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https://www.jiskha.com/search?query=the+activity+of+a+sample+of+carbon+has+one-eighth+of+the+initial+activity.+carbon-14+has+a+half-life+of+5730+yr.+how+old+is+the+sample+in+yr%3F | 1,534,430,970,000,000,000 | text/html | crawl-data/CC-MAIN-2018-34/segments/1534221211000.35/warc/CC-MAIN-20180816132758-20180816152758-00083.warc.gz | 909,541,915 | 12,822 | # the activity of a sample of carbon has one-eighth of the initial activity. carbon-14 has a half-life of 5730 yr. how old is the sample in yr?
42,855 results
1. ## college physics part 2
the activity of a sample of carbon has one-eighth of the initial activity. carbon-14 has a half-life of 5730 yr. how old is the sample in yr?
2. ## ChemB
The activity of carbon 14 in living tissue is 15.3 disintegrations per minute per gram of carbon. The limit for reliable determination of age is based on carbon 14 is .10 disintegration per min per gram of carbon. Calculate the max age of a sample that can
3. ## science
The half-life of carbon 14 is 5730 years. if a 1 g sample of old carbon is 1/8 as radioactive as 1 g of a current sample, then the age of the old sample is about ___________years. 22,900 17,200 11,500 716
4. ## geology
suppose you have a sample of clamshell at a paleoindian site and you measure the 14c activity of aa 100-gram sample of carbon as 320 disintegretions per scond (or 3.2 disingtegrations per gram of carbon per second). a. what was the activity(in
5. ## Physicr
A 10 kg sample from a living plant has actiuity 30 000 Bq due to Carbon-14. A 500g sample of the same type of plant but dead has activity 1 000 Bq. Calculate the age of the dead sample given that the half life of Carbon-14 is 5568 years
6. ## nuclear
Calculate the age of a plant sample that shows about one-eighth of the carbon 14 of a living sample. The half-life of carbon-14 is about 5760 a. Help please...
7. ## nuclear physics
Calculate the age of a plant sample that shows about one-eighth of the carbon 14 of a living sample. The half-life of carbon 14 is about 5760a How do you do this?
8. ## physics
A sample has a activity of 0.0065 Bq per gram of carbon. (a) Find the age of the sample, assuming that the activity per gram of carbon in a living organism has been constant at a value of 0.23 Bq. (b) Evidence suggests that the value of 0.23 Bq might have
9. ## physics 2
A sample has a activity of 0.0065 Bq per gram of carbon. (a) Find the age of the sample, assuming that the activity per gram of carbon in a living organism has been constant at a value of 0.23 Bq. (b) Evidence suggests that the value of 0.23 Bq might have
Beryllium-7 has a half-life of 53 D. A sample was observed for one minute and there were 26,880 decays. a.) what is the activity level of the sample? b.) what will the activity level of the sample be after 265 d? c.) after how many days will be activity
11. ## Chemistry
Carbon-14 has a half-life of 5730 y. How much of a 144 g sample of a carbon-14 will remain after 1.719 (times) 10 4y?
12. ## Chemistry
Carbon-14 has a half-life of 5730 y. How much of a 144 g sample of a carbon-14 will remain after 1.719 (times) 10 4y?
13. ## Physics
When any radioactive dating method is used, experimental error in the measurement of the sample's activity leads to error in the estimated age. In an application of the radiocarbon dating technique to certain fossils, an activity of 0.15 Bq per gram of
14. ## chemistry
A wooden object from a prehistoric site has a carbon-14 activity of 10 counts per min.(cpm) compared to 40 cpm for new wood. If carbon-14 has a half life of 5730 years what is the age of the wood? Please get me started. Thank you
15. ## chem
Can someone please help me with the following questions? 1:Suppose you were given an ancient wooden box. If you analyze the box for carbon-14 activity and find that it is 50% of that of a new piece of wood of the same size, how old is the wood in the box?
16. ## chemistry
The half-life for the radioactive decay of calcium-47 is 4.5 days.If a sample has an activity of 4.00uCi after 13.5 days, what was the initial activity of the sample?
17. ## college geology help please
I was the same person from yesterday. I need help on a question. I don't type very good so I have one of my host family do it for me. so please help us. Suppose you have a sample of clamshell at a Paleoindian site and you measure the 14C activity of a
18. ## college Geol 101
Suppose you have a sample of clamshell at a Paleoindian site and you measure the 14C activity of a 100-gram sample of carbon as 320 disintegrations per minute (or 3.2 disintegrations per gram of carbon per minute). a.What was the activity (in
19. ## physics
The half-life of carbon-14 is 5730 years. How much of a 50 g sample of carbon-14 is present after 11,460 years?
20. ## calculus
Carbon-14 is a radioactive substance produced in the Earth's atmosphere and then absorbed by plants and animals on the surface of the earth. It has a half-life (the time it takes for half the amount of a sample to decay) of approximately 5730 years. Using
21. ## Physics
The isotope carbon-14, 146C, is radioactive and has a half-life of 5730 years. If you start with a sample of 1000 carbon-14 nuclei, how many will still be around in 22920 years? I got 62.5 atoms, am I correct?? Thank you!!
The activity of a sample of Ba-137m has decreased by 75% from its initial activity after 5.10 minutes. What is the half-life of Ba-137m? What fraction of activity remains after 6.25 minutes? (A=Aoe (-kt); k = .693/t1/2)
23. ## Physics
University students, studying the activity of a particular radioactive isotope which had a half-life of 12.0 hours. If the original activity of the sample was 448 kBq, what would the activity be 3.00 days later?
24. ## science
The half-life of carbon-14 is 5730 years. If we start with 10 grams of carbon-14, after 5730 years, we will have _____ of carbon-14 left.
25. ## science
The half-life of carbon-14 is 5730 years. If we start with 10 grams of carbon-14, after 5730 years, we will have _____ of carbon-14 left.
26. ## half-life
ok so i got... the half life of carbon-14 is 5730 years, the relation c+(1/2)^ N/5730 is used to calc. the concentration, c, in parts per trillion remaining n years after death determine the carbon concentration in a 11460 year old bone. please help :)
27. ## half-life
ok so i got... the half life of carbon-14 is 5730 years, the relation c+(1/2)^ N/5730 is used to calc. the concentration, c, in parts per trillion remaining n years after death determine the carbon concentration in a 11460 year old bone. please help :)
28. ## chemistry
A 1.00-g sample of carbon from a modern source gave 15.3 disintegrations per minute. A sample of carbon from an “old” source gave 920 disintegrations per hour. What is the age of the “old” sample of carbon? The half-life of carbon-14 is 5.73×103
29. ## chemistry
A 1.00-g sample of carbon from a modern source gave 15.3 disintegrations per minute. A sample of carbon from an “old” source gave 920 disintegrations per hour. What is the age of the “old” sample of carbon? The half-life of carbon-14 is 5.73×103
30. ## Nuclear Physics
An investigator receives Co-60 (5.27 year half life) for use in a research study. Unfortunately the Co-60 is contaminated with Cs-137 (30.0 year half life). The initial Co-60 activity is 400 times the initial Cs-137 activity. How long after the initial
31. ## physics
Suppose 32000 radioactive nuclei are in a sample. About how many remain after two days if the half-life is 22 hrs? What is the initial activity of the sample in decays per minute?
32. ## physics
How do I do this ? Calculate the age of a plant sample that shows about one-eigth of the carbon 14 of a living sample. The half-life of carbon-14 is about 5760a I don't have the notes on how to do this one... Help
33. ## physics
After 1.84 days, the activity of a sample of an unknown type radioactive material has decreased to 85.8% of the initial activity. What is the half-life of this material? (in days)
34. ## Chemistry
The cloth shroud from around a mummy is found to have a carbon-14 activity of 8.1 disintegrations per minute per gram of carbon as compared with living organisms that undergo 15.2 disintegrations per minute per gram of carbon. From the half-life for
35. ## Algebra
An artifact was found and tested for its carbon-14 content. If 74% of the orginal carbon-14 was still present, what is its probable age (to the nearest 100 years)? (Carbon-14 has a half life of 5730 years).
36. ## physics
before 1900 the activity per mass of atmospheric carbon due to the presence of carbon-14 averaged about 0.255bq/g of carbon 1. what fraction of carbon is carbon-14
37. ## physics
before 1900 the activity per mass of atmospheric carbon due to the presence of carbon-14 averaged about 0.255bq/g of carbon 1. what fraction of carbon is carbon-14
38. ## Pre Calculus
The burial cloth of an Egyptian mummy is estimated to contain 56% of the carbon-14 it contained originally. How long ago was the mummy buried? (the half-life of carbon-14 is 5730). Please round the answer to the nearest tenth. I have figured that: m(t) =
39. ## physics
A wooden artifact is found in an ancient tomb. Its carbon-14 activity is measured to be 60.0% of that in a fresh sample of wood from the same region. Assuming the same amount of carbon-14 was initially present in the wood from which the artifact was made,
40. ## Math
Cosmic ray bombardment of the atmosphere produces neutrons, which in turn react w/ nitrogen to produce radioactive carbon-14. Radioactive carbon-14 enters all living tissue through carbon dioxide. As long as it is alive, carbon-14 is maintained in the
41. ## Math
The half-life of carbon-14, which is used in dating archaeological finds, is 5730 yr. Assume that 100% of the carbon-14 is present at time 0 yr, or x=0. Write the equation that expresses the percentage of carbon-14 remaining as a function of time.
42. ## Calculus
An artifact was found with 63.8% of Carbon 14, how old is the mummy, assuming the half-life of Carbon 14 is 5730 years.
43. ## Chemistry
A piece of wood found in an ancient city has a carbon-14 to carbon-12 ratio that is one-eighth the carbon-14 to carbon-12 ratio of a tree growing nearby. How old is the piece of wood? (The half-life of carbon-14 is 5,715 years.)
44. ## Physics
Carbon-15 has a half-life of 5730 years. As observed from Earth, what would the half-life of carbon-15 be if it traveled through space at 25% of the speed of light, relative to Earth?
45. ## Calculus
The amount of carbon-14 still present in a sample after t years is given by the function where C0 is the initial amount. Estimate the age of a sample of wood discovered by an archeologist if the carbon level in the sample is only 18% of its original
46. ## Chem
Living organisms give a Carbon-14 decay rate of 15.3 counts/min for each gram of carbon in the sample. A sample of bristle cone pine wood has a decay rate of 3.20 counts/min per gram of carbon. Calculate the age of the wood from the radiochemical evidence.
47. ## Biology
The half-life of Carbon-14 is 5730 years. What is the age of a fossil containing 1/16 the amount of Carbon-14 of living organisms? Explain your calculation.
48. ## Physics (Inside the atom)
A sample of radioactive isotope I is to be used for medical diagnosis of the kidneys. The isotope has a half-life of 8.0 days, and the sample is required to have an activity of 8 x 10^5 per second at the time it is given to the patient. Calculate the mass
49. ## chemistry
The half-life of oxygen-15 is 124 s. If a sample of oxygen-15 has an activity of 4800 Bq, how many minutes will elapse before it has an activity of 600 Bq?
50. ## chem
the half life of oxygen-15 is 124 s. if a sample of oxygen-15 has an activity of 4000 Bq, how many minutes will elapse before it reaches an activity of 500Bq
51. ## ChemB
measurements of carbon 14 taken from linen wrappings of the book of isaiah from the dead sea scrolls indicate that the scrolls contain 79.5% of the carbon 14 expected in living tissue. how old are these scrolls if the half life of carbon 14 is 5730 years?
52. ## chem
A sample of radon has an activity of 80,000 Bq. If the half-life of radon is 15 h, how long before the sample's activity is 5,000 Bq?
By comparing the amount of carbon-14 to amount of carbon-12, one can determine approx how long ago the organism died. The half-life of carbon-14 is 5730 years. Assume the initial quantity of carbon-14 is 600 milligrams. the equation is A (t)=600*(.5)^(t)
54. ## Physics
(a)-A fossilised tree was tested and contains 10 grams of Carbon-14. Given that there was 12 grams of Carbon-14 present when it died, determine the age of the fossil? Half life of Carbon-14 is 5700 years. (b)How much Carbon-14 will be present in the sample
55. ## Physics
(a)-A fossilised tree was tested and contains 10 grams of Carbon-14. Given that there was 12 grams of Carbon-14 present when it died, determine the age of the fossil? Half life of Carbon-14 is 5700 years. (b)How much Carbon-14 will be present in the sample
56. ## Chemistry
Radium-223 has a half-life of 11.4 days.Approximately how long would it take for the activity of a sample of 223Ra to decrease to 2.00 % of its initial value?
57. ## Chemistry
Radium-223 has a half-life of 11.4 days. Approximately how long would it take for the activity of a sample of 223Ra to decrease to 2.00 % of its initial value?
58. ## Intermediate Maths
(a)-A fossilised tree was tested and contains 10 grams of Carbon-14. Given that there was 12 grams of Carbon-14 present when it died, determine the age of the fossil? Half life of Carbon-14 is 5700 years. (b)How much Carbon-14 will be present in the sample
59. ## Final Maths
(a)-A fossilised tree was tested and contains 10 grams of Carbon-14. Given that there was 12 grams of Carbon-14 present when it died, determine the age of the fossil? Half life of Carbon-14 is 5700 years. (b)How much Carbon-14 will be present in the sample
60. ## Chemistry
What is the activity of a 18.9 μCi sample of carbon-14 in becquerels?
61. ## math: pre-calculus
You have 5 grams of carbon-14; whose half-life is 5730 years. a)Write the rule of the function that gives the amount of carbon-14 remaining after x years. b)How much carbon-14 will be left after 4,000 years? c)When will there be just 1 gram left?
62. ## PreCalculus
The half life of Carbon-14 is 5730 years. a. find the rule of the function that gives the amount remaining from an initial quantity of 100 milligrams of carbon14 after t years. b. the burial cloth of an egyptian mummy i sestimated to contain 59% of the
63. ## Chemistry
A sample of sodium-24 with an activity of 12 mCi is used to study the rate of blow flow in the circulatory system. If sodium -24 has a half-life of 15 hours, what is the activity of the sodium after 2.5 d ?
64. ## Chemistry Numerical
The half life period of a radioactive element is 27.96 days. Calculate the time taken by a given sample to reduce to 1/8th of its initial activity
65. ## chemistry
a sample of sodium-24 with an activity of 12 mCi is used to study the rate of blood flow in the circulatory system. If sodium-24 has a half-life of 15 h, what is the activity of the sodium after 2.5 days. please show work.
66. ## math
only 5% of the carbon-14 in a small wooden bowl remains , how old is the bowl? Hint, half-life for carbon –14 us 5730 years
67. ## math
Carbon-14 has a half-life of 5730 years. How long will it take 17 grams of carbon-14 to be reduced to 10 grams? Round to the nearest integer.
68. ## Math
A plant fossil lost 40 % of its carbon-14. How old is the fossil? (Half-life of carbon-14 is 5730 years.)
69. ## physics
If an archaeologist finds an ancient fire pit containing partially consumed firewood and the 14C content of the wood is only 10% of an equal carbon sample from present day tree, what is the age of ancient site. 14 C has half life of 5730 years
70. ## physical science
a scientist found a fossilized bison. using Carbon-14 dating, she found that the fossil was about 45,840 years old. Carbon-14 has a half-life of 5730 years. how many half-lives have passed?
71. ## chemistry
The amount of organic carbon in a sample can be obtained by IR analysis of the carbon dioxide (CO2) released following complete combustion of the sample in oxygen. A reference sample of an organic compound is usually used to calibrate the instrument
72. ## Precalculus
The burial cloth of an Egyptian mummy is estimated to contain 57% of the carbon-14 it contained originally. How long ago was the mummy buried? (The half-life of carbon-14 is 5730 years.)
73. ## Precalculus
The burial cloth of an Egyptian mummy is estimated to contain 57% of the carbon-14 it contained originally. How long ago was the mummy buried? (The half-life of carbon-14 is 5730 years.)
74. ## calculus
A wooden artifact recovered from a tomb contains 29% of the carbon-14 that is present in living trees. The half life of carbon-14 is 5730 years. How long ago was the artifact made?
75. ## Physics
A radioactive isotope of Bismuth undergoes Beta Decay with a half-life of 22 days. How long (in days) will it take the Activity (A) of the sample to decrease to one-ninth of its original value? Assume that the original activity is A0.
76. ## Chemistry
One last question...even though no one seems to be willing to help me out without being rude. The blood volume in a cancer patient was measured by injecting 5.0 mL of Na2SO4(aq) labeled with 35S (t1/2 = 87.4 d). The activity of the sample was 300 µCi.
77. ## chemistry
The radioactive decay of carbon-14 is first-order and the half-life is 5800 years. While a plant or animal is living, it has a constant proportion of carbon-14 (relative to carbon-12) in its composition. When the organism dies, the proportion of carbon-14
78. ## Chemistry
A sample of charcoal is found to have only 1/8th of Carbon-14. Half-life of Carbon-14 is 5730yrs, what is the age of the charcoal?
79. ## Chemistry
Cobalt-60, which undergoes beta decay, has a half-life of 5.26 yr. How many beta particles are emitted in 190s by a 3.10mg sample of Co-60? What is the activity of the sample in Bq?
80. ## Chemistry
Cobalt-60, which undergoes beta decay, has a half-life of 5.26 yr. How many beta particles are emitted in 190s by a 3.10mg sample of Co-60? What is the activity of the sample in Bq?
81. ## Chemistry
Cobalt-60, which undergoes beta decay, has a half-life of 5.26 yr. How many beta particles are emitted in 190s by a 3.10mg sample of Co-60? What is the activity of the sample in Bq?
82. ## Chemistry
Cobalt-60, which undergoes beta decay, has a half-life of 5.26 yr. How many beta particles are emitted in 190s by a 3.10mg sample of Co-60? What is the activity of the sample in Bq?
83. ## math
A wooden artifact from an ancient tomb contains 70% of the carbon-14 that is present in living trees. How long ago was the artifact made? (The half-life of carbon-14 is 5730 years. Round your answer to the nearest whole number.)
84. ## Biology
The half-life of carbon-14 is 5,700 years. If a sample originally had 26 g of carbon-14, how much would it contain after 22,800 years?
85. ## chem
A typical dose of a radioactive sample is 27.0 mCi. How long does it take for the activity to reduce to 0.100 mCi? The half life of the sample is 211,000 y.
86. ## MATH 123
A wooden artifact from an ancient tomb contains 55% of the carbon-14 that is present in living trees. How long ago was the artifact made? (The half-life of carbon-14 is 5730 years. Round your answer to the nearest whole number.)
87. ## Intro to Astronomy
The half-life of carbon 14, which is commonly used to date organic materials, is 5700 years. What is the minimum age of sample in which less than 1% of the organic carbon 14 is left?
88. ## Chemistry
The strontium-90 isotope decays by the reaction below. It has a half-life of 28 yr. If the initial activity of this isotope was 168dpm, what would the activity be after 28.0 yr?
89. ## Chemistry
Radium-223 has a half-life of 11.4 days.Approximately how long would it take for the activity of a sample of Radium-223 to decrease to 1.00% of its initial value?
90. ## Calculus
A fragment of bone is discovered to contain 20% of the usual carbon-14 concentration. Estimate the age of the bone to the nearest hundred years, given that Carbon-1 is radioactive with half-life of 5730 years and the rate of decay is given by the following
91. ## College Algebra
This exercise uses the radioactive decay model. A wooden artifact from an ancient tomb contains 80% of the carbon-14 that is present in living trees. How long ago was the artifact made? (The half-life of carbon-14 is 5730 years. Round your answer to the
92. ## chem
Radioactive substances decay by first-order kinetics. How many years would be required for a sample containing strontium-90 to decrease to 58.32% of its initial activity? The half-life of strontium-90 is 2.88e1 years.
93. ## Physics 30
The activity of a sample of a radioactive isotope is 1800Bq. If this isotope has a half-life of 16 days, what is the activity after 16 days?, 24 days?, and 60 days?
1. A granite rock is thought to be about 2 billion years old. why is it not possible to determine the age of the Rock using carbon-14 dating? 2. A hair sample has 80% of its original carbon-14 present. what is the age of the sample? 3. A bone fragment has
95. ## Chem
If you have a 12.01g sample carbon. What would be the average mass of a carbon atoms if it is 1.994 x 10 to the 23 power g. How many carbon atoms are in the sample?
96. ## math
1.The remains of an old campfire are unearthed and it is found that there is only 80% as much radioactive carbon-14 in the charcoal samples from the campfire as there is in modern living trees. If the half-life of carbon- 14 is 5730 years, how
97. ## Chemistry
An artifact has a carbon-14 to carbon-12 ratio that is one-fourth the carbon-14 to carbon-12 ratio of a similar modern object. How old is the artifact? (The half-life of carbon-14 is 5,715 years.)
98. ## Chemistry
Q1. The blood volume in a cancer patient was measured by injecting 5.0 mL of Na2SO4(aq) labeled with 35S (t1/2 = 87.4 d). The activity of the sample was 300 µCi. After 22 min, 12.9 mL of blood was withdrawn from the man and the activity of that sample was
99. ## chemistry
You have a 12.01 g sample of carbon. The average mass of a carbon atoms is 1.994 x 1023 g. How many carbon atoms are in the sample?
100. ## chemistry
Assayed for LDH activity were 5 microliters of a sample that was diluted 6 to 1. The activity in the reaction vessel, which has a volume of 3 mililiters, is 0.30 U. What is the ΔA/min observed? What is the relative activity of the original sample? | 6,016 | 22,391 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.578125 | 4 | CC-MAIN-2018-34 | latest | en | 0.921395 | # the activity of a sample of carbon has one-eighth of the initial activity. carbon-14 has a half-life of 5730 yr. how old is the sample in yr?. 42,855 results. 1. ## college physics part 2. the activity of a sample of carbon has one-eighth of the initial activity. carbon-14 has a half-life of 5730 yr. how old is the sample in yr?. 2. ## ChemB. The activity of carbon 14 in living tissue is 15.3 disintegrations per minute per gram of carbon. The limit for reliable determination of age is based on carbon 14 is .10 disintegration per min per gram of carbon. Calculate the max age of a sample that can. 3. ## science. The half-life of carbon 14 is 5730 years. if a 1 g sample of old carbon is 1/8 as radioactive as 1 g of a current sample, then the age of the old sample is about ___________years. 22,900 17,200 11,500 716. 4. ## geology. suppose you have a sample of clamshell at a paleoindian site and you measure the 14c activity of aa 100-gram sample of carbon as 320 disintegretions per scond (or 3.2 disingtegrations per gram of carbon per second). a. what was the activity(in. 5. ## Physicr. A 10 kg sample from a living plant has actiuity 30 000 Bq due to Carbon-14. A 500g sample of the same type of plant but dead has activity 1 000 Bq. Calculate the age of the dead sample given that the half life of Carbon-14 is 5568 years. 6. ## nuclear. Calculate the age of a plant sample that shows about one-eighth of the carbon 14 of a living sample. The half-life of carbon-14 is about 5760 a. Help please.... 7. ## nuclear physics. Calculate the age of a plant sample that shows about one-eighth of the carbon 14 of a living sample. The half-life of carbon 14 is about 5760a How do you do this?. 8. ## physics. A sample has a activity of 0.0065 Bq per gram of carbon. (a) Find the age of the sample, assuming that the activity per gram of carbon in a living organism has been constant at a value of 0.23 Bq. (b) Evidence suggests that the value of 0.23 Bq might have. 9. ## physics 2. A sample has a activity of 0.0065 Bq per gram of carbon. (a) Find the age of the sample, assuming that the activity per gram of carbon in a living organism has been constant at a value of 0.23 Bq. (b) Evidence suggests that the value of 0.23 Bq might have. Beryllium-7 has a half-life of 53 D. A sample was observed for one minute and there were 26,880 decays. a.) what is the activity level of the sample? b.) what will the activity level of the sample be after 265 d? c.) after how many days will be activity. 11. ## Chemistry. Carbon-14 has a half-life of 5730 y. How much of a 144 g sample of a carbon-14 will remain after 1.719 (times) 10 4y?. 12. ## Chemistry. Carbon-14 has a half-life of 5730 y. How much of a 144 g sample of a carbon-14 will remain after 1.719 (times) 10 4y?. 13. ## Physics. When any radioactive dating method is used, experimental error in the measurement of the sample's activity leads to error in the estimated age. In an application of the radiocarbon dating technique to certain fossils, an activity of 0.15 Bq per gram of. 14. ## chemistry. A wooden object from a prehistoric site has a carbon-14 activity of 10 counts per min.(cpm) compared to 40 cpm for new wood. If carbon-14 has a half life of 5730 years what is the age of the wood? Please get me started. Thank you. 15. ## chem. Can someone please help me with the following questions? 1:Suppose you were given an ancient wooden box. If you analyze the box for carbon-14 activity and find that it is 50% of that of a new piece of wood of the same size, how old is the wood in the box?. 16. ## chemistry. The half-life for the radioactive decay of calcium-47 is 4.5 days.If a sample has an activity of 4.00uCi after 13.5 days, what was the initial activity of the sample?. 17. ## college geology help please. I was the same person from yesterday. I need help on a question. I don't type very good so I have one of my host family do it for me. so please help us. Suppose you have a sample of clamshell at a Paleoindian site and you measure the 14C activity of a. 18. ## college Geol 101. Suppose you have a sample of clamshell at a Paleoindian site and you measure the 14C activity of a 100-gram sample of carbon as 320 disintegrations per minute (or 3.2 disintegrations per gram of carbon per minute). a.What was the activity (in. 19. ## physics. The half-life of carbon-14 is 5730 years. How much of a 50 g sample of carbon-14 is present after 11,460 years?. 20. ## calculus. Carbon-14 is a radioactive substance produced in the Earth's atmosphere and then absorbed by plants and animals on the surface of the earth. It has a half-life (the time it takes for half the amount of a sample to decay) of approximately 5730 years. Using. 21. ## Physics. The isotope carbon-14, 146C, is radioactive and has a half-life of 5730 years. If you start with a sample of 1000 carbon-14 nuclei, how many will still be around in 22920 years? I got 62.5 atoms, am I correct?? Thank you!!. The activity of a sample of Ba-137m has decreased by 75% from its initial activity after 5.10 minutes. What is the half-life of Ba-137m? What fraction of activity remains after 6.25 minutes? (A=Aoe (-kt); k = .693/t1/2). 23. ## Physics. University students, studying the activity of a particular radioactive isotope which had a half-life of 12.0 hours. If the original activity of the sample was 448 kBq, what would the activity be 3.00 days later?. 24. ## science. The half-life of carbon-14 is 5730 years. If we start with 10 grams of carbon-14, after 5730 years, we will have _____ of carbon-14 left.. 25. ## science. The half-life of carbon-14 is 5730 years. If we start with 10 grams of carbon-14, after 5730 years, we will have _____ of carbon-14 left.. 26. ## half-life. ok so i got... the half life of carbon-14 is 5730 years, the relation c+(1/2)^ N/5730 is used to calc. the concentration, c, in parts per trillion remaining n years after death determine the carbon concentration in a 11460 year old bone. please help :). 27. ## half-life. ok so i got... the half life of carbon-14 is 5730 years, the relation c+(1/2)^ N/5730 is used to calc. the concentration, c, in parts per trillion remaining n years after death determine the carbon concentration in a 11460 year old bone. please help :). 28. ## chemistry. A 1.00-g sample of carbon from a modern source gave 15.3 disintegrations per minute. A sample of carbon from an “old” source gave 920 disintegrations per hour. What is the age of the “old” sample of carbon? The half-life of carbon-14 is 5.73×103. 29. ## chemistry. A 1.00-g sample of carbon from a modern source gave 15.3 disintegrations per minute. A sample of carbon from an “old” source gave 920 disintegrations per hour. What is the age of the “old” sample of carbon? The half-life of carbon-14 is 5.73×103. 30. ## Nuclear Physics. An investigator receives Co-60 (5.27 year half life) for use in a research study. Unfortunately the Co-60 is contaminated with Cs-137 (30.0 year half life). The initial Co-60 activity is 400 times the initial Cs-137 activity. How long after the initial. 31. ## physics. Suppose 32000 radioactive nuclei are in a sample. About how many remain after two days if the half-life is 22 hrs? What is the initial activity of the sample in decays per minute?. 32. ## physics. How do I do this ? Calculate the age of a plant sample that shows about one-eigth of the carbon 14 of a living sample. The half-life of carbon-14 is about 5760a I don't have the notes on how to do this one... Help. 33. ## physics. After 1.84 days, the activity of a sample of an unknown type radioactive material has decreased to 85.8% of the initial activity. What is the half-life of this material? (in days). 34. ## Chemistry. The cloth shroud from around a mummy is found to have a carbon-14 activity of 8.1 disintegrations per minute per gram of carbon as compared with living organisms that undergo 15.2 disintegrations per minute per gram of carbon. From the half-life for. 35. ## Algebra. An artifact was found and tested for its carbon-14 content. If 74% of the orginal carbon-14 was still present, what is its probable age (to the nearest 100 years)? (Carbon-14 has a half life of 5730 years).. 36. ## physics. before 1900 the activity per mass of atmospheric carbon due to the presence of carbon-14 averaged about 0.255bq/g of carbon 1. what fraction of carbon is carbon-14. 37. ## physics. before 1900 the activity per mass of atmospheric carbon due to the presence of carbon-14 averaged about 0.255bq/g of carbon 1. what fraction of carbon is carbon-14. 38. ## Pre Calculus. The burial cloth of an Egyptian mummy is estimated to contain 56% of the carbon-14 it contained originally. How long ago was the mummy buried? (the half-life of carbon-14 is 5730). Please round the answer to the nearest tenth. I have figured that: m(t) =. 39. ## physics. A wooden artifact is found in an ancient tomb. Its carbon-14 activity is measured to be 60.0% of that in a fresh sample of wood from the same region. Assuming the same amount of carbon-14 was initially present in the wood from which the artifact was made,. 40. ## Math. Cosmic ray bombardment of the atmosphere produces neutrons, which in turn react w/ nitrogen to produce radioactive carbon-14. Radioactive carbon-14 enters all living tissue through carbon dioxide. As long as it is alive, carbon-14 is maintained in the. 41. ## Math. The half-life of carbon-14, which is used in dating archaeological finds, is 5730 yr. Assume that 100% of the carbon-14 is present at time 0 yr, or x=0. Write the equation that expresses the percentage of carbon-14 remaining as a function of time.. 42. ## Calculus. An artifact was found with 63.8% of Carbon 14, how old is the mummy, assuming the half-life of Carbon 14 is 5730 years.. 43. ## Chemistry. A piece of wood found in an ancient city has a carbon-14 to carbon-12 ratio that is one-eighth the carbon-14 to carbon-12 ratio of a tree growing nearby. How old is the piece of wood? (The half-life of carbon-14 is 5,715 years.). 44. ## Physics. Carbon-15 has a half-life of 5730 years. As observed from Earth, what would the half-life of carbon-15 be if it traveled through space at 25% of the speed of light, relative to Earth?. 45. ## Calculus. The amount of carbon-14 still present in a sample after t years is given by the function where C0 is the initial amount. Estimate the age of a sample of wood discovered by an archeologist if the carbon level in the sample is only 18% of its original. 46. ## Chem. Living organisms give a Carbon-14 decay rate of 15.3 counts/min for each gram of carbon in the sample. A sample of bristle cone pine wood has a decay rate of 3.20 counts/min per gram of carbon. Calculate the age of the wood from the radiochemical evidence.. 47. ## Biology. The half-life of Carbon-14 is 5730 years. What is the age of a fossil containing 1/16 the amount of Carbon-14 of living organisms? Explain your calculation.. 48. ## Physics (Inside the atom). A sample of radioactive isotope I is to be used for medical diagnosis of the kidneys. The isotope has a half-life of 8.0 days, and the sample is required to have an activity of 8 x 10^5 per second at the time it is given to the patient. Calculate the mass. 49. ## chemistry. The half-life of oxygen-15 is 124 s. If a sample of oxygen-15 has an activity of 4800 Bq, how many minutes will elapse before it has an activity of 600 Bq?. 50. ## chem. the half life of oxygen-15 is 124 s. if a sample of oxygen-15 has an activity of 4000 Bq, how many minutes will elapse before it reaches an activity of 500Bq. | 51. ## ChemB. measurements of carbon 14 taken from linen wrappings of the book of isaiah from the dead sea scrolls indicate that the scrolls contain 79.5% of the carbon 14 expected in living tissue. how old are these scrolls if the half life of carbon 14 is 5730 years?. 52. ## chem. A sample of radon has an activity of 80,000 Bq. If the half-life of radon is 15 h, how long before the sample's activity is 5,000 Bq?. By comparing the amount of carbon-14 to amount of carbon-12, one can determine approx how long ago the organism died. The half-life of carbon-14 is 5730 years. Assume the initial quantity of carbon-14 is 600 milligrams. the equation is A (t)=600*(.5)^(t). 54. ## Physics. (a)-A fossilised tree was tested and contains 10 grams of Carbon-14. Given that there was 12 grams of Carbon-14 present when it died, determine the age of the fossil? Half life of Carbon-14 is 5700 years. (b)How much Carbon-14 will be present in the sample. 55. ## Physics. (a)-A fossilised tree was tested and contains 10 grams of Carbon-14. Given that there was 12 grams of Carbon-14 present when it died, determine the age of the fossil? Half life of Carbon-14 is 5700 years. (b)How much Carbon-14 will be present in the sample. 56. ## Chemistry. Radium-223 has a half-life of 11.4 days.Approximately how long would it take for the activity of a sample of 223Ra to decrease to 2.00 % of its initial value?. 57. ## Chemistry. Radium-223 has a half-life of 11.4 days. Approximately how long would it take for the activity of a sample of 223Ra to decrease to 2.00 % of its initial value?. 58. ## Intermediate Maths. (a)-A fossilised tree was tested and contains 10 grams of Carbon-14. Given that there was 12 grams of Carbon-14 present when it died, determine the age of the fossil? Half life of Carbon-14 is 5700 years. (b)How much Carbon-14 will be present in the sample. 59. ## Final Maths. (a)-A fossilised tree was tested and contains 10 grams of Carbon-14. Given that there was 12 grams of Carbon-14 present when it died, determine the age of the fossil? Half life of Carbon-14 is 5700 years. (b)How much Carbon-14 will be present in the sample. 60. ## Chemistry. What is the activity of a 18.9 μCi sample of carbon-14 in becquerels?. 61. ## math: pre-calculus. You have 5 grams of carbon-14; whose half-life is 5730 years. a)Write the rule of the function that gives the amount of carbon-14 remaining after x years. b)How much carbon-14 will be left after 4,000 years? c)When will there be just 1 gram left?. 62. ## PreCalculus. The half life of Carbon-14 is 5730 years. a. find the rule of the function that gives the amount remaining from an initial quantity of 100 milligrams of carbon14 after t years. b. the burial cloth of an egyptian mummy i sestimated to contain 59% of the. 63. ## Chemistry. A sample of sodium-24 with an activity of 12 mCi is used to study the rate of blow flow in the circulatory system. If sodium -24 has a half-life of 15 hours, what is the activity of the sodium after 2.5 d ?. 64. ## Chemistry Numerical. The half life period of a radioactive element is 27.96 days. Calculate the time taken by a given sample to reduce to 1/8th of its initial activity. 65. ## chemistry. a sample of sodium-24 with an activity of 12 mCi is used to study the rate of blood flow in the circulatory system. If sodium-24 has a half-life of 15 h, what is the activity of the sodium after 2.5 days. please show work.. 66. ## math. only 5% of the carbon-14 in a small wooden bowl remains , how old is the bowl? Hint, half-life for carbon –14 us 5730 years. 67. ## math. Carbon-14 has a half-life of 5730 years. How long will it take 17 grams of carbon-14 to be reduced to 10 grams? Round to the nearest integer.. 68. ## Math. A plant fossil lost 40 % of its carbon-14. How old is the fossil? (Half-life of carbon-14 is 5730 years.). 69. ## physics. If an archaeologist finds an ancient fire pit containing partially consumed firewood and the 14C content of the wood is only 10% of an equal carbon sample from present day tree, what is the age of ancient site. 14 C has half life of 5730 years. 70. ## physical science. a scientist found a fossilized bison. using Carbon-14 dating, she found that the fossil was about 45,840 years old. Carbon-14 has a half-life of 5730 years. how many half-lives have passed?. 71. ## chemistry. The amount of organic carbon in a sample can be obtained by IR analysis of the carbon dioxide (CO2) released following complete combustion of the sample in oxygen. A reference sample of an organic compound is usually used to calibrate the instrument. 72. ## Precalculus. The burial cloth of an Egyptian mummy is estimated to contain 57% of the carbon-14 it contained originally. How long ago was the mummy buried? (The half-life of carbon-14 is 5730 years.). 73. ## Precalculus. The burial cloth of an Egyptian mummy is estimated to contain 57% of the carbon-14 it contained originally. How long ago was the mummy buried? (The half-life of carbon-14 is 5730 years.). 74. ## calculus. A wooden artifact recovered from a tomb contains 29% of the carbon-14 that is present in living trees. The half life of carbon-14 is 5730 years. How long ago was the artifact made?. 75. ## Physics. A radioactive isotope of Bismuth undergoes Beta Decay with a half-life of 22 days. How long (in days) will it take the Activity (A) of the sample to decrease to one-ninth of its original value? Assume that the original activity is A0.. 76. ## Chemistry. One last question...even though no one seems to be willing to help me out without being rude. The blood volume in a cancer patient was measured by injecting 5.0 mL of Na2SO4(aq) labeled with 35S (t1/2 = 87.4 d). The activity of the sample was 300 µCi.. 77. ## chemistry. The radioactive decay of carbon-14 is first-order and the half-life is 5800 years. While a plant or animal is living, it has a constant proportion of carbon-14 (relative to carbon-12) in its composition. When the organism dies, the proportion of carbon-14. 78. ## Chemistry. A sample of charcoal is found to have only 1/8th of Carbon-14. Half-life of Carbon-14 is 5730yrs, what is the age of the charcoal?. 79. ## Chemistry. Cobalt-60, which undergoes beta decay, has a half-life of 5.26 yr. How many beta particles are emitted in 190s by a 3.10mg sample of Co-60? What is the activity of the sample in Bq?. 80. ## Chemistry. Cobalt-60, which undergoes beta decay, has a half-life of 5.26 yr. How many beta particles are emitted in 190s by a 3.10mg sample of Co-60? What is the activity of the sample in Bq?. 81. ## Chemistry. Cobalt-60, which undergoes beta decay, has a half-life of 5.26 yr. How many beta particles are emitted in 190s by a 3.10mg sample of Co-60? What is the activity of the sample in Bq?. 82. ## Chemistry. Cobalt-60, which undergoes beta decay, has a half-life of 5.26 yr. How many beta particles are emitted in 190s by a 3.10mg sample of Co-60? What is the activity of the sample in Bq?. 83. ## math. A wooden artifact from an ancient tomb contains 70% of the carbon-14 that is present in living trees. How long ago was the artifact made? (The half-life of carbon-14 is 5730 years. Round your answer to the nearest whole number.). 84. ## Biology. The half-life of carbon-14 is 5,700 years. If a sample originally had 26 g of carbon-14, how much would it contain after 22,800 years?. 85. ## chem. A typical dose of a radioactive sample is 27.0 mCi. How long does it take for the activity to reduce to 0.100 mCi? The half life of the sample is 211,000 y.. 86. ## MATH 123. A wooden artifact from an ancient tomb contains 55% of the carbon-14 that is present in living trees. How long ago was the artifact made? (The half-life of carbon-14 is 5730 years. Round your answer to the nearest whole number.). 87. ## Intro to Astronomy. The half-life of carbon 14, which is commonly used to date organic materials, is 5700 years. What is the minimum age of sample in which less than 1% of the organic carbon 14 is left?. 88. ## Chemistry. The strontium-90 isotope decays by the reaction below. It has a half-life of 28 yr. If the initial activity of this isotope was 168dpm, what would the activity be after 28.0 yr?. 89. ## Chemistry. Radium-223 has a half-life of 11.4 days.Approximately how long would it take for the activity of a sample of Radium-223 to decrease to 1.00% of its initial value?. 90. ## Calculus. A fragment of bone is discovered to contain 20% of the usual carbon-14 concentration. Estimate the age of the bone to the nearest hundred years, given that Carbon-1 is radioactive with half-life of 5730 years and the rate of decay is given by the following. 91. ## College Algebra. This exercise uses the radioactive decay model. A wooden artifact from an ancient tomb contains 80% of the carbon-14 that is present in living trees. How long ago was the artifact made? (The half-life of carbon-14 is 5730 years. Round your answer to the. 92. ## chem. Radioactive substances decay by first-order kinetics. How many years would be required for a sample containing strontium-90 to decrease to 58.32% of its initial activity? The half-life of strontium-90 is 2.88e1 years.. 93. ## Physics 30. The activity of a sample of a radioactive isotope is 1800Bq. If this isotope has a half-life of 16 days, what is the activity after 16 days?, 24 days?, and 60 days?. 1. A granite rock is thought to be about 2 billion years old. why is it not possible to determine the age of the Rock using carbon-14 dating? 2. A hair sample has 80% of its original carbon-14 present. what is the age of the sample? 3. A bone fragment has. 95. ## Chem. If you have a 12.01g sample carbon. What would be the average mass of a carbon atoms if it is 1.994 x 10 to the 23 power g. How many carbon atoms are in the sample?. 96. ## math. 1.The remains of an old campfire are unearthed and it is found that there is only 80% as much radioactive carbon-14 in the charcoal samples from the campfire as there is in modern living trees. If the half-life of carbon- 14 is 5730 years, how. 97. ## Chemistry. An artifact has a carbon-14 to carbon-12 ratio that is one-fourth the carbon-14 to carbon-12 ratio of a similar modern object. How old is the artifact? (The half-life of carbon-14 is 5,715 years.). 98. ## Chemistry. Q1. The blood volume in a cancer patient was measured by injecting 5.0 mL of Na2SO4(aq) labeled with 35S (t1/2 = 87.4 d). The activity of the sample was 300 µCi. After 22 min, 12.9 mL of blood was withdrawn from the man and the activity of that sample was. 99. ## chemistry. You have a 12.01 g sample of carbon. The average mass of a carbon atoms is 1.994 x 1023 g. How many carbon atoms are in the sample?. 100. ## chemistry. Assayed for LDH activity were 5 microliters of a sample that was diluted 6 to 1. The activity in the reaction vessel, which has a volume of 3 mililiters, is 0.30 U. What is the ΔA/min observed? What is the relative activity of the original sample?. |
https://gateoverflow.in/220957/iit-m-video-questions | 1,576,133,642,000,000,000 | text/html | crawl-data/CC-MAIN-2019-51/segments/1575540537212.96/warc/CC-MAIN-20191212051311-20191212075311-00055.warc.gz | 380,315,592 | 18,309 | 81 views
P(x,y,z), xy=z, Universe is interger;
write in logic form
If xy=x for all y, then x =0.
Thank you
| 81 views
+1 vote
It's a simple "If----then" statement.
Hence, the formulation would be of type $A \rightarrow B$
Here, $A$ is "xy=x for all y"...Or rephrasing, "For all y, xy = x"
Hence, $A$ = $\forall y (P(x,y,x))$
And $B$ is "$x = 0$"
So, "If xy=x for all y, then x =0" $\equiv$ $\forall y (P(x,y,x))$ $\rightarrow$ ($x = 0$)
You can check the above Propositional expression is Always True.
by Boss (26.4k points)
0
'=' operator is used here too
0
'=' operator is used here too
I have also used...see.. ∀y(P(x,y,x)) → (x=0)
Since, Universe is integer, You could use $x = 0$ if need be.
0
Sir, what about ${\forall y (P(x,y,x)) \to P(x,1,0)}$? Can it be a solution?
$\forall y\exists x\left (\left (P\left ( x ,y,z\right )=x\right )\rightarrow\left ( xy=x \right )\Lambda \left ( x=0 \right ) \right )$
by Veteran (117k points)
edited by
0
What "=" stands for ??
And What will be the English interpretation of this expression?
0
= is just for the interpretation of statement
May be a bracket need to clear the statement "If xy=x for all y, then x =0."
0
P(x,y,z)=x
What does it mean?
0
ultimately we need to get x as result and we are operating on function P(x,y,z) i.e. P(x,y,z)=x
and for that conditions are (xy=x) and (x=0)
I think it is resolution method http://nptel.ac.in/courses/106106140/39
1 | 487 | 1,440 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.03125 | 4 | CC-MAIN-2019-51 | longest | en | 0.806885 | 81 views. P(x,y,z), xy=z, Universe is interger;. write in logic form. If xy=x for all y, then x =0.. Thank you. | 81 views. +1 vote. It's a simple "If----then" statement.. Hence, the formulation would be of type $A \rightarrow B$. Here, $A$ is "xy=x for all y"...Or rephrasing, "For all y, xy = x". Hence, $A$ = $\forall y (P(x,y,x))$. And $B$ is "$x = 0$". So, "If xy=x for all y, then x =0" $\equiv$ $\forall y (P(x,y,x))$ $\rightarrow$ ($x = 0$). You can check the above Propositional expression is Always True.. by Boss (26.4k points). 0. '=' operator is used here too. 0. '=' operator is used here too. I have also used...see.. ∀y(P(x,y,x)) → (x=0). Since, Universe is integer, You could use $x = 0$ if need be. | 0. Sir, what about ${\forall y (P(x,y,x)) \to P(x,1,0)}$? Can it be a solution?. $\forall y\exists x\left (\left (P\left ( x ,y,z\right )=x\right )\rightarrow\left ( xy=x \right )\Lambda \left ( x=0 \right ) \right )$. by Veteran (117k points). edited by. 0. What "=" stands for ??. And What will be the English interpretation of this expression?. 0. = is just for the interpretation of statement. May be a bracket need to clear the statement "If xy=x for all y, then x =0.". 0. P(x,y,z)=x. What does it mean?. 0. ultimately we need to get x as result and we are operating on function P(x,y,z) i.e. P(x,y,z)=x. and for that conditions are (xy=x) and (x=0). I think it is resolution method http://nptel.ac.in/courses/106106140/39. 1. |
https://eftradioonline.com/mph-to-degrees-per-second-2022.html | 1,660,339,132,000,000,000 | text/html | crawl-data/CC-MAIN-2022-33/segments/1659882571758.42/warc/CC-MAIN-20220812200804-20220812230804-00081.warc.gz | 225,399,126 | 18,297 | # Mph To Degrees Per Second 2022
Mph To Degrees Per Second 2022. For 250057 mph the best unit of measurement is metres per second, and the amount is 111785.48128 mps. Miles per hour to speed.
Once you know what 1 mph is in feet per second, you can. You can also go to the universal conversion page. A distance of one international mile or 1 760 international yards or exactly 1609.344 meters travelled in one hour or exactly 3 600 seconds.
### 2 Miles Per Second = 7200 Miles Per Hour:
If not, is it better to express the speed of rotation in degrees or rpms?” using linear speed, like miles per hour, to describe a rotating. To switch the unit simply find the one you want on the page and click it. For example, here's how to convert 5 miles per hour to feet per second using the formula above.
### To Get The Distance Travelled During One Minute, The Previous Value Must Be Multiplied By 60.
Meters per second is a unit of speed or velocity in the metric system. You can also go to the universal conversion page. In that case, m/sec = (degrees/sec *.
### 2500 Miles Per Second = 8999998.71 Miles Per Hour:
Miles per hour or mile/second. Then click the convert me button. In this case, all you need to know is that 1 mph is equal to 1.4666679325038 ftps.
### The Speed In Feet Per Second Is Equal To The Miles Per Hour Multiplied By 1.466667.
We all use different units of measurement every day. We assume you are converting between mile/hour and mile/second. Once you know what 1 mph is in feet per second, you can.
### 1 Miles Per Second = 3600 Miles Per Hour:
What is meters per second (m/s)? 1 degree per second is comparative to 0.00277777777777778 hertz. 1,000 degrees per second to radians per second = 17.4533. | 446 | 1,731 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.515625 | 4 | CC-MAIN-2022-33 | latest | en | 0.840815 | # Mph To Degrees Per Second 2022. Mph To Degrees Per Second 2022. For 250057 mph the best unit of measurement is metres per second, and the amount is 111785.48128 mps. Miles per hour to speed.. Once you know what 1 mph is in feet per second, you can. You can also go to the universal conversion page. A distance of one international mile or 1 760 international yards or exactly 1609.344 meters travelled in one hour or exactly 3 600 seconds.. ### 2 Miles Per Second = 7200 Miles Per Hour:. If not, is it better to express the speed of rotation in degrees or rpms?” using linear speed, like miles per hour, to describe a rotating. To switch the unit simply find the one you want on the page and click it. For example, here's how to convert 5 miles per hour to feet per second using the formula above.. ### To Get The Distance Travelled During One Minute, The Previous Value Must Be Multiplied By 60.. Meters per second is a unit of speed or velocity in the metric system. You can also go to the universal conversion page. | In that case, m/sec = (degrees/sec *.. ### 2500 Miles Per Second = 8999998.71 Miles Per Hour:. Miles per hour or mile/second. Then click the convert me button. In this case, all you need to know is that 1 mph is equal to 1.4666679325038 ftps.. ### The Speed In Feet Per Second Is Equal To The Miles Per Hour Multiplied By 1.466667.. We all use different units of measurement every day. We assume you are converting between mile/hour and mile/second. Once you know what 1 mph is in feet per second, you can.. ### 1 Miles Per Second = 3600 Miles Per Hour:. What is meters per second (m/s)? 1 degree per second is comparative to 0.00277777777777778 hertz. 1,000 degrees per second to radians per second = 17.4533. |
http://mathhelpforum.com/pre-calculus/132596-x-iy.html | 1,480,736,483,000,000,000 | text/html | crawl-data/CC-MAIN-2016-50/segments/1480698540804.14/warc/CC-MAIN-20161202170900-00367-ip-10-31-129-80.ec2.internal.warc.gz | 177,726,939 | 8,798 | 1. ## x + iy
just a quick question on expressing $(1 + i) ^3$ in the form x + iy
the answer i came to was:
$2 + 4i + i^2 + i^2
= 2 + 4i -1 -1
= 0 + 4i$
however im not sure if this is correct...
2. Originally Posted by murielx
just a quick question on expressing $(1 + i) ^3$ in the form x + iy
the answer i came to was:
$2 + 4i + i^2 + i^2
= 2 + 4i -1 -1
= 0 + 4i$
however im not sure if this is correct...
I am not sure how you expanded the above but it can be treated like a polynomial in i.
Using the binomial theorem or by the distributive law you get
$(1+i)^3=\sum_{n=0}^{3}\binom{3}{n}1^{3-n}i^{n}=1+3i+3i^2+i^3=1+3i-3-i=-2+2i$ | 253 | 639 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 5, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.765625 | 4 | CC-MAIN-2016-50 | longest | en | 0.84213 | 1. ## x + iy. just a quick question on expressing $(1 + i) ^3$ in the form x + iy. the answer i came to was:. $2 + 4i + i^2 + i^2. = 2 + 4i -1 -1. = 0 + 4i$. however im not sure if this is correct.... 2. Originally Posted by murielx. | just a quick question on expressing $(1 + i) ^3$ in the form x + iy. the answer i came to was:. $2 + 4i + i^2 + i^2. = 2 + 4i -1 -1. = 0 + 4i$. however im not sure if this is correct.... I am not sure how you expanded the above but it can be treated like a polynomial in i.. Using the binomial theorem or by the distributive law you get. $(1+i)^3=\sum_{n=0}^{3}\binom{3}{n}1^{3-n}i^{n}=1+3i+3i^2+i^3=1+3i-3-i=-2+2i$. |
https://edurev.in/studytube/Class-12-Mathematics-CBSE-Sample-Question-Paper-Te/1e4c95ba-724c-4822-8449-85038c149f86_t | 1,722,944,553,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722640484318.27/warc/CC-MAIN-20240806095414-20240806125414-00797.warc.gz | 171,727,324 | 72,286 | Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 1
# Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 1 | Mathematics (Maths) Class 12 - JEE PDF Download
Table of contents Class-XII Time: 90 Minutes Max. Marks: 40 Section - A Section - B Section - C
## Max. Marks: 40
General Instructions :
1. This question paper contains three sections – A, B and C. Each part is compulsory.
2. Section - A has 20 MCQs, attempt any 16 out of 20.
3. Section - B has 20 MCQs, attempt any 16 out of 20.
4. Section - C has 10 MCQs, attempt any 8 out of 10.
5. There is no negative marking.
6. All questions carry equal marks
## Section - A
Q.1: 1. What is the principal value branch of sec–1 x ?
(a) (–1, 1)
(b) [–1, 1]
(c)
(d) [0, π]
The sec function is periodic so to calculate its inverse function we need to make the function bijective. For that we have to consider an interval in which all values of the function exist and do not repeat. For sec function this interval is considered as
Thus when we take the inverse of the function the domain becomes range and the range becomes domain. Hence the principal value branch is the range of sec–1x that is
Q.2: What is the derivative of the function y = xtanx ?
(a) xtanx(xsecx + sec x logx)
(b)
(c) xtanx (2x sec x + tanx log x))
(d)
y = xtan x
log y = tanx logx
Differentiating both side w.r.t. x.
Q.3: Matrix is a square matrix if
(a) m > n
(b) m < n
(c) m = 1
(d) m = n
Given matrix is said to be square matrix if number of rows are equal to number of columns. Therefore, is a square matrix only if m = n.
Q.4: Calculate the determinant of the given matrix
(a) 1/2
(b) -1/2
(c) 3/2
(d) None of the above
Q.5: Absolute maximum of the function 2x + 5 in [5, 10] ?
(a) 5
(b) 10
(c) 20
(d) 25
Given, f '(x) = 2x + 5
Therefore, f '(x) = 2 > 0
Since, f '(x) > 0 in the maximum value is at upper and point f(10) = 2 × 10 + 5 = 25
Q.6: if then the value of x is:
(a) –6
(b) –36
(c) 6
(d) 36
For any matrices A and B of suitable orders, we have
(a) (A')' = A
(b) (A + B)' = A' + B'
(c) (kA)' = kA' (where k is any constant)
(d) (A B)' = B'A'
Q.7: Given set A = {a, b, c}. An identity relation in set A is:
(a) R= {(a, b), (a, c)}
(b) R= {(a, a), (b, b), (c, c)}
(c) R= {(a, a), (b, b), (c, c), (a, c)}
(d) R= {(c, a), (b, a), (a, a)}
Identity relation is function that always returns the same value that was used as its argument. That is, f(x) = x for all elements in set A.
Q.8: For a square matrix A = [aij] the quantity calculated for any element aij in A as the product of (-1)i+j and determinant of the square sub-matrix of order (n-1) obtained by leaving the ith row and jth column of A is known as
(a) Cofactor
(b) Minor
(c) Coefficient
(d) Elements
The cofactor of an element aij in A is calculated as the product of ( -1)i+j and determinant of the square sub-matrix of order (n-1) obtained by leaving the ith row and jth column of A.
Q.9: What is the absolute minimum of the function |x – 3| in the interval [4, 5] ?
(a) 2
(b) 4
(c) 6
(d) 8
Since the given function is increasing continuously in the given interval, maximum value is at the extreme end point.
Q.10: What is the general interval for sine function to become a bijective function?
(a)
(b)
(c)
(d)
The sine function is periodic so to calculate its inverse function we need to make the function bijective. For that we have to consider an interval in which all values of the function exist and do not repeat.
Q.11: Let R be relation from R to R the set of real numbers defined by R = {(x, y): x, y ∈ R and x – y + √3 is an irrational number}. Then, R is:
(a) Reflexive
(b) Transitive
(c) Symmetric
(d) An equivalence relation
For reflexive, let (x, x) ∈ R
⇒ x - x + √3 = √3 which is an irrational number. Hence, it is reflexive.
For symmetric, let f(x, y) ∈ R
⇒ x - y + √3 which is an irrational number.
This means y - x + √3 is an irrational number. So, f(y, x) ∈ R. Hence, it is symmetric.
For transitive, let f(x, y)∈ R
⇒ x - y + √3 and f(y, z) ∈ R
⇒ y - z + √3. Now adding these equations, we will get x - z + √3
⇒ (x, z)∈ R. Hence, it is transitive. Therefore, it is an equivalence relation.
Q.12: if x = at4, y = at3 then dy/dx will be
(a) 3/4t
(b) 3/4t2
(c) 3/4
(d) 3t/4
Q.13: Every Identity matrix is a:
(a) Zero matrix
(b) Row matrix
(c) Scalar matrix
(d) Column matrix
A scalar matrix is an identity matrix when k = 1. But every identity matrix is clearly a scalar matrix.
Q.14: If y = sin x log x then the value of dy/dx is
(a) sin x log x – 1
(b)
(c)
(d)
y = sinx logx
Q.15: For Matrix (adj A)' is equal to
(a)
(b)
(c)
(d)
Q.16: Which of the following line perpendicular to the tangent to curve y = x2 – 5 at x=1.
(a) 2y+x - 35 = 0
(b) 2x−3y+35 = 0
(c) 4x+7y+35 = 0
(d) 3x+7y+21= 0
Slope of tangent = dy/dx = 2x at x = 1, dy/dx = 2
slope of the perpendicular is - 1/slope
= - 1/2
Required equation is 2y + x – 35 =0
Q.17: Calculate the value of x such that the matrix is singular.
(a) –1, 2
(b) 2, 3
(c) 1
(d) No such value exist
+ 1[1 – x + 1] = 0
⇒ (x – 1)(x2 + 1 – 2x – 1) – x + 2 + 2 – x = 0
⇒ (x – 1)(x2 – 2x) – 2(x – 2) = 0
⇒ (x – 2)(x2 – x – 2) = 0
Q.18: If then dy/dx is equal to
(a)
(b)
(c)
(d)
Given that,
Differentiate with respect to x, we have
Q.19: Maximize Z = x + y, subject to x – y ≤ –1, –x + y ≤ 0, x, y ≥ 0.
(a) the value of z is minimum at every point on line x – y = –1
(b) there is no feasible region with these constraints.
(c) the value of z is minimum at every point on line –x + y = 1
(d) None
The region determined by the constraints, is as follows. There is no feasible region and thus, Z has
x – y ≤ –1, –x + y ≤ 0, x, y≥ 0
Q.20: Which of the following is true for the given function?
(a) Continuous at x = 0
(b) Not continuous at 0
(c) differentiable at 0
(d) None of the above
Given,
## Section - B
Q.21: Let A = {a, b, c} and B = {1, 2, 3} and f: A→ B is defined by f = {(a, 2), (b, 1), (c, 3)}. Is the function oneone and onto.
(a) both one-one and onto
(b) only one-one
(c) only onto
(d) neither of them
All the elements in the domain has a unique value in the range. Also the codomain of the function is equal to its range.
Q.22: Find the dy/dx of yx+xy = 0 ?
(a)
(b)
(c) 0
(d) None of these
yx+xy = 0
or exlogy + eylogx = 0
Differentiating both sides w.r.t. x.
Q.23: Corner points of the feasible region for an LPP are (0, 2), (3, 0), (6, 0), (6, 8) and (0, 5). Let F = 4x + 6y be the objective function.
The minimum value of F occurs at
(a) (0, 2) only
(b) (3, 0) only
(c) the mid-point of the line segment joining the points (0, 2) and (3, 0) only
(d) any point on the line segment joining the points (0, 2) and (3, 0)
Hence, minimum value of F occurs at any points on the line segment joining the points (0, 2) and (3, 0).
Q.24: Consider the curve y = x2/4. The Slope of the line parallel to tangent to the curve at x = 1 is
(a) 1/4
(b) 1/3
(c) - 1/2
(d) 1/2
y = x2/4
Slope of the curve
Parallel lines have same slopes
∴ Slope of tangent = 1/2
Q.25: if then the value of x is
(a) 3
(b) ±3
(c) ±6
(d) 6
The process described in the reason statement is the correct procedure to solve the given question. For the given determinant,
2x2 – 40 = 32
2x2 = 72
x = ±6
Q.26: Given a function f (x)= 2x3 −21x2 +60x+48, it has local maximum at x =
(a) 2
(b) 3
(c) 5
(d) 4
f(x) = 2x3 – 21x2 + 60x + 48
f'(x) = 6x2 – 42x + 60
f'(x) = 0
⇒ 6x2 – 42x + 60 = 0
6 (x2 – 7x + 10) = 0
6 (x – 2) (x – 5) = 0
x = 2, 5
f''(x) = 12x – 42
f''(2) = –18 < 0
f''(5) = 60 – 42
= 18 > 0
∴ f(x) is maximum at x = 2.
Q.27: The principal value of
(a) π/4
(b) π/6
(c) -π/4
(d) π/3
The principal value of means that we need to find an angle in the principal branch of the function where the sine function is equal to - 1/√2. Hence the required value is -π/4.
Q.28: Suppose P and Q are two different matrices of order 3 × n and n × p, then the order of the matrix P × Q is ?
(a) 3 × p
(b) p × 3
(c) n × n
(d) 3 × 3
Q.29: Let f(x) = |sin x|, then
(a) f is everywhere differentiable
(b) f is everywhere continuous but not differentiable at x = n π, n ∈ Z.
(c) f is everywhere continuous but not differentiable at
(d) none of these
Given that, f(x) = |sin x|
The functions |x| and sin x are continuous function for all real value of x.
Thus, the function f(x) = |sin x| is continuous function everywhere.
Now, |x| is non-differentiable function at x = 0.
Since f(x) = |sin x| is non-differentiable function at sin x = 0
Thus, f is everywhere continuous but not differentiable at x = n π, n ∈ Z.
Q.30: If function f : R → R defined as f(x) = x2 then f(x) is
(a) onto
(b) one-one and onto
(c) one-one
(d) None of these
f(x) is a one-one function
if f(x1) = f(x2) ⇒ x1= x2
Let f(x1) = f(x2) for some x1, x2 ∈ R
⇒(x1)2=(x2)2
⇒ x1 = ±x2
Hence f(x) is one-one.
Q.31: Which of these intervals, the function f (x)= √2 cos x+x−35 is monotonic?
(a)
(b)
(c)
(d)
A function is Monotonic if its first derivative’s sign doesn’t change in the given interval.
Q.32: If then x equals
(a) 0
(b) -2
(c) -1
(d) 2
Q.33: Objective function:
Maximise Z = 1000x + 600y
Constraints:
x + y ≥ 200
y ≥ 20, x ≥ 0
4x
Z is maximum at point
(a) (20, 80)
(b) (20, 180)
(c) (0, 0)
(d) (40, 160)
The corner points are A(20, 180), B(40, 160), C(20, 80)
Evaluating the objective function Z = 1,000x + 600y at A, B and C
At A(20, 180),
Z = 1,000 × 20 + 600 × 180 = 20,000 + 1,08,000 = ₹1,28,000
At B(40, 160), Z = 1,000 × 40 + 600 × 160 = 40,000 + 96,000 = ₹1,36,000 (max.)
At C(20, 80), Z = 1000 × 20 + 600 × 80 = 20,000 + 48,000 = ₹68,000 or
Z is maximum, when x = 40, y = 160.
Q.34: A particle moves along the curve x2 = 2y. The point at which, ordinate increases at the same rate as the abscissa is ________
(a) (1,2)
(b) (1/2, 1)
(c) (1/2, 1/2)
(d) (1, 1/2)
Q.35: If then AB + XY equals
(a) [28]
(b) [24]
(c) 28
(d) 24
Given, A = [2 -3 4] ,
= [6 – 6 + 8] + [2 + 6 + 12]
= [8] + [20]
= [28]
Q.36: If function Then the domain of the function is:
(a)
(b) R
(c) R - {1}
(d) R - {5}
10xy – 2y = 2x + 5
10xy – 2x = 5 + 2y
2x(5y – 1) = 5 + 2y
Q.37: The maximum number of equivalence relations on the set A = {1, 2, 3} are
(a) 1
(b) 2
(c) 3
(d) 5
Given that, A = {1, 2, 3}
Now, number of equivalence relations are as follows:
R1 = {(1, 1), (2, 2), (3, 3)}
R2 = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 1)}
R3 = {(1, 1), (2, 2), (3, 3), (1, 3), (3, 1)}
R4 = {(1, 1), (2, 2), (3, 3), (2, 3), (3, 2)}
R5 = {(1, 2, 3) ⇔ A × A = A2}
∴ Maximum number of equivalence relations on the set A = {1, 2, 3} = 5
Q.38: If A is any square matrix of order 3 × 3 such that |A| = 3, then the value of |adj A| is?
(a) 3
(b) 1/3
(c) 9
(d) 27
|A| = 3, n = 3
|adj A| = |A|2 = 32 = 9
Q.39: The equation of tangent to the curve y(1 + x2) = 2 – x, where it crosses x-axis is:
(a) x + 5y = 2
(b) x – 5y = 2
(c) 5x – y = 2
(d) 5x + y = 2
Given that the equation of curve is
y(1 + x2) = 2 – x ...(i)
On differentiating with respect to x, we get
Since, the given curve passes through -axis,
i.e y = 0
∴ 0(1 + x2) = 2 - x [by using eq. (i) ]
⇒ x = 2
So the curve passes through the point (2, 0).
∴ Equation of tangent to the curve passsing through (2, 0) is
Q.40: A = [aij]m×n is a square matrix, if
(a) m < n
(b) m > n
(c) m = n
(d) None of these
It is known that a given matrix is said to be a square matrix if the number of rows is equal to the number of columns.
Therefore,
A = [aij]m x n is a square matrix, if m = n.
## Section - C
Q.41: For an objective function Z = ax + by, where a, b > 0; the corner points of the feasible region determined by a set of constraints (linear inequalities) are (0, 20), (10, 10), (30, 30) and (0, 40). The condition on a and b such that the maximum Z occurs at both the points (30, 30) and (0, 40) is:
(a) b − 3a = 0
(b) a = 3b
(c) a + 2b = 0
(d) 2a − b = 0
As Z is maximum at (30, 30) and (0, 40)
⇒ 30a + b = 40b
⇒ b – 3a = 0
Q.42: For which value of m is the line y = mx + 1 a tangent to the curve y2 = 4x?
(a) 1 2
(b) 1
(c) 2
(d) 3
y = mx + 1 ...(i)
and y2 = 4x ...(ii)
Substituting (i) in (ii) :
(mx + 1)2 = 4x
⇒ m2x2 + (2m – 4)x + 1 = 0 ...(iii)
As line is tangent to the curve
⇒ line touches the curve at only one point
⇒ (2m – 4)2 – 4m2 = 0
⇒ m = 1
Q.43: The maximum value of [x(x+1)+1]1/3, 0 ≤ x ≤ 1 is:
(a) 0
(b) 1/2
(c) 1
(d)
Let f(x) = [x(x – 1) + 1]1/3,0 ≤ x ≤ 1
Q.44: In a linear programming problem, the constraints on the decision variables x and y are x − 3y ≥ 0, y ≥ 0, 0 ≤ x ≤ 3. The feasible region
(a) is not in the first quadrant
(b) is bounded in the first quadrant
(c) is unbounded in the first quadrant
(d) does not exist
Feasible region is bounded in the first quadrant
Q.45: Let where 0 ≤ α ≤ 2π, then:
(A) |A|= 0
(B) |A| ∈ (2, ∞)
(C) |A| ∈ (2, 4)
(D) |A| ∈ [2, 4]
|A| = 2 + 2sin2θ
As –1 ≤ sin θ ≤ 1, ∀ 0 ≤ θ ≤ 2π
⇒ 2 ≤ 2 + 2sin2θ ≤ 4
⇒ |A|∈ [2, 4]
Questions 46-50 are based on a Case-Study
Case-Study
The fuel cost per hour for running a train is proportional to the square of the speed it generates in km per hour. If the fuel costs ₹48 per hour at speed 16 km per hour and the fixed charges to run the train amount to ₹1200 per hour. Assume the speed of the train as v km/h. Based on the given information, answer the following questions.
Q.46: Given that the fuel cost per hour is k times the square of the speed the train generates in km/h, the value of k is:
(a) 16/3
(b) 1/3
(c) 3
(d) 3/16
Fuel cost = k(speed)2
⇒ 48 = k.162
⇒ k = 3/16
Q.47: If the train has travelled a distance of 500km, then the total cost of running the train is given by function:
(a)
(b)
(c)
(d)
Total cost of running train
Distance covered = 500 km
Q.48: The most economical speed to run the train is:
(a) 18km/h
(b) 5km/h
(c) 80km/h
(d) 40km/h
Q.49: The fuel cost for the train to travel 500 km at the most economical speed is: (a) ₹3750
(b) 750
(c) 7500
(d) 75000
Fuel cost for running 500 km
Q.50: The total cost of the train to travel 500km at the most economical speed is:
(a) 3750
(b) 75000
(c) 7500
(d) 15000
Total cost for running 500 km
The document Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 1 | Mathematics (Maths) Class 12 - JEE is a part of the JEE Course Mathematics (Maths) Class 12.
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; | 5,594 | 14,633 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.4375 | 4 | CC-MAIN-2024-33 | latest | en | 0.783867 | Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 1. # Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 1 | Mathematics (Maths) Class 12 - JEE PDF Download. Table of contents Class-XII Time: 90 Minutes Max. Marks: 40 Section - A Section - B Section - C. ## Max. Marks: 40. General Instructions :. 1. This question paper contains three sections – A, B and C. Each part is compulsory.. 2. Section - A has 20 MCQs, attempt any 16 out of 20.. 3. Section - B has 20 MCQs, attempt any 16 out of 20.. 4. Section - C has 10 MCQs, attempt any 8 out of 10.. 5. There is no negative marking.. 6. All questions carry equal marks. ## Section - A. Q.1: 1. What is the principal value branch of sec–1 x ?. (a) (–1, 1). (b) [–1, 1]. (c). (d) [0, π]. The sec function is periodic so to calculate its inverse function we need to make the function bijective. For that we have to consider an interval in which all values of the function exist and do not repeat. For sec function this interval is considered as. Thus when we take the inverse of the function the domain becomes range and the range becomes domain. Hence the principal value branch is the range of sec–1x that is. Q.2: What is the derivative of the function y = xtanx ?. (a) xtanx(xsecx + sec x logx). (b). (c) xtanx (2x sec x + tanx log x)). (d). y = xtan x. log y = tanx logx. Differentiating both side w.r.t. x.. Q.3: Matrix is a square matrix if. (a) m > n. (b) m < n. (c) m = 1. (d) m = n. Given matrix is said to be square matrix if number of rows are equal to number of columns. Therefore, is a square matrix only if m = n.. Q.4: Calculate the determinant of the given matrix. (a) 1/2. (b) -1/2. (c) 3/2. (d) None of the above. Q.5: Absolute maximum of the function 2x + 5 in [5, 10] ?. (a) 5. (b) 10. (c) 20. (d) 25. Given, f '(x) = 2x + 5. Therefore, f '(x) = 2 > 0. Since, f '(x) > 0 in the maximum value is at upper and point f(10) = 2 × 10 + 5 = 25. Q.6: if then the value of x is:. (a) –6. (b) –36. (c) 6. (d) 36. For any matrices A and B of suitable orders, we have. (a) (A')' = A. (b) (A + B)' = A' + B'. (c) (kA)' = kA' (where k is any constant). (d) (A B)' = B'A'. Q.7: Given set A = {a, b, c}. An identity relation in set A is:. (a) R= {(a, b), (a, c)}. (b) R= {(a, a), (b, b), (c, c)}. (c) R= {(a, a), (b, b), (c, c), (a, c)}. (d) R= {(c, a), (b, a), (a, a)}. Identity relation is function that always returns the same value that was used as its argument. That is, f(x) = x for all elements in set A.. Q.8: For a square matrix A = [aij] the quantity calculated for any element aij in A as the product of (-1)i+j and determinant of the square sub-matrix of order (n-1) obtained by leaving the ith row and jth column of A is known as. (a) Cofactor. (b) Minor. (c) Coefficient. (d) Elements. The cofactor of an element aij in A is calculated as the product of ( -1)i+j and determinant of the square sub-matrix of order (n-1) obtained by leaving the ith row and jth column of A.. Q.9: What is the absolute minimum of the function |x – 3| in the interval [4, 5] ?. (a) 2. (b) 4. (c) 6. (d) 8. Since the given function is increasing continuously in the given interval, maximum value is at the extreme end point.. Q.10: What is the general interval for sine function to become a bijective function?. (a). (b). (c). (d). The sine function is periodic so to calculate its inverse function we need to make the function bijective. For that we have to consider an interval in which all values of the function exist and do not repeat.. Q.11: Let R be relation from R to R the set of real numbers defined by R = {(x, y): x, y ∈ R and x – y + √3 is an irrational number}. Then, R is:. (a) Reflexive. (b) Transitive. (c) Symmetric. (d) An equivalence relation. For reflexive, let (x, x) ∈ R. ⇒ x - x + √3 = √3 which is an irrational number. Hence, it is reflexive.. For symmetric, let f(x, y) ∈ R. ⇒ x - y + √3 which is an irrational number.. This means y - x + √3 is an irrational number. So, f(y, x) ∈ R. Hence, it is symmetric.. For transitive, let f(x, y)∈ R. ⇒ x - y + √3 and f(y, z) ∈ R. ⇒ y - z + √3. Now adding these equations, we will get x - z + √3. ⇒ (x, z)∈ R. Hence, it is transitive. Therefore, it is an equivalence relation.. Q.12: if x = at4, y = at3 then dy/dx will be. (a) 3/4t. (b) 3/4t2. (c) 3/4. (d) 3t/4. Q.13: Every Identity matrix is a:. (a) Zero matrix. (b) Row matrix. (c) Scalar matrix. (d) Column matrix. A scalar matrix is an identity matrix when k = 1. But every identity matrix is clearly a scalar matrix.. Q.14: If y = sin x log x then the value of dy/dx is. (a) sin x log x – 1. (b). (c). (d). y = sinx logx. Q.15: For Matrix (adj A)' is equal to. (a). (b). (c). (d). Q.16: Which of the following line perpendicular to the tangent to curve y = x2 – 5 at x=1.. (a) 2y+x - 35 = 0. (b) 2x−3y+35 = 0. (c) 4x+7y+35 = 0. (d) 3x+7y+21= 0. Slope of tangent = dy/dx = 2x at x = 1, dy/dx = 2. slope of the perpendicular is - 1/slope. = - 1/2. Required equation is 2y + x – 35 =0. Q.17: Calculate the value of x such that the matrix is singular.. (a) –1, 2. (b) 2, 3. (c) 1. (d) No such value exist. + 1[1 – x + 1] = 0. ⇒ (x – 1)(x2 + 1 – 2x – 1) – x + 2 + 2 – x = 0. ⇒ (x – 1)(x2 – 2x) – 2(x – 2) = 0. ⇒ (x – 2)(x2 – x – 2) = 0. Q.18: If then dy/dx is equal to. (a). (b). (c). (d). Given that,. Differentiate with respect to x, we have. Q.19: Maximize Z = x + y, subject to x – y ≤ –1, –x + y ≤ 0, x, y ≥ 0.. (a) the value of z is minimum at every point on line x – y = –1. (b) there is no feasible region with these constraints.. (c) the value of z is minimum at every point on line –x + y = 1. (d) None. The region determined by the constraints, is as follows. There is no feasible region and thus, Z has. x – y ≤ –1, –x + y ≤ 0, x, y≥ 0. Q.20: Which of the following is true for the given function?. (a) Continuous at x = 0. (b) Not continuous at 0. (c) differentiable at 0. (d) None of the above. Given,. ## Section - B. Q.21: Let A = {a, b, c} and B = {1, 2, 3} and f: A→ B is defined by f = {(a, 2), (b, 1), (c, 3)}. Is the function oneone and onto.. (a) both one-one and onto. (b) only one-one. (c) only onto. (d) neither of them. All the elements in the domain has a unique value in the range. Also the codomain of the function is equal to its range.. Q.22: Find the dy/dx of yx+xy = 0 ?. (a). (b). (c) 0. (d) None of these. yx+xy = 0. or exlogy + eylogx = 0. Differentiating both sides w.r.t. x.. Q.23: Corner points of the feasible region for an LPP are (0, 2), (3, 0), (6, 0), (6, 8) and (0, 5). Let F = 4x + 6y be the objective function.. The minimum value of F occurs at. (a) (0, 2) only. (b) (3, 0) only. (c) the mid-point of the line segment joining the points (0, 2) and (3, 0) only. (d) any point on the line segment joining the points (0, 2) and (3, 0). Hence, minimum value of F occurs at any points on the line segment joining the points (0, 2) and (3, 0).. Q.24: Consider the curve y = x2/4. The Slope of the line parallel to tangent to the curve at x = 1 is. (a) 1/4. (b) 1/3. (c) - 1/2. (d) 1/2. y = x2/4. Slope of the curve. Parallel lines have same slopes. ∴ Slope of tangent = 1/2. Q.25: if then the value of x is. (a) 3. (b) ±3. (c) ±6. (d) 6. The process described in the reason statement is the correct procedure to solve the given question. For the given determinant,. 2x2 – 40 = 32. 2x2 = 72. x = ±6. Q.26: Given a function f (x)= 2x3 −21x2 +60x+48, it has local maximum at x =. (a) 2. (b) 3. (c) 5. (d) 4. f(x) = 2x3 – 21x2 + 60x + 48. f'(x) = 6x2 – 42x + 60. f'(x) = 0. ⇒ 6x2 – 42x + 60 = 0. 6 (x2 – 7x + 10) = 0. 6 (x – 2) (x – 5) = 0. x = 2, 5. f''(x) = 12x – 42. f''(2) = –18 < 0. f''(5) = 60 – 42. = 18 > 0. ∴ f(x) is maximum at x = 2.. Q.27: The principal value of. (a) π/4. (b) π/6. | (c) -π/4. (d) π/3. The principal value of means that we need to find an angle in the principal branch of the function where the sine function is equal to - 1/√2. Hence the required value is -π/4.. Q.28: Suppose P and Q are two different matrices of order 3 × n and n × p, then the order of the matrix P × Q is ?. (a) 3 × p. (b) p × 3. (c) n × n. (d) 3 × 3. Q.29: Let f(x) = |sin x|, then. (a) f is everywhere differentiable. (b) f is everywhere continuous but not differentiable at x = n π, n ∈ Z.. (c) f is everywhere continuous but not differentiable at. (d) none of these. Given that, f(x) = |sin x|. The functions |x| and sin x are continuous function for all real value of x.. Thus, the function f(x) = |sin x| is continuous function everywhere.. Now, |x| is non-differentiable function at x = 0.. Since f(x) = |sin x| is non-differentiable function at sin x = 0. Thus, f is everywhere continuous but not differentiable at x = n π, n ∈ Z.. Q.30: If function f : R → R defined as f(x) = x2 then f(x) is. (a) onto. (b) one-one and onto. (c) one-one. (d) None of these. f(x) is a one-one function. if f(x1) = f(x2) ⇒ x1= x2. Let f(x1) = f(x2) for some x1, x2 ∈ R. ⇒(x1)2=(x2)2. ⇒ x1 = ±x2. Hence f(x) is one-one.. Q.31: Which of these intervals, the function f (x)= √2 cos x+x−35 is monotonic?. (a). (b). (c). (d). A function is Monotonic if its first derivative’s sign doesn’t change in the given interval.. Q.32: If then x equals. (a) 0. (b) -2. (c) -1. (d) 2. Q.33: Objective function:. Maximise Z = 1000x + 600y. Constraints:. x + y ≥ 200. y ≥ 20, x ≥ 0. 4x. Z is maximum at point. (a) (20, 80). (b) (20, 180). (c) (0, 0). (d) (40, 160). The corner points are A(20, 180), B(40, 160), C(20, 80). Evaluating the objective function Z = 1,000x + 600y at A, B and C. At A(20, 180),. Z = 1,000 × 20 + 600 × 180 = 20,000 + 1,08,000 = ₹1,28,000. At B(40, 160), Z = 1,000 × 40 + 600 × 160 = 40,000 + 96,000 = ₹1,36,000 (max.). At C(20, 80), Z = 1000 × 20 + 600 × 80 = 20,000 + 48,000 = ₹68,000 or. Z is maximum, when x = 40, y = 160.. Q.34: A particle moves along the curve x2 = 2y. The point at which, ordinate increases at the same rate as the abscissa is ________. (a) (1,2). (b) (1/2, 1). (c) (1/2, 1/2). (d) (1, 1/2). Q.35: If then AB + XY equals. (a) [28]. (b) [24]. (c) 28. (d) 24. Given, A = [2 -3 4] ,. = [6 – 6 + 8] + [2 + 6 + 12]. = [8] + [20]. = [28]. Q.36: If function Then the domain of the function is:. (a). (b) R. (c) R - {1}. (d) R - {5}. 10xy – 2y = 2x + 5. 10xy – 2x = 5 + 2y. 2x(5y – 1) = 5 + 2y. Q.37: The maximum number of equivalence relations on the set A = {1, 2, 3} are. (a) 1. (b) 2. (c) 3. (d) 5. Given that, A = {1, 2, 3}. Now, number of equivalence relations are as follows:. R1 = {(1, 1), (2, 2), (3, 3)}. R2 = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 1)}. R3 = {(1, 1), (2, 2), (3, 3), (1, 3), (3, 1)}. R4 = {(1, 1), (2, 2), (3, 3), (2, 3), (3, 2)}. R5 = {(1, 2, 3) ⇔ A × A = A2}. ∴ Maximum number of equivalence relations on the set A = {1, 2, 3} = 5. Q.38: If A is any square matrix of order 3 × 3 such that |A| = 3, then the value of |adj A| is?. (a) 3. (b) 1/3. (c) 9. (d) 27. |A| = 3, n = 3. |adj A| = |A|2 = 32 = 9. Q.39: The equation of tangent to the curve y(1 + x2) = 2 – x, where it crosses x-axis is:. (a) x + 5y = 2. (b) x – 5y = 2. (c) 5x – y = 2. (d) 5x + y = 2. Given that the equation of curve is. y(1 + x2) = 2 – x ...(i). On differentiating with respect to x, we get. Since, the given curve passes through -axis,. i.e y = 0. ∴ 0(1 + x2) = 2 - x [by using eq. (i) ]. ⇒ x = 2. So the curve passes through the point (2, 0).. ∴ Equation of tangent to the curve passsing through (2, 0) is. Q.40: A = [aij]m×n is a square matrix, if. (a) m < n. (b) m > n. (c) m = n. (d) None of these. It is known that a given matrix is said to be a square matrix if the number of rows is equal to the number of columns.. Therefore,. A = [aij]m x n is a square matrix, if m = n.. ## Section - C. Q.41: For an objective function Z = ax + by, where a, b > 0; the corner points of the feasible region determined by a set of constraints (linear inequalities) are (0, 20), (10, 10), (30, 30) and (0, 40). The condition on a and b such that the maximum Z occurs at both the points (30, 30) and (0, 40) is:. (a) b − 3a = 0. (b) a = 3b. (c) a + 2b = 0. (d) 2a − b = 0. As Z is maximum at (30, 30) and (0, 40). ⇒ 30a + b = 40b. ⇒ b – 3a = 0. Q.42: For which value of m is the line y = mx + 1 a tangent to the curve y2 = 4x?. (a) 1 2. (b) 1. (c) 2. (d) 3. y = mx + 1 ...(i). and y2 = 4x ...(ii). Substituting (i) in (ii) :. (mx + 1)2 = 4x. ⇒ m2x2 + (2m – 4)x + 1 = 0 ...(iii). As line is tangent to the curve. ⇒ line touches the curve at only one point. ⇒ (2m – 4)2 – 4m2 = 0. ⇒ m = 1. Q.43: The maximum value of [x(x+1)+1]1/3, 0 ≤ x ≤ 1 is:. (a) 0. (b) 1/2. (c) 1. (d). Let f(x) = [x(x – 1) + 1]1/3,0 ≤ x ≤ 1. Q.44: In a linear programming problem, the constraints on the decision variables x and y are x − 3y ≥ 0, y ≥ 0, 0 ≤ x ≤ 3. The feasible region. (a) is not in the first quadrant. (b) is bounded in the first quadrant. (c) is unbounded in the first quadrant. (d) does not exist. Feasible region is bounded in the first quadrant. Q.45: Let where 0 ≤ α ≤ 2π, then:. (A) |A|= 0. (B) |A| ∈ (2, ∞). (C) |A| ∈ (2, 4). (D) |A| ∈ [2, 4]. |A| = 2 + 2sin2θ. As –1 ≤ sin θ ≤ 1, ∀ 0 ≤ θ ≤ 2π. ⇒ 2 ≤ 2 + 2sin2θ ≤ 4. ⇒ |A|∈ [2, 4]. Questions 46-50 are based on a Case-Study. Case-Study. The fuel cost per hour for running a train is proportional to the square of the speed it generates in km per hour. If the fuel costs ₹48 per hour at speed 16 km per hour and the fixed charges to run the train amount to ₹1200 per hour. Assume the speed of the train as v km/h. Based on the given information, answer the following questions.. Q.46: Given that the fuel cost per hour is k times the square of the speed the train generates in km/h, the value of k is:. (a) 16/3. (b) 1/3. (c) 3. (d) 3/16. Fuel cost = k(speed)2. ⇒ 48 = k.162. ⇒ k = 3/16. Q.47: If the train has travelled a distance of 500km, then the total cost of running the train is given by function:. (a). (b). (c). (d). Total cost of running train. Distance covered = 500 km. Q.48: The most economical speed to run the train is:. (a) 18km/h. (b) 5km/h. (c) 80km/h. (d) 40km/h. Q.49: The fuel cost for the train to travel 500 km at the most economical speed is: (a) ₹3750. (b) 750. (c) 7500. (d) 75000. Fuel cost for running 500 km. Q.50: The total cost of the train to travel 500km at the most economical speed is:. (a) 3750. (b) 75000. (c) 7500. (d) 15000. Total cost for running 500 km. The document Class 12 Mathematics: CBSE Sample Question Paper- Term I (2021-22)- 1 | Mathematics (Maths) Class 12 - JEE is a part of the JEE Course Mathematics (Maths) Class 12.. All you need of JEE at this link: JEE. ## Mathematics (Maths) Class 12. 204 videos|288 docs|139 tests. ## Mathematics (Maths) Class 12. 204 videos|288 docs|139 tests. ### Up next. Explore Courses for JEE exam. Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.. 10M+ students study on EduRev. Related Searches. ,. ,. ,. ,. ,. ,. ,. ,. ,. ,. ,. ,. ,. ,. ,. ,. ,. ,. ,. ,. ,. ;. |
https://www.jiskha.com/questions/642516/almost-everyone-at-the-bright-corporation-reads-a-daily-newspaper-on-a-regular-basis-in | 1,638,423,966,000,000,000 | text/html | crawl-data/CC-MAIN-2021-49/segments/1637964361169.72/warc/CC-MAIN-20211202054457-20211202084457-00468.warc.gz | 878,495,449 | 5,563 | # math
Almost everyone at the Bright Corporation reads a daily newspaper on a regular basis. In fact, altogether te company employs 2,940 people,of whom70% read The Daily News,45% read The Courier and 60% read The inquirer.
One fourth of the employees reads The Daily News and The Courier, and 30% read The Inquirer and The Courier, and 35% read The Daily News and The Inquirer. One tenth of the people read all three newspapers on a regular basis.
a. how many people read only The Daily news?
b. How many people read only The Courier?
c. How many people read on The Inquirer?
d. How many people don't read any newspaper?
1. 👍
2. 👎
3. 👁
1. Draw your 3-circle Venn diagram. Label the circles D,C,I
DCI = .1
so
DC only = .15 (.25-.10)
CI only = .20 (.30-.10)
DI only = .25 (.35-.10)
D only = .20 (.70 - .15 - .10 - .25)
C only = .00 (.45 - .15 - .10 - .20)
I only = .05 (.60 - .25 - .10 - .20)
Add up all the percentages and it is clear that only 90% of the employees read any papers.
That makes .9*2940 = 2646 readers.
So,
a. D only = .2*2940 = 588
b. C only = 0
c. I only = .05*2940 = 147
d. None = .10*2940 = 294
1. 👍
2. 👎
2. 95% of the employees read any newspaper, therefore 5% don't read and newspaper. D should be 147
1. 👍
2. 👎
## Similar Questions
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HI JISKHA, just got my first course for next year. this is my first writing assignment: Think about your personal food choices: How do you decide what you will eat on a daily basis? What sorts of things influence your decision? | 1,076 | 4,177 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.9375 | 4 | CC-MAIN-2021-49 | latest | en | 0.927123 | # math. Almost everyone at the Bright Corporation reads a daily newspaper on a regular basis. In fact, altogether te company employs 2,940 people,of whom70% read The Daily News,45% read The Courier and 60% read The inquirer.. One fourth of the employees reads The Daily News and The Courier, and 30% read The Inquirer and The Courier, and 35% read The Daily News and The Inquirer. One tenth of the people read all three newspapers on a regular basis.. a. how many people read only The Daily news?. b. How many people read only The Courier?. c. How many people read on The Inquirer?. d. How many people don't read any newspaper?. 1. 👍. 2. 👎. 3. 👁. 1. Draw your 3-circle Venn diagram. Label the circles D,C,I. DCI = .1. so. DC only = .15 (.25-.10). CI only = .20 (.30-.10). DI only = .25 (.35-.10). D only = .20 (.70 - .15 - .10 - .25). C only = .00 (.45 - .15 - .10 - .20). I only = .05 (.60 - .25 - .10 - .20). Add up all the percentages and it is clear that only 90% of the employees read any papers.. That makes .9*2940 = 2646 readers.. So,. a. D only = .2*2940 = 588. b. C only = 0. c. I only = .05*2940 = 147. d. None = .10*2940 = 294. 1. 👍. 2. 👎. 2. 95% of the employees read any newspaper, therefore 5% don't read and newspaper. D should be 147. 1. 👍. 2. 👎. ## Similar Questions. 1. ### social studies (check my answers). What is the definition of civic-mindedness? paying attention to the needs of one's community treating others with respect following the newspaper on a daily basis following and showing respect for the law. 2. ### English. 1. | My father reads the newspaper every day. [Does this sentence mean that he reads the same newspaper every day{gain and again}? Or was 'the newspaper' in generic use?] 2. My father reads a newspaper every day. [What about this. 3. ### Math. in a survey of 290 newspaper readers, 181 of them read the Daily Times, 142 Read the Guardian 117 read punch and each reads at least one of the three papers if 75 read the Daily Times, and the Guardian, 60 read the Daily Times and. 4. ### English. What distinguishes a fact from an opinion? -A fact can be proven true. -A fact can be changed over time. -A fact can be supported with evidence. -A fact can be supported with examples.. 1. ### Art. Art can serve many purposes. here, an artist created bowls and plates that are used every day. what other artistic creations are used on a daily basis? clothing****** sculptures paintings drawings The ****** is what i think my. 2. ### Mathematics. In a surveyor of 200 newspaper readers,181 of them read daily times,142 read the guardian,117 read the punch and each reads at least one of the three papers. If 75 read the daily times and the guardian,60 read the daily times and. 3. ### Sta. A regular feature in a newspaper asks readers to respond via e-mail to a survey that requires a yes or no response. In the following day's newspaper, the percentage of yes and no responses are reported. discuss why we should. 4. ### English. 1. My father reads the newspaper every day. (What does it mean? 2. My father reads the same newspaper everyday. 3. My father reads a newspaper every day. Does #1 mean #2 or #3? Is 'the newspaper' the generic term? ). 1. ### History. "The Daily News- March 14, 1904 Supreme Court Rules Northern Securities in Violation of Sherman Antitrust Act" Which statement best explains the significance of the newspaper headline? a.)The ruling provided a legal basis for. 2. ### finance 2 questions. 9. When Patricia sells her General Motors common stock at the same time that Brian purchases the same amount of General Motor's stock, General Motors receives: A. The spread between the bid and ask of the transaction B. The dollar. 3. ### English. e.g. My father reads the newspaper every day. (What is the meaning of the sentence above? #1 or #2?) 1. My father reads the same/specific newspaper every day /repeatedly. 2. My father reads newspapers every day. He reads newly. 4. ### nutrition and wellness. HI JISKHA, just got my first course for next year. this is my first writing assignment: Think about your personal food choices: How do you decide what you will eat on a daily basis? What sorts of things influence your decision?. |
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Wednesday, December 27, 2006
Microsoft Interview Question : Polar Bear
One of the most asked and well known microsoft interview question is that of the walking bear.The question is still asked because a lot of people have either not heard of it or most of them don't know the correct solution yet.
If a bear walks one mile south, turns left and walks one mile to the east and then turns left again and walks one mile north and arrives at its original position, what is the color of the bear.
Well,from the very framing of the question it is evident that we r talking about the poles,and all polar bears are white.You can also very well argue that any bear or man walking the same path will reach the same starting position if he is at north
pole.The question can also be extended and that's what we are interested in.
The question is how many such points exists on the surface of the globe.
Jim Miles said...
Infinity.
There is indeed the one point exactly on the north pole where walking 1 mile south, 1 mile east then 1 mile north returns you to the starting position but there is also a circle of infinity points in the southern hemisphere.
Let us call this circle 'A'. It is formed by the points 1 mile north of another circle 'B' of circumference 1, parallel to the equator and between the equator and the south pole.
Suppose you are on 'A'. Then going 1 mile south puts you on 'B'. Travelling 1 mile east lands you up exactly where you just were on the circle (because the circumference of 'B' is 1). Then travelling north puts you back where you started.
However, 'A' is not the only circle of such points. In the same way that we constructed 'A' by taking the points 1 mile north of the circle 'B' of circumference 1, parallel to the equator, between the equator and the south pole we may take any circle 'A_n' of points 1 mile north of the circle 'B_n' of circumference 1/n (for any n in the natural numbers), parallel to the equator, between the equator and the south pole.
Suman said...
Thats a good question and i agree with jim miles solution.
----------------
My blog:
http://justriddles.blogspot.com
http://justfungames.blogspot.com
----------------
hugo bowne-anderson said...
great, jim.
so: as your n gets really, really big, the circle B_n gets closer and closer to the south pole.
so in the limit as n goes to infinity, we find another solution!, which is:
start at any point on the circle A' which is all points 1mile north of the south pole.
then when you get to the south pole, walking east is doing nothing!
Narendran Kumaragurunathan said...
The bear is white because, there are no bears on south pole.
Eighth Wonder said...
There r no polar bears in Antarctica.
Answer is north pole,which is exactly a point on earth.
Thiep said...
First of all. Thanks very much for your useful post.
I just came across your blog and wanted to drop you a note telling you how impressed I was with the information you have posted here.
Please let me introduce you some info related to this post and I hope that it is useful for community.
Source: Microsoft interview questions
Thanks again
Ngo
aashish said...
To add: Somebody might think that such a circle (of unit circumference) can exist in northern hemisphere also all the points lying on circle one mile above(the circle of unit radius) will also be the answer but it is not possible because the distance of north pole from this circle would be 1/2*pi which is less than 1 so only one point in northern hemisphere and i.e north pole.
aashish said...
ohhhh sry instead of radius it should be circumference at one place
Lily said...
My husband became like a polar bear he is like an iceberg with me so I had to suggest him Viagra Online because I just need to be with my old sweetheart husband.
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guddu said...
infinity...as we earth is as a hemisphere so we cannot say there is one point.
lavesh said...
Hi I got inspired by your blog and created my own puzzle blog
Quiz
Lauraine said...
That bear should be white. Bcoz it started one mile south from north. So it lives in north. That's it should been white.
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Chankey Pathak said...
Color: White (North pole's bear are white and also there are no bears in south pole)
sophia-yang said...
AT THE FIRST SIGHT IF THIS ARTICLE, I THINK OF A SONG POLAR BEAR OUR FOREIGN TEACHER TOUGHT US EVER. IT IS A SO WARM MEMORY FOR ME NOW!
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Rajesh said...
excellent solution given by Jim!
Hats off..
Ashutosh Mukherjee said...
but y do we consider that bear statred off from north pole...not obviously soth but it can be any place and then how do we come to the conclusion
Ashutosh Mukherjee said...
and how do we arrive at this...
we may take any circle 'A_n' of points 1 mile north of the circle 'B_n' of circumference 1/n (for any n in the natural numbers), parallel to the equator, between the equator and the south pole.
Ian Webb said...
It would be very difficult to find any bears at the Magnetic North Pole, considering it is in the middle of the sea!
Amazing solution, Jim ! Just out of curiosity, how much distance south would one need to travel to reach the South Pole from the Circle B ( with a 1 mile circumference) ?
Amazing solution, Jim ! Just out of curiosity, how much distance south would one need to travel to reach the South Pole from the Circle B ( with a 1 mile circumference) ?
Amazing solution, Jim ! Just out of curiosity, how much distance south would one need to travel to reach the South Pole from the Circle B ( with a 1 mile circumference) ?
Amazing solution, Jim ! Just out of curiosity, how much distance south would one need to travel to reach the South Pole from the Circle B ( with a 1 mile circumference) ?
Amazing solution, Jim ! Just out of curiosity, how much distance south would one need to travel to reach the South Pole from the Circle B ( with a 1 mile circumference) ?
Realmatri.com said...
You are on north pole, it can’t be south pole because being at south, you can’t go south.
Eldhose Baby said...
HemanT AgrawaL said...
Nice puzzle.. my puzzle collection is here...
Top Logical Puzzles
Unknown said...
There is one more point , barring that vicinity circle concept, where in with these three movements you will come to original point??Wait for ans
Unknown said...
There is one more point , barring that vicinity circle concept, where in with these three movements you will come to original point??Wait for ans | 1,546 | 6,792 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.859375 | 4 | CC-MAIN-2017-09 | longest | en | 0.952276 | Classic Puzzles. Wednesday, December 27, 2006. Microsoft Interview Question : Polar Bear. One of the most asked and well known microsoft interview question is that of the walking bear.The question is still asked because a lot of people have either not heard of it or most of them don't know the correct solution yet.. If a bear walks one mile south, turns left and walks one mile to the east and then turns left again and walks one mile north and arrives at its original position, what is the color of the bear.. Well,from the very framing of the question it is evident that we r talking about the poles,and all polar bears are white.You can also very well argue that any bear or man walking the same path will reach the same starting position if he is at north. pole.The question can also be extended and that's what we are interested in.. The question is how many such points exists on the surface of the globe.. Jim Miles said.... Infinity.. There is indeed the one point exactly on the north pole where walking 1 mile south, 1 mile east then 1 mile north returns you to the starting position but there is also a circle of infinity points in the southern hemisphere.. Let us call this circle 'A'. It is formed by the points 1 mile north of another circle 'B' of circumference 1, parallel to the equator and between the equator and the south pole.. Suppose you are on 'A'. Then going 1 mile south puts you on 'B'. Travelling 1 mile east lands you up exactly where you just were on the circle (because the circumference of 'B' is 1). Then travelling north puts you back where you started.. However, 'A' is not the only circle of such points. In the same way that we constructed 'A' by taking the points 1 mile north of the circle 'B' of circumference 1, parallel to the equator, between the equator and the south pole we may take any circle 'A_n' of points 1 mile north of the circle 'B_n' of circumference 1/n (for any n in the natural numbers), parallel to the equator, between the equator and the south pole.. Suman said.... Thats a good question and i agree with jim miles solution.. ----------------. My blog:. http://justriddles.blogspot.com. http://justfungames.blogspot.com. ----------------. hugo bowne-anderson said.... great, jim.. so: as your n gets really, really big, the circle B_n gets closer and closer to the south pole.. so in the limit as n goes to infinity, we find another solution!, which is:. start at any point on the circle A' which is all points 1mile north of the south pole.. then when you get to the south pole, walking east is doing nothing!. Narendran Kumaragurunathan said.... The bear is white because, there are no bears on south pole.. Eighth Wonder said.... There r no polar bears in Antarctica.. Answer is north pole,which is exactly a point on earth.. Thiep said.... First of all. Thanks very much for your useful post.. I just came across your blog and wanted to drop you a note telling you how impressed I was with the information you have posted here.. Please let me introduce you some info related to this post and I hope that it is useful for community.. Source: Microsoft interview questions. Thanks again. Ngo. aashish said.... To add: Somebody might think that such a circle (of unit circumference) can exist in northern hemisphere also all the points lying on circle one mile above(the circle of unit radius) will also be the answer but it is not possible because the distance of north pole from this circle would be 1/2*pi which is less than 1 so only one point in northern hemisphere and i.e north pole.. aashish said.... ohhhh sry instead of radius it should be circumference at one place. Lily said.... My husband became like a polar bear he is like an iceberg with me so I had to suggest him Viagra Online because I just need to be with my old sweetheart husband.. power balance. silly bandz. Raymond Weil Watches. | concord papillon. rolex datejust 36mm. wedding dresses develop quality for discerning customers and Experience the comfort, free shipping.. Buy evening dresses with a price guarantee and top rated customer service.. guddu said.... infinity...as we earth is as a hemisphere so we cannot say there is one point.. lavesh said.... Hi I got inspired by your blog and created my own puzzle blog. Quiz. Lauraine said.... That bear should be white. Bcoz it started one mile south from north. So it lives in north. That's it should been white.. Formspring Clone Script. Formspring Backgrounds. Chankey Pathak said.... Color: White (North pole's bear are white and also there are no bears in south pole). sophia-yang said.... AT THE FIRST SIGHT IF THIS ARTICLE, I THINK OF A SONG POLAR BEAR OUR FOREIGN TEACHER TOUGHT US EVER. IT IS A SO WARM MEMORY FOR ME NOW!. Dell laptop keyboard. Gateway laptop keyboard. Rajesh said.... excellent solution given by Jim!. Hats off... Ashutosh Mukherjee said.... but y do we consider that bear statred off from north pole...not obviously soth but it can be any place and then how do we come to the conclusion. Ashutosh Mukherjee said.... and how do we arrive at this.... we may take any circle 'A_n' of points 1 mile north of the circle 'B_n' of circumference 1/n (for any n in the natural numbers), parallel to the equator, between the equator and the south pole.. Ian Webb said.... It would be very difficult to find any bears at the Magnetic North Pole, considering it is in the middle of the sea!. Amazing solution, Jim ! Just out of curiosity, how much distance south would one need to travel to reach the South Pole from the Circle B ( with a 1 mile circumference) ?. Amazing solution, Jim ! Just out of curiosity, how much distance south would one need to travel to reach the South Pole from the Circle B ( with a 1 mile circumference) ?. Amazing solution, Jim ! Just out of curiosity, how much distance south would one need to travel to reach the South Pole from the Circle B ( with a 1 mile circumference) ?. Amazing solution, Jim ! Just out of curiosity, how much distance south would one need to travel to reach the South Pole from the Circle B ( with a 1 mile circumference) ?. Amazing solution, Jim ! Just out of curiosity, how much distance south would one need to travel to reach the South Pole from the Circle B ( with a 1 mile circumference) ?. Realmatri.com said.... You are on north pole, it can’t be south pole because being at south, you can’t go south.. Eldhose Baby said.... HemanT AgrawaL said.... Nice puzzle.. my puzzle collection is here.... Top Logical Puzzles. Unknown said.... There is one more point , barring that vicinity circle concept, where in with these three movements you will come to original point??Wait for ans. Unknown said.... There is one more point , barring that vicinity circle concept, where in with these three movements you will come to original point??Wait for ans. |
http://mathhelpforum.com/differential-geometry/170304-lebesgue-integrability-showing-limit-x-approaches-f-x-0-a-print.html | 1,513,055,216,000,000,000 | text/html | crawl-data/CC-MAIN-2017-51/segments/1512948515165.6/warc/CC-MAIN-20171212041010-20171212061010-00648.warc.gz | 195,525,003 | 5,182 | # lebesgue integrability and showing limit as x approaches +/-∞ of F(x) = 0.
• Feb 5th 2011, 08:04 PM
oblixps
lebesgue integrability and showing limit as x approaches +/-∞ of F(x) = 0.
a) let f be L-integrable on R. show that F(x) = integral (from 0 to x) f(t)dt is continuous.
b)show that if F is L-integrable, then lim (as x approaches +/-∞) of F(x) = 0.
i am having trouble proving these statements. i'm not sure but i think part a) involves the property of differentiating under the integral sign which is justified by the dominated convergence theorem for lebesgue integrals. but the hypothesis of the differentiating under the integral sign property requires that the derivative of f (the integrand) exists for almost all x. i don't know if it satisfies this since the only information given is that f is L integrable. as for part b) i am stuck as well and don't know how to go about it. please help.
• Feb 5th 2011, 09:51 PM
TheEmptySet
Quote:
Originally Posted by oblixps
a) let f be L-integrable on R. show that F(x) = integral (from 0 to x) f(t)dt is continuous.
b)show that if F is L-integrable, then lim (as x approaches +/-∞) of F(x) = 0.
i am having trouble proving these statements. i'm not sure but i think part a) involves the property of differentiating under the integral sign which is justified by the dominated convergence theorem for lebesgue integrals. but the hypothesis of the differentiating under the integral sign property requires that the derivative of f (the integrand) exists for almost all x. i don't know if it satisfies this since the only information given is that f is L integrable. as for part b) i am stuck as well and don't know how to go about it. please help.
for a) you will want to use sequential continuity.
Let $x_n \to x$ and consider the function
$\displaystyle F(x_n)=\lim_{n \to \infty}\int f \chi_{[0,x_n]}d\lambda$
Now since $f(x)\chi_{[0,x_n]} \le f(x)$ and $f(x) \in L^1$
Just use DCT and $F(x_n) \to F(x)$
For b) what would happen it the function didn't go to zero?
• Feb 5th 2011, 11:40 PM
chisigma
Quote:
Originally Posted by oblixps
a) let f be L-integrable on R. show that F(x) = integral (from 0 to x) f(t)dt is continuous.
b)show that if F is L-integrable, then lim (as x approaches +/-∞) of F(x) = 0.
i am having trouble proving these statements. i'm not sure but i think part a) involves the property of differentiating under the integral sign which is justified by the dominated convergence theorem for lebesgue integrals. but the hypothesis of the differentiating under the integral sign property requires that the derivative of f (the integrand) exists for almost all x. i don't know if it satisfies this since the only information given is that f is L integrable. as for part b) i am stuck as well and don't know how to go about it. please help.
Examples of function L-integrable on R that doesn't tend to 0 if x tends to infinity are given in...
http://www.mathhelpforum.com/math-he...tml#post597107
Kind regards
$\chi$ $\sigma$
• Feb 6th 2011, 12:22 AM
Tinyboss
Quote:
Originally Posted by chisigma
Examples of function L-integrable on R that doesn't tend to 0 if x tends to infinity are given in...
http://www.mathhelpforum.com/math-he...tml#post597107
Kind regards
$\chi$ $\sigma$
Exactly...the function could do anything at all on a set of measure zero and not affect the Lebesgue integral.
• Feb 7th 2011, 01:07 PM
oblixps
for part b) would the reason be along these lines: since F is L-integrable it can be written as the infinite sum of the integrals of L-integrable functions and in order for the infinite sum to converge the individual integrals in the sum must approach 0 as n approaches infinite. I'm a little confused though since it is x in F(x) that is approaching infinite. i have looked at the thread you have provided me and near the bottom i saw that F(x) must approach 0 since if it didn't the integral of |F| would not be finite. although i can intuitively see that, i am trying to reconcile that with the definitions provided in my book and that is what is causing me some confusion.
my book does not use measure sets to motivate the lebesgue integral but defines it as: let f_k be a sequence of R integrable functions such that the infinite sum of the integral (-infinite, infinite) |f_k|dx < infinite, then the lebesgue integral of f = infinite sum of f_k is:
integral of f(x) dx = infinite sum of integral of f_k dx.
can you help me make sense of this problem given my book's definition? thanks in advance.
• Feb 7th 2011, 04:21 PM
Jose27
So, apparently condition b) indeed holds, but functions that satisfy the hypothesis are quite limited:
Assume for the moment $f\geq 0$ then if there exists a measurable set $M \subset \mathbb{R}$ such that $\int_{M} f >0$ then $\int_{[0,\infty )} f >0$ and so $F$ can't be integrable there (take a sequence in $M$ tending to infinity and apply dominated convergence to obtain a contradiction, if $M$ is bounded it's easier still) and from this we deduce $F\notin L^1(\mathbb{R})$ contradicting the assumption. We conclude $f=0$ a.e. In the same way we deal with the case $f\leq 0$.
Now, for any function $g$, we define $g^+=\max \{ g,0\}$ and $g^-=\min \{ g,0 \}$. It's a standard result that $g\in L^1(\mathbb{R})$ iff $g^+,g^-\in L^1(\mathbb{R})$, so we get $F(x)= \int_0^x f^+(t)dt + \int_0^x f^-(t)dt = F^+(x) + F^-(x)$ (this is easily seen to be the case because the integral is monotone), but $F^+ \in L^1(\mathbb{R})$ iff $f= 0$ a.e., and analogous for $F^-$. We therefore must have $f= 0$ a.e. if $F\in L^1(\mathbb{R})$, in which case the conclusion trivially holds.
On the other hand if you ask that $F+c \in L^1(\mathbb{R})$ for some constant c, then the problem is more difficult (read I don't have a proof for this case), but certainly interesting. As an example take $f(t)=2|t|e^{-t^2}$ and $F(x)=1-e^{-x^2}$, then $F$ is not integrable but $F(x)-1$ is.
Edit: There is a mistake in the argument, it only works if the hypothesis are satisfied by $G(x)= \int_0^x |f(t)|dt$. I'm not sure if the argument can be adapted.
• Feb 8th 2011, 12:42 AM
oblixps
why does $\int_{M} f >0$ imply $\int_{[0,\infty )} f >0$? also i am not sure how to obtain the contradiction. so i take a sequence of functions f_k but each of them have to be bounded by an integrable function and i'm not sure how to pick that. i also have trouble seeing how because of this F(x) is not L-integrable.
• Feb 8th 2011, 07:11 AM
Tinyboss
Are you sure (b) isn't something like, if f is Lebesgue integrable, then $\lim_{x\to\infty}\int_x^\infty f(t)dt=0$?
• Feb 8th 2011, 10:19 AM
oblixps
yes i double checked. b) is:
let f, F be as in part a. Show that if F(x) = $\int_0^x f(t)dt$ is L-integrable, then $lim_{x\to\infty} F(x) = 0$.
i wasn't sure how to type it but, the limit is actually as x approaches +/- infinite. | 2,011 | 6,851 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 41, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.609375 | 4 | CC-MAIN-2017-51 | longest | en | 0.941461 | # lebesgue integrability and showing limit as x approaches +/-∞ of F(x) = 0.. • Feb 5th 2011, 08:04 PM. oblixps. lebesgue integrability and showing limit as x approaches +/-∞ of F(x) = 0.. a) let f be L-integrable on R. show that F(x) = integral (from 0 to x) f(t)dt is continuous.. b)show that if F is L-integrable, then lim (as x approaches +/-∞) of F(x) = 0.. i am having trouble proving these statements. i'm not sure but i think part a) involves the property of differentiating under the integral sign which is justified by the dominated convergence theorem for lebesgue integrals. but the hypothesis of the differentiating under the integral sign property requires that the derivative of f (the integrand) exists for almost all x. i don't know if it satisfies this since the only information given is that f is L integrable. as for part b) i am stuck as well and don't know how to go about it. please help.. • Feb 5th 2011, 09:51 PM. TheEmptySet. Quote:. Originally Posted by oblixps. a) let f be L-integrable on R. show that F(x) = integral (from 0 to x) f(t)dt is continuous.. b)show that if F is L-integrable, then lim (as x approaches +/-∞) of F(x) = 0.. i am having trouble proving these statements. i'm not sure but i think part a) involves the property of differentiating under the integral sign which is justified by the dominated convergence theorem for lebesgue integrals. but the hypothesis of the differentiating under the integral sign property requires that the derivative of f (the integrand) exists for almost all x. i don't know if it satisfies this since the only information given is that f is L integrable. as for part b) i am stuck as well and don't know how to go about it. please help.. for a) you will want to use sequential continuity.. Let $x_n \to x$ and consider the function. $\displaystyle F(x_n)=\lim_{n \to \infty}\int f \chi_{[0,x_n]}d\lambda$. Now since $f(x)\chi_{[0,x_n]} \le f(x)$ and $f(x) \in L^1$. Just use DCT and $F(x_n) \to F(x)$. For b) what would happen it the function didn't go to zero?. • Feb 5th 2011, 11:40 PM. chisigma. Quote:. Originally Posted by oblixps. a) let f be L-integrable on R. show that F(x) = integral (from 0 to x) f(t)dt is continuous.. b)show that if F is L-integrable, then lim (as x approaches +/-∞) of F(x) = 0.. i am having trouble proving these statements. i'm not sure but i think part a) involves the property of differentiating under the integral sign which is justified by the dominated convergence theorem for lebesgue integrals. but the hypothesis of the differentiating under the integral sign property requires that the derivative of f (the integrand) exists for almost all x. i don't know if it satisfies this since the only information given is that f is L integrable. as for part b) i am stuck as well and don't know how to go about it. please help.. Examples of function L-integrable on R that doesn't tend to 0 if x tends to infinity are given in.... http://www.mathhelpforum.com/math-he...tml#post597107. | Kind regards. $\chi$ $\sigma$. • Feb 6th 2011, 12:22 AM. Tinyboss. Quote:. Originally Posted by chisigma. Examples of function L-integrable on R that doesn't tend to 0 if x tends to infinity are given in.... http://www.mathhelpforum.com/math-he...tml#post597107. Kind regards. $\chi$ $\sigma$. Exactly...the function could do anything at all on a set of measure zero and not affect the Lebesgue integral.. • Feb 7th 2011, 01:07 PM. oblixps. for part b) would the reason be along these lines: since F is L-integrable it can be written as the infinite sum of the integrals of L-integrable functions and in order for the infinite sum to converge the individual integrals in the sum must approach 0 as n approaches infinite. I'm a little confused though since it is x in F(x) that is approaching infinite. i have looked at the thread you have provided me and near the bottom i saw that F(x) must approach 0 since if it didn't the integral of |F| would not be finite. although i can intuitively see that, i am trying to reconcile that with the definitions provided in my book and that is what is causing me some confusion.. my book does not use measure sets to motivate the lebesgue integral but defines it as: let f_k be a sequence of R integrable functions such that the infinite sum of the integral (-infinite, infinite) |f_k|dx < infinite, then the lebesgue integral of f = infinite sum of f_k is:. integral of f(x) dx = infinite sum of integral of f_k dx.. can you help me make sense of this problem given my book's definition? thanks in advance.. • Feb 7th 2011, 04:21 PM. Jose27. So, apparently condition b) indeed holds, but functions that satisfy the hypothesis are quite limited:. Assume for the moment $f\geq 0$ then if there exists a measurable set $M \subset \mathbb{R}$ such that $\int_{M} f >0$ then $\int_{[0,\infty )} f >0$ and so $F$ can't be integrable there (take a sequence in $M$ tending to infinity and apply dominated convergence to obtain a contradiction, if $M$ is bounded it's easier still) and from this we deduce $F\notin L^1(\mathbb{R})$ contradicting the assumption. We conclude $f=0$ a.e. In the same way we deal with the case $f\leq 0$.. Now, for any function $g$, we define $g^+=\max \{ g,0\}$ and $g^-=\min \{ g,0 \}$. It's a standard result that $g\in L^1(\mathbb{R})$ iff $g^+,g^-\in L^1(\mathbb{R})$, so we get $F(x)= \int_0^x f^+(t)dt + \int_0^x f^-(t)dt = F^+(x) + F^-(x)$ (this is easily seen to be the case because the integral is monotone), but $F^+ \in L^1(\mathbb{R})$ iff $f= 0$ a.e., and analogous for $F^-$. We therefore must have $f= 0$ a.e. if $F\in L^1(\mathbb{R})$, in which case the conclusion trivially holds.. On the other hand if you ask that $F+c \in L^1(\mathbb{R})$ for some constant c, then the problem is more difficult (read I don't have a proof for this case), but certainly interesting. As an example take $f(t)=2|t|e^{-t^2}$ and $F(x)=1-e^{-x^2}$, then $F$ is not integrable but $F(x)-1$ is.. Edit: There is a mistake in the argument, it only works if the hypothesis are satisfied by $G(x)= \int_0^x |f(t)|dt$. I'm not sure if the argument can be adapted.. • Feb 8th 2011, 12:42 AM. oblixps. why does $\int_{M} f >0$ imply $\int_{[0,\infty )} f >0$? also i am not sure how to obtain the contradiction. so i take a sequence of functions f_k but each of them have to be bounded by an integrable function and i'm not sure how to pick that. i also have trouble seeing how because of this F(x) is not L-integrable.. • Feb 8th 2011, 07:11 AM. Tinyboss. Are you sure (b) isn't something like, if f is Lebesgue integrable, then $\lim_{x\to\infty}\int_x^\infty f(t)dt=0$?. • Feb 8th 2011, 10:19 AM. oblixps. yes i double checked. b) is:. let f, F be as in part a. Show that if F(x) = $\int_0^x f(t)dt$ is L-integrable, then $lim_{x\to\infty} F(x) = 0$.. i wasn't sure how to type it but, the limit is actually as x approaches +/- infinite. |
https://www.enotes.com/homework-help/find-equation-line-which-passes-through-4-1-an-767643 | 1,695,554,743,000,000,000 | text/html | crawl-data/CC-MAIN-2023-40/segments/1695233506632.31/warc/CC-MAIN-20230924091344-20230924121344-00800.warc.gz | 846,925,883 | 17,720 | # Find the equation of the line which passes through (-4,1) and is at an angle of 135° with the positive direction of the x axis.
The angle essentially gives the slope. If you consider, slope is a measure of the steepness of a line, a lot like a hill, which will go up at a certain angle. To use it for the slope, we need to take tangent function (from trigonometry) of the angle:
`tan135 = -1`
So, in the equation for the line, slope = m = -1
So, we have m = -1 with a point on the line (-4,1).
Various ways to get the equation from there. We could put this information into the equation`y=mx+b`:
`1 = -1*-4 + b`
So, we can solve that for b:
`1 = 4 + b`
`b = -3`
So, then, we have m and b. So, we can write the equation for the line:
`y = -x - 3` | 232 | 762 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.3125 | 4 | CC-MAIN-2023-40 | latest | en | 0.935487 | # Find the equation of the line which passes through (-4,1) and is at an angle of 135° with the positive direction of the x axis.. The angle essentially gives the slope. If you consider, slope is a measure of the steepness of a line, a lot like a hill, which will go up at a certain angle. To use it for the slope, we need to take tangent function (from trigonometry) of the angle:. `tan135 = -1`. So, in the equation for the line, slope = m = -1. So, we have m = -1 with a point on the line (-4,1).. Various ways to get the equation from there. We could put this information into the equation`y=mx+b`:. | `1 = -1*-4 + b`. So, we can solve that for b:. `1 = 4 + b`. `b = -3`. So, then, we have m and b. So, we can write the equation for the line:. `y = -x - 3`. |
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# lec 1 - Tuesday January 3 Lecture 1 Integration by...
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Tuesday, January 3 Lecture 1: Integration by substitution (Refers to 6.1 in your text) After having practiced using the concepts of this lecture the student should be able to: define the differential of a function, integrate indefinite integrals by making appropriate change of variables (substitution), integrate definite integrals by appropriate change of variables. Summary of what we have learned about the notion of integration . - Our study of integration began with attempts at finding the area of the region bounded by the curve of f ( x ) and the x -axis over an interval [ a , b ]. To do this we introduced the notion of a Riemann sum. But computing areas in this way is inefficient. - The Fundamental theorem of calculus presented an alternate way to compute such numbers. This important theorem is presented into two parts. - The second part of the Fundamental theorem of calculus says that to find the area of the region bounded by the curve of f ( x ) and the x -axis over an interval [ a , b ] it suffices to find an anti-derivative of the function f ( x ), evaluating it at the limits of integration and subtracting the results. That is, if f ( x ) is continuous on [ a , b ] and F ( x ) is an anti- derivative of f ( x ) then - The first part of the Fundamental theorem of calculus says that, if f ( x ) is continuous on [ a , b ] and as x ranges over [ a , b ], then This can also be expressed by - The first part of the FTC appears to be unrelated to our initial inquiry. In these notes we used it to provide an easier proof of the second part of the FTC. But it is worth remembering it since we occasionally invoke it in particular situations. It is a more
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Ask a homework question - tutors are online | 513 | 2,267 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.875 | 4 | CC-MAIN-2018-09 | latest | en | 0.926176 | {[ promptMessage ]}. Bookmark it. {[ promptMessage ]}. # lec 1 - Tuesday January 3 Lecture 1 Integration by.... This preview shows pages 1–2. Sign up to view the full content.. Tuesday, January 3 Lecture 1: Integration by substitution (Refers to 6.1 in your text) After having practiced using the concepts of this lecture the student should be able to: define the differential of a function, integrate indefinite integrals by making appropriate change of variables (substitution), integrate definite integrals by appropriate change of variables. Summary of what we have learned about the notion of integration . - Our study of integration began with attempts at finding the area of the region bounded by the curve of f ( x ) and the x -axis over an interval [ a , b ]. To do this we introduced the notion of a Riemann sum. But computing areas in this way is inefficient. - The Fundamental theorem of calculus presented an alternate way to compute such numbers. This important theorem is presented into two parts. - The second part of the Fundamental theorem of calculus says that to find the area of the region bounded by the curve of f ( x ) and the x -axis over an interval [ a , b ] it suffices to find an anti-derivative of the function f ( x ), evaluating it at the limits of integration and subtracting the results. That is, if f ( x ) is continuous on [ a , b ] and F ( x ) is an anti- derivative of f ( x ) then - The first part of the Fundamental theorem of calculus says that, if f ( x ) is continuous on [ a , b ] and as x ranges over [ a , b ], then This can also be expressed by - The first part of the FTC appears to be unrelated to our initial inquiry. In these notes we used it to provide an easier proof of the second part of the FTC. But it is worth remembering it since we occasionally invoke it in particular situations. | It is a more. This preview has intentionally blurred sections. Sign up to view the full version.. View Full Document. This is the end of the preview. Sign up to access the rest of the document.. {[ snackBarMessage ]}. ### Page1 / 9. lec 1 - Tuesday January 3 Lecture 1 Integration by.... This preview shows document pages 1 - 2. Sign up to view the full document.. View Full Document. Ask a homework question - tutors are online. |
https://www.brainkart.com/article/Kutzbach-criterion,-Grashoff-s-law-Kutzbach-criterion_6272/ | 1,685,231,913,000,000,000 | text/html | crawl-data/CC-MAIN-2023-23/segments/1685224643388.45/warc/CC-MAIN-20230527223515-20230528013515-00088.warc.gz | 753,347,541 | 7,344 | Home | | Kinematics of Machinery | Kutzbach criterion, Grashoff's law Kutzbach criterion
# Kutzbach criterion, Grashoff's law Kutzbach criterion
Fundamental Equation for 2-D Mechanisms: M = 3(L – 1) – 2J1 – J2
Kutzbach criterion, Grashoff's law Kutzbach criterion:
· Fundamental Equation for 2-D Mechanisms: M = 3(L – 1) – 2J1 – J2
Can we intuitively derive Kutzbach’s modification of Grubler’s equation? Consider a rigid link constrained to move in a plane. How many degrees of freedom does the link have? (3: translation in x and y directions, rotation about z-axis)
· If you pin one end of the link to the plane, how many degrees of freedom does it now have?
· Add a second link to the picture so that you have one link pinned to the plane and one free to move in the plane. How many degrees of freedom exist between the two links? (4 is the correct answer)
· Pin the second link to the free end of the first link. How many degrees of freedom do you now have?
· How many degrees of freedom do you have each time you introduce a moving link? How many degrees of freedom do you take away when you add a simple joint? How many degrees of freedom would you take away by adding a half joint? Do the different terms in equation make sense in light of this knowledge?
Grashoff's law:
· Grashoff 4-bar linkage: A linkage that contains one or more links capable of undergoing a full rotation. A linkage is Grashoff if: S + L < P + Q (where: S = shortest link length, L = longest, P, Q = intermediate length links). Both joints of the shortest link are capable of 360 degrees of rotation in a Grashoff linkages. This gives us 4 possible linkages: crank-rocker (input rotates 360), rocker-crank-rocker (coupler rotates 360), rocker-crank (follower); double crank (all links rotate 360). Note that these mechanisms are simply the possible inversions (section 2.11, Figure 2-16) of a Grashoff mechanism.
· Non Grashoff 4 bar: No link can rotate 360 if: S + L > P + Q
Let’s examine why the Grashoff condition works:
· Consider a linkage with the shortest and longest sides joined together. Examine the linkage when the shortest side is parallel to the longest side (2 positions possible, folded over on the long side and extended away from the long side). How long do P and Q have to be to allow the linkage to achieve these positions?
· Consider a linkage where the long and short sides are not joined. Can you figure out the required lengths for P and Q in this type of mechanism
Study Material, Lecturing Notes, Assignment, Reference, Wiki description explanation, brief detail
Mechanical : Kinematics of Machinery : Basics of Mechanisms : Kutzbach criterion, Grashoff's law Kutzbach criterion | | 668 | 2,766 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.78125 | 4 | CC-MAIN-2023-23 | longest | en | 0.830054 | Home | | Kinematics of Machinery | Kutzbach criterion, Grashoff's law Kutzbach criterion. # Kutzbach criterion, Grashoff's law Kutzbach criterion. Fundamental Equation for 2-D Mechanisms: M = 3(L – 1) – 2J1 – J2. Kutzbach criterion, Grashoff's law Kutzbach criterion:. · Fundamental Equation for 2-D Mechanisms: M = 3(L – 1) – 2J1 – J2. Can we intuitively derive Kutzbach’s modification of Grubler’s equation? Consider a rigid link constrained to move in a plane. How many degrees of freedom does the link have? (3: translation in x and y directions, rotation about z-axis). · If you pin one end of the link to the plane, how many degrees of freedom does it now have?. · Add a second link to the picture so that you have one link pinned to the plane and one free to move in the plane. How many degrees of freedom exist between the two links? (4 is the correct answer). · Pin the second link to the free end of the first link. How many degrees of freedom do you now have?. · How many degrees of freedom do you have each time you introduce a moving link? How many degrees of freedom do you take away when you add a simple joint? How many degrees of freedom would you take away by adding a half joint? Do the different terms in equation make sense in light of this knowledge?. | Grashoff's law:. · Grashoff 4-bar linkage: A linkage that contains one or more links capable of undergoing a full rotation. A linkage is Grashoff if: S + L < P + Q (where: S = shortest link length, L = longest, P, Q = intermediate length links). Both joints of the shortest link are capable of 360 degrees of rotation in a Grashoff linkages. This gives us 4 possible linkages: crank-rocker (input rotates 360), rocker-crank-rocker (coupler rotates 360), rocker-crank (follower); double crank (all links rotate 360). Note that these mechanisms are simply the possible inversions (section 2.11, Figure 2-16) of a Grashoff mechanism.. · Non Grashoff 4 bar: No link can rotate 360 if: S + L > P + Q. Let’s examine why the Grashoff condition works:. · Consider a linkage with the shortest and longest sides joined together. Examine the linkage when the shortest side is parallel to the longest side (2 positions possible, folded over on the long side and extended away from the long side). How long do P and Q have to be to allow the linkage to achieve these positions?. · Consider a linkage where the long and short sides are not joined. Can you figure out the required lengths for P and Q in this type of mechanism. Study Material, Lecturing Notes, Assignment, Reference, Wiki description explanation, brief detail. Mechanical : Kinematics of Machinery : Basics of Mechanisms : Kutzbach criterion, Grashoff's law Kutzbach criterion |. |
https://wiki.haskell.org/index.php?title=Euler_problems/1_to_10&diff=51650&oldid=51649 | 1,500,672,101,000,000,000 | text/html | crawl-data/CC-MAIN-2017-30/segments/1500549423809.62/warc/CC-MAIN-20170721202430-20170721222430-00342.warc.gz | 724,218,855 | 8,937 | # Euler problems/1 to 10
(Difference between revisions)
## 1 Problem 1
Add all the natural numbers below 1000 that are multiples of 3 or 5.
Two solutions using sum:
```problem_1 = sum [x | x <- [1..999], x `mod` 3 == 0 || x `mod` 5 == 0]
import Data.List (union)
problem_1' = sum (union [3,6..999] [5,10..999])```
Another solution which uses algebraic relationships:
```problem_1 = sumStep 3 999 + sumStep 5 999 - sumStep 15 999
where
sumStep s n = s * sumOnetoN (n `div` s)
sumOnetoN n = n * (n+1) `div` 2```
## 2 Problem 2
Find the sum of all the even-valued terms in the Fibonacci sequence which do not exceed one million.
Solution:
```problem_2 =
sum [ x | x <- takeWhile (<= 1000000) fibs,
even x]
where
fibs = 1 : 1 : zipWith (+) fibs (tail fibs)```
The following two solutions use the fact that the even-valued terms in the Fibonacci sequence themselves form a Fibonacci-like sequence that satisfies
evenFib 0 = 0, evenFib 1 = 2, evenFib (n+2) = evenFib n + 4 * evenFib (n+1)
.
```problem_2_v2 = sumEvenFibs \$ numEvenFibsLessThan 1000000
sumEvenFibs n = (evenFib n + evenFib (n+1) - 2) `div` 4
evenFib n = round \$ (2 + sqrt 5) ** (fromIntegral n) / sqrt 5
numEvenFibsLessThan n =
floor \$ (log (fromIntegral n - 0.5) + 0.5*log 5) / log (2 + sqrt 5)```
The first two solutions work because 10^6 is small. The following solution also works for much larger numbers (up to at least 10^1000000 on my computer):
```problem_2 = sumEvenFibsLessThan 1000000
sumEvenFibsLessThan n = (a + b - 1) `div` 2
where
n2 = n `div` 2
(a, b) = foldr f (0,1)
. takeWhile ((<= n2) . fst)
. iterate times2E \$ (1, 4)
f x y | fst z <= n2 = z
| otherwise = y
where z = x `addE` y
addE (a, b) (c, d) = (a*d + b*c - 4*ac, ac + b*d)
where ac=a*c
times2E (a, b) = addE (a, b) (a, b)```
## 3 Problem 3
Find the largest prime factor of 317584931803.
Solution:
```primes = 2 : filter ((==1) . length . primeFactors) [3,5..]
primeFactors n = factor n primes
where
factor n (p:ps)
| p*p > n = [n]
| n `mod` p == 0 = p : factor (n `div` p) (p:ps)
| otherwise = factor n ps
problem_3 = last (primeFactors 317584931803)```
Another solution, not using recursion, is:
```problem_3 = (m !! 0) `div` (m !! 1)
where
m = reverse \$
takeWhile (<=n) (scanl1 (*) [ x | x <- 2:[3,5..], (n `mod` x) == 0 ])
n = 600851475143```
## 4 Problem 4
Find the largest palindrome made from the product of two 3-digit numbers.
Solution:
```problem_4 = maximum [ x | y <- [100..999],
z <- [y..999],
let x = y * z,
let s = show x,
s == reverse s ]```
## 5 Problem 5
What is the smallest number divisible by each of the numbers 1 to 20?
Solution:
```--http://www.research.att.com/~njas/sequences/A003418
problem_5 = foldr1 lcm [1..20]```
## 6 Problem 6
What is the difference between the sum of the squares and the square of the sums?
Solution:
```fun n = a - b
where
a = (sum [1..n])^2
b = sum (map (^2) [1..n])
problem_6 = fun 100```
## 7 Problem 7
Find the 10001st prime.
Solution:
```--primes in problem_3
problem_7 = primes !! 10000```
## 8 Problem 8
Discover the largest product of five consecutive digits in the 1000-digit number.
Solution:
```import Data.Char
groupsOf _ [] = []
groupsOf n xs =
take n xs : groupsOf n ( tail xs )
problem_8 x = maximum . map product . groupsOf 5 \$ x
main = do t <- readFile "p8.log"
let digits = map digitToInt \$concat \$ lines t
print \$ problem_8 digits```
## 9 Problem 9
There is only one Pythagorean triplet, {a, b, c}, for which a + b + c = 1000. Find the product abc.
Solution:
```triplets l = [[a,b,c] | m <- [2..limit],
n <- [1..(m-1)],
let a = m^2 - n^2,
let b = 2*m*n,
let c = m^2 + n^2,
a+b+c==l]
where limit = floor . sqrt . fromIntegral \$ l
problem_9 = product . head . triplets \$ 1000```
## 10 Problem 10
Calculate the sum of all the primes below one million.
Solution:
```--http://www.research.att.com/~njas/sequences/A046731
problem_10 = sum (takeWhile (< 1000000) primes)``` | 1,389 | 3,954 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.28125 | 4 | CC-MAIN-2017-30 | latest | en | 0.715954 | # Euler problems/1 to 10. (Difference between revisions). ## 1 Problem 1. Add all the natural numbers below 1000 that are multiples of 3 or 5.. Two solutions using sum:. ```problem_1 = sum [x | x <- [1..999], x `mod` 3 == 0 || x `mod` 5 == 0]. import Data.List (union). problem_1' = sum (union [3,6..999] [5,10..999])```. Another solution which uses algebraic relationships:. ```problem_1 = sumStep 3 999 + sumStep 5 999 - sumStep 15 999. where. sumStep s n = s * sumOnetoN (n `div` s). sumOnetoN n = n * (n+1) `div` 2```. ## 2 Problem 2. Find the sum of all the even-valued terms in the Fibonacci sequence which do not exceed one million.. Solution:. ```problem_2 =. sum [ x | x <- takeWhile (<= 1000000) fibs,. even x]. where. fibs = 1 : 1 : zipWith (+) fibs (tail fibs)```. The following two solutions use the fact that the even-valued terms in the Fibonacci sequence themselves form a Fibonacci-like sequence that satisfies. evenFib 0 = 0, evenFib 1 = 2, evenFib (n+2) = evenFib n + 4 * evenFib (n+1). .. ```problem_2_v2 = sumEvenFibs \$ numEvenFibsLessThan 1000000. sumEvenFibs n = (evenFib n + evenFib (n+1) - 2) `div` 4. evenFib n = round \$ (2 + sqrt 5) ** (fromIntegral n) / sqrt 5. numEvenFibsLessThan n =. floor \$ (log (fromIntegral n - 0.5) + 0.5*log 5) / log (2 + sqrt 5)```. The first two solutions work because 10^6 is small. The following solution also works for much larger numbers (up to at least 10^1000000 on my computer):. ```problem_2 = sumEvenFibsLessThan 1000000. sumEvenFibsLessThan n = (a + b - 1) `div` 2. where. n2 = n `div` 2. (a, b) = foldr f (0,1). . takeWhile ((<= n2) . fst). . iterate times2E \$ (1, 4). f x y | fst z <= n2 = z. | otherwise = y. where z = x `addE` y. addE (a, b) (c, d) = (a*d + b*c - 4*ac, ac + b*d). where ac=a*c. times2E (a, b) = addE (a, b) (a, b)```. ## 3 Problem 3. Find the largest prime factor of 317584931803.. Solution:. ```primes = 2 : filter ((==1) . length . primeFactors) [3,5..]. primeFactors n = factor n primes. where. factor n (p:ps). | p*p > n = [n]. | n `mod` p == 0 = p : factor (n `div` p) (p:ps). | otherwise = factor n ps. problem_3 = last (primeFactors 317584931803)```. Another solution, not using recursion, is:. ```problem_3 = (m !! 0) `div` (m !! 1). where. | m = reverse \$. takeWhile (<=n) (scanl1 (*) [ x | x <- 2:[3,5..], (n `mod` x) == 0 ]). n = 600851475143```. ## 4 Problem 4. Find the largest palindrome made from the product of two 3-digit numbers.. Solution:. ```problem_4 = maximum [ x | y <- [100..999],. z <- [y..999],. let x = y * z,. let s = show x,. s == reverse s ]```. ## 5 Problem 5. What is the smallest number divisible by each of the numbers 1 to 20?. Solution:. ```--http://www.research.att.com/~njas/sequences/A003418. problem_5 = foldr1 lcm [1..20]```. ## 6 Problem 6. What is the difference between the sum of the squares and the square of the sums?. Solution:. ```fun n = a - b. where. a = (sum [1..n])^2. b = sum (map (^2) [1..n]). problem_6 = fun 100```. ## 7 Problem 7. Find the 10001st prime.. Solution:. ```--primes in problem_3. problem_7 = primes !! 10000```. ## 8 Problem 8. Discover the largest product of five consecutive digits in the 1000-digit number.. Solution:. ```import Data.Char. groupsOf _ [] = []. groupsOf n xs =. take n xs : groupsOf n ( tail xs ). problem_8 x = maximum . map product . groupsOf 5 \$ x. main = do t <- readFile "p8.log". let digits = map digitToInt \$concat \$ lines t. print \$ problem_8 digits```. ## 9 Problem 9. There is only one Pythagorean triplet, {a, b, c}, for which a + b + c = 1000. Find the product abc.. Solution:. ```triplets l = [[a,b,c] | m <- [2..limit],. n <- [1..(m-1)],. let a = m^2 - n^2,. let b = 2*m*n,. let c = m^2 + n^2,. a+b+c==l]. where limit = floor . sqrt . fromIntegral \$ l. problem_9 = product . head . triplets \$ 1000```. ## 10 Problem 10. Calculate the sum of all the primes below one million.. Solution:. ```--http://www.research.att.com/~njas/sequences/A046731. problem_10 = sum (takeWhile (< 1000000) primes)```. |
https://vectormap.net/map_design_tutorials/a-free-hand-drawing-with-simultaneous-projection-of-predicted-guideline/ | 1,618,465,068,000,000,000 | text/html | crawl-data/CC-MAIN-2021-17/segments/1618038083007.51/warc/CC-MAIN-20210415035637-20210415065637-00176.warc.gz | 695,452,873 | 23,773 | # A free-hand drawing with simultaneous projection of predicted guideline
Graphical projection is a protocol by which an image of a three-dimensional object is projected onto a planar surface without the aid of mathematical calculation, used in technical drawing. In mathematics, a parabola is a conic section, created from the intersection of a right circular conical surface and a plane parallel to a generating straight line of that surface. Another way to generate a parabola is to examine a point and a line on a plane. The locus of points in that plane that are equidistant from both the line and point is a parabola. In mathematics, an ellipse (from Greek ¿¿¿¿¿¿¿¿ elleipsis, a ‘falling short’) is a plane curve that results from the intersection of a cone by a plane in a way that produces a closed curve. Circles are special cases of ellipses, obtained when the cutting plane is orthogonal to the cone’s axis. An ellipse is also the locus of all points of the plane whose distances to two fixed points add to the same constant. A circle is a simple shape of Euclidean geometry consisting of those points in a plane that are equidistant from a given point, the centre. The distance between any of the points and the centre is called the radius. Circles are simple closed curves which divide the plane into two regions: an interior and an exterior. The notion of line or straight line was introduced by ancient mathematicians to represent straight objects with negligible width and depth. Lines are an idealization of such objects. Thus, until seventeenth century, lines were defined like this: ‘The line is the first species of quantity, which has only one dimension, namely length, without any width nor depth, and is nothing else than the flow or run of the point which [… … In mathematics, a curve (also called a curved line in older texts) is, generally speaking, an object similar to a line but which is not required to be straight. This entails that a line is a special case of curve, namely a curve with null curvature. Often curves in two-dimensional or three-dimensional (space curves) Euclidean space are of interest. Drawing is a form of visual art that makes use of any number of drawing instruments to mark a two-dimensional medium. Common instruments include graphite pencils, pen and ink, inked brushes, wax color pencils, crayons, charcoal, chalk, pastels, various kinds of erasers, markers, styluses, and various metals. An artist who practices or works in drawing may be called a draftsman or draughtsman. A small amount of material is released onto the two dimensional medium, leaving a visible mark. Canvas is an extremely heavy-duty plain-woven fabric used for making sails, tents, marquees, backpacks, and other items for which sturdiness is required. It is also popularly used by artists as a painting surface, typically stretched across a wooden frame. It is also used in such fashion objects as handbags and shoes. Source. | 621 | 2,956 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.796875 | 4 | CC-MAIN-2021-17 | latest | en | 0.946529 | # A free-hand drawing with simultaneous projection of predicted guideline. Graphical projection is a protocol by which an image of a three-dimensional object is projected onto a planar surface without the aid of mathematical calculation, used in technical drawing. In mathematics, a parabola is a conic section, created from the intersection of a right circular conical surface and a plane parallel to a generating straight line of that surface. Another way to generate a parabola is to examine a point and a line on a plane. The locus of points in that plane that are equidistant from both the line and point is a parabola. In mathematics, an ellipse (from Greek ¿¿¿¿¿¿¿¿ elleipsis, a ‘falling short’) is a plane curve that results from the intersection of a cone by a plane in a way that produces a closed curve. Circles are special cases of ellipses, obtained when the cutting plane is orthogonal to the cone’s axis. An ellipse is also the locus of all points of the plane whose distances to two fixed points add to the same constant. A circle is a simple shape of Euclidean geometry consisting of those points in a plane that are equidistant from a given point, the centre. The distance between any of the points and the centre is called the radius. Circles are simple closed curves which divide the plane into two regions: an interior and an exterior. The notion of line or straight line was introduced by ancient mathematicians to represent straight objects with negligible width and depth. Lines are an idealization of such objects. | Thus, until seventeenth century, lines were defined like this: ‘The line is the first species of quantity, which has only one dimension, namely length, without any width nor depth, and is nothing else than the flow or run of the point which [… … In mathematics, a curve (also called a curved line in older texts) is, generally speaking, an object similar to a line but which is not required to be straight. This entails that a line is a special case of curve, namely a curve with null curvature. Often curves in two-dimensional or three-dimensional (space curves) Euclidean space are of interest. Drawing is a form of visual art that makes use of any number of drawing instruments to mark a two-dimensional medium. Common instruments include graphite pencils, pen and ink, inked brushes, wax color pencils, crayons, charcoal, chalk, pastels, various kinds of erasers, markers, styluses, and various metals. An artist who practices or works in drawing may be called a draftsman or draughtsman. A small amount of material is released onto the two dimensional medium, leaving a visible mark. Canvas is an extremely heavy-duty plain-woven fabric used for making sails, tents, marquees, backpacks, and other items for which sturdiness is required. It is also popularly used by artists as a painting surface, typically stretched across a wooden frame. It is also used in such fashion objects as handbags and shoes. Source. |
http://www.dailykos.com/story/2013/11/17/1256193/-Snarky-Opinion-on-Statistics?detail=hide | 1,432,776,663,000,000,000 | text/html | crawl-data/CC-MAIN-2015-22/segments/1432207929176.79/warc/CC-MAIN-20150521113209-00097-ip-10-180-206-219.ec2.internal.warc.gz | 387,346,480 | 18,026 | A personal opinion on statistics inspired by the excellent Kos diary "Vaccinate Yourself Against Statistics" which I recommend follows. Yeah, following is just my opinion, based on that dwem LaPlace's writing on probability and a stubborn streak about real facts.
A Snarky Treat(ise) on Statistics
Winning Powerball versus Committing Suicide
Powerball Odds ***Compared to U. S. Committing Suicide Odds ****
175,223,510 24,530 times more likely to commit suicide than win Jackpot
5,153,632 721 times more likely to commit suicide than win \$1 million
648,975 91 times more likely to commit suicide than win \$10,000
19,087 2.67 times more likely to commit suicide than win \$100
12,244 1.71 times more likely to commit suicide than win \$100 red ball
706 (only) 10 times more likely to win \$7 with red ball than commit suicide
360 (only) 20 times more likely to win \$7 without red than commit suicide
110 (only) 65 times more likely to win \$4 without red than commit suicide
55 (only) 130 times more likely to win \$4 with red ball than commit suicide
"LIkely" based on 14 suicides per 100,000, the tenth leading cause of death in US.
Suicide rate from http://www.bbc.co.uk/...
Which reported U.S. Center for Disease Control Statistics. May 2, 2013
Powerball odds from http://www.powerball.com/...
Calculations as follows: 14 per 100,000 equals 1 per 7,143 persons commit suicide.
Comparison of odds = powerball odds (per 1) divided by suicide odds of 7,143 (per 1).
Huh? In addition to the obvious, shows that comparison of statistical subjects has close to zero meaning for an individual, a way in which statistics mislead. For example, for a person who will definitely not commit suicide the comparison of statistics is invalid, his number will not change them. The powerball odds stay the same, the suicide odds stay the same. If he does win powerball then his odds of winning were 100%, there was just no way to know that in advance. If the individual does commit suicide, his odds were 100% in retrospect. At some point that person knew in advance.
What are the odds that the sun will rise tomorrow? Rise versus not-rise, like flip of a coin, 50/50. I hear in the Anthropology Museum in Ciudad Mexico that the Aztec priests realized this 50/50 statistic and prayed without ceasing, that the sun would rise tomorrow, which worked, as the sun kept rising. Heart rending. Same as with suicide as above, there are other factors than the 50/50. Statistics are to inform opinions, not twist them.
As seen here, comparing statistics does not work. The struck by lightning trope among thousands of other stats "more likely" is B.S.. When do stats work? In my opinion, only on an agreed common base, like cards, then only in a special way of guessing. Same for surveys, sports. Now if they rise the same way every day...for awhile...same base...
One person believed that if she has a certain gene her "risk of getting alzheimer's 'increases'. Huh? Wait a minute. No, no, some reasoning missing here. You can figure it out, and other "stats" too.
So more people have been killed by falling sandcastles than sharks? Did I get that right? Hm, if true what am I to conclude? Something fishy here. Some can check that out, saw it on BBC net. I won't bother.
May your chi-square be one or two dots. May your sun rise tomorrow.
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Are you sure you want to save these changes to the published diary? | 1,351 | 5,828 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.6875 | 4 | CC-MAIN-2015-22 | latest | en | 0.853319 | A personal opinion on statistics inspired by the excellent Kos diary "Vaccinate Yourself Against Statistics" which I recommend follows. Yeah, following is just my opinion, based on that dwem LaPlace's writing on probability and a stubborn streak about real facts.. A Snarky Treat(ise) on Statistics. Winning Powerball versus Committing Suicide. Powerball Odds ***Compared to U. S. Committing Suicide Odds ****. 175,223,510 24,530 times more likely to commit suicide than win Jackpot. 5,153,632 721 times more likely to commit suicide than win \$1 million. 648,975 91 times more likely to commit suicide than win \$10,000. 19,087 2.67 times more likely to commit suicide than win \$100. 12,244 1.71 times more likely to commit suicide than win \$100 red ball. 706 (only) 10 times more likely to win \$7 with red ball than commit suicide. 360 (only) 20 times more likely to win \$7 without red than commit suicide. 110 (only) 65 times more likely to win \$4 without red than commit suicide. 55 (only) 130 times more likely to win \$4 with red ball than commit suicide. "LIkely" based on 14 suicides per 100,000, the tenth leading cause of death in US.. Suicide rate from http://www.bbc.co.uk/.... Which reported U.S. Center for Disease Control Statistics. May 2, 2013. Powerball odds from http://www.powerball.com/.... Calculations as follows: 14 per 100,000 equals 1 per 7,143 persons commit suicide.. Comparison of odds = powerball odds (per 1) divided by suicide odds of 7,143 (per 1).. Huh? In addition to the obvious, shows that comparison of statistical subjects has close to zero meaning for an individual, a way in which statistics mislead. For example, for a person who will definitely not commit suicide the comparison of statistics is invalid, his number will not change them. The powerball odds stay the same, the suicide odds stay the same. If he does win powerball then his odds of winning were 100%, there was just no way to know that in advance. If the individual does commit suicide, his odds were 100% in retrospect. At some point that person knew in advance.. What are the odds that the sun will rise tomorrow? Rise versus not-rise, like flip of a coin, 50/50. I hear in the Anthropology Museum in Ciudad Mexico that the Aztec priests realized this 50/50 statistic and prayed without ceasing, that the sun would rise tomorrow, which worked, as the sun kept rising. Heart rending. Same as with suicide as above, there are other factors than the 50/50. Statistics are to inform opinions, not twist them.. As seen here, comparing statistics does not work. The struck by lightning trope among thousands of other stats "more likely" is B.S.. When do stats work? In my opinion, only on an agreed common base, like cards, then only in a special way of guessing. Same for surveys, sports. Now if they rise the same way every day...for awhile...same base.... One person believed that if she has a certain gene her "risk of getting alzheimer's 'increases'. Huh? Wait a minute. No, no, some reasoning missing here. | You can figure it out, and other "stats" too.. So more people have been killed by falling sandcastles than sharks? Did I get that right? Hm, if true what am I to conclude? Something fishy here. Some can check that out, saw it on BBC net. I won't bother.. May your chi-square be one or two dots. May your sun rise tomorrow.. #### Tags. EMAIL TO A FRIEND X. You must add at least one tag to this diary before publishing it.. Add keywords that describe this diary. Separate multiple keywords with commas.. Tagging tips - Search For Tags - Browse For Tags. ?. More Tagging tips:. A tag is a way to search for this diary. If someone is searching for "Barack Obama," is this a diary they'd be trying to find?. Use a person's full name, without any title. Senator Obama may become President Obama, and Michelle Obama might run for office.. If your diary covers an election or elected official, use election tags, which are generally the state abbreviation followed by the office. CA-01 is the first district House seat. CA-Sen covers both senate races. NY-GOV covers the New York governor's race.. Tags do not compound: that is, "education reform" is a completely different tag from "education". A tag like "reform" alone is probably not meaningful.. Consider if one or more of these tags fits your diary: Civil Rights, Community, Congress, Culture, Economy, Education, Elections, Energy, Environment, Health Care, International, Labor, Law, Media, Meta, National Security, Science, Transportation, or White House. If your diary is specific to a state, consider adding the state (California, Texas, etc). Keep in mind, though, that there are many wonderful and important diaries that don't fit in any of these tags. Don't worry if yours doesn't.. You can add a private note to this diary when hotlisting it:. Are you sure you want to remove this diary from your hotlist?. Are you sure you want to remove your recommendation? You can only recommend a diary once, so you will not be able to re-recommend it afterwards.. Rescue this diary, and add a note:. Are you sure you want to remove this diary from Rescue?. Choose where to republish this diary. The diary will be added to the queue for that group. Publish it from the queue to make it appear.. You must be a member of a group to use this feature.. Add a quick update to your diary without changing the diary itself:. Are you sure you want to remove this diary?. Unpublish Diary (The diary will be removed from the site and returned to your drafts for further editing.) Delete Diary (The diary will be removed.). Are you sure you want to save these changes to the published diary?. |
http://www.jiskha.com/display.cgi?id=1394425835 | 1,498,412,085,000,000,000 | text/html | crawl-data/CC-MAIN-2017-26/segments/1498128320545.67/warc/CC-MAIN-20170625170634-20170625190634-00680.warc.gz | 563,008,688 | 3,621 | # physics
posted by .
A piece of metal has a mass of 85cg and a volume of 450L. What is its density in g/cm3? What would be the mass of 300 cm3 of this metal? What would be the volume of 00 ounces of this metal?
• physics -
m = 85 kg?
V = 450 L.
V = 450L * 1000cm^3/L = 450,000cm^3
D = 85,000g/450,000cm^3 = 0.189 g/cm^3.
Mass = 300cm^3 * 0.189g/cm^3 = 56.67 g =
0.0567 kg. | 152 | 380 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.625 | 4 | CC-MAIN-2017-26 | latest | en | 0.896695 | # physics. posted by .. A piece of metal has a mass of 85cg and a volume of 450L. What is its density in g/cm3? What would be the mass of 300 cm3 of this metal? What would be the volume of 00 ounces of this metal?. • physics -. m = 85 kg?. | V = 450 L.. V = 450L * 1000cm^3/L = 450,000cm^3. D = 85,000g/450,000cm^3 = 0.189 g/cm^3.. Mass = 300cm^3 * 0.189g/cm^3 = 56.67 g =. 0.0567 kg. |
https://unemployedtutors.org/you-are-fishing-off-a-bridge-and-feel-a-tug-on-the-vertical-line-this-time-your-lucky-catch-is-an-old-boot-2/ | 1,660,635,987,000,000,000 | text/html | crawl-data/CC-MAIN-2022-33/segments/1659882572221.38/warc/CC-MAIN-20220816060335-20220816090335-00391.warc.gz | 526,770,722 | 10,087 | # You are fishing off a bridge and feel a tug on the vertical line. This time, your lucky catch is an old boot. |
You are fishing off a bridge and feel a tug on the vertical line. This time, your lucky catch is an old boot. (a) Assume that the boot is not punctured, so that as you lift it out of the water at constant speed, you haul up one bootful, or 7500 cm^3, of water along with the boot. If the neoprene rubber making up the boot has volume 435 cm^3 and density 1240 kg/m^3, then what is the tension on your fishing line after you pull the boot out of the water? Answer in Newton. Do NOT give me the answer 1.02N on yahoo, that is for part b..button {background-color: #4CAF50;border: none;color: white;padding: 10px 20px;text-align: center;text-decoration: none;display: inline-block;font-size: 16px;margin: 4px 2px;cursor: pointer;border-radius: 10px;} “Are you looking for this answer? We can Help click Order Now” | 250 | 926 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.546875 | 4 | CC-MAIN-2022-33 | latest | en | 0.845599 | # You are fishing off a bridge and feel a tug on the vertical line. This time, your lucky catch is an old boot. |. You are fishing off a bridge and feel a tug on the vertical line. This time, your lucky catch is an old boot. | (a) Assume that the boot is not punctured, so that as you lift it out of the water at constant speed, you haul up one bootful, or 7500 cm^3, of water along with the boot. If the neoprene rubber making up the boot has volume 435 cm^3 and density 1240 kg/m^3, then what is the tension on your fishing line after you pull the boot out of the water? Answer in Newton. Do NOT give me the answer 1.02N on yahoo, that is for part b..button {background-color: #4CAF50;border: none;color: white;padding: 10px 20px;text-align: center;text-decoration: none;display: inline-block;font-size: 16px;margin: 4px 2px;cursor: pointer;border-radius: 10px;} “Are you looking for this answer? We can Help click Order Now”. |
https://www.racehotwheels.com/2016/01/hot-wheels-stem-lesson-plan-scientific.html | 1,718,998,959,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198862157.88/warc/CC-MAIN-20240621191840-20240621221840-00805.warc.gz | 823,944,256 | 21,691 | ## Thursday, January 28, 2016
### Introduction and background
After I have taught/reviewed the scientific method with my students, we do a lab using Hot Wheels cars to give them practice using the scientific method.
The question they are trying to answer is: On which surface will my Hot Wheels car roll furthest after going down a ramp: 60 grit sandpaper, carpet, or cedar fencing?
You could do this lab with any number or type of surfaces that you choose. Also, depending on the time you have and resources available you could let the students completely design the experiment, coming up with the surfaces and the set-up. If this is the case, you could reword the question to: On which surface will my Hot Wheels car roll furthest after going down a ramp.
For our lab, due to time constraints, I have designed the initial set-up of the lab and the surfaces for the cars.
### The Lab
The purpose of the lab is: To show understanding of the scientific method by designing a lab sheet (and possibly the lab itself), completing the experiment, then analyzing the data and reporting on the lab.
After showing the students the initial set-up, I have the students use a word processor to design a lab sheet that includes the following headings:
• Problem/Question
• Hypothesis
• Independent and Dependent Variables
• Constants
• Procedure
• Data
• Analysis
• Conclusion
The students need to have information under each heading through the Procedure as well as a data table that they can fill out during the experiment done and printed out before I will let them proceed with the experiment. An example may look like this.
#### Hot Wheels Scientific Method Lab
Problem/Question
On which surface will my Hot Wheels car roll furthest after going down a ramp: 60 grit sandpaper, carpet, or cedar fencing?
Hypothesis
My hypothesis is that the Hot Wheels car will roll the furthest on the 60 grit sandpaper.
Independent and Dependent Variables
The independent variable in this experiment is the surfaces the car is traveling on. The dependent variable is the distance the car goes.
Constants
Some things that need to remain constant are:
The car I use.
Where/how high the car starts on the ramp.
How I release the car.
How I measure the distance including to the front or back of the car and the units I use.
Procedure
Line the back of the car up with back edge of the track. Without pushing the car, release it so that it rolls down the orange track. Let it roll on the surface until it comes to a stop. Measure from the end of the orange track to the back of the car and record the distance in centimeters. Repeat 5 times for each surface. Use the same car for each trial and each surface.
Data
Analysis
Conclusion
Once they have this much done and printed out, I let them start the experiment. They should record the data on in their table. When they have finished the experiment, it's back to the computer for them to do their analysis and write up their conclusion. When the lab paper is finished I have them print it out and turn it in.
### Notes
• Remember, this lab is not really about what surface the cars go further on. The students are not graded on getting the "right" surface. It's about the scientific method. How well did they organize their lab sheet? How well did they pay attention to the constants. How well did they perform the procedure. How well did they analyze the experiment and discuss the problems. These are the things that I pay attention to and grade them on.
• The set-up I used is not perfect by design. I like that there are problems with the set-up and hope that the students notice these and address them in their analysis and conclusion. One of the potential problems is that on the wood and the sandpaper, sometimes the cars veer off the surface. The most common ways the students try to deal with these are to just do more trials until they get their specified number on the surface; or they will put "railings" on the edge to keep the car on the surface. Hopefully they realize that rubbing on their "railing" will cause the car not to go as far and perhaps skew their results. I usually don't talk to them about this, but do look to see if they discussed how their solution may have affected their data. Using yard sticks to guide the cars
Another issue with the experiment is that I've taped several pieces of sandpaper together. Where they come together the seams aren't always smooth and sometime there are little ridges. That could also affect their data. Again, I don't talk to them about it. I just watch to see if they notice. There are a few other small possible problems with this set-up, but the key is, do the students notice, what if anything do they do to solve them, and most importantly, do they talk about them in their analysis and conclusion. This is how they learn about experiments and what make a good one.
• Make sure that all the constants listed are addressed in the procedure.
• I don't mention how many trials they should do. I let them decided. This let's me know how well they understand the scientific method and how important multiple trials are. I always have a few who only do one trial. Most do 2 or 3. Once in a while I get students who will do 5 or more. | 1,155 | 5,275 | {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 4.03125 | 4 | CC-MAIN-2024-26 | latest | en | 0.923837 | ## Thursday, January 28, 2016. ### Introduction and background. After I have taught/reviewed the scientific method with my students, we do a lab using Hot Wheels cars to give them practice using the scientific method.. The question they are trying to answer is: On which surface will my Hot Wheels car roll furthest after going down a ramp: 60 grit sandpaper, carpet, or cedar fencing?. You could do this lab with any number or type of surfaces that you choose. Also, depending on the time you have and resources available you could let the students completely design the experiment, coming up with the surfaces and the set-up. If this is the case, you could reword the question to: On which surface will my Hot Wheels car roll furthest after going down a ramp.. For our lab, due to time constraints, I have designed the initial set-up of the lab and the surfaces for the cars.. ### The Lab. The purpose of the lab is: To show understanding of the scientific method by designing a lab sheet (and possibly the lab itself), completing the experiment, then analyzing the data and reporting on the lab.. After showing the students the initial set-up, I have the students use a word processor to design a lab sheet that includes the following headings:. • Problem/Question. • Hypothesis. • Independent and Dependent Variables. • Constants. • Procedure. • Data. • Analysis. • Conclusion. The students need to have information under each heading through the Procedure as well as a data table that they can fill out during the experiment done and printed out before I will let them proceed with the experiment. An example may look like this.. #### Hot Wheels Scientific Method Lab. Problem/Question. On which surface will my Hot Wheels car roll furthest after going down a ramp: 60 grit sandpaper, carpet, or cedar fencing?. Hypothesis. My hypothesis is that the Hot Wheels car will roll the furthest on the 60 grit sandpaper.. Independent and Dependent Variables. | The independent variable in this experiment is the surfaces the car is traveling on. The dependent variable is the distance the car goes.. Constants. Some things that need to remain constant are:. The car I use.. Where/how high the car starts on the ramp.. How I release the car.. How I measure the distance including to the front or back of the car and the units I use.. Procedure. Line the back of the car up with back edge of the track. Without pushing the car, release it so that it rolls down the orange track. Let it roll on the surface until it comes to a stop. Measure from the end of the orange track to the back of the car and record the distance in centimeters. Repeat 5 times for each surface. Use the same car for each trial and each surface.. Data. Analysis. Conclusion. Once they have this much done and printed out, I let them start the experiment. They should record the data on in their table. When they have finished the experiment, it's back to the computer for them to do their analysis and write up their conclusion. When the lab paper is finished I have them print it out and turn it in.. ### Notes. • Remember, this lab is not really about what surface the cars go further on. The students are not graded on getting the "right" surface. It's about the scientific method. How well did they organize their lab sheet? How well did they pay attention to the constants. How well did they perform the procedure. How well did they analyze the experiment and discuss the problems. These are the things that I pay attention to and grade them on.. • The set-up I used is not perfect by design. I like that there are problems with the set-up and hope that the students notice these and address them in their analysis and conclusion. One of the potential problems is that on the wood and the sandpaper, sometimes the cars veer off the surface. The most common ways the students try to deal with these are to just do more trials until they get their specified number on the surface; or they will put "railings" on the edge to keep the car on the surface. Hopefully they realize that rubbing on their "railing" will cause the car not to go as far and perhaps skew their results. I usually don't talk to them about this, but do look to see if they discussed how their solution may have affected their data. Using yard sticks to guide the cars. Another issue with the experiment is that I've taped several pieces of sandpaper together. Where they come together the seams aren't always smooth and sometime there are little ridges. That could also affect their data. Again, I don't talk to them about it. I just watch to see if they notice. There are a few other small possible problems with this set-up, but the key is, do the students notice, what if anything do they do to solve them, and most importantly, do they talk about them in their analysis and conclusion. This is how they learn about experiments and what make a good one.. • Make sure that all the constants listed are addressed in the procedure.. • I don't mention how many trials they should do. I let them decided. This let's me know how well they understand the scientific method and how important multiple trials are. I always have a few who only do one trial. Most do 2 or 3. Once in a while I get students who will do 5 or more. |
https://madwirebuild.com/solved-how-much-time-does-it-take-an-electromagnetic-gentle/ | 1,695,519,064,000,000,000 | text/html | crawl-data/CC-MAIN-2023-40/segments/1695233506539.13/warc/CC-MAIN-20230923231031-20230924021031-00655.warc.gz | 427,240,786 | 17,971 | Solved How Much Time Does It Take An Electromagnetic Gentle
Okay, So this query requested, how long wouldn’t it soak up minutes for radio wave to journey from Venice to the earth? Now we all know that according query, it’s 28 million miles between Venus and Earth. So we need to make certain that those air in the identical items. All right, so we know that there’s for every one mile, there are 1.sixty one kilometers. Okay, so now if we have been to cease right here, we now have been kilometers, however we wanted in meters. So we know that for each kilometer based mostly on the the tens scale of the metric system, there will be one thousand meters, so that can give us after we plug that in.
In the earlier couple of years scientists have found that the water molecules in the environment additionally generate waves of light busiest travel days around christmas 2018. Compute the angular momentum of the earth arising from the next motions. Earth’s orbital movement around the solar.
Any radio wave is transferring at the velocity of sunshine, whatever the frequency, so the frequency must be superfluous info. AM radio waves have larger wavelengths (some as massive as a kilometer!). It is normally easier to get reception for AM waves in mountain areas compared to FM waves which have shorter wavelengths. Explain why this is so utilizing your data of diffraction.
Describe how the motions of the particles that make up an object change when the object’s temperature will increase. Astronomers observe the chromosphere of the Sun with a filter that passes the pink hydrogen spectral line of wavelength 656.three nm, known as the $\mathrm _$ line. The filter consists of a clear dielectric of thickness d held between two partially aluminized glass plates. The filter is saved at a constant temperature. The dielectric may also pass what near-visible wavelength?
The pace of sunshine is 299,792,458 metres per second – which is 1,079,252,849km/hour. The Earth is the source of every wave that has ever been created, however that’s not all that makes the Earth particular. It is the supply of the next largest wave, but the Earth is the source of the second largest wave, which is the wave that’s traveling to the moon. Scientist typically agree that earth is getting warmer as a end result of what call the green house effectt. Why is the Curie temperature such a significant property of magnetic materials?
• 69 | 509 | 2,426 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.5 | 4 | CC-MAIN-2023-40 | latest | en | 0.935842 | Solved How Much Time Does It Take An Electromagnetic Gentle. Okay, So this query requested, how long wouldn’t it soak up minutes for radio wave to journey from Venice to the earth? Now we all know that according query, it’s 28 million miles between Venus and Earth. So we need to make certain that those air in the identical items. All right, so we know that there’s for every one mile, there are 1.sixty one kilometers. Okay, so now if we have been to cease right here, we now have been kilometers, however we wanted in meters. So we know that for each kilometer based mostly on the the tens scale of the metric system, there will be one thousand meters, so that can give us after we plug that in.. In the earlier couple of years scientists have found that the water molecules in the environment additionally generate waves of light busiest travel days around christmas 2018. Compute the angular momentum of the earth arising from the next motions. Earth’s orbital movement around the solar.. Any radio wave is transferring at the velocity of sunshine, whatever the frequency, so the frequency must be superfluous info. AM radio waves have larger wavelengths (some as massive as a kilometer!). It is normally easier to get reception for AM waves in mountain areas compared to FM waves which have shorter wavelengths. Explain why this is so utilizing your data of diffraction. | Describe how the motions of the particles that make up an object change when the object’s temperature will increase. Astronomers observe the chromosphere of the Sun with a filter that passes the pink hydrogen spectral line of wavelength 656.three nm, known as the $\mathrm _$ line. The filter consists of a clear dielectric of thickness d held between two partially aluminized glass plates. The filter is saved at a constant temperature. The dielectric may also pass what near-visible wavelength?. The pace of sunshine is 299,792,458 metres per second – which is 1,079,252,849km/hour. The Earth is the source of every wave that has ever been created, however that’s not all that makes the Earth particular. It is the supply of the next largest wave, but the Earth is the source of the second largest wave, which is the wave that’s traveling to the moon. Scientist typically agree that earth is getting warmer as a end result of what call the green house effectt. Why is the Curie temperature such a significant property of magnetic materials?. • 69. |
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