6.11: Finding Evidence
- Describe strategies for preliminary research on a topic
A critical step in the writing process is to find evidence that supports and explains the claim you make in your thesis statement. Often, this means doing research and finding information, facts, stories, data, and reports related to your topic, but sometimes, especially in narrative writing, it means adding support through your own experiences and examples.
Support and Elaboration
Support and elaboration consist of the specific details and information writers use to develop their topic. The key to developing support and elaboration is getting specific . Good writers use concrete, specific details, and relevant information to establish mental images for their readers.
Sufficiency and Relatedness
Two important concepts in support and elaboration are sufficiency and relatedness .
Sufficiency refers the amount of detail — is there enough detail to support the topic? Any parent who has asked his or her child what happened at school knows how hard it is to get a child to elaborate on a subject. Good writers supply their readers with sufficient details to comprehend what they have written. In narrative writing, this means providing enough descriptive details for the reader to construct a picture of the story in their mind. In expository writing, this means not only finding enough information to support your purpose, whether it is to inform or persuade your audience, but also finding information that is credible and accurate.
Sufficiency, however, is not enough. The power of your information is determined less by the quantity of details than by their quality . Look for evidence that is accurate and comes from credible sources.
Relatedness refers to the quality of the details and their relevance to the topic. Good writers select only the details that will support their focus, deleting irrelevant information. In narrative writing, details should be included only if they are concrete, specific details that contribute to, rather than detract from, the picture provided by the narrative. In expository writing, information should be included only if it is relevant to the writer’s goal and strengthens rather than weakens the writer’s ability to meet that goal.
FOR NARRATIVE WRITING:
- Is your story developed with specific details that are related to the main event?
- Do all of the details move the story along?
- Does your story have enough elaboration so that your reader can see and feel what is happening? Can you show me an example where your reader can see or feel what is happening?
FOR INFORMATIONAL WRITING:
- Is your essay developed with specific information (facts, statistics, etc.) that is related to the main topic?
- Does all of the information support the main topic?
- Does your essay have enough information to fulfill your reader’s needs?
FOR ARGUMENTATIVE WRITING:
- Is your essay developed with specific details that are related to the main topic?
- Does all of the information support the main argument?
- Does your essay have enough supporting evidence to persuade your reader?
Finding Evidence
Your research strategy for finding supporting evidence should be based on the research requirements your professor provides. Some formal research essays should include peer-reviewed journal articles only; however, there are some research papers that may allow you to use a wider variety of sources, including sources from the World Wide Web.
Primary and Secondary Sources
Some assignments require you to find primary sources only, while others allow you to rely on secondary sources . Primary sources are original sources and documents that were created at the time of study or that were created by someone experiencing an event first-hand. For example, a historical primary source would be a document, manuscript, recording, autobiography, photograph, or letter directly from the time period; if you were studying the Civil War, then a letter from Abraham Lincoln or a journal entry from a soldier would both be primary sources. More current primary sources include descriptions of events by those who experienced it in person—for example, an essay written by someone at the World Trade Center during 9/11. In the sciences, results of research studies and experiments are also primary sources.
Secondary sources are secondhand accounts of primay sources and involve generalization, analysis, interpretation, or evaluation of the original information. For example, a secondary source about the Civil War would be a biography on Abraham Lincoln or a scholarly journal from someone analyzing battle plans. A news article about a scientific breakthrough would also be a secondary source.
Popular and Scholarly Sources
A popular source is meant for a general audience. Popular sources include newspaper and magazine articles, your Yahoo or Google newsfeed, and blogs. A scholarly source would be one that has been written by a professional in the field; the author may hold a doctoral degree or have a great amount of expertise in the field you are studying. Oftentimes, an author’s credentials will be listed as a footnote within the source, but if not, an Internet search may reveal whether the writer can be determined to be a scholarly author or one that has done a vast amount of research on the topic.
The author of the source will always be an important consideration, as your view of the quality of the article may change depending upon the author’s credibility. In addition, you must ask yourself whether your source is popular or scholarly, and be sure to meet any requirements the project demands regarding source types.
In many fields, there will be a number of academic journals, periodicals and organizations that publish scholarly articles related to the subject. By discovering and accessing these journals, you can be sure that the piece from which you are quoting is a scholarly source. Many colleges and universities pay fees in order to provide their students with access to these journals in their electronic form, and an even greater number of university libraries will shelve current and back issues of these journals.
Furthermore, conducting an Internet search of these journals and articles may prove fruitful. Search engines such as Google offer the option of searching “Google Scholar” in order to access only these scholarly articles. Finding these sources online, depending on the journal and the site, may require that you pay a fee to view the article. This is where university libraries come in handy, as they offer free access to the same materials. If you cannot access a university library, some clever hunting of the Internet may still yield what you are looking for at no cost.
If your professor has not established research requirements for your assignment, it’s a good idea to ask. You can start with a general search using Google or Wikipedia to understand the basics about your topic, but you’ll want to do specific research to find the type of evidence needed to give credibility to your argument. This will probably include using both print and electronic sources, in the form of books, scholarly journals, magazines, newspapers, and websites.
Contributors and Attributions
- Introduction to text. Provided by : Lumen Learning. License : CC BY: Attribution
- Support and elaboration. Authored by : Kathleen Cali. Located at : http://www.learnnc.org/lp/editions/few/685 . License : CC BY-NC-SA: Attribution-NonCommercial-ShareAlike
- Research Strategies. Provided by : Excelsior College Online Writing Lab. Located at : https://owl.excelsior.edu/research/research-strategies/ . License : CC BY: Attribution
- Popular and Scholarly Sources from Horse of a Different Color: English Composition and Rhetoric . Authored by : Marianne Botos, Lynn McClelland, Stephanie Polliard, and Pamela Osback . Located at : https://pvccenglish.files.wordpress.com/2010/09/eng-101-inside-pages-proof2-no-pro.pdf . License : CC BY: Attribution
- Image of iphone. Authored by : Markus Spiske. Provided by : Pexels. Located at : www.pexels.com/photo/hand-smartphone-summer-internet-230860/. License : Other . License Terms : www.pexels.com/photo-license/


1.7: Angles
Our next goal is to introduce angles and angle measures; after that, the statement “we can measure angles” will become rigorous; see (iii) on Section 1.1 .
An ordered pair of half-lines that start at the same point is called an angle. The angle \(AOB\) (also denoted by \(\angle AOB\)) is the pair of half-lines \([OA)\) and \([OB)\). In this case the point \(O\) is called the vertex of the angle.
Intuitively, the angle measure tells how much one has to rotate the first half-line counterclockwise, so it gets the position of the second half-line of the angle. The full turn is assumed to be \(2 \cdot \pi\); it corresponds to the angle measure in radians. (For a while you may think that \(\pi\) is a positive real number that measures the size of a half turn in certain units. Its concrete value \(\pi \approx 3.14\) will not be important for a long time.
The angle measure of \(\angle AOB\) is denoted by \(\measuredangle AOB\); it is a real number in the interval \((-\pi, \pi]\).
The notations \(\angle AOB\) and \(\measuredangle AOB\) look similar; they also have close but different meanings which better not be confused. For example, the equality \(\angle AOB = \angle A'O'B'\) means that \([OA) = [O'A')\) and \([OB) = [O'B')\); in particular, \(O = O'\). On the other hand the equality \(\measuredangle AOB = \measuredangle A'O'B'\) means only equality of two real numbers; in this case \(O\) may be distinct from \(O'\).
Here is the first property of angle measure which will become a part of the axiom.
Given a half-line \([OA)\) and \(\alpha \in (-\pi, \pi]\) there is a unique half-line \([OB)\) such that \(\measuredangle AOB = \alpha\).


9.10: Center of Mass (Part 2)
Center of Mass of Continuous Objects
If the object in question has its mass distributed uniformly in space, rather than as a collection of discrete particles, then m j → dm, and the summation becomes an integral:
\[\vec{r}_{CM} = \frac{1}{M} \int \vec{r} dm \ldotp \label{9.34}\]
In this context, r is a characteristic dimension of the object (the radius of a sphere, the length of a long rod). To generate an integrand that can actually be calculated, you need to express the differential mass element dm as a function of the mass density of the continuous object, and the dimension r. An example will clarify this.
Find the center of mass of a uniform thin hoop (or ring) of mass \(M\) and radius \(r\).
Strategy
First, the hoop’s symmetry suggests the center of mass should be at its geometric center. If we define our coordinate system such that the origin is located at the center of the hoop, the integral should evaluate to zero.
We replace dm with an expression involving the density of the hoop and the radius of the hoop. We then have an expression we can actually integrate. Since the hoop is described as “thin,” we treat it as a one-dimensional object, neglecting the thickness of the hoop. Therefore, its density is expressed as the number of kilograms of material per meter. Such a density is called a linear mass density , and is given the symbol \(\lambda\); this is the Greek letter “lambda,” which is the equivalent of the English letter “l” (for “linear”).
Since the hoop is described as uniform, this means that the linear mass density \(\lambda\) is constant. Thus, to get our expression for the differential mass element dm, we multiply \(\lambda\) by a differential length of the hoop, substitute, and integrate (with appropriate limits for the definite integral).
Solution
First, define our coordinate system and the relevant variables (Figure \(\PageIndex{1}\)).
The center of mass is calculated with Equation \ref{9.34}:
\[\vec{r}_{CM} = \frac{1}{M} \int_{a}^{b} \vec{r} dm \ldotp\]
We have to determine the limits of integration a and b. Expressing \(\vec{r}\) in component form gives us
\[\vec{r}_{CM} = \frac{1}{M} \int_{a}^{b} \big[ (r \cos \theta) \hat{i} + (R \sin \theta) \hat{j} \big] dm \ldotp\]
In the diagram, we highlighted a piece of the hoop that is of differential length ds; it therefore has a differential mass dm = \(\lambda\)ds. Substituting:
\[\vec{r}_{CM} = \frac{1}{M} \int_{a}^{b} \big[ (r \cos \theta) \hat{i} + (R \sin \theta) \hat{j} \big] \lambda ds \ldotp\]
However, the arc length ds subtends a differential angle d\(theta\), so we have
\[ds = rd \theta\]
and thus
\[\vec{r}_{CM} = \frac{1}{M} \int_{a}^{b} \big[ (r \cos \theta) \hat{i} + (R \sin \theta) \hat{j} \big] \lambda rd \theta \ldotp\]
One more step: Since \(\lambda\) is the linear mass density, it is computed by dividing the total mass by the length of the hoop:
\[\lambda = \frac{M}{2 \pi r}\]
giving us
\[\begin{split} \vec{r}_{CM} & = \frac{1}{M} \int_{a}^{b} \big[ (r \cos \theta) \hat{i} + (R \sin \theta) \hat{j} \big] \left(\dfrac{M}{2 \pi r}\right) rd \theta \\ & = \frac{1}{2 \pi} \int_{a}^{b} \big[ (r \cos \theta) \hat{i} + (R \sin \theta) \hat{j} \big] d \theta \ldotp \end{split}\]
Notice that the variable of integration is now the angle \(\theta\). This tells us that the limits of integration (around the circular hoop) are θ = 0 to \(\theta\) = 2\(\pi\), so a = 0 and b = 2\(\pi\). Also, for convenience, we separate the integral into the x- and y-components of \(\vec{r}_{CM}\). The final integral expression is
\[\begin{split} \vec{r}_{CM} & = r_{CM,x} \hat{i} + r_{CM,y} \hat{j} \\ & = \Big[ \frac{1}{2 \pi} \int_{0}^{2 \pi} (2 \cos \theta d \theta \Big] \hat{i} + \Big[ \frac{1}{2 \pi} \int_{0}^{2 \pi} (2 \sin \theta d \theta \Big] \hat{j} \\ & = 0 \hat{i} + 0 \hat{j} = \vec{0} \end{split}\]
as expected.
Center of Mass and Conservation of Momentum
How does all this connect to conservation of momentum?
 The center of mass of the objects is
\[\vec{r}_{CM} = \frac{1}{M} \sum_{j = 1}^{N} m_{j} \vec{r}_{j} \ldotp\]
Its velocity is
\[\vec{v}_{CM} = \frac{d \vec{r}_{CM}}{dt} = \frac{1}{M} \sum_{j = 1}^{N} m_{j} \frac{d \vec{r}_{j}}{dt} \label{9.35}\]
and thus the initial momentum of the center of mass is
\[\begin{split} \Big[ M \frac{d \vec{r}_{CM}}{dt} \Big]_{i} & = \sum_{j = 1}^{N} m_{j} \frac{d \vec{r}_{j,i}}{dt} \\ M \vec{v}_{CM,i} & = \sum_{j = 1}^{N} m_{j} \vec{v}_{j,i} \ldotp \end{split}\]
After these masses move and interact with each other, the momentum of the center of mass is
\[M \vec{v}_{CM,f} = \sum_{j = 1}^{N} m_{j} \vec{v}_{j,f} \ldotp\]
But conservation of momentum tells us that the right-hand side of both equations must be equal, which says
\[M \vec{v}_{CM,f} = M \vec{v}_{CM,i} \ldotp \label{9.36}\]
This result implies that conservation of momentum is expressed in terms of the center of mass of the system. Notice that as an object moves through space with no net external force acting on it, an individual particle of the object may accelerate in various directions, with various magnitudes, depending on the net internal force acting on that object at any time. (Remember, it is only the vector sum of all the internal forces that vanishes, not the internal force on a single particle.) Thus, such a particle’s momentum will not be constant—but the momentum of the entire extended object will be, in accord with Equation \ref{9.36}.
Equation \ref{9.36} implies another important result: Since M represents the mass of the entire system of particles, it is necessarily constant. (If it isn’t, we don’t have a closed system, so we can’t expect the system’s momentum to be conserved.) As a result, Equation \ref{9.36} implies that, for a closed system,
\[\vec{v}_{CM,f} = \vec{v}_{CM,i} \ldotp \label{9.37}\]
That is to say, in the absence of an external force, the velocity of the center of mass never changes .
You might be tempted to shrug and say, “Well yes, that’s just Newton’s first law,” but remember that Newton’s first law discusses the constant velocity of a particle, whereas Equation \ref{9.37} applies to the center of mass of a (possibly vast) collection of interacting particles, and that there may not be any particle at the center of mass at all! So, this really is a remarkable result.
When a fireworks rocket explodes, thousands of glowing fragments fly outward in all directions, and fall to Earth in an elegant and beautiful display (Figure \(\PageIndex{2}\)). Describe what happens, in terms of conservation of momentum and center of mass.
The picture shows radial symmetry about the central points of the explosions; this suggests the idea of center of mass. We can also see the parabolic motion of the glowing particles; this brings to mind projectile motion ideas.
Solution
Initially, the fireworks rocket is launched and flies more or less straight upward; this is the cause of the more-or-less-straight, white trail going high into the sky below the explosion in the upper-right of the picture (the yellow explosion). This trail is not parabolic because the explosive shell, during its launch phase, is actually a rocket; the impulse applied to it by the ejection of the burning fuel applies a force on the shell during the rise-time interval. (This is a phenomenon we will study in the next section.) The shell has multiple forces on it; thus, it is not in free-fall prior to the explosion.
At the instant of the explosion, the thousands of glowing fragments fly outward in a radially symmetrical pattern. The symmetry of the explosion is the result of all the internal forces summing to zero \((\sum_{j} \vec{f}_{j}^{int} = 0)\); for every internal force, there is another that is equal in magnitude and opposite in direction.
However, as we learned above, these internal forces cannot change the momentum of the center of mass of the (now exploded) shell. Since the rocket force has now vanished, the center of mass of the shell is now a projectile (the only force on it is gravity), so its trajectory does become parabolic. The two red explosions on the left show the path of their centers of mass at a slightly longer time after explosion compared to the yellow explosion on the upper right.
In fact, if you look carefully at all three explosions, you can see that the glowing trails are not truly radially symmetric; rather, they are somewhat denser on one side than the other. Specifically, the yellow explosion and the lower middle explosion are slightly denser on their right sides, and the upper-left explosion is denser on its left side. This is because of the momentum of their centers of mass; the differing trail densities are due to the momentum each piece of the shell had at the moment of its explosion. The fragment for the explosion on the upper left of the picture had a momentum that pointed upward and to the left; the middle fragment’s momentum pointed upward and slightly to the right; and the right-side explosion clearly upward and to the right (as evidenced by the white rocket exhaust trail visible below the yellow explosion).
Finally, each fragment is a projectile on its own, thus tracing out thousands of glowing parabolas.
Significance
In the discussion above, we said, “…the center of mass of the shell is now a projectile (the only force on it is gravity)….” This is not quite accurate, for there may not be any mass at all at the center of mass; in which case, there could not be a force acting on it. This is actually just verbal shorthand for describing the fact that the gravitational forces on all the particles act so that the center of mass changes position exactly as if all the mass of the shell were always located at the position of the center of mass.
How would the firework display change in deep space, far away from any source of gravity?
You may sometimes hear someone describe an explosion by saying something like, “the fragments of the exploded object always move in a way that makes sure that the center of mass continues to move on its original trajectory.” This makes it sound as if the process is somewhat magical: how can it be that, in every explosion, it always works out that the fragments move in just the right way so that the center of mass’ motion is unchanged? Phrased this way, it would be hard to believe no explosion ever does anything differently.
The explanation of this apparently astonishing coincidence is: We defined the center of mass precisely so this is exactly what we would get. Recall that first we defined the momentum of the system:
\[\vec{p}_{CM} = \sum_{j = 1}^{N} \frac{d \vec{p}_{j}}{dt} \ldotp\]
We then concluded that the net external force on the system (if any) changed this momentum:
\[\vec{F} = \frac{d \vec{p}_{CM}}{dt}\]
and then—and here’s the point—we defined an acceleration that would obey Newton’s second law. That is, we demanded that we should be able to write
\[\vec{a} = \frac{\vec{F}}{M}\]
which requires that
\[\vec{a} = \frac{d^{2}}{dt^{2}} \left(\dfrac{1}{M} \sum_{j = 1}^{N} m_{j} \vec{r}_{j}\right) \ldotp\]
where the quantity inside the parentheses is the center of mass of our system. So, it’s not astonishing that the center of mass obeys Newton’s second law; we defined it so that it would.


8.10: Watching, Rating, and Providing Feedback for a Page
While the LibreTexts team has a curation sub-team that cultivates the content on the library (in coordination with contributing authors), community curation is also a key aspect in keeping our content "living" rather than stagnating (e.g., in a dead format). There are three key aspects to facilitate: Watching pages, Rating Page, and providing Feedback on Pages.
Watching Pages
- Navigate to the page you want to subscribe to.
- Click the Page Notifications (star) icon in the upper right-hand corner of the page and select the appropriate radio button to set your subscription.
If you are on a Category or Guide page and want to receive notifications on all content in that Category or Guide, select the option for This page and all subpages . To subscribe to all content on your site, navigate to each top-level Category or Guide from your homepage and subscribe to all subpages.
Figure \(\PageIndex{1}\)
Rating Pages
Article ratings and feedback enable users to indicate if an article was helpful or not and provide optional comments. To rate an article go to the bottom of the page and click either Yes (smiley face) or No (sad face) to indicate if an article was helpful or not. Logged in users can also select Leave Feedback to include a comment and indicate their preference to be contacted regarding their feedback.
Figure \(\PageIndex{2}\)
Feedback on Pages
Feedback is only enabled for logged in users to prohibit spam bots from submitting feedback. Emails are sent to the development team and then addressed at that level or forwarded to the relevant curators.


5.10: Current and Resistance (Answers)
Conceptual Questions
1. If a wire is carrying a current, charges enter the wire from the voltage source’s positive terminal and leave at the negative terminal, so the total charge remains zero while the current flows through it.
3. Using one hand will reduce the possibility of “completing the circuit” and having current run through your body, especially current running through your heart.
5. Even though the electrons collide with atoms and other electrons in the wire, they travel from the negative terminal to the positive terminal, so they drift in one direction. Gas molecules travel in completely random directions.
7. In the early years of light bulbs, the bulbs are partially evacuated to reduce the amount of heat conducted through the air to the glass envelope. Dissipating the heat would cool the filament, increasing the amount of energy needed to produce light from the filament. It also protects the glass from the heat produced from the hot filament. If the glass heats, it expands, and as it cools, it contacts. This expansion and contraction could cause the glass to become brittle and crack, reducing the life of the bulbs. Many bulbs are now partially filled with an inert gas. It is also useful to remove the oxygen to reduce the possibility of the filament actually burning. When the original filaments were replaced with more efficient tungsten filaments, atoms from the tungsten would evaporate off the filament at such high temperatures. The atoms collide with the atoms of the inert gas and land back on the filament.
9. In carbon, resistivity increases with the amount of impurities, meaning fewer free charges. In silicon and germanium, impurities decrease resistivity, meaning more free electrons.
11. Copper has a lower resistivity than aluminum, so if length is the same, copper must have the smaller diameter.
13. Device B shows a linear relationship and the device is ohmic.
15. Although the conductors have a low resistance, the lines from the power company can be kilometers long. Using a high voltage reduces the current that is required to supply the power demand and that reduces line losses.
17. The resistor would overheat, possibly to the point of causing the resistor to burn. Fuses are commonly added to circuits to prevent such accidents.
Problems
21. a. \(\displaystyle v=4.38×10^5\frac{m}{s}\);
b. \(\displaystyle Δq=5.00×10^{−3}C\),no. of protons=\(\displaystyle 3.13×10^{16}\)
23. \(\displaystyle I=\frac{ΔQ}{Δt},ΔQ=12.00C\), no. of electrons=\(\displaystyle 7.46×10^{19}\)
25. \(\displaystyle I(t)=0.016\frac{C}{s^4}t^3−0.001\frac{C}{s}\) \(\displaystyle I(3.00s)=0.431A\)
27. \(\displaystyle I(t)=−I_{max}sin(ωt+ϕ)\)
29. \(\displaystyle |J|=15.92A/m^2\)
31. \(\displaystyle I=3.98×10^{−5} A\)
33. a. \(\displaystyle |J|=7.60×10^5\frac{A}{m^2}\);
b. \(\displaystyle v_d=5.60×10^{−5}\frac{m}{s}\)
35. \(\displaystyle R=6.750kΩ\)
37. \(\displaystyle R=0.10Ω\)
39. \(\displaystyle R=ρ\frac{L}{A}\); \(\displaystyle L=3cm\)
41. \(\displaystyle \frac{R_{Al}/L_{Al}}{R_{Cu}/L_{Cu}}\)\(\displaystyle =\frac{ρ_{Al}\frac{1}{π(\frac{D_{Al}}{2})^2}}{ρ_{Cu}\frac{1}{π(\frac{D_{Cu}}{2})^2}}\)\(\displaystyle =\frac{ρ_{Al}}{ρ_{Cu}}(\frac{D_{Cu}}{D_{Al}})^2=1\)\(\displaystyle ,\frac{D_{Al}}{D_{Cu}}=\sqrt{\frac{ρ_{AI}}{ρ_{Cu}}}\)
43. a. \(\displaystyle R=R_0(1+αΔT),2=1+αΔT,ΔT=256.4°C,T=276.4°C\);
b. Under normal conditions, no it should not occur.
45. \(\displaystyle R=R_0(1+αΔT)\) \(\displaystyle α=0.006°C^{−1}\), iron
47. a. \(\displaystyle R=ρ\frac{L}{A},ρ=2.44×10^{−}8Ω⋅m\), gold; \(\displaystyle R=ρ\frac{L}{A}(1+αΔT)\)
b. \(\displaystyle R=2.44×10^{−8}Ω⋅m(\frac{25m}{π(\frac{0.100×10^{−3}m}{2})^2})(1+0.0034°C^{−1}(150°C−20°C))R=112Ω\)
49. \(\displaystyle R_{Fe}=0.525Ω,R_{Cu}=0.500Ω,α_{Fe}=0.0065°C^{−1},α_{Cu}=0.0039°C^{−1},R_{Fe}=R_{Cu},R_{0Fe}(1+α_{Fe}(T−T_0))=R_{0Cu}(1+α_{Cu}(T−T_0)),\frac{R_{0Fe}}{R_{0Cu}}(1+α_{Fe}(T−T_0))=1+α_{Cu}(T−T_0),T=2.91°C\)
51. \(\displaystyle R_{min}=2.375×10^5Ω,I_{min}=12.63μA\)
\(\displaystyle R_{max}=2.625×10^5Ω,I_{max}=11.43μA\)
53. \(\displaystyle R = 100Ω\)
55. a. \(\displaystyle I =2 mA\);
b. \(\displaystyle P =0.04 mW\);
c. \(\displaystyle P = 0.04 mW\);
d. It is converted into heat.
57. \(\displaystyle P=\frac{V^2}{R},R=40Ω, A=2.08mm^2, ρ=100×10^{−8}Ω⋅m, R=ρ\frac{L}{A},L=83m\)
59. \(\displaystyle I=0.14A,V=14V\)
61. a. \(\displaystyle I≈3.00A+\frac{100W}{110V}+\frac{60W}{110V}+\frac{3.00W}{110V}=4.48A\)
\(\displaystyle P=493W\)
\(\displaystyle R=9.91Ω,\)
\(\displaystyle P_{loss}=200.W\)
\(\displaystyle %loss=40%\)
b. \(\displaystyle P=493W\)
\(\displaystyle I=0.0045A\)
\(\displaystyle R=9.91Ω\)
\(\displaystyle P_{loss}=201μW\)
\(\displaystyle %loss=0.00004%\)
Additional Problems
69. \(\displaystyle dR=\frac{ρ}{2πrL}dr\)
\(\displaystyle R=\frac{ρ}{2πL}ln\frac{r_o}{r_i}\)
\(\displaystyle R=2.21×10^{11}Ω\)
71. a. \(\displaystyle R_0=0.003Ω\);
b. \(\displaystyle T_c=37.0°C\) \(\displaystyle R=0.00302Ω\)
73. \(\displaystyle ρ=5.00×10^{−8}Ω⋅m\)
75. \(\displaystyle ρ=1.71×10^{−8}Ω⋅m\)
77. \(\displaystyle a. V=6000V\);
b. \(\displaystyle V=60V\)
79. \(\displaystyle P=\frac{W}{t},W=8.64J\)
Challenge Problems
81. \(\displaystyle V=7.09cm^3\) \(\displaystyle n=8.49×10^{28}\frac{electrons}{m^2}\) \(\displaystyle v_d=7.00×10^{−5}\frac{m}{s}\)
83. a. \(\displaystyle v=4.38×10^{7} m/s \);
b. \(\displaystyle v = 5.81×10^{13} \: \frac{protons}{m^3}\);
c. 1.25 \(\frac{electrons}{m^3}\)
85. \(\displaystyle E=75kJ\)
87. a. \(\displaystyle P=52W\) \(\displaystyle R=36Ω\);
b. \(\displaystyle V=43.54V\)
89. a. \(\displaystyle R=\frac{ρ}{2πL}ln(\frac{R_0}{R_i})\);
b. \(\displaystyle R=2.5mΩ\)
91. a. \(\displaystyle I=0.870A\);
b. #electrons \(\displaystyle =2.54×10^{23}\)
c. \(\displaystyle R=132Ω\);
d. \(\displaystyle q=4.68×10^6J\)
93. \(\displaystyle P=1045W,P=\frac{V^2}{R},R=12.27Ω\)
Contributors and Attributions
Samuel J. Ling (Truman State University), Jeff Sanny (Loyola Marymount University), and Bill Moebs with many contributing authors. This work is licensed by OpenStax University Physics under a
Creative Commons Attribution License (by 4.0)
.


13.4: The History of Studying Galaxies
The study and discussions of galaxies goes back millennia. Abd al-Rahman al-Sufi , a Muslim astronomer from Persia (modern Iran), was the first to recognize the Large Magellanic Cloud, an irregular galaxy, and in 964 AD made the earliest observation of the Andromeda Galaxy, in which al-Sufi described Andromeda as a small cloud . Al-Sufi was the first to observe other galaxies than the Milky Way galaxy.
In his text, al-Sufi discusses a number of astronomical observations and topics, including his observations of what he called Al Bakr, the Large Magellanic Cloud.
Thomas Wright hypothesized in 1750 that the Milky Way galaxy was a flattened disk of stars. Wright also thought that some of the ‘nebulae’ observed were actually objects like the Milky Way. (Nebulae was the term used to describe all of these nebula-like objects, many of which are now known to be galaxies. ) Five years later, in 1755, Immanuel Kant coined the term Island Universe to describe these ‘nebulae’ that Wright had hypothesized.
During the search for comets from 1771 to 1784, Charles Messier completed a catalog listing of a number of bright nebulae. Several of the Messier Objects are now known to be galaxies. When William Herschel created his 1786 catalogue of deep sky objects, he used the phrase spiral nebula for a number of the objects, such as the Andromeda nebula. This indicated that Herschel was able to discern the spiral nature of these objects. Lord Rosse completed a new, large telescope in 1845 and was able to differentiate between elliptical and spiral nebulae.
Deep sky objects are those objects other than Solar System and stellar system objects, and individual stars. These include objects such as star clusters, nebulae, and galaxies.


7.8: Mergers and Acquisitions
What you’ll learn to do: describe the two types of mergers and acquisitions
One of the quickest ways for a business to expand into other markets or products lines is either to merge or acquire/purchase another company. Although this is common in today’s business environment, there are still many complex factors to consider before deciding whether a merger or acquisition is the optimal solution.
Learning Objectives
- Define acquisition as a business strategy
- Explain why companies undertake vertical mergers and acquisitions
Mergers and Acquisitions
Integration Strategies: Mergers and Acquisitions
When businesses acquire other businesses or operations that were previously competitors, suppliers, buyers, or sellers, they are engaging in a strategy known as integration . This strategy is based on the possibility of synergy, the idea that the sum of two entities will be greater than their individual parts—often expressed as 1 + 1 = 3. Integration can be accomplished in two primary ways: through mergers or acquisitions. A merger is the consolidation of two companies that, prior to the merger, were operating as independent entities. A merger usually creates one larger company, and one of the original companies ceases to exist. Mergers can be either horizontal or vertical.
A horizontal merger occurs between companies in the same industry. This type of merger is essentially a consolidation of two or more businesses that operate in the same market space, often as competitors offering the same good or service. Horizontal mergers are common in industries with fewer firms, since competition tends to be higher, and the synergies and potential market-share gains are much greater in those industries.
facebook + Instagram = horizontal merger
When Facebook acquired Instagram in 2012 for a reported $1 billion, Facebook was looking to strengthen its position in the social-media and social-sharing space. Both Facebook and Instagram operated in the same industry and were in similar positions with regard to their photo-sharing services. Facebook clearly saw Instagram as an opportunity to grow its market share, increase its product line, reduce competition, and access new markets.
A vertical merger is characterized by the merger of two organizations that have a buyer-seller relationship or, more generally, two or more firms that are operating at different levels within an industry’s supply chain. Most often the logic behind the merger is to increase synergies by merging firms that would be more efficient operating as one.
apple: The King of Vertical Integration
Apple Inc. is famous for perfecting the art of vertical integration. The company manufactures its custom A-series chips for its iPhones and iPads . It also manufactures its custom touch ID fingerprint sensor. Apple opened up a laboratory in Taiwan for the development of LCD and OLED screen technologies in 2015. It also paid $18.2 million for a 70,000-square-foot manufacturing facility in North San Jose in 2015. These investments (i.e., mergers) enable Apple to move along the supply chain in a backward integration, giving it flexibility and freedom in its manufacturing capabilities. [1]
An acquisition , on the other hand, occurs when a company purchases the assets of another business (such as stock, property, plants, equipment) and usually permits the acquired company to continue operating as it did prior to the acquisition. Acquisition usually refers to a purchase of a smaller firm by a larger one. Sometimes, however, a smaller firm will acquire management control of a larger and/or longer-established company and retain the name of the latter for the post-acquisition combined entity.
Reasons for Mergers and Acquisitions
There are many good reasons for growing your business through an acquisition or merger. These include:
- Obtaining quality staff or additional skills, knowledge of your industry or sector, and other business intelligence. For instance, a business with good management and process systems will be useful to a buyer who wants to improve their own. Ideally, the business you choose should have systems that complement your own and that will adapt to running a larger business.
- Accessing funds or valuable assets for new development. Better production or distribution facilities are often less expensive to buy than to build. Look for target businesses that are only marginally profitable and have large unused capacity that can be bought at a small premium-to-net-asset value.
- Your business is underperforming. For example, if you are struggling with regional or national growth, it may well be less expensive to buy an existing business than to expand internally.
- Accessing a wider customer base and increasing your market share. Your target business may have distribution channels and systems you can use for your own offers.
- Diversification of the products, services, and long-term prospects of your business. A target business may be able to offer you products or services that you can sell through your own distribution channels.
- Reducing your costs and overheads through shared marketing budgets, increased purchasing power, and lower costs.
- Reducing competition. Buying up new intellectual property, products, or services may be cheaper than developing these yourself.
- Organic growth (i.e., the existing business plan for growth needs to be accelerated). Businesses in the same sector or location can combine resources to reduce costs, eliminate duplicated facilities or departments, and increase revenue.


2.A: Review questions
Complete as directed.
Fill in the Blanks:
1. Under the provisions of Subpart C, every employer must ensure that each employee does not work under conditions which are ________ , ________ or otherwise dangerous to their safety or health.
2. Employees required to handle or use poisons, caustics, and other harmful substances shall be ________ regarding the safe handling and use, and be made aware of the potential hazards, personal hygiene, and personal protective measures required.
3. True or False...Employers who are only performing demolition work are not responsible for the development and maintenance of a fire protection and prevention program at the job site.
4. Combustible scrap and debris shall be removed at regular ________ during the course of construction.
5. Which of the following construction areas are required to be lit with either natural or artificial lighting during construction periods?
a. Aisles
b. Ramps
c. Runways
d. Storage areas
e. All of the above
6. In general, the medical record for each employee shall be preserved and maintained for at least the duration of employment plus ________ years.
a. 5 b. 10 c. 20 d. 30
7. Means of ________ shall be continually maintained free of all obstructions or impediments to full instant use in the case of fire or other emergency.
8. The employer shall establish in the emergency action plan the types of ________ to be used in emergency circumstances.
9. For the purposes of Subpart C, Define a "confined space."


2.1: Chapter Introduction
-
- Last updated
- Save as PDF
In the first chapter we briefly examined the concern of many psychologists that the field of psychology has been slow to embrace the value of cross-cultural research (see Lee et al., 1999; Sue, 1999; Triandis & Suh, 2002). This concern is by no means new. In 1936, Ralph Linton wrote that “different societies seem to show differences in the relative frequency of occurrence of the various psychological types” (pg. 484), and in 1973, Robert LeVine suggested that “this is a moment at which even those who are skeptical about the value of culture and personality study might consider stretching their curiosity in this direction” (pg. ix). Throughout this textbook we will examine a number of theorists who emphasized studying cultural differences as a significant part of their careers and, often, their personality theories as well.
However, it remains true that cross-cultural studies in psychology have only recently moved closer to the mainstream of psychological research and clinical practice. As of 2002, the American Psychological Association has “Guidelines on Multicultural Education, Training, Research, Practice, and Organizational Change for Psychologists” (www.apa.org/pi/multiculturalguidelines/homepage.html). To cite just a few examples of the range of current interest in cross-cultural psychology, we now have a Dictionary of Multicultural Psychology (Hall, 2005) and books on the relationships between culture, mental illness, and counseling (Axelson, 1999; Castillo, 1997), as well as on the relationships between race, class, and the social and personal development of women (Jordan, 1997b; Pack-Brown, Whittington-Clark, & Parker, 1998). There are also major new texts on African American psychology (Belgrave & Allison, 2006) and racism, prejudice, and discrimination in America (Miller & Garran, 2008; Whitley & Kite, 2006).
The fact that studying cross-cultural factors in personality has always been present in the careers and theories of certain individuals, while not becoming a mainstream focus of attention, is more than just an historical curiosity. By emphasizing biological factors (i.e., genetics), Freud’s theory did not allow for cultural differences. Behavioral theorists emphasized environmental factors, a seemingly cultural approach, but they did not allow themselves to address factors beyond immediate scientific control. Thus, they defined with great precision the role of reinforcement, punishment, discriminative stimuli, etc., while not allowing for the richness of cognition and cultural experiences. Likewise, cognitive theorists clung to the scientific approach of the behaviorists, rather than embracing the potential of sociocultural perspectives. In other words, because strict Freudian theorists, as well as behavioral and cognitive theorists, believed that their theories applied to all people equally, they typically chose not to address differences between people. Thus, those who wished to bring sociocultural perspectives on the development of personality into the field of personality theory faced a degree of direct opposition. And yet, their perseverance is now being fulfilled.
In this chapter, we will briefly examine some of the issues facing personality psychologists who wish to examine personality development in a sociocultural context. The United States, Canada, and Western Europe represent only about one tenth of the world’s population. Ralph Linton, a renowned anthropologist with an interest in cultural influences on personality (see Linton, 1945), also edited a book entitled Most of the World: The Peoples of Africa, Latin America, and the East Today (Linton, 1949). Thus, it is essential that we consider the influence of different cultures around the world if we are going to claim that we have really examined human personality in all its variations.


3.1: Successfully Logging In
Before editing a page, you must first log in to the LibreTexts with an account that has editing capabilities. If you do not have an account register at https://register.libretexts.org for an Instructor's account. Please remember to specify ONE library to use as your home library (content you create can be moved to other libraries) and provide a URL that shows your name as an instructor/teacher/faculty member. Once provided, sign in to a library by entering your credentials into the toolbar below the list of libraries. If you have forgotten your password, hover your cursor over the "door" symbol next to the sign in button and select to have a reset password link sent to you.
If the bar is grey after you sign in (like above), you do not have editing capabilities; in that case, you can write<EMAIL_ADDRESS>to request your permissions to be updated. After you log in you should see a black bar
Now you can navigate to your sandbox by pulling down the menu under your userID (TestBox in this case)
My preferences lets you change your password.
The SSO system is coupled to accept both google and microsoft authenticated networks so that if your campus is part of either, you can use your campus account to sign in. However, Microsoft provide additional freedoms to campuses to verify vendors (like LibreTexts) to access campus authentication.
Below is what it looks like for an admin to “Consent on behalf of your organization”.
Even though LibreTexts, Inc. is already verified with Microsoft, in this case it also has to verify with the local IT department of the campus. That can be a fast or slow process. If instant access is needed (and Google isn't an option), we can provide local authentication. Contact<EMAIL_ADDRESS>for help.


4.3: Electric Sector/Double Focusing Mass Spectrometers
Electric Sector/Double Focusing Mass Spectrometers (1). An electric sector consists of two concentric curved plates. A voltage is applied across these plates to bend the ion beam as it travels through the analyzer. The voltage is set so that the beam follows the curve of the analyzer. The radius of the ion trajectory (r) depends up on the kinetic energy of the ion (V) and the potential field (E) applied across the plates.
\[r=\frac{2 V}{E} \nonumber \]
Equation \(\PageIndex{1}\) shows that an electric sector will not separate ions accelerated to a uniform kinetic energy. The radius of the ion beam is indep endent of the ion’s mass to charge ratio so the electric sector is not useful as a standalone mass analyzer.* An electric sector is, however, useful in series with a magnetic sector. The mass resolution of a magnetic sector is limited by the kinetic energy distribution ( \(\mathrm{V}\) ) of the ion beam. This kinetic energy distribution results from variations in the acceleration of ions produced at different locations in the source and from the initial kinetic energy distribution of the molecules. An electric sector significantly imp roves the resolution of the magnetic sector by reducing the kinetic energy distribution of the ions**. These high resolutions experiments are discussed in the section on mass spectral interpretation. The effect of the electric sector is shown in Figure \(\PageIndex{1}\) for a reverse geometry (BE) instrument with the magnetic sector \((B)\) located before the electric sector \((\mathrm{E})\) .
*The electric sector is a kinetic energy analyzer. In the source region of the mass spectrometer all ions are accelerated to the same kinetic energy. Because they have the same kinetic energy, they are not separated by an electric sector. A magnetic sector will resolve different mass ions accelerated to a uniform kinetic energy because it separates ions based upon their momentum (See 4.2: Magnetic Sector ).
**Ion optics are complex and interested readers are referred to the literature for more detail. The model presented here provides a framework for understanding many high resolution and tandem mass spectrometry experiments. The article by Nier (1) provides an excellent introduction, a historical perspective, and many references for the development and theory of these instruments.
References
- Nier, A. J Am Soc Mass Spectrum 1991 , 2 , 447-452.
- Hercules, D.M.; Day, R.J.; Balasanmugam, K.; Dang, T.A.; Li, C.P. Anal. Chem. 1982 , 54 , 280A-305A.


1.14.31: Helmholtz Energy
Gibbs energy is defined with practical chemistry in mind because the definition centres on closed systems held at constant temperature and constant pressure. A similar interest prompt definition of the Helmholtz energy, symbol \(\mathrm{F}\). By definition,
\[\mathrm{F}=\mathrm{U}-\mathrm{T} \, \mathrm{S} \nonumber \]
Physicists use the term ‘Helmholtz Function’. The old term ‘Helmholtz free energy’ is not encouraged [1]. If a closed system is displaced to a neighboring state, the differential change in Helmholtz energy is given by equation (b).
\[\mathrm{dF}=\mathrm{dU}-\mathrm{T} \, \mathrm{dS}-\mathrm{S} \, \mathrm{dT} \nonumber \]
But the differential change in thermodynamic energy is given by the Master Equation. By incorporating the latter into equation (b), we obtain equation (c), the memorable “all-minus” equation.
\[\begin{aligned}
&\mathrm{dF}=-\mathrm{S} \, \mathrm{dT}-\mathrm{p} \, \mathrm{dV}-\mathrm{A} \, \mathrm{d} \xi \\
&\mathrm{A} \, \mathrm{d} \xi \geq 0
\end{aligned} \nonumber \]
At fixed temperature and fixed volume (isothermal and isochoric conditions),
\[\mathrm{dF}=-\mathrm{A} \, \mathrm{d} \xi \nonumber \]
All spontaneous processes at fixed temperature and fixed volume lower the Helmholtz energy of a closed system. In practical terms, for a closed system held at constant volume and temperature, chemical reaction (molecular reorganization) lowers the Helmholtz energy of the system [2]. We presume that the pressure inside the reaction vessel will change, decreasing for some systems and increasing for other systems. As it stands thermodynamics offers no generalization concerning how the pressure changes. In fact if we want to use the Helmholtz energy as an indicator of the direction of spontaneous change we would build the reaction vessel with thick steel walls. This is a practical possibility and so the Helmholtz energy is a practical thermodynamic potential. For equilibrium transformations (i.e. at constant A = zero),
\[S=-\left(\frac{\partial \mathrm{F}}{\partial \mathrm{T}}\right)_{\mathrm{V}, \mathrm{A}=0} \nonumber \]
Similarly [3]
\[\mathrm{p}=-\left(\frac{\partial \mathrm{F}}{\partial \mathrm{V}}\right)_{\mathrm{T}, \mathrm{A}=0} \nonumber \]
Footnotes
[1] Since the product \(\mathrm{T} \, \mathrm{S}\) is the linked energy, equation (a) shows that \(\mathrm{F}\) is the ‘free energy’ of the system.
[2] An interesting literature discusses the analysis of experimental data in terms of an isochoric condition.
- Liquid transport; A. F. M. Barton, Rev. Pure Appl. Chem., 1971, 21 , 49.
- Ionic Conductances in Solution. F. Barreira and G. J. Hills, Trans. Faraday Soc.,1968, 64 ,1539, and references therein
-
Chemical kinetics
- M. G. Evans and M. Polanyi, Trans. Faraday Soc.,1935, 31 , 873.
- E. Whalley, Ber. Bunsenges. Phys. Chem., 1966. 70 , 958, and references therein.
- P. G. Wright, J. Chem. Soc. Faraday Trans. 1, 1986, 82 , 2557, and 2563.
- L. M. P. C. Albuquerque and J. C. R. Reis, J. Chem. Soc. Faraday Trans.1, 1989, 85 , 207; 1991, 87 , 1553.
- J. B. F. N. Engberts, J. R. Haak, M. J. Blandamer, J. Burgess and H. J. Cowles, J. Chem. Soc .Perkin Trans, 2.1990,1059, and references therein.
- Chemical Equilibria. M. J. Blandamer, J. Burgess, B. Clarke and J. M. W. Scott, J. Chem. Soc. Faraday 1984, 80 , 3359, and references therein..
[3] A similar set of equations describes the differential change in \(\mathrm{F}\) at constant molecular composition (molecular organization). Thus
\[\mathrm{S}=-\left(\frac{\partial \mathrm{F}}{\partial \mathrm{T}}\right)_{\mathrm{V}, \xi} \text { and, } \mathrm{p}=-\left(\frac{\partial \mathrm{F}}{\partial \mathrm{V}}\right)_{\mathrm{T}, \xi} \nonumber \]


 Each tablet of supplement A contains 1000 mg of calcium, 400 mg of magnesium, and 15 mg of zinc, and each tablet of supplement B contains 800 mg of calcium, 500 mg of magnesium, and 20 mg of zinc.}
- Represent the amount of calcium, magnesium and zinc in each tablet as a \(2 \times 3\) matrix.
- Represent the number of tablets in each bottle as a row matrix.
- Use matrix multiplication to find the total amount of calcium, magnesium, and zinc in both bottles.
-
Let matrix \(A=\left[\begin{array}{rrr}1 & -1 & 3 \\
3 & -2 & 1
\end{array}\right]\) and \(B=\left[\begin{array}{ccc}
3 & 3 & -1 \\
1 & 4 & -3
\end{array}\right]\). Find the following.- \(\frac{1}{2}(A+B)\)
- \(3A = 2B\)
-
Let matrix \(\mathrm{C}=\left[\begin{array}{ccc} 1 & 1 & -1 \\
2 & 1 & 1 \\
1 & 0 & 1
\end{array}\right]\) and \(D=\left[\begin{array}{rrr}
2 & -3 & -1 \\
3 & -1 & -2 \\
3 & -3 & -2
\end{array}\right]\). Find the following.- \(2(C-D)\)
- \(C-3D\)
-
Let matrix \(E=\left[\begin{array}{cc}1 & -1 \\
2 & 3 \\
1 & 2
\end{array}\right]\) and \(\mathrm{F}=\left[\begin{array}{ccc}
2 & 1 & -1 \\
1 & 2 & -3
\end{array}\right]\). Find the following.- \(2EF\)
- \(3FE\)
-
Let matrix \(G=\left[\begin{array}{ccc}
1 & -1 & 3 \\
3 & 2 & 1
\end{array}\right]\) and \(H=\left[\begin{array}{ll}
a & b \\
c & d \\
e & f
\end{array}\right]\). Find the following.- \(2GH\)
- \(HG\)
-
Solve the following systems using the Gauss-Jordan Method.
-
\[\begin{array}{r}
x+3 y-2 z=7 \\
2 x+7 y-5 z=16 \\
x+5 y-3 z=10
\end{array}\nonumber \] -
\[\begin{array}{rr}
2 x-4 y+4 z=2 \\
2 x+y+9 z=17 \\
3 x-2 y+2 z=7
\end{array}\nonumber \]
-
\[\begin{array}{r}
- An apple, a banana and three oranges or two apples, two bananas, and an orange, or four bananas and two oranges cost $2. Find the price of each.
-
Solve the following systems. If a system has an infinite number of solutions, first express the solution in parametric form, and then determine one particular solution.
-
\[\begin{array}{r}
x+y+z=6 \\
2 x-3 y+2 z=12 \\
3 x-2 y+3 z=18
\end{array}\nonumber \] -
\[\begin{array}{rr}
x+y+3 z&= 4 \\
x +z&=1 \\
2 x-y & =2
\end{array}\nonumber \]
-
\[\begin{array}{r}
- Elise has a collection of 12 coins consisting of nickels, dimes and quarters. If the total worth of the coins is $1.80, how many are there of each? Find all possible solutions.
SECTION 2.7 PROBLEM SET: CHAPTER REVIEW
-
Solve the following systems. If a system has an infinite number of solutions, first express the solution in parametric form, and then find a particular solution.
-
\[\begin{array}{l}
2 x+y-2 z=0 \\
2 x+2 y-3 z=0 \\
6 x+4 y-7 z=0
\end{array}\nonumber \] -
\[\begin{array}{r}
3 x+4 y-3 z=5 \\
2 x+3 y-z=4 \\
x+2 y+z=1
\end{array}\nonumber \]
-
\[\begin{array}{l}
-
Solve the following systems. If a system has an infinite number of solutions, first express the solution in parametric form, and then provide one particular solution.
-
\[\begin{array}{l}
2 x+y-2 z=0 \\
2 x+2 y-3 z=0 \\
6 x+4 y-7 z=0
\end{array}\nonumber \] -
\[\begin{array}{r}
3 x+4 y-3 z=5 \\
2 x+3 y-z=4 \\
x+2 y+z=1
\end{array}\nonumber \]
-
\[\begin{array}{l}
-
Find the inverse of the following matrices:
-
\[\left[\begin{array}{ll}
2 & 3 \\
3 & 5
\end{array}\right]\nonumber \] -
\[\left[\begin{array}{lll}
1 & 1 & 1 \\
1 & 2 & 1 \\
2 & 3 & 1
\end{array}\right]\nonumber \]
-
\[\left[\begin{array}{ll}
-
Solve the following systems using the matrix inverse method.
-
\begin{aligned}
2 x+3 y+z &=12 \\
x+2 y+z &=9 \\
x+y+z &=5
\end{aligned} -
\begin{aligned}
x+2 y-3 z+w&= \\
x -z&=4 \\
x-2 y+z= & 0 \\
y-2 z+w= & -11=0
\end{aligned}
-
\begin{aligned}
-
Use matrix \(A\) to encode the following messages. The space between the letters is represented by the number 27, and all punctuation is ignored. \[A=\left[\begin{array}{lll}
1 & 2 & 0 \\
1 & 2 & 1 \\
0 & 1 & 0
\end{array}\right] \nonumber \]- TAKE IT AND RUN
- GET OUT QUICK
-
Decode the following messages that were encoded using matrix \(A\) in the above problem.
- 44, 71, 15, 18, 27, 1, 68, 82, 27, 69, 76, 27, 19, 33, 9
- 37, 64, 15, 36, 54, 15, 67, 75, 20, 59, 66, 27, 39, 43, 12
- Chris, Bob, and Matt decide to help each other study during the final exams. Chris's favorite subject is chemistry, Bob loves biology, and Matt knows his math. Each studies his own subject as well as helps the others learn their subjects. After the finals, they realize that Chris spent 40% of his time studying his own subject chemistry, 30% of his time helping Bob learn chemistry, and 30% of the time helping Matt learn chemistry. Bob spent 30% of his time studying his own subject biology, 30% of his time helping Chris learn biology, and 40% of the time helping Matt learn biology. Matt spent 20% of his time studying his own subject math, 40% of his time helping Chris learn math, and 40% of the time helping Bob learn math. If they originally agreed that each should work about 33 hours, how long did each work?
- As in the previous problem, Chris, Bob, and Matt decide to not only help each other study during the final exams, but also tutor others to make a little money. Chris spends 30% of his time studying chemistry, 15% of his time helping Bob with chemistry, and 25% helping Matt with chemistry. Bob spends 25% of his time studying biology, 15% helping Chris with biology, and 30% helping Matt. Similarly, Matt spends 20% of his time on his own math, 20% helping Chris, and 20% helping Bob. If they spend respectively, 12, 12, and 10 hours tutoring others, how many total hours are they going to end up working?


12.3: Lab Report
Exercise A
Employing Steps in the Scientific Method:
- Record the Question that is being investigated in this experiment.
- Record a Hypothesis for the question stated above.
- Predict the results of the experiment based on your hypothesis (if/then).
- Fill in your data below.
|
Indicator Used: |
||||
|---|---|---|---|---|
|
Tube contents |
Initial color of indicator |
Color after 2 hrs |
Color after 24 hrs |
Acidic or basic? |
|
||||
|
||||
|
5. What is the color of the indicator at at A) neutral pH, B) Basic pH and C) Acidic pH?
6. What was the purpose of Tube #1 ?
7. What specifically was produced as a result of cellular respiration that changed the color of the indicator?
8. How is carbon dioxide an indicator that cellular respiration is taking place in these peas?
9. Germination is the process by which a dormant seed begins to sprout and grow into a seedling. What are some possible metabolic processes that are required for seed germination?
10. During respiration, a seed metabolizes sugars. What is the source of the sugar metabolized by the seed?
11. What variables do you think may affect the respiration rate of the seeds?
12. The equation for cellular respiration is: C6H12O6 + 6O2 → 6CO2 + 6H2O + 32ATP (1.8.2). The energy released from the complete oxidation of glucose under standard conditions is 686 kcal/mol. The energy released from the hydrolysis of ATP to ADP and inorganic phosphate under standard conditions is 7.3 kcal/mol. Using the equation for cellular respiration above, calculate the efficiency of respiration (i.e. the percentage of chemical energy in glucose that is transferred to ATP). For help with answering this question, refer to the course textbook.
13. How might the process of photosynthesis affect pH? Form a hypothesis.
Exercise B
1. In the space below, draw and label several yeast cells undergoing aerobic respiration and several yeast cells not undergoing aerobic respiration. Label the cytoplasm and nucleus if visible.
Exercise C
Employing Steps in the Scientific Method:
- Record the Question that is being investigated in this experiment.
- Record a Hypothesis for the question stated above.
- Predict the results of the experiment based on your hypothesis (if/then).
- Record your data below.
| Time (min.) | Sacch. 1 | Sacch. 2 | Sacch. 3 | Sacch. 4 |
|
0 (initial) |
||||
|
2 |
||||
|
4 |
||||
|
6 |
||||
|
8 |
||||
|
10 |
||||
|
12 |
||||
|
14 |
||||
|
16 |
||||
|
18 |
||||
|
20 |
The results of this experiment can be presented graphically. The presentation of your data in a graph will assist you in interpreting your results. Based on your results, you can complete the final step of scientific investigation, in which you must be able to propose a logical argument that either allows you to support or reject your initial hypothesis.
5. Graph your results using the data from Table 3.
6. What is the dependent variable? Which axis is used to graph this data?
7. What is your independent variable? Which axis is used to graph this data?
Exercise D
|
Time (min.) |
Sacch. 1 |
Sacch. 2 |
Sacch. 3 |
|---|---|---|---|
|
0 (initial) |
|||
|
2 |
|||
|
4 |
|||
|
6 |
|||
|
8 |
|||
|
10 |
|||
|
12 |
|||
|
14 |
|||
|
16 |
|||
|
18 |
|||
|
20 |
The results of this experiment can be presented graphically. The presentation of your data in a graph will assist you in interpreting your results. Based on your results, you can complete the final step of scientific investigation, in which you must be able to propose a logical argument that either allows you to support or reject your initial hypothesis.
5. Graph your results using the data from Table 5.
6. What is the dependent variable? Which axis is used to graph this data?
7. What is your independent variable? Which axis is used to graph this data?
8. Fermentation involves redox reactions . Explain what happens to electrons during a redox reaction and how this changes a molecule’s potential energy.
9. Why did we add the Saccharomyces cerevisiae (baker's yeast) to the fermentation tubes? Specifically, what did the yeast provide to the fermentation mixture?
10. What is the purpose of Saccharomyces cerevisiae (“baker’s yeast) in the bread-making process?
11. We measured the formation of what end product to determine the fermentation rate? Name the end product that we measured.
12. List two specific factors (as they relate to the experiment performed in our lab) that affect the rate of fermentation.
13. What other variables could be investigated that might affect the rate of alcoholic fermentation by yeast?


1.6: Chapter 6 – Financing Entrepreneurship
Money is like gasoline during a road trip. You don’t want to run out of gas on your trip, but you’re not doing a tour of gas stations. – Tim O’Reilly, founder and CEO of O’Reilly Media
Chase the vision, not the money; the money will end up following you. – Tony Hsieh, CEO of Zappos
Learning Objectives
After completing this chapter you will be able to
- Describe the financing considerations for entrepreneurs
- Describe the advantages and disadvantages of debt financing and of equity financing
- List and describe the forms of financing appropriate for the different phases of business development
Overview
Securing needed financing is one of the most important functions related to starting a business. It is important, then, to understand what sources of financing exist at various stages of venture development. It is also important to determine what kinds of financing provide the most value for the entrepreneur and the new venture. Debt and equity financing decisions must be considered in relation to the cost of the financing and the amount of control that the owner is willing to sacrifice to get the needed resources.
Financing
Starting Capital
Entrepreneurs almost always require starting capital to move their ideas forward to the point where they can start their ventures. Determining the amount of money that is actually needed is tricky because that requirement can change as plans evolve. Other challenges include actually securing the amount desired and getting it when it is needed. If an entrepreneur is unable to secure the required amount or cannot get the funding when needed, they must develop new plans.
Once a venture begins to make cash sales or it starts to receive the money earned through credit sales, it can use those resources to fund some of its activities. Until then, it must get the money it needs through other sources.
Bootstrap financing is when entrepreneurs use their ingenuity to make their existing resources, including money and time, stretch as far as possible—usually out of necessity until they can transform their venture into one that outside investors will find appealing enough to invest in.
Personal Money
Entrepreneurs will almost always have to invest their own personal money into their start-up before others will give them any financial help. Sometimes entrepreneurs form businesses as partnerships or as multi-owner corporations with other individual entrepreneurs who also contribute their own personal funds to the venture.
Love Money
Love money refers to money provided by friends and family who want to support an entrepreneur, often when they have no other ready source of funding after using as much of their own personal money as possible to support their start-up.
Grants and Start-up Prize Money
In some cases, grants that do not need to be repaid might be provided by government or other agencies to support new venture start-ups. Sometimes entrepreneurs can enter business planning or similar competitions in which they might win money and other benefits, like free office or retail space, or free legal or accounting services for a set period of time.
Debt Financing
From an entrepreneur’s perspective, the cost of debt financing is the interest that they pay for the use of the money that they borrow. From an investor’s perspective, their reward, or return on debt financing, is the interest that they gain in addition to the return of the money that they lent to an entrepreneur or other borrower.
To provide some protection for the investor (lender) to enable them to accept an interest rate that is also acceptable for the entrepreneur (borrower), the borrower must often pledge collateral so that if they do not pay back the loan along with interest as arranged, the lender has a way to get all or some of the money they are owed. If a borrower defaults on a loan, the lender can become the owner of the property pledged as collateral. A key objective for an entrepreneur seeking debt financing is to provide sufficient collateral to get the loan, but not pledge so much that they put essential property at risk.
When entrepreneurs borrow money, they must pay it back subject to the terms of the loan. The loan terms include the specific interest rate that will be charged and the time period within which the loan needs to be repaid. Several other terms or features of the loan that can be negotiated between lender and borrowers. One such feature is whether the loan can be converted to equity at a particular point in time and according to certain criteria and subject to specific terms.
Sometimes debt financing can be in the form of trade credit, where a supplier provides product to a business but does not require payment for a specific length of time, or perhaps even until the business has sold the product to a customer. Another form of debt financing is customer advances. This might involve a customer paying in advance for a product or service so that the businesses has those funds available to use to pay its suppliers.
Advantages of Debt Financing
One advantage of debt financing is that the entrepreneur is not sacrificing ownership and some control of their venture when they take out a loan.
Another advantage of debt financing is the certainty of the payments the borrower needs to make during the term of the loan. If the borrower takes out a loan for $20,000 over a five-year term at a fixed interest rate of 6.2% with a monthly payment schedule designed to pay off the entire loan by the end of its five-year term, they know that each month they must pay $389 and that over the five years they will have paid back the entire $20,000 loan amount plus a total of $3,340 in interest. With this certainty, the business can accurately budget its payback amount for this loan over the five years.
Yet another advantage of debt financing is that it allows companies to trad e on equity . Trading on equity enhances the rate of return on common shareholders’ equity by using debt to financing asset purchases or to take other measures that are expected to cost less than the earnings generated by the action taken. For example, if a company borrows $20,000 at 6.2% interest and uses that money to purchase a machine it will use to increase its return on equity by 20%, then it is trading on equity. In this case, the company is financially better off than it would have been if it had not taken out the loan. Of course, the inherent risk involved with this strategy is lowered when income streams are relatively stable.
Disadvantages of Debt Financing
A disadvantage of borrowing money is the need to report to those from whom you borrowed the money. This might be particularly true when lenders, often bankers, have interests or incentives—mainly getting their money back plus at all of the interest owed to them during the loan term through regular monthly blended loan payments—that might not fully align with the interests and incentives of the borrower, which might include being able to pay the money back when they are best able to do so without also impacting other parts of their business, like the need to pay their employees or their facility lease payment at the end of a month when an expected customer payment did not arrive as planned.
Another disadvantage of borrowing is that the business’s ownership of the property it pledged as collateral for the loan is placed at risk. For many new ventures, a loan is only possible to acquire if the owner provides their personal guarantee that the money will be paid back as determined in the loan agreement, thus putting personal property at risk.
Equity financing
From an entrepreneur’s perspective, the cost of equity financing is the loss of some control over their venture as they must now share ownership of the business. From an investor’s perspective, their reward in exchange for purchasing an ownership interest in the business is the potential to share in the business’s anticipated future success by possibly receiving dividends (a portion of the profit that is distributed to owners) and by possibly being able to sell their ownership interest to another investor for more than the amount they purchased that ownership interest for originally.
The protection for the investor, who might be a shareholder if the ownership interest is represented in the form of shares in the business, is in the influence they can exert in the company’s decision-making processes. This influence is normally proportionate to their share of the ownership in the overall business. Equity investors normally seek to earn a competitive return on their investment that is in line with the level of risk they assume by investing in the business. The riskier the investment, the higher the return the investor expects.
Public Offering
Stock investors might invest in a public offering where the company’s shares are made available to the public—and by which the company becomes a public company . An initial public offering (IPO) is where a company’s stock (its shares) are sold to institutional investors who then resell them to the public, usually through a securities exchange like the Toronto Stock Exchange (TSX).
When an IPO occurs, a company goes through a legal process to sell shares in its company for the purpose of raising capital. This is called going public . An important part of going public is setting the initial price for the shares being offered for sale (the offering price ). The amount that the company will raise is the price they sell the new stock at multiplied by the number of shares they sell less any fees and other expenses incurred to make the sale. If they set the initial selling price of the shares too high, they might not sell all of the shares and the company won’t raise as much capital as anticipated. If they happen to sell all of the overvalued shares, the share price will fall once it begins trading on the exchange. Setting the offering price too high indicates that the company and its agents helping it with its IPO, called underwriters , have valued the company higher than investors in the marketplace value it. If the company sets the offering price too low, it will raise the amount of money planned, but will find out too late that it could have raised much more capital by setting the offering price higher. In this case, the company and its underwriters have undervalued the company and the initial investors will make all of the gains that the company could have when they sell the shares on the exchange almost immediately after they purchased them for more money than they purchased them for.
Private Offering
Stock investors might also invest in a private offering (or private placement ) where the shares are sold to a few investors rather than to the general public through an exchange. Institutional private placements involve selling the shares to institutional investors like insurance companies. Private offerings cost less and are subject to less stringent regulation than public offerings, mainly because it is expected that private investors will be more diligent on their own and require less regulatory protection than do public investors.
Venture Capital
Venture capital is raised when investors pool their money. The venture capital fund is then used to very carefully invest in existing but usually young companies that are expected to experience high growth. The venture capital company does not expect to invest for long and it expects to generate a large return. For example, it might expect to invest in an opportunity for a period of up to five years and then get out of the investment with five times the money it originally invested. Of course, only some investment opportunities will generate the returns hoped for and others will return far less than expected.
Venture capitalists might exert some ownership control by influencing some business decisions in cases where they believe that by doing so they can protect their investment or cause the investment to produce greater returns, but they generally prefer to invest in companies that are going to be well-run and will not require them to be involved in decisions. Venture capitalists might also provide some assistance, such as business advice, to the companies in which they invest.
A venture round refers to a phase of financing that institutional investors like venture capitalists provide to entrepreneurs. The first phase (sometimes following a seed round in which entrepreneurs themselves provide the start-up capital and then an angel round where angel investors invest in the company) is called Series A . Subsequent venture rounds are called Series B , Series C , and so on.
Angel Investors
Angel investors are wealthy individuals who on their own, or often along with other angel investors in a network—like the Saskatchewan Capital Network—invest in new ventures in exchange for an ownership interest in the business. Sometimes angels invest in companies in exchange for convertible debt, an investment that starts off as a loan, usually in the form of a bond, that they can exercise an option to convert to an equity interest in the company at a particular point in time for a pre-determined number of shares. Angel investors are generally less restricted in what kinds of investments they will consider as opposed to venture capitalists, who are using other people’s pooled money. Like venture capitalists, however, they normally undertake a rigorous due diligence process to determine whether to invest in the opportunities they are considering.
Equity Crowd Funding
Equity crowd funding is a relatively new way for entrepreneurs to raise capital. It involves using online methods to promote equity interests in ventures to potential investors.
Due Diligence
Investors follow due diligence processes to assess the risk and potential return associated with the investments they are considering. As such, entrepreneurs should maintain a due diligence file or binder that they can quickly draw upon when a desirable potential investor expresses an interest in their venture.
A due diligence file or binder will include copies of many of the legal papers and other important documents that a venture has accumulated that tell the story of the enterprise. These documents will include those related to incorporation, securities it has issued or is in the process of issuing, loans, important contracts, intellectual property documents, tax information, financial statements, and other important documentation.
Advantages of Equity Financing
One important benefit to equity financing is that it does not normally require a regular payback from cash flow. Unlike with debt financing, equity investments do not usually give rise to a regular encumbrance that can increase the difficulty a young company might have in meeting its regular monthly expenses.
Second, when a firm uses equity financing, it does not need to pledge collateral, which means that the company’s assets are not placed at risk.
A potential advantage with equity financing is that, depending upon the form of financing and who the investors are, a firm might gain valued advisers. In addition, investors who exercise their ownership rights to have a say in the operations of the company, or who otherwise provide advise and mentorship to entrepreneurs starting ventures, are usually highly motivated to help the company succeed. Investors expect to benefit only when the companies they invest in succeed, meaning that their financing incentives are aligned with those of the entrepreneur and other owners.
Disadvantages of Equity Financing
Equity financing is often more difficult to raise than debt financing. Second, when they share ownership in exchange for investment into their business, entrepreneurs give up a portion of the value that they create. If things do not go as planned, entrepreneurs can lose control of their companies to their investors.
Sources of Financing for Different Phases of Development
Different financing sources are used at different phases of business development. The appropriate and available financing sources depend upon the risks and opportunities available to both the entrepreneur and to the investors.
Idea Development Phase
- Personal sources (savings and other income)
- Extended personal sources (family, friends, employees, partners)
-
Angel investors (possibly)
- also called informal investors
- wealthy individuals interested in investing their own money in early-stage companies as convertible debt holders or equity investors
- convertible debt (convertible bond, convertible note, convertible debenture) allows the bondholder to convert their debt into an equity interest at an agreed-upon price
-
can be a win-win arrangement
- If the company is successful, investor has opportunity to participate as equity investor, but if company is only marginally successful, they get their money back with interest.
- If entrepreneurs have difficulty borrowing money, they can add the convertible feature as a sweetener.
-
Strategic partners
- might include potential customers or potential suppliers who want to have access to a business like the one proposed (and therefore might fund part of its development)—i.e. a building owner (supplier) might help a business develop which will be a tenant
- might include complementary businesses who feel helping the new business get started might help their own businesses—i.e. a hotel investing in a spa next door to their facility
Start-Up Phase
- Angel investors
- Strategic partners
-
Customers (possibly)
- They might place orders for services or products and pay for them up-front, thereby providing financing for the new business.
- They might want your business to succeed so it can support their business. For example, a general contractor (future customer) might help a new plumber get started if there is now a shortage of plumbers affecting the building industry.
-
Venture Capitalists (possibly)
- These organizations acquire pools of money to invest, so they differ from angel investors in that those making the decisions are not investing their own money; this means they usually consider investment options which have shown some success already (which isn’t usually the case in the start-up phase).
-
Asset-Based lenders
- lend money secured by the assets of the borrower – i.e. plant and equipment
- sometimes this can be done quite creatively – i.e. secure a loan with assets that will turn into money … like through accounts receivable or inventories, etc.
- Equipment Leasing Companies
- Suppliers
Early Operations
- Venture Capitalists (possibly)
- Asset-Based Lenders
- Equipment Leasing Companies
- Suppliers
-
Small Business Investment Companies
- U.S. term – developed to bridge the gap between when small businesses need money and the time later on when venture capitalists might provide financing to small businesses
- SBICs are privately owned companies in the United States that are licensed by the Small Business Administration (U.S. Government) to supply equity capital, long-term loans, and management assistance to qualifying small businesses
- Canadian equivalent = Community Futures Corporations
-
Trade Credit
- The supplier provides product now on terms so the retailer does not need to pay the supplier for perhaps 30 or 60 or 90 days
- The retailer can then sell the product and collecting the money from the customer before the retailer needs to pay supplier for it the product.
-
Factoring
- when a business sells its accounts receivable (its invoices) to a third party (called a factor) at a discount in exchange for immediate money
-
differs from bank loan in three ways
- The factor is interested in the value of the receivables; a bank is interested in the firm’s creditworthiness.
- Factoring is not a loan; it is the purchase of a financial asset (the receivables).
- A bank loan involves two parties (lender and borrower); factoring involves three (the business, the factor, and those who owe the money).
Growth Phase
- Venture Capitalists
- Asset-Based Lenders
- Equipment Leasing Companies
- Suppliers
- Small Business Investment Companies
- Trade Credit
- Factoring
-
Mezzanine Lenders
- used to fill the financing gap between relatively expensive equity financing and less expensive forms of financing like secured loans
- structured either as an unsecured or subordinated debt instrument or as preferred stock
- represents a claim on assets which is senior only to that of the common shares
- mezzanine debt holders require a higher return than is the case with holders of secured debt (maybe close to 20% or more – because the risk is higher)
- usually issued as private placements (i.e. fewer legal requirements than with public placements)
- can be used by smaller companies
- mezzanine lenders might have right to convert the debt instrument to an equity instrument
- mezzanine lenders work with companies to ensure the high return they require doesn’t cripple the company, so they might take an equity interest or might defer loan payments until the end of loan term or until the company is sold
Exit or Harvest Phase
- Mezzanine Lenders
- Public Debt
-
Initial Public Offerings (IPOs)
- issuing common stock or shares to the public
- used by companies seeking capital to expand (or by privately-owned companies wanting to become publicly traded)
-
a major challenge is to figure out how to value the shares offered so underwriting firms are often used to help deal with this challenge
- if the price is set too high maybe all the shares will not be sold (and the desired amount of money will not be raised)
- if the price is set too low the company might lose out on money it could have had (if all the shares sold had of been sold at a higher price)
- money from initial sale of shares goes to the company, but after that the shares are traded between shareholders (the company doesn’t get any of this money)
- the money never has to be repaid, but the owners of the shares have a right to any distributed profits (dividends declared) and to residual dissolution proceeds (what is left over after the debt holders and everyone else is paid off if the company assets are sold)
-
Acquisition, Leveraged Buy-Outs (LBO), Management Buy-Outs (MBO)
- LBOs are when the controlling interest in the company is purchased using mainly borrowed money (the assets of the company being purchased are often used as the loan collateral).
- MBOs are often a form of LBOs where the purchasers are the current managers of the company.