13.5: The Origin and Fate of Comets and Related Objects
By the end of this section, you will be able to:
- Describe the traits of the centaur objects
- Chronicle the discovery and describe the composition of the Oort cloud
- Describe trans-Neptunian and Kuiper-belt objects
- Explain the proposed fate of comets that enter the inner solar system
The comets we notice when they come near Earth (especially the ones coming for the first time) are probably the most primitive objects we can study, preserved unchanged for billions of years in the deep freeze of the outer solar system. However, astronomers have discovered many other objects that orbit the Sun beyond the planets.
Centaurs and TNOs
In the outer solar system, where most objects contain large amounts of water ice, the distinction between asteroids and comets breaks down. Astronomers initially still used the name “asteroids” for new objects discovered going around the Sun with orbits that carry them far beyond Jupiter. The first of these objects is Chiron , found in 1977 on a path that carries it from just inside the orbit of Saturn at its closest approach to the Sun out to almost the distance of Uranus (Figure 13.26). The diameter of Chiron is estimated to be about 200 kilometers, much larger than any known comet.
In 1992, a still-more-distant object named Pholus was discovered with an orbit that takes it 33 AU from the Sun, beyond the orbit of Neptune. Pholus has the reddest surface of any object in the solar system, indicating a strange (and still unknown) surface composition. As more objects are discovered in these distant reaches, astronomers decided that they will be given the names of centaurs from classical mythology; this is because the centaurs were half human, half horse, and these new objects display some of the properties of both asteroids and comets.
Beyond the orbit of Neptune lies a cold, dark realm populated by objects called simply trans-Neptunian objects (TNOs). The first discovered, and best known, of these TNOs is the dwarf planet Pluto . We discussed Pluto and the New Horizons spacecraft encounter with it in Rings, Moons, and Pluto. The second TNO was discovered in 1992, and now more than a thousand are known, most of them smaller than Pluto. In late 2018, a team of astronomers announced the discovery of the most distant TNO found so far, orbiting at 120 Astronomical Units, or 3 ½ times the distance of Pluto; they nicknamed it “farout.”
The largest ones after Pluto—named Eris , Makemake , and Haumea —are also classed as dwarf planets. Except for their small size, dwarf planets have many properties in common with the larger planets. Pluto has five moons, and two moons have been discovered orbiting Haumea and one each circling Eris and Makemake.
The Kuiper Belt and the Oort Cloud
TNOs are a part of what is called the Kuiper belt , a large area of space beyond Neptune that is also the source of many comets. Astronomers study the Kuiper belt in two ways. New, more powerful telescopes allow us to discover many of the larger members of the Kuiper belt directly. We can also measure the composition of short-period comets that are thought to originate in the Kuiper belt, where small gravitational perturbations from Neptune can gradually shift their orbits until they can penetrate the inner solar system. More than a thousand Kuiper belt objects have been discovered, and astronomers estimate that there are more than 100,000 with diameters larger than 100 kilometers, in a disk extending out to about 50 AU from the Sun.
Following its successful flyby of Pluto, the New Horizons spacecraft explored the Kuiper Belt. The team eventually identified a member of the belt, 2014 MU16 (subsequently named Arrokoth), that could be reached by a slight change in the spacecraft trajectory. New Horizons flew past Arrokoth on January 1, 2019, at a distance of only 3,500 km, obtaining images and other data. The target turned out to be a contact binary, something new and unexpected (see photo).
By following their orbits backward, we can calculate that the aphelia (points farthest from the Sun) of newly discovered comets typically have values near 50,000 AU (more than a thousand times farther than Pluto). This clustering of aphelion distances was first noted by Dutch astronomer Jan Oort , who, in 1950, proposed an idea for the origin of those comets that is still accepted today (Figure 13.27).
It is possible to calculate that a star’s gravitational sphere of influence —the distance within which it can exert sufficient gravitation to hold onto orbiting objects—is about one third of its distance to the nearest other stars. Stars in the vicinity of the Sun are spaced in such a way that the Sun’s sphere of influence extends a little beyond 50,000 AU, or about 1 light-year. At such great distances, however, objects in orbit about the Sun can be perturbed by the gravity of passing stars. Some of the perturbed objects can then take on orbits that bring them much closer to the Sun (while others might be lost to the solar system forever).
Oort suggested, therefore, that the new comets we were seeing were examples of objects orbiting the Sun near the edge of its sphere of influence, whose orbits had been disturbed by nearby stars, eventually bringing them close to the Sun where we can see them. 1 The reservoir of ancient icy objects from which such comets are derived is now called the Oort cloud .
Astronomers estimate that there are about a trillion comets in the Oort cloud. In addition, we estimate that about 10 times this number of icy objects could be orbiting the Sun in the volume of space between the Kuiper belt (which is gravitationally linked to Neptune) and the Oort cloud. These objects remain undiscovered because they are too faint to be seen directly and their orbits are too stable to permit any of them to be deflected inward close to the Sun. The total number of icy or cometary objects in the outer reaches of our solar system could thus be on the order of 10 trillion , a very large number indeed.
What is the mass represented by comets? We can make an estimate if we assume something about comet sizes and masses. Let us suppose that the nucleus of Comet Halley is typical. Its observed volume is about 600 km 3 . If the primary constituent is water ice with a density of about 1 g/cm 3 , then the total mass of Halley’s nucleus must be about kilograms. This is about one ten billionth of the mass of Earth.
If our estimate is reasonable and there are comets with this mass out there, their total mass would be equal to about 1000 Earths—comparable to the mass of all the planets put together. Therefore, icy, cometary material could be the most important constituent of the solar system after the Sun itself.
Suppose the Oort cloud contains 10 12 comets with an average diameter of 10 km each. Let’s estimate the mass of the total Oort cloud.
Solution
We can start by assuming that typical comets are about the size of Comets Halley and Borrelly, with a diameter of 10 km and a density appropriate to water ice, which is about 1 g/cm 3 or 1000 kg/m 3 . We know that , the volume of a sphere, and the radius, Therefore, for each comet,
Given that , each comet’s mass is
To calculate the total mass of the cloud, we multiply this typical mass for one comet by the number of comets:
How does the total mass we calculated above compare to the mass of Jupiter? To the mass of the Sun? (Give a numerical answer.)
- Answer
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The mass of Jupiter is about . The mass of the Oort cloud calculated above is kg. So the cloud would contain about half a Jupiter of mass. The mass of the Sun is . This means the Oort cloud would be
Early Evolution of the Planetary System
Comets from the Oort cloud help us sample material that formed very far from the Sun, whereas the short-period comets from the Kuiper belt sample materials that were planetesimals in the solar nebula disk but did not form planets. Studies of the Kuiper belt also are influencing our understanding of the early evolution of our planetary system.
The objects in the Oort cloud and the Kuiper belt have different histories, and they may therefore have different compositions. Astronomers are therefore very interested in comparing detailed measurements of the comets derived from these two source regions. Most of the bright comets that have been studied in the past (such as Hyakutake and Hale-Bopp) are Oort cloud comets, but P67 and several other comets targeted for spacecraft measurements in the next decade are Jupiter -family comets from the Kuiper belt (see Table 13.2).
The Kuiper belt is made up of ice-and-rock planetesimals, a remnant of the building blocks of the planets. Since it is gravitationally linked to Neptune, it can help us understand the formation and history of the solar system. As the giant planets formed, their gravity profoundly influenced the orbits of Kuiper belt objects. Computer simulations of the early evolution of the planetary system suggest that the gravitational interactions between the giant planets and the remaining planetesimals caused the orbit of Jupiter to drift inward, whereas the orbits of Saturn, Uranus, and Neptune all expanded, carrying the Kuiper belt with them.
Another hypotheses involves a fifth giant planet that was expelled from the solar system entirely as the planetary orbits shifted. Neptune’s retrograde (backward-orbiting) moon Triton (which is nearly as large as Pluto) may have been a Kuiper belt object captured by Neptune during the period of shifting orbits. It clearly seems that the Kuiper belt may carry important clues to the way our solar system reached its present planetary configuration.
When amateur astronomer David Levy (Figure 13.28), the co-discoverer of Comet Shoemaker-Levy 9 , found his first comet, he had already spent 928 fruitless hours searching through the dark night sky. But the discovery of the first comet only whetted his appetite. Since then, he has found 8 others on his own and 13 more working with others. Despite this impressive record, he ranks only third in the record books for number of comet discoveries. But David hopes to break the record someday.
All around the world, dedicated amateur observers spend countless nights scanning the sky for new comets. Astronomy is one of the very few fields of science where amateurs can still make a meaningful contribution, and the discovery of a comet is one of the most exciting ways they can establish their place in astronomical history. Don Machholz, a California amateur (and comet hunter) who has been making a study of comet discoveries, reported that between 1975 and 1995, 38% of all comets discovered were found by amateurs. Those 20 years yielded 67 comets for amateurs, or almost 4 per year. That might sound pretty encouraging to new comet hunters, until they learn that the average number of hours the typical amateur spent searching for a comet before finding one was about 420. Clearly, this is not an activity for impatient personalities.
What do comet hunters do if they think they have found a new comet? First, they must check the object’s location in an atlas of the sky to make sure it really is a comet. Since the first sighting of a comet usually occurs when it is still far from the Sun and before it sports a significant tail, it will look like only a small, fuzzy patch. And through most amateur telescopes, so will nebulae (clouds of cosmic gas and dust) and galaxies (distant groupings of stars). Next, they must check that they have not come across a comet that is already known, in which case, they will only get a pat on the back instead of fame and glory. Then they must re-observe or re-image it sometime later to see whether its motion in the sky is appropriate for comets.
Often, comet hunters who think they have made a discovery get another comet hunter elsewhere in the country to confirm it. If everything checks out, the place they contact is the Central Bureau for Astronomical Telegrams at the Harvard-Smithsonian Center for Astrophysics in Cambridge, Massachusetts ( http://www.cbat.eps.harvard.edu/ ). If the discovery is confirmed, the bureau will send the news out to astronomers and observatories around the world. One of the unique rewards of comet hunting is that the discoverer’s name becomes associated with the new comet—a bit of cosmic fame that few hobbies can match.
The Fate of Comets
Any comet we see today will have spent nearly its entire existence in the Oort cloud or the Kuiper belt at a temperature near absolute zero. But once a comet enters the inner solar system, its previously uneventful life history begins to accelerate. It may, of course, survive its initial passage near the Sun and return to the cold reaches of space where it spent the previous 4.5 billion years. At the other extreme, it may collide with the Sun or come so close that it is destroyed on its first perihelion passage (several such collisions have been observed with space telescopes that monitor the Sun). Sometimes, however, the new comet does not come that close to the Sun but instead interacts with one or more of the planets.
SOHO (the Solar and Heliospheric Observatory) has an excellent collection of videos of comets that come near the Sun. At this site, comet ISON approaches the Sun and is believed to be destroyed in its passage.
A comet that comes within the gravitational influence of a planet has three possible fates. It can (1) impact the planet, ending the story at once; (2) speed up and be ejected, leaving the solar system forever; or (3) be perturbed into an orbit with a shorter period. In the last case, its fate is sealed. Each time it approaches the Sun, it loses part of its material and also has a significant chance of collision with a planet. Once the comet is in this kind of short-period orbit, its lifetime starts being measured in thousands, not billions, of years.
A few comets end their lives catastrophically by breaking apart (sometimes for no apparent reason) (Figure 13.29). Especially spectacular was the fate of the faint Comet Shoemaker-Levy 9 , which broke into about 20 pieces when it passed close to Jupiter in July 1992. The fragments of Shoemaker-Levy were actually captured into a very elongated, two-year orbit around Jupiter, more than doubling the number of known jovian moons. This was only a temporary enrichment of Jupiter’s family, however, because in July 1994, all the comet fragments crashed unto Jupiter, releasing energy equivalent to millions of megatons of TNT.
As each cometary fragment streaked into the jovian atmosphere at a speed of 60 kilometers per second, it disintegrated and exploded, producing a hot fireball that carried the comet dust as well as atmospheric gases to high altitudes. These fireballs were clearly visible in profile, with the actual point of impact just beyond the jovian horizon as viewed from Earth (Figure 13.30). As each explosive plume fell back into Jupiter, a region of the upper atmosphere larger than Earth was heated to incandescence and glowed brilliantly for about 15 minutes, a glow we could detect with infrared-sensitive telescopes.
After this event, dark clouds of debris settled into the stratosphere of Jupiter, producing long-lived “bruises” (each still larger than Earth) that could be easily seen through even small telescopes (Figure 13.31). Millions of people all over the world peered at Jupiter through telescopes or followed the event via television or online. Another, smaller, impact feature was seen on Jupiter in summer 2009 (and six more since), indicating that the 1994 events were by no means unique. Seeing these large, impact explosions on Jupiter helps us to appreciate the disaster that would happen to our planet if we were hit by a comet or asteroid.
For comets that do not meet so dramatic an end, measurements of the amount of gas and dust in their atmospheres permit us to estimate the total losses during one orbit. Typical loss rates are up to a million tons per day from an active comet near the Sun, adding up to some tens of millions of tons per orbit. At that rate, a typical comet will be gone after a few thousand orbits. This will probably be the fate of Comet Halley in the long run.
Earlier we mentioned that comets can also escape the solar system. In 2019, astronomers discovered comet 2I/Borisov, which came from a planetary system other than ours. It is only the second interstellar object we have found, and the first that is rich in volatile materials such as water and carbon compounds. The presence of an atmosphere allowed its composition to be studied. Borisov contains much more carbon monoxide than normal solar system comets, which tells us that it was probably formed in a cooler location, perhaps around a red dwarf star.
Watch this 4-minute NASA retrospective on the collision of Comet Shoemaker-Levy 9 with Jupiter History Channel video to learn more.
Footnotes
- 1 We now know that not every comet we see originates in the Kuiper Belt or Oort Cloud. In 2017 and 2019, astronomers discovered two “interstellar comets,” (named 1I/Oumuamua and 2I/Borisov) whose orbits indicated that they came from outside the solar system! (Oumoumua means scout or messenger in Hawaiian.)


24: Black Holes and Curved Spacetime
For most of the twentieth century, black holes seemed the stuff of science fiction, portrayed either as monster vacuum cleaners consuming all the matter around them or as tunnels from one universe to another. But the truth about black holes is almost stranger than fiction. As we continue our voyage into the universe, we will discover that black holes are the key to explaining many mysterious and remarkable objects—including collapsed stars and the active centers of giant galaxies.
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- 24.2: Spacetime and Gravity
- By considering the consequences of the equivalence principle, Einstein concluded that we live in a curved spacetime. The distribution of matter determines the curvature of spacetime; other objects (and even light) entering a region of spacetime must follow its curvature. Light must change its path near a massive object not because light is bent by gravity, but because spacetime is.
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- 24.3: Tests of General Relativity
- In weak gravitational fields, the predictions of general relativity agree with the predictions of Newton’s law of gravity. However, in the stronger gravity of the Sun, general relativity makes predictions that differ from Newtonian physics and can be tested. For example, general relativity predicts that light or radio waves will be deflected when they pass near the Sun, and that the position where Mercury is at perihelion would change by 43 arcsec per century even if there were no other planets
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- 24.4: Time in General Relativity
- General relativity predicts that the stronger the gravity, the more slowly time must run. Experiments on Earth and with spacecraft have confirmed this prediction with remarkable accuracy. When light or other radiation emerges from a compact smaller remnant, such as a white dwarf or neutron star, it shows a gravitational redshift due to the slowing of time.
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- 24.5: Black Holes
- Theory suggests that stars with stellar cores more massive than three times the mass of the Sun at the time they exhaust their nuclear fuel will collapse to become black holes. The surface surrounding a black hole, where the escape velocity equals the speed of light, is called the event horizon, and the radius of the surface is called the Schwarzschild radius. Nothing, not even light, can escape through the event horizon from the black hole. At its center, each black hole is thought to have a si
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- 24.6: Evidence for Black Holes
- The best evidence of stellar-mass black holes comes from binary star systems in which (1) one star of the pair is not visible, (2) the flickering X-ray emission is characteristic of an accretion disk around a compact object, and (3) the orbit and characteristics of the visible star indicate that the mass of its invisible companion is greater than 3 MSun. A number of systems with these characteristics have been found. Black holes with masses of millions to billions of solar masses are found in th
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- 24.7: Gravitational Wave Astronomy
- Another part of Einstein’s ideas about gravity can be tested as a way of checking the theory that underlies black holes. According to general relativity, the geometry of spacetime depends on where matter is located. Any rearrangement of matter—say, from a sphere to a sausage shape—creates a disturbance in spacetime. This disturbance is called a gravitational wave, and relativity predicts that it should spread outward at the speed of light.
Thumbnail: The artist’s illustration on the right shows the black hole pulling material away from a massive blue companion star. This material forms a disk (shown in red and orange) that rotates around the black hole before falling into it or being redirected away from the black hole in the form of powerful jets. The material in the disk (before it falls into the black hole) is so hot that it glows with X-rays, explaining why this object is an X-ray source (credit modification of work by NASA/CXC/M.Weiss).


4.4: Global Patterns of Insolation, Net radiation, and Heat
Patterns of insolation and net radiation which determine the location of plants, animals, climate, soils and other elements of our physical environment can be discerned from Figures \(\PageIndex{1}\) through \(\PageIndex{3}\). Figure \(\PageIndex{1}\) illustrates the latitudinal distribution of incoming solar radiation and outgoing terrestrial radiation. From approximately 35 o N to 35 o S latitude (the red area of the graph) there is a surplus of energy as incoming radiation exceeds outgoing. The blue regions indicate that there is more outgoing energy than incoming, yielding a net loss of energy from the Earth's surface. One might ask then why the middle to higher latitudes aren't getting colder through time as a result of the net loss, and the subtropical to equatorial regions getting constantly hotter due to the net gain. The reason is that the energy is redistributed by circulation of the atmosphere and oceans. Heat gained in the tropics is transported poleward by the global circulation of air and warm ocean currents to heat higher latitude regions. Cooler air from the higher latitudes and cold ocean currents push equatorward to cool the lower latitudes. This process of redistributing energy in the Earth system helps maintain a long-term energy balance.
Insolation
Figure \(\PageIndex{1}\) simplifies the geographic distribution of insolation. For the Earth as a whole, particular patterns can be accounted for by variation in surface features that impact insolation. Insolation maxima are found in the tropical and subtropical deserts of the earth. Here, high sun angles and a lack of cloud cover in desert regions allow much solar radiation to the surface. Insolation decreases to a minimum at the poles where low sun angles and the fact that the Sun doesn't rise above the horizon nearly half the year reduces annual insolation.
Net radiation
Net radiation exhibits a different pattern from that of insolation. Maximum net radiation is found over the tropical and subtropical oceans. The sun angle is always high over the tropical oceans so the surface receives intense radiation throughout the year. With an high sun angle the albedo of the surface is low and absorption is high. However, the energy received is partitioned into warming the surface as well as evaporating water. The result is a lower surface temperature than one might expect with such high sun angles. Additionally, the high specific heat of water means that it takes much more energy to heat a unit mass of water than that of land, resulting in lower ocean surface temperatures. With lower surface temperatures the water surface does not radiate as much longwave radiation out to the atmosphere as nearby land at the same latitude. With much radiation coming in and little going out, the net value is large compared to land at the same latitude. Net radiation is at a minimum over the poles as the sunlight that comes in at a low angle is reflected from the ice-covered surface. Combined with the long polar night, very little net radiation is found at these latitudes.


10.3.1: Regular Markov Chains (Exercises)
SECTION 10.3 PROBLEM SET: REGULAR MARKOV CHAINS
- Determine whether the following matrices are regular Markov chains.
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- Company I and Company II compete against each other, and the transition matrix for people switching from Company I to Company II is given below.
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- Suppose the transition matrix for a tennis player is as follows, where C denotes the cross-court shots and D denotes down-the-line shots.
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- Professor Hay never orders eggs two days in a row, but if he orders tofu one day, then there is an equal probability that he will order tofu or eggs the next day.
Find the following:
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- In a bikeshare program with 3 bike stations, A, B, and C, people can borrow a bicycle at one station and return it to the same station or either of the other two stations. The transition matrix is:
Find the following:
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- Suppose that a country has 3 political parties: the Conservative (C), Liberal (L), and National (N) parties. If a person votes for the candidate from one party in an election, that person may decide to vote for the same party in the next election or may switch to vote for a candidate from another party in the next election. The transition matrix is:
Assume there is an election every year, so the transition time is one year. Find the following.
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Question 7 refers to the following:
Markov chains play an important role in online search.
“PageRank is an algorithm used by Google Search to rank websites in their search engine results. PageRank was named after Larry Page, one of the founders of Google. PageRank is a way of measuring the importance of website pages”
Source:
https://en.Wikipedia.org/wiki/PageRank
under the Creative Commons Attribution-ShareAlike License;
The theory behind PageRank is that pages that are linked to more often are more important and useful; identifying those that are linked to more often about a topic helps identify the pages that should be presented as most pertinent in a search.
In real world search, there are thousands or millions of pages linking together, resulting in huge transition matrices. Because of the size and other properties of these matrices, the mathematics behind PageRank is more sophisticated than the small example we examine here with only four websites. However our example is adequate to convey the main concept of PageRank and its use in search algorithms.
It should be noted that real world search algorithms, PageRank or similar Markov chain ranking schemes are only one of a variety of methodsused.
Suppose we have 4 webpages that contains links to each other. We call the pages A, B, C, D.
- From page A, 30% of people link to page B, 50% link to page C, and 20% link to page D
- From page B, 50% of popele link to page A and 50% link to page D
- From page C, 10% of people link to page B, 70% link to page C, and 20% link to page D
- From page D, 20% of people link to page A, 40% to page B, 10% to page C, and 30% link to page D
(In this example, when a page links to itself, it means that a person viewing the page stays at that page and does not link to another page.)
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4.9: Classical Theme Types - Thematic Function Reference
This page is a quick-reference. For examples of these functions in musical contexts, see the resource on Classical theme types .
Initiating Functions
Presentation
Presentation function comes at the beginning of a theme or phrase. It involves the establishment of the primary melodic material (usually through the use of one or more statements of a basic idea ) and the establishment of the tonality of the theme (usually through tonic prolongation ).
Antecedent
Antecedent function comes at the beginning of a theme or phrase. It involves the statement of a basic idea followed by a contrasting idea. An antecedent should close with a weak cadence, usually a HC or IAC.
Medial Functions
Continuation
Continuation function comes in the middle of a phrase or theme. It typically involves the breakdown of the primary melodic material and harmonic acceleration towards the cadence.
Following are important terms/concepts associated with continuation function. Not all need be present for a passage to express continuation function, but some should be.
- Fragmentation – Breaking the melodic unit into smaller chunks (for example, following two-bar basic ideas in the presentation with one-bar melodic ideas). Note: fragmentation references the breakdown of the size of the units. Those units are not necessarily related melodically.
- Liquidation – Gradually replacing the characteristic or unique parts of a melody with conventional or common elements.
- Sequential repetition – Repeating the same melodic or harmonic element two or three times, transposed to different pitch levels. This is often used in conjunction with fragmentation.
- Acceleration of melodic rhythm – Changing from predominately quarter notes and eighth notes in the melody to predominately eighth notes and sixteenth notes, for example.
- Acceleration of harmonic rhythm – Chord changes coming more frequently (changing from one chord per bar to two chords per bar, for example).
#Closing Functions
Cadential
Cadential function comes at the end of a theme or phrase. It typically involves a cadential harmonic progression and a conventional, descending melodic pattern .
A classical cadential progression begins with the last chord of tonic prolongation and ends with a cadential arrival . The three typical types of cadential arrival in Classical music are the perfect authentic cadence (PAC), the imperfect authentic cadence (IAC), and the half cadence (HC).
A half-cadential progression will begin with the final T chord, progress (optionally) through S , and arrive on a cadential D chord ( always D5 : V or V 7 ):
T__ (S__) D5
An authentic-cadential progression will begin with the final T chord, progress (optionally) through S , and end with the cadential D T progression ( always D5 T1 : V (7) I ):
T_ (S_) D5 T1
Consequent
Consequent function resembles antecedent function in that it involves the presentation of a basic idea followed by a contrasting one. Unlike the antecedent function , however, consequent function brings completion to a thematic unit. Therefore, it ends with a strong cadence, typically a PAC.


2.4: Inorganic Compounds Essential to Human Functioning
Learning Objectives
- Compare and contrast inorganic and organic compounds
- Identify the properties of water that make it essential to life
- Explain the role of salts in body functioning
- Distinguish between acids and bases, and explain their role in pH
- Discuss the role of buffers in helping the body maintain pH homeostasis
The concepts you have learned so far in this chapter govern all forms of matter, and would work as a foundation for geology as well as biology. This section of the chapter narrows the focus to the chemistry of human life; that is, the compounds important for the body’s structure and function. In general, these compounds are either inorganic or organic.
- An inorganic compound is a substance that does not contain both carbon and hydrogen. A great many inorganic compounds do contain hydrogen atoms, such as water (H 2 O) and the hydrochloric acid (HCl) produced by your stomach. In contrast, only a handful of inorganic compounds contain carbon atoms. Carbon dioxide (CO 2 ) is one of the few examples.
- An organic compound , then, is a substance that contains both carbon and hydrogen. Organic compounds are synthesized via covalent bonds within living organisms, including the human body. Recall that carbon and hydrogen are the second and third most abundant elements in your body. You will soon discover how these two elements combine in the foods you eat, in the compounds that make up your body structure, and in the chemicals that fuel your functioning.
The following section examines the three groups of inorganic compounds essential to life: water, salts, acids, and bases. Organic compounds are covered later in the chapter.
Water
As much as 70 percent of an adult’s body weight is water. This water is contained both within the cells and between the cells that make up tissues and organs. Its several roles make water indispensable to human functioning.
Water as a Lubricant and Cushion
Water is a major component of many of the body’s lubricating fluids. Just as oil lubricates the hinge on a door, water in synovial fluid lubricates the actions of body joints, and water in pleural fluid helps the lungs expand and recoil with breathing. Watery fluids help keep food flowing through the digestive tract, and ensure that the movement of adjacent abdominal organs is friction free.
Water also protects cells and organs from physical trauma, cushioning the brain within the skull, for example, and protecting the delicate nerve tissue of the eyes. Water cushions a developing fetus in the mother’s womb as well.
Water as a Heat Sink
A heat sink is a substance or object that absorbs and dissipates heat but does not experience a corresponding increase in temperature. In the body, water absorbs the heat generated by chemical reactions without greatly increasing in temperature. Moreover, when the environmental temperature soars, the water stored in the body helps keep the body cool. This cooling effect happens as warm blood from the body’s core flows to the blood vessels just under the skin and is transferred to the environment. At the same time, sweat glands release warm water in sweat. As the water evaporates into the air, it carries away heat, and then the cooler blood from the periphery circulates back to the body core.
Water as a Component of Liquid Mixtures
A mixture is a combination of two or more substances, each of which maintains its own chemical identity. In other words, the constituent substances are not chemically bonded into a new, larger chemical compound. The concept is easy to imagine if you think of powdery substances such as flour and sugar; when you stir them together in a bowl, they obviously do not bond to form a new compound. The room air you breathe is a gaseous mixture, containing three discrete elements—nitrogen, oxygen, and argon—and one compound, carbon dioxide. There are three types of liquid mixtures, all of which contain water as a key component. These are solutions, colloids, and suspensions.
For cells in the body to survive, they must be kept moist in a water-based liquid called a solution. In chemistry, a liquid solution consists of a solvent that dissolves a substance called a solute. An important characteristic of solutions is that they are homogeneous; that is, the solute molecules are distributed evenly throughout the solution. If you were to stir a teaspoon of sugar into a glass of water, the sugar would dissolve into sugar molecules separated by water molecules. The ratio of sugar to water in the left side of the glass would be the same as the ratio of sugar to water in the right side of the glass. If you were to add more sugar, the ratio of sugar to water would change, but the distribution—provided you had stirred well—would still be even.
Water is considered the “universal solvent” and it is believed that life cannot exist without water because of this. Water is certainly the most abundant solvent in the body; essentially all of the body’s chemical reactions occur among compounds dissolved in water. Because water molecules are polar, with regions of positive and negative electrical charge, water readily dissolves ionic compounds and polar covalent compounds. Such compounds are referred to as hydrophilic, or “water-loving.” As mentioned above, sugar dissolves well in water. This is because sugar molecules contain regions of hydrogen-oxygen polar bonds, making it hydrophilic. Nonpolar molecules, which do not readily dissolve in water, are called hydrophobic, or “water-fearing.”
Concentrations of Solutes
Various mixtures of solutes and water are described in chemistry. The concentration of a given solute is the number of particles of that solute in a given space (oxygen makes up about 21 percent of atmospheric air). In the bloodstream of humans, glucose concentration is usually measured in milligram (mg) per deciliter (dL), and in a healthy adult averages about 100 mg/dL. Another method of measuring the concentration of a solute is by its molarilty—which is moles (M) of the molecules per liter (L). The mole of an element is its atomic weight, while a mole of a compound is the sum of the atomic weights of its components, called the molecular weight. An often-used example is calculating a mole of glucose, with the chemical formula C 6 H 12 O 6 . Using the periodic table, the atomic weight of carbon (C) is 12.011 grams (g), and there are six carbons in glucose, for a total atomic weight of 72.066 g. Doing the same calculations for hydrogen (H) and oxygen (O), the molecular weight equals 180.156g (the “gram molecular weight” of glucose). When water is added to make one liter of solution, you have one mole (1M) of glucose. This is particularly useful in chemistry because of the relationship of moles to “Avogadro’s number.” A mole of any solution has the same number of particles in it: 6.02 × 10 23 . Many substances in the bloodstream and other tissue of the body are measured in thousandths of a mole, or millimoles (mM).
A colloid is a mixture that is somewhat like a heavy solution. The solute particles consist of tiny clumps of molecules large enough to make the liquid mixture opaque (because the particles are large enough to scatter light). Familiar examples of colloids are milk and cream. In the thyroid glands, the thyroid hormone is stored as a thick protein mixture also called a colloid.
A suspension is a liquid mixture in which a heavier substance is suspended temporarily in a liquid, but over time, settles out. This separation of particles from a suspension is called sedimentation. An example of sedimentation occurs in the blood test that establishes sedimentation rate, or sed rate. The test measures how quickly red blood cells in a test tube settle out of the watery portion of blood (known as plasma) over a set period of time. Rapid sedimentation of blood cells does not normally happen in the healthy body, but aspects of certain diseases can cause blood cells to clump together, and these heavy clumps of blood cells settle to the bottom of the test tube more quickly than do normal blood cells.
The Role of Water in Chemical Reactions
Two types of chemical reactions involve the creation or the consumption of water: dehydration synthesis and hydrolysis.
- In dehydration synthesis, one reactant gives up an atom of hydrogen and another reactant gives up a hydroxyl group (OH) in the synthesis of a new product. In the formation of their covalent bond, a molecule of water is released as a byproduct (Figure \(\PageIndex{1}\) ). This is also sometimes referred to as a condensation reaction.
- In hydrolysis, a molecule of water disrupts a compound, breaking its bonds. The water is itself split into H and OH. One portion of the severed compound then bonds with the hydrogen atom, and the other portion bonds with the hydroxyl group.
These reactions are reversible, and play an important role in the chemistry of organic compounds (which will be discussed shortly).
Salts
Recall that salts are formed when ions form ionic bonds. In these reactions, one atom gives up one or more electrons, and thus becomes positively charged, whereas the other accepts one or more electrons and becomes negatively charged. You can now define a salt as a substance that, when dissolved in water, dissociates into ions other than H + or OH – . This fact is important in distinguishing salts from acids and bases, discussed next.
A typical salt, NaCl, dissociates completely in water (Figure \(\PageIndex{2}\)). The positive and negative regions on the water molecule (the hydrogen and oxygen ends respectively) attract the negative chloride and positive sodium ions, pulling them away from each other. Again, whereas nonpolar and polar covalently bonded compounds break apart into molecules in solution, salts dissociate into ions. These ions are electrolytes; they are capable of conducting an electrical current in solution. This property is critical to the function of ions in transmitting nerve impulses and prompting muscle contraction.
Many other salts are important in the body. For example, bile salts produced by the liver help break apart dietary fats, and calcium phosphate salts form the mineral portion of teeth and bones.
Acids and Bases
Acids and bases, like salts, dissociate in water into electrolytes. Acids and bases can very much change the properties of the solutions in which they are dissolved.
Acids
An acid is a substance that releases hydrogen ions (H + ) in solution (Figure \(\PageIndex{3.a}\) ). Because an atom of hydrogen has just one proton and one electron, a positively charged hydrogen ion is simply a proton. This solitary proton is highly likely to participate in chemical reactions. Strong acids are compounds that release all of their H + in solution; that is, they ionize completely. Hydrochloric acid (HCl), which is released from cells in the lining of the stomach, is a strong acid because it releases all of its H + in the stomach’s watery environment. This strong acid aids in digestion and kills ingested microbes. Weak acids do not ionize completely; that is, some of their hydrogen ions remain bonded within a compound in solution. An example of a weak acid is vinegar, or acetic acid; it is called acetate after it gives up a proton.
Bases
A base is a substance that releases hydroxyl ions (OH – ) in solution, or one that accepts H + already present in solution (see Figure \(\PageIndex{3.b}\)). The hydroxyl ions or other base combine with H + present to form a water molecule, thereby removing H + and reducing the solution’s acidity. Strong bases release most or all of their hydroxyl ions; weak bases release only some hydroxyl ions or absorb only a few H + . Food mixed with hydrochloric acid from the stomach would burn the small intestine, the next portion of the digestive tract after the stomach, if it were not for the release of bicarbonate (HCO 3 – ), a weak base that attracts H + . Bicarbonate accepts some of the H + protons, thereby reducing the acidity of the solution.
The Concept of pH
The relative acidity or alkalinity of a solution can be indicated by its pH. A solution’s pH is the negative, base-10 logarithm of the hydrogen ion (H + ) concentration of the solution. As an example, a pH 4 solution has an H + concentration that is ten times greater than that of a pH 5 solution. That is, a solution with a pH of 4 is ten times more acidic than a solution with a pH of 5. The concept of pH will begin to make more sense when you study the pH scale, like that shown in Figure \(PageIndex{4}\). The scale consists of a series of increments ranging from 0 to 14. A solution with a pH of 7 is considered neutral—neither acidic nor basic. Pure water has a pH of 7. The lower the number below 7, the more acidic the solution, or the greater the concentration of H + . The concentration of hydrogen ions at each pH value is 10 times different than the next pH. For instance, a pH value of 4 corresponds to a proton concentration of 10 –4 M, or 0.0001M, while a pH value of 5 corresponds to a proton concentration of 10 –5 M, or 0.00001M. The higher the number above 7, the more basic (alkaline) the solution, or the lower the concentration of H + . Human urine, for example, is ten times more acidic than pure water, and HCl is 10,000,000 times more acidic than water.
Buffers
The pH of human blood normally ranges from 7.35 to 7.45, although it is typically identified as pH 7.4. At this slightly basic pH, blood can reduce the acidity resulting from the carbon dioxide (CO 2 ) constantly being released into the bloodstream by the trillions of cells in the body. Homeostatic mechanisms (along with exhaling CO 2 while breathing) normally keep the pH of blood within this narrow range. This is critical, because fluctuations—either too acidic or too alkaline—can lead to life-threatening disorders.
All cells of the body depend on homeostatic regulation of acid–base balance at a pH of approximately 7.4. The body therefore has several mechanisms for this regulation, involving breathing, the excretion of chemicals in urine, and the internal release of chemicals collectively called buffers into body fluids. A buffer is a solution of a weak acid and its conjugate base. A buffer can neutralize small amounts of acids or bases in body fluids. For example, if there is even a slight decrease below 7.35 in the pH of a bodily fluid, the buffer in the fluid—in this case, acting as a weak base—will bind the excess hydrogen ions. In contrast, if pH rises above 7.45, the buffer will act as a weak acid and contribute hydrogen ions.
HOMEOSTATIC IMBALANCES
Acids and Bases
Excessive acidity of the blood and other body fluids is known as acidosis. Common causes of acidosis are situations and disorders that reduce the effectiveness of breathing, especially the person’s ability to exhale fully, which causes a buildup of CO 2 (and H + ) in the bloodstream. Acidosis can also be caused by metabolic problems that reduce the level or function of buffers that act as bases, or that promote the production of acids. For instance, with severe diarrhea, too much bicarbonate can be lost from the body, allowing acids to build up in body fluids. In people with poorly managed diabetes (ineffective regulation of blood sugar), acids called ketones are produced as a form of body fuel. These can build up in the blood, causing a serious condition called diabetic ketoacidosis. Kidney failure, liver failure, heart failure, cancer, and other disorders also can prompt metabolic acidosis.
In contrast, alkalosis is a condition in which the blood and other body fluids are too alkaline (basic). As with acidosis, respiratory disorders are a major cause; however, in respiratory alkalosis, carbon dioxide levels fall too low. Lung disease, aspirin overdose, shock, and ordinary anxiety can cause respiratory alkalosis, which reduces the normal concentration of H + .
Metabolic alkalosis often results from prolonged, severe vomiting, which causes a loss of hydrogen and chloride ions (as components of HCl). Medications also can prompt alkalosis. These include diuretics that cause the body to lose potassium ions, as well as antacids when taken in excessive amounts, for instance by someone with persistent heartburn or an ulcer.
Chapter Review
Inorganic compounds essential to human functioning include water, salts, acids, and bases. These compounds are inorganic; that is, they do not contain both hydrogen and carbon. Water is a lubricant and cushion, a heat sink, a component of liquid mixtures, a byproduct of dehydration synthesis reactions, and a reactant in hydrolysis reactions. Salts are compounds that, when dissolved in water, dissociate into ions other than H + or OH – . In contrast, acids release H + in solution, making it more acidic. Bases accept H + , thereby making the solution more alkaline (caustic).
The pH of any solution is its relative concentration of H + . A solution with pH 7 is neutral. Solutions with pH below 7 are acids, and solutions with pH above 7 are bases. A change in a single digit on the pH scale (e.g., from 7 to 8) represents a ten-fold increase or decrease in the concentration of H + . In a healthy adult, the pH of blood ranges from 7.35 to 7.45. Homeostatic control mechanisms important for keeping blood in a healthy pH range include chemicals called buffers, weak acids and weak bases released when the pH of blood or other body fluids fluctuates in either direction outside of this normal range.
Review Questions
Q. CH 4 is methane. This compound is ________.
A. inorganic
B. organic
C. reactive
D. a crystal
Q. Which of the following is most likely to be found evenly distributed in water in a homogeneous solution?
A. sodium ions and chloride ions
B. NaCl molecules
C. salt crystals
D. red blood cells
Q. Jenny mixes up a batch of pancake batter, then stirs in some chocolate chips. As she is waiting for the first few pancakes to cook, she notices the chocolate chips sinking to the bottom of the clear glass mixing bowl. The chocolate-chip batter is an example of a ________.
A. solvent
B. solute
C. solution
D. suspension
Q. A substance dissociates into K + and Cl – in solution. The substance is a(n) ________.
A. acid
B. base
C. salt
D. buffer
Q. Ty is three years old and as a result of a “stomach bug” has been vomiting for about 24 hours. His blood pH is 7.48. What does this mean?
A. Ty’s blood is slightly acidic.
B. Ty’s blood is slightly alkaline.
C. Ty’s blood is highly acidic.
D. Ty’s blood is within the normal range
Critical Thinking Questions
Q. The pH of lemon juice is 2, and the pH of orange juice is 4. Which of these is more acidic, and by how much? What does this mean?
A. Lemon juice is one hundred times more acidic than orange juice. This means that lemon juice has a one hundred-fold greater concentration of hydrogen ions.
Q. During a party, Eli loses a bet and is forced to drink a bottle of lemon juice. Not long thereafter, he begins complaining of having difficulty breathing, and his friends take him to the local emergency room. There, he is given an intravenous solution of bicarbonate. Why?
A. Lemon juice, like any acid, releases hydrogen ions in solution. As excessive H + enters the digestive tract and is absorbed into blood, Eli’s blood pH falls below 7.35. Recall that bicarbonate is a buffer, a weak base that accepts hydrogen ions. By administering bicarbonate intravenously, the emergency department physician helps raise Eli’s blood pH back toward neutral.
Glossary
- acid
- compound that releases hydrogen ions (H + ) in solution
- base
- compound that accepts hydrogen ions (H + ) in solution
- buffer
- solution containing a weak acid or a weak base that opposes wide fluctuations in the pH of body fluids
- colloid
- liquid mixture in which the solute particles consist of clumps of molecules large enough to scatter light
- inorganic compound
- substance that does not contain both carbon and hydrogen
- organic compound
- substance that contains both carbon and hydrogen
- pH
- negative logarithm of the hydrogen ion (H + ) concentration of a solution
- solution
- homogeneous liquid mixture in which a solute is dissolved into molecules within a solvent
- suspension
- liquid mixture in which particles distributed in the liquid settle out over time


2.5: How to Write an Annotation
One of the greatest challenges students face is adjusting to college reading expectations. Unlike high school, students in college are expected to read more “academic” type of materials in less time and usually recall the information as soon as the next class.
The problem is many students spend hours reading and have no idea what they just read. Their eyes are moving across the page, but their mind is somewhere else. The end result is wasted time, energy, and frustration…and having to read the text again.
Although students are taught how to read at an early age, many are not taught how to actively engage with written text or other media. Annotation is a tool to help you learn how to actively engage with a text or other media.
View the following video about how to annotate a text.
Annotating a text or other media (e.g. a video, image, etc.) is as much about you as it is the text you are annotating. What are YOUR responses to the author’s writing, claims and ideas? What are YOU thinking as you consider the work? Ask questions, challenge, think!
When we annotate an author’s work, our minds should encounter the mind of the author, openly and freely. If you met the author at a party, what would you like to tell to them; what would you like to ask them? What do you think they would say in response to your comments? You can be critical of the text, but you do not have to be. If you are annotating properly, you often begin to get ideas that have little or even nothing to do with the topic you are annotating. That’s fine: it’s all about generating insights and ideas of your own. Any good insight is worth keeping because it may make for a good essay or research paper later on.
The Secret is in the Pen
One of the ways proficient readers read is with a pen in hand. They know their purpose is to keep their attention on the material by:
- Predicting what the material will be about
- Questioning the material to further understanding
- Determining what’s important
- Identifying key vocabulary
- Summarizing the material in their own words, and
- Monitoring their comprehension (understanding) during and after engaging with the material
The same applies for mindfully viewing a film, video, image or other media.
Annotating a Text
Review the video, “How to Annotate a Text.” Pay attention to both how to make annotations and what types of thoughts and ideas may be part of your annotations as you actively read a written text.
Example Assignment Format: Annotating a Written Text
For the annotation of reading assignments in this class, you will cite and comment on a minimum of FIVE (5) phrases, sentences or passages from notes you take on the selected readings.
Here is an example format for an assignment to annotate a written text:
| Passage # | Quotation and Location | My Comments / Ideas |
|---|---|---|
| 1 | Direct quote (paragraph #) | Add your comments here |
| 2 | Direct quote (paragraph #) | Add your comments here |
| 3 | Direct quote (paragraph #) | Add your comments here |
| 4 | Direct quote (paragraph #) | Add your comments here |
| 5 | Direct quote (paragraph #) | Add your comments here |
Example Assignment Format: Annotating Media
In addition to annotating written text, at times you will have assignments to annotate media (e.g., videos, images or other media). For the annotation of media assignments in this class, you will cite and comment on a minimum of THREE (3) statements, facts, examples, research or any combination of those from the notes you take about selected media.
Here is an example format for an assignment to annotate media:
| Passage # | Describe Passage | My Comments / Ideas |
|---|---|---|
| 1 | Passage Description | Add your comments here |
| 2 | Passage Description | Add your comments here |
| 3 | Passage Description | Add your comments here |


2.1E: Linear Functions (Exercises)
1. A town's population has been growing linearly. In 2003, the population was 45,000, and the population has been growing by 1700 people each year. Write an equation,
\(P(t)\), for the population \(t\) years after 2003.
2. A town's population has been growing linearly. In 2005, the population was 69,000, and the population has been growing by 2500 people each year. Write an equation,
\(P(t)\), for the population \(t\) years after 2005.
3. Sonya is currently 10 miles from home, and is walking further away at 2 miles per hour. Write an equation for her distance from home \(t\) hours from now.
4. A boat is 100 miles away from the marina, sailing directly towards it at 10 miles per hour. Write an equation for the distance of the boat from the marina after \(t\) hours.
5. Timmy goes to the fair with $40. Each ride costs $2. How much money will he have left after riding n rides?
6. At noon, a barista notices she has $20 in her tip jar. If she makes an average of $0.50 from each customer, how much will she have in her tip jar if she serves \(n\) more customers during her shift?
Determine if each function is increasing or decreasing
7. \(f(x) = 4x + 3\)
8. \(g(x) = 5x + 6\)
9. \(a(x) = -2x + 4\)
10. \(b(x) = 8 - 3x\)
11. \(h(x) = -2x + 4\)
12. \(h(x) = -4x + 1\)
13. \(j(x) = \dfrac{1}{2}x - 3\)
14. \(p(x) = \dfrac{1}{4} x - 5\)
15. \(n(x) = -\dfrac{1}{3} x - 2\)
16. \(m(x) = -\dfrac{3}{8} x + 3\)
Find the slope of the line that passes through the two given points
17. (2, 4) and (4, 10)
18. (1, 5) and (4, 11)
19. (-1, 4) and (5, 2)
20. (-2, 8) and (4, 6)
21. (6, 11) and (-4, 3)
22. (9, 10) and (-6, -12)
Find the slope of the lines graphed
23. 24.
25. Sonya is walking home from a friend’s house. After 2 minutes she is 1.4 miles from home. Twelve minutes after leaving, she is 0.9 miles from home. What is her rate?
26. A gym membership with two personal training sessions costs $125, while gym membership with 5 personal training sessions costs $260. What is the rate for personal training sessions?
27. A city's population in the year 1960 was 287,500. In 1989 the population was 275,900. Compute the slope of the population growth (or decline) and make a statement about the population rate of change in people per year.
28. A city's population in the year 1958 was 2,113,000. In 1991 the population was 2,099,800. Compute the slope of the population growth (or decline) and make a statement about the population rate of change in people per year.
29. A phone company charges for service according to the formula: \(C(n) = 24 0.+1n\), where \(n\) is the number of minutes talked, and \(C(n)\) is the monthly charge, in dollars. Find and interpret the rate of change and initial value.
30. A phone company charges for service according to the formula: \(C(n) = 26 0.+04n\), where \(n\) is the number of minutes talked, and \(C(n)\) is the monthly charge, in dollars. Find and interpret the rate of change and initial value.
31. Terry is skiing down a steep hill. Terry's elevation, \(E(t)\), in feet after \(t\) seconds is given by \(E(t) = 3000 - 70t\).Write a complete sentence describing Terry’s starting elevation and how it is changing over time.
32. Maria is climbing a mountain. Maria's elevation, \(E(t)\), in feet after \(t\) minutes is given by \(E(t) =1200 + 40t\). Write a complete sentence describing Maria’s starting elevation and how it is changing over time.
Given each set of information, find a linear equation satisfying the conditions, if possible
33. \(f(-5) = -4\), and \(f(5) = 2\)
34. \(f(-1) = 4\), and \(f(5) = 1\)
35. Passes through (2, 4) and (4, 10)
36. Passes through (1, 5) and (4, 11)
37. Passes through (-1, 4) and (5, 2)
38. Passes through (-2, 8) and (4, 6)
39. \(x\) intercept at (-2, 0) and \(y\) intercept at (0, -3)
40. \(x\) intercept at (-5, 00 and \(y\) intercept at (0, 4)
Find an equation for the function graphed
41. 42.
43. 44.
45. A clothing business finds there is a linear relationship between the number of shirts, \(n\), it can sell and the price, \(p\), it can charge per shirt. In particular, historical data shows that 1000 shirts can be sold at a price of $30, while 3000 shirts can be sold at a price of $22 . Find a linear equation in the form \(p = mn + b\) that gives the price \(p\) they can charge for \(n\) shirts.
46. A farmer finds there is a linear relationship between the number of bean stalks, \(n\), she plants and the yield, \(y\), each plant produces. When she plants 30 stalks, each plant yields 30 oz of beans. When she plants 34 stalks, each plant produces 28 oz of beans. Find a linear relationships in the form \(y = mn + b\) that gives the yield when \(n\) stalks are planted.
47. Which of the following tables could represent a linear function? For each that could be linear, find a linear equation models the data.
48. Which of the following tables could represent a linear function? For each that could be linear, find a linear equation models the data.
49. While speaking on the phone to a friend in Oslo, Norway, you learned that the current temperature there was -23 Celsius (-23\({}^{o}\)C). After the phone conversation, you wanted to convert this temperature to Fahrenheit degrees, oF, but you could not find a reference with the correct formulas. You then remembered that the relationship between \({}^{o}\)F and \({}^{o}\)C is linear. [UW]
Using this and the knowledge that 32\({}^{o}\)F = 0 \({}^{o}\)C and 212 \({}^{o}\)F = 100 \({}^{o}\)C, find an equation that computes Celsius temperature in terms of Fahrenheit; i.e. an equation of the form C = “an expression involving only the variable F.”
Likewise, find an equation that computes Fahrenheit temperature in terms of Celsius temperature; i.e. an equation of the form F = “an expression involving only the variable C.”
How cold was it in Oslo in \({}^{o}\)F?
- Answer
-
1. \(P(t) = 1700t + 45000\)
3. \(D(t) = 10 + 2t\)
5. \(M(n) = 40 - 2n\)
7. Increasing
9. Decreasing
11. Decreasing
13. Increasing
15. Decreasing
17. 3
19. \(-\dfrac{1}{3}\)
21. \(\dfrac{4}{3}\)
23. \(\dfrac{2}{3}\)
25. -0.05 mph (or 0.05 miles per hour toward her home)
27. Population is decreasing by 400 people per year
29. Monthly charge in dollars has an initial base charge of $24, and increases by $0.10 for each minute talked
31. Terry started at an elevation of 3,000 ft and is descending by 70ft per second.
33. \(y = \dfrac{3}{5} x - 1\)
35. \(y = 3x - 2\)
37. \(y = -\dfrac{1}{3}x + \dfrac{11}{3}\)
39. \(y = -1.5x - 3\)
41. \(y = \dfrac{2}{3} x + 1\)
43. \(y = -2x + 3\)
45. \(P(n) = -0.004n + 34\)
47. The \(1^{\text{st}}\), \(3^{\text{rd}}\) & \(4^{\text{th}}\) tables are linear: respectively
1. \(g(x) = -3x + 5\)
3. \(f(x) = 5x - 5\)
4. \(k(x) = 3x - 2\)49a. \(C = \dfrac{5}{9} F - \dfrac{160}{9}\)
b. \(F = \dfrac{9}{5} C + 32\)
c. \(-9.4^{\circ} F\)


1.2A: Anatomical Position
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When an organism is in its standard anatomical position, positional descriptive terms are used to indicate regions and features.
Learning Objectives
- Describe the standard position in human anatomy
Key Points
- In standard anatomical position, the limbs are placed similarly to the supine position imposed on cadavers during autopsy.
- The anatomical position of the skull is the Frankfurt plane. In this position, the lower margins of the orbitals (eye sockets), the lower margin of the orbits, and the upper margins of the ear canals (poria) lie in the same horizontal plane.
- Because animals can change orientation with respect to their environments and appendages can change position with respect to the body, positional descriptive terms refer to the organism only in its standard anatomical position to prevent confusion.
Key Terms
- appendage : A limb of the body.
- supine : Lying on its back, reclined.
- anatomical position : The standard position in which the body is standing with feet together, arms to the side, and head, eyes, and palms facing forward.
The Need for Standardization
Standard anatomical position is the body orientation used when describing an organism’s anatomy. Standardization is necessary to avoid confusion since most organisms can take on many different positions that may change the relative placement of organs. All descriptions refer to the organism in its standard anatomical position, even when the organism’s appendages are in another position. Thus, the standard anatomical position provides a “gold standard” when comparing the anatomy of different members of the same species.
Relative location in the anatomical position : Many terms are used to describe relative location on the body. Cranial refers to features closer to the head, while caudal refers to features closer to the feet. The front of the body is referred to as anterior or ventral, while the back is referred to as posterior or dorsal. Proximal and distal describe relative position on the limbs. Proximal refers to a feature that is closer to the torso, while distal refers to a feature that is closer to the fingers/toes. Medial and lateral refer to position relative to the midline, which is a vertical line drawn through the center of the forehead, down through the belly button to the floor. Medial indicates a feature is closer to this line, while lateral indicates features further from this line.
Standard Anatomical Position in Humans
The standard anatomical position is agreed upon by the international medical community. In this position, a person is standing upright with the lower limbs together or slightly apart, feet flat on the floor and facing forward, upper limbs at the sides with the palms facing forward and thumbs pointing away from the body, and head and eyes directed straight ahead. In addition, the arms are usually placed slightly apart from the body so that the hands do not touch the sides. The positions of the limbs, particularly the arms, have important implications for directional terms in those appendages.
The basis for the standard anatomical position in humans comes from the supine position used for examining human cadavers during autopsies. Dissection of cadavers was one of the primary ways humans learned about anatomy throughout history, which has tremendously influenced the ways by which anatomical knowledge has developed into the scientific field of today.
Standard anatomical position : The regions of the body in standard anatomical position, in which the body is erect.
In humans, the standard anatomical position of the skull is called the Frankfurt plane. In this position, the orbitales (eye sockets), lower margins of the orbits, and the poria (ear canal upper margins) all lie in the same horizontal plane. This orientation represents the position of the skull if the subject were standing upright and looking straight ahead.
It is important to note that all anatomical descriptions are based on the standard anatomical position unless otherwise stated.


15.5: Shoot Development
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Learning Objective
- Define the roles of the shoot apical meristem, leaf primordia, intercalary meristems, and axillary buds in shoot development.
- Explain the mechanism of the ABCDE model of floral development.
Some plant parts, such as stems and roots, continue to grow throughout a plant’s life: a phenomenon called indeterminate growth . Other plant parts, such as leaves and flowers, exhibit determinate growth, which ceases when a plant part reaches a particular size.
Stem and Leaf Development
In comparison to roots, in which cell division, elongation, and maturation occur in distinct regions (see Internal Root Structure ), growth in stems occurs in several regions. Rapid cell division occurs at the shoot apical meristem of the shoot tip. Some of the cells produced from these divisions give rise to leaf primordia , which ultimately develop into leaves. Division, elongation, and cell differentiation (maturation) also occurs at the intercalary meristems of internodes , the stem segments between nodes , the points where leaves attach. As a result, multiple internodes can lengthen simultaneously. Under certain circumstances, the axillary buds at each node can become active and produce axillary shoots, which branch from the main stem.
Flower Development
Changes in gene expression can cause a shoot apical meristem to develop into a floral meristem, which leads to flowering. The ABCDE model (ABC model) of floral development directs the formation of each of the four whorls of a complete flower. From outside to inside, these whorls are the calyx (sepals), corolla (petals), androecium (stamens), and gynoecium (carpels). (See Angiosperms for more details; Figure \(\PageIndex{1}\).) Each unit of these whorls (sepal, petal, etc.) developmentally and evolutionarily originated from the leaf.
The ABCDE model refers to five groups of homeotic genes, each represented by one letter. Homeotic genes are those that control the development and organization of body parts (body plan). Each of the five groups of genes that encode the transcription factors (proteins required for gene expression), which turn on the genes for development of each whorl. Genetic analysis of mutants especially those found in the Arabidopsis thaliana and in the snapdragon ( Antirrhinum ) support the ABCDE model of flowering. Each group of genes has a distinct role as follows (Figure \(\PageIndex{2}\)):
- A genes are needed for sepal and petal development
- B genes are needed for petal and stamen development.
- C gene are needed for stamen and carpel (including ovules) development.
- D genes are need for ovule development (part of the carpels).
- E genes are needed to produce any of the floral whorls.
Thus, each whorl results from the expression of a different gene combination as follows:
- Expression of A and E genes produce sepals.
- Expression of A, B, and E genes produce petals.
- Expression of B, C, and E genes produce stamens.
- Expression of C and E genes produce carpels. To produce ovules, which are considered part of the carpels, D genes must also be expressed (C+D+E = ovules).
In summary, the formation of a flower requires a cascade of sequential gene activity that gradually converts a mass of undifferentiated cells (the shoot apical meristem) into the parts of a flower. The genes encode transcription factors that act as master switches, turning on (or off) downstream genes that ultimately make each part of the flower in its appropriate location.
Attributions
Curated and authored by Melissa Ha using the following sources:
- 16.4D Flowering from Biology by John W. Kimball ( CC-BY )
- 30.2 Stems from Biology 2e by OpenStax (licensed CC-BY ). Access for free at openstax.org .