9.3: Religion and Culture- Difference and Similarity
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We have explored elements of religion and culture and offered various brief examples from an individual, national and international perspective. While it has been important to consider each concept separately, highlighting the particular ways that religion and culture influence international relations, there are clear interlinkages between them. Theorists have long drawn such links and these are useful for our consideration here. For example, the anthropologist Clifford Geertz famously described religion as a ‘cultural system’ composed of myths, rituals, symbols and beliefs created by humans as a way of giving our individual and collective lives a sense of meaning (Woodhead 2011, 124). Consider the similarities between the elements of religion and culture described in this chapter such as the role of symbols and stories in both accounts, and the pursuit of life according to what either faith or culture determine to be the higher standards of living.
An important question to ask is whether ‘culture’ should be necessarily understood as the larger more significant category in international relations, always casting ‘religion’ as a subset within it. Such a view makes sense because no one religion encompasses an entire society in the world today, and no society lives entirely according to one set of sacred rules and practices. On the other hand, in some contexts religious authority and identity can be more significant than any other cultural element. For example, when American soldiers moved into the Iraqi city of Najaf in 2003 to negotiate security arrangements, it was not the town mayor or the police chief that had most influence. Rather, it was the reclusive religious leader Grand Ayatollah Ali al-Sistani, whose authority influenced not only the city but much of the fracturing nation itself. Taking another example, when Communist authorities confronted striking dock workers in Poland in the 1980s, it was not only unions that opposed them but also the Catholic Church, whose priests performed sacred rituals and stood in solidarity with strikers in open defiance of the government. In both these examples, the elements of religion are equally – if not more – prominent than the elements of culture. Perhaps the most useful approach, therefore, is to see the elements of religion and the elements of culture in constant interaction with one another.
We have explored just four elements for each category. What might some other elements be and what are the impacts of these elements on individual and international life? There are some excellent resources to assist us in exploring such questions. These include an introduction to religion in IR by Toft, Philpott and Shah (2011), an examination of religion in a globalised world by Haynes (2012), a large compendium of essential readings on religion and foreign affairs edited by Hoover and Johnston (2012), and E-International Relations’ edited collection Nations Under God (Herrington, McKay and Haynes 2015). However, the simple outline we have provided so far will enable us to begin answering the ‘what’ and ‘how’ questions about religion and culture in global affairs and draw some connections between them.


5.8: Outcome- Ensuring Ethical Marketing and Sales
What you’ll learn to do: describe measures companies take to encourage ethical behavior
Ethical issues arise at both an organizational level and an individual level. A single individual can engage in unethical behavior, but most ethical breaches that have significant impact on a business occur when many individuals come together to act unethically. This section will review the steps that businesses take at each level to define ethical behavior and create a culture that encourages employees to do the right thing.
The way to gain a good reputation is to endeavor to be what you desire to appear.—Socrates
The specific things you’ll learn in this section include:
- Explain the importance of ethics policies and a culture of accountability for all employees
- Identify the unique ethical considerations and roles for company executives
- Describe how companies manage ethical behavior of marketing employees
Learning Activities
The learning activities for this section include the following:
- Reading: A Culture of Accountability
- Reading: Executive Role in Ethics
- Reading: Ethics for Marketing Employees
- Simulation: Ethics
- Self Check: Ensuring Ethical Marketing and Sales
Contributors and Attributions
- Outcome: Ensuring Ethical Marketing and Sales. Provided by : Lumen Learning. License : CC BY: Attribution


3.3: Obtain dimensions from drawings
The best way to get exact dimensions from drawings is to use the explicit dimensions (in millimeters or in feet and inches) written between the dimension lines. Any measurements that you need should be somewhere on the drawings. Drawings normally only give each dimension once. If there are a number of parallel lengths, only one will have a measurement. To find the dimension you need, you may need to refer to other views or you may have to add or subtract other dimensions.
Measuring lines on a drawing to determine the measurement is not an accurate way to extract dimensions. This is because the drawing is only a representation and may not be exact. Photocopies of drawings may not be to the scale of the original.
The scale of the drawing and your accuracy in measuring will lead to inaccuracies. For example, if the scale of a drawing is 1/8 " = 1 ' -0 " , an error of 1/32 " in measuring the plan amounts to 3 " of error in the object measured. Detail drawings permit more exactness because they are proportionately larger. Details, however, often require more exactness and usually contain any needed dimensions.
When accuracy is not required and approximate dimensions are adequate, measuring plans is a quick method of taking off material for estimating the cost of a job. In such cases, 10% is usually added for cut-off and waste allowance.
If you use the scale of the drawing, it will be simple to read off the measurements. However, in the field you will often need approximate measurements and the only measuring tool at hand will be a measuring tape.
A steel pocket tape measure has a movable hook on the end that allows accurate measuring both when butted against a surface or when hooked on the end of an object (Figure 9). The end of the flexible tape itself is shortened to allow for the hook.


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Learning Objectives
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Identify the organs of the alimentary canal from proximal to distal
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Identify the accessory digestive organs
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20.1: Overview
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This page explains the digestive system's primary role in breaking down food and absorbing nutrients, with the small intestine being the key site for these processes. It categorizes digestive organs into the alimentary canal and accessory organs, highlighting that, although termed "accessory," these organs are vital for efficient digestion and nutrient absorption.
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20.2: Alimentary Canal Organs
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This page discusses the alimentary canal, a 7.62-meter-long tube essential for digestion, detailing its processing of food from mouth to anus through organs like the pharynx, esophagus, stomach, and intestines. It highlights accessory organs such as teeth, tongue, and salivary glands that aid digestion, as well as the canal's four basic tissue layers—mucosa, submucosa, muscularis, and serosa—vital for function and nutrient absorption.
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20.3: Stomach
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This page outlines the stomach's anatomy, describing its four main regions: the cardia, fundus, body, and pylorus, as well as their functions. It highlights the role of the pyloric sphincter in regulating emptying into the duodenum and details the stomach wall's structure, including the unique inner oblique muscle layer. Additionally, it explains the mucosa's gastric pits and glands that produce gastric juice, which contains hydrochloric acid and enzymes essential for digestion.
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20.4: Small Intestine
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This page describes the anatomy and structure of the small intestine, detailing its three regions: duodenum, jejunum, and ileum. It highlights the four-layered wall of the small intestine and emphasizes the specialized mucosal and submucosal features, such as circular folds, villi, and microvilli, which significantly increase absorptive surface area, primarily in the proximal two-thirds, where absorption is most extensive.
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20.5: Large Intestine
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This page describes the anatomy and histology of the large intestine, which includes the cecum, colon, and rectum. Although shorter than the small intestine, it has a larger diameter. It features teniae coli, haustra, and epiploic appendages. The mucosa is made up of simple columnar epithelium with enterocytes and many goblet cells for mucus secretion, aiding in fecal movement and the absorption of water, salts, and vitamins produced by intestinal bacteria.
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20.6: Exercises
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This page provides exercises for labeling anatomical and histological structures of the digestive system, including hollow organs, the oral cavity, teeth, salivary glands, stomach, liver, bile and pancreatic pathways, colon, rectum, and liver histology. It highlights the complexity and organization of the digestive system through a structured identification process for various components.
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20.7: MODELS- Hollow Organs, Teeth, Live/Gall Bladder, Upright Torsos, Mid-Sagittal Head
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This page details the anatomy and histology of the digestive system, covering structures like the oral cavity, stomach, intestines, pancreas, liver, and salivary glands. It discusses various tissue layers, histological features of organs, and includes a dental formula, as well as the organization of salivary glands and the peritoneal cavity.


9.3: Unit 9 Practice Problems
Exercise 1
An associative mechanism is favored when
a) the oxidation state of the metal is high
b) the coordination number of the metal is low
c) the complex has bulky ligands
d) the metal –ligand bonds are labile.
- Answer
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b) the coordination number of the metal is low
Exercise 2
Which of the following metal-ligand bonds would you expect to have the highest thermodynamic stability?
a) Hg-S
b) Hg-O
c) Hg-N
d) Hg-F
- Answer
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a) Hg-S
Exercise 3
Chelate complexes are thermodynamically particularly stable because
a) The substitution of a simple ligand by a chelating ligand is enthalpically particularly favorable.
b) The substitution of a simple ligand by a chelating ligand is entropically particularly favorable.
c) Chelating ligands are more inert than simple ligands.
- Answer
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b) The substitution of a simple ligand by a chelating ligand is entropically particularly favorable.
Exercise 4
What is true about complexes that undergo metal to ligand charge transfer?
a) The metal ion has no or few d electrons
b) The ligands are good pi-acceptors
c) The metal ions have a high charge.
- Answer
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b) The ligands are good pi-acceptors


2.3: Forces as Interactions
Stepping Back
From previous sections, we now have a definition of force (push or pull between two objects), a notion of fundamental (between particles) vs. composite (between clusters of particles), and a description of all the types of composite forces we are going to encounter in this class. In this section, we will back away from the specifics of the previous section, and explore more general features of force. We will find that our faulty human intuition and imprecise language when it comes to physical concepts will give us some challenges, but hopefully this section will provide some tools for overcoming them.
Newton's Third Law
As is implied by the name “first law,” Newton was not finished – he posited two other laws of motion as well. We’ll return to the second law in a future section, but first we will discuss the third law. You have almost certainly heard it before:
Newton's Third Law
For every action there is an equal and opposite reaction.
This is an extremely unfortunate use of language, and this law has been misinterpreted for hundreds of years as a result. It is often heard quoted in movies to essentially express how natural it is to seek retribution.
ALERT
The idea of a “reaction” as we understand it in common parlance is that it is a consequence of a previous action, but this is not the way that Newton meant it.
Okay, then, so how did Newton mean it? Forces are interactions , and just as it is impossible for a single hand to clap, it is equally impossible for a single object to be the sole participant in a force interaction. So if one object experiences a force from another, there must be a reciprocal force also felt in the other direction at exactly the same moment, with precisely the same magnitude and in precisely the opposite direction (remember, forces are vectors). So for every force you can name, there exists an evil twin that acts in the opposite direction with equal magnitude. These "twins" we will refer to as Newton’s third law force pairs . It is important to note that while all third law pairs are forces equal in magnitude and opposite in direction, not all pairs of forces equal in magnitude and opposite in direction to each other are third law pairs with each other . That is, "equal-and-opposite" is a necessary (restrictive), but not sufficient (defining) condition. It is also worth noting that this law doesn't depend upon the force being fundamental between particles, or composite between objects – it is just a general feature of force itself.
What follows is a very useful tool in our study of force, and in particular for identification of third law pairs:
The "Force Phrase"
"...\(\left<type\;of\;force\right>\) on \(\left<object\;experiencing\;force\right>\) by \(\left<object\;exerting\;force\right>\)..."
By "type of force", we mean one of the macroscopic forces listed in the previous section (gravity, contact, tension, etc.), and since two objects are always involved, both must be listed here. In addition, the specific force between the two objects must be indicated, meaning that the phrase specifies which object is doing the pushing or pulling, and which object is being pushed or pulled. Of course they are both pushed or pulled, but that just means there are two forces involved (one acting on each object), and this force phrase singles out one of them.
This phrase can be used to great effect to identify third law pairs. If one can correctly describe a force using the force phrase, then its third-law pair is the force whose phrase simply reverses the "on" and "by" objects. Naturally the type of force must be the same for both, as they are two halves of the same single interaction.
Conceptual Question
A child sits on a swing, swinging back-and forth. At the bottom of the swing, which of the following forces is the Newton’s 3rd law pair to the contact force the child exerts on the seat of the swing?
- the tension force on the seat by the chain of the swing
- the gravitational force on the child by the Earth
- the gravitational force on the Earth by the child
- the centripetal force on the child by the seat
- none of these
- Solution
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(e) The contact force on the seat by the child is a result of the interaction of the seat and the child. The third law pair is therefore the contact force on the child by the seat. Forces (a)-(c) aren't the same interaction as the one given, and (d) is not even a type of force!
Conceptual Question
A block weighing 12lb travels in a circular path in a vertical plane. As the block does this, it slides along a frictionless circular track, and it is also attached to a string, the other end of which is attached to a fixed point at the center of the circle. When the block is at the bottom of its circular path, the contact force exerted on it by the track equals the tension force exerted on it by the string, and both are equal to 12lb. Which of the following forces is the Newton’s 3rd Law pair corresponding to the gravity force on the block?
- the normal force on the block
- the tension force on the block
- Either (a) or (b) can be considered a third law pair for the gravity force.
- the sum of (a) and (b)
- None of the above is a third law pair to the gravity force on the block.
- Solution
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(e) Don't let all the special information provided and coincidental numbers fool you! Just reverse the "on" and the "by" in the force phrase. The gravity force interaction is between the block and the earth, so the third law pair of the gravity force on the block by the earth is the gravity force on the earth by the block.
Free-Body Diagrams
Possibly our most powerful tool for analyzing forces and their effects on the motions of objects is the free-body diagram (or FBD for short). This is a diagram that consists of a single system (the "free-body," which can be a single object or a collection of objects with the same collective fate), with arrows representing force vectors drawn on it. There are a few rules to drawing an accurate FBD:
- It must include only an isolated "system." This system can consist of one object or many, but the analysis that follows applies to the system as a whole, and nothing outside this system – whatever its role in the physics – is included in the diagram.
- The force vectors must be “real” forces. If you can’t name the force with one of the forces mentioned earlier, then you are probably trying to fix something that isn’t broken by inventing a force. Also, no forces calculated from aggregates of other forces should be included – just separate, physically-describable forces.
- Only forces on the system can be included – never forces by the system. If every vector is labeled using the force phrase, there is no way to go wrong here.
- For now, where the force vectors are located on the system is not important, so the entire system can be reduced to a single dot for simplicity (we will discuss why we are allowed to do this for systems of particles in the next section). But later this quarter the location where the force acts will become important, so it might be a good idea to try to place the force vectors properly right away. Since the type of force and its basic nature are related to where it acts on an system, this will also help confirm that you are dealing with the right forces, and are not trying to invent a force that doesn't exist.
Okay, let's consider the following puzzling question... Suppose two people engage in a tug-o-war. According to Newton's third law, the tension force on person #1 by person #2 equals the tension force on person #2 by person #1. This is inescapable. But then how does anyone ever win , if both always pull with the same force? Let’s draw a FBD to see if we can see why.
The first step is to isolate a single object (the "free body") – we will therefore choose one of the two competitors. Then we need to think about the physical situation, and name all the forces on (not by !) that object, and add vector arrows to the diagram to represent those forces. Only then can we decide how the motion of the free body might be affected by these forces.
Figure 2.3.1 – Analyzing a Tug-o-War Using a FBD
The reason the question is confusing is that we think that the two forces that are equal-and-opposite must always cancel out, but how exactly do forces “cancel?” They have to act on the same system to be added together and cancel . By drawing a careful force diagram in which we only include the forces on the system in question (in this case, the blue-headed stick figure), we see that in fact the third law pairs that are equal and opposite are split between two FBDs, and therefore cannot cancel each other. The real determining factor of whether an individual wins the tug-o-war is whether that individual receives a friction force from the ground that is greater than or less than the tension force, unbalancing the total horizontal force on them.
Does this mean the person is at the whim of the ground, that either decides to provide a big or small friction force? Of course not! The friction force on our feet by the ground is equal-and-opposite to the friction force our feet exert on the ground, and we do this by leaning back and sliding (or push our foot forward as if to slide it) across the ground. We can see that this is the case, because even the strongest human in the world cannot win a tug-o-war against a small child if the strong person is on ice or on some rolling device that doesn’t allow them to push horizontally (and thereby be pushed back the opposite way).
Exercise
A pickup truck with the tailgate down carries two identical sheets of plywood stacked in its bed as it accelerates horizontally. The plywood sheets do not slide within the bed or across each other.
a. Draw a free-body diagram for both sheets of plywood, labeling the vector arrows using the force phase.
b. Indicate which forces in your diagrams are third-law force pairs of each other.
- Solution
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4.3E: Fitting Linear Models to Data (Exercises)
Draw a scatter plot for the data in Table 2. Then determine whether the data appears to be linearly related.
| 0 | -105 |
| 2 | -50 |
| 4 | 1 |
| 6 | 55 |
| 8 | 105 |
| 10 | 160 |
35 .
Draw a scatter plot for the data in Table 3. If we wanted to know when the population would reach 15,000, would the answer involve interpolation or extrapolation?
| Year | Population |
|---|---|
| 1990 | 5,600 |
| 1995 | 5,950 |
| 2000 | 6,300 |
| 2005 | 6,600 |
| 2010 | 6,900 |
Eight students were asked to estimate their score on a 10-point quiz. Their estimated and actual scores are given in Table 4. Plot the points, then sketch a line that fits the data.
| Predicted | Actual |
|---|---|
| 6 | 6 |
| 7 | 7 |
| 7 | 8 |
| 8 | 8 |
| 7 | 9 |
| 9 | 10 |
| 10 | 10 |
| 10 | 9 |
37. Draw a best-fit line for the plotted data.
For the following exercises, consider the data in Table 5, which shows the percent of unemployed in a city of people 25 years or older who are college graduates is given below, by year.
| Year | 2000 | 2002 | 2005 | 2007 | 2010 |
| Percent Graduates | 6.5 | 7.0 | 7.4 | 8.2 | 9.0 |
Determine whether the trend appears to be linear. If so, and assuming the trend continues, find a linear regression model to predict the percent of unemployed in a given year to three decimal places.
39 .In what year will the percentage exceed 12%?
40 .Based on the set of data given in Table 6, calculate the regression line using a calculator or other technology tool, and determine the correlation coefficient to three decimal places.
| xx | 17 | 20 | 23 | 26 | 29 |
| yy | 15 | 25 | 31 | 37 | 40 |
Based on the set of data given in Table 7, calculate the regression line using a calculator or other technology tool, and determine the correlation coefficient to three decimal places.
| xx | 10 | 12 | 15 | 18 | 20 |
| yy | 36 | 34 | 30 | 28 | 22 |
For the following exercises, consider this scenario: The population of a city increased steadily over a ten-year span. The following ordered pairs show the population and the year over the ten-year span (population, year) for specific recorded years:
\[(3,600,2000) ;(4,000,2001) ;(4,700,2003) ;(6,000,2006)\]
42. Use linear regression to determine a function \(y,\) where the year depends on the population, to three decimal places of accuracy.
43. Predict when the population will hit 12,000.
44. What is the correlation coefficient for this model to three decimal places of accuracy?
45. According to the model, what is the population in \(2014 ?\)


16.3: Biogeochemical Cycles
By the end of this section, you will be able to do the following:
- Discuss the biogeochemical cycles of water, carbon, nitrogen, phosphorus, and sulfur
- Explain how human activities have impacted these cycles and the resulting potential consequences for Earth
Energy flows directionally through ecosystems, entering as sunlight (or inorganic molecules for chemoautotrophs) and leaving as heat during the transfers between trophic levels. Rather than flowing through an ecosystem, the matter that makes up living organisms is conserved and recycled. The six most common elements associated with organic molecules—carbon, nitrogen, hydrogen, oxygen, phosphorus, and sulfur—take a variety of chemical forms and may exist for long periods in the atmosphere, on land, in water, or beneath Earth’s surface. Geologic processes, such as weathering, erosion, water drainage, and the subduction of the continental plates, all play a role in the cycling of elements on Earth. Because geology and chemistry have major roles in the study of this process, the recycling of inorganic matter between living organisms and their nonliving environment is called a biogeochemical cycle.
Water, which contain s hydrogen and oxygen, is essential to all living processes. The hydrosphere is the area of Earth where water movement and storage occurs: as liquid water on the surface (rivers, lakes, oceans) and beneath the surface (groundwater) or ice, (polar ice caps and glaciers), and as water vapor in the atmosphere. Carbon is found in all organic macromolecules and is an important constituent of fossil fuels. Nitrogen is a major component of our nucleic acids and proteins and is critical to human agriculture. Phosphorus, a major component of nucleic acids, is one of the main ingredients (along with nitrogen) in artificial fertilizers used in agriculture, which has environmental impacts on our surface water. Sulfur, critical to the three-dimensional folding of proteins (as in disulfide binding), is released into the atmosphere by the burning of fossil fuels.
The cycling of these elements is interconnected. For example, the movement of water is critical for the leaching of nitrogen and phosphate into rivers, lakes, and oceans. The ocean is also a major reservoir for carbon. Thus, mineral nutrients are cycled, either rapidly or slowly, through the entire biosphere between the biotic and abiotic world and from one living organism to another.
CONCEPT IN ACTION
Click the link to explore the Third National Climate Assessment (new window) and learn more about biogeochemical cycles.
The Water Cycle
Water is essential for all living processes. The human body is more than one-half water and human cells are more than 70 percent water. Thus, most land animals need a supply of fresh water to survive. Of the stores of water on Earth, 97.5 percent is salt water (Figure \(\PageIndex{1}\)). Of the remaining water, 99 percent is locked as underground water or ice. Thus, less than one percent of fresh water is present in lakes and rivers. Many living things are dependent on this small amount of surface fresh water supply, a lack of which can have important effects on ecosystem dynamics. Humans, of course, have developed technologies to increase water availability, such as digging wells to harvest groundwater, storing rainwater, and using desalination to obtain drinkable water from the ocean. Although this pursuit of drinkable water has been ongoing throughout human history, the supply of fresh water continues to be a major issue in modern times.
The various processes that occur during the cycling of water are illustrated in Figure \(\PageIndex{2}\). The processes include the following:
- evaporation and sublimation
- condensation and precipitation
- subsurface water flow
- surface runoff and snowmelt
- streamflow
The water cycle is driven by the Sun’s energy as it warms the oceans and other surface waters. This leads to evaporation (water to water vapor) of liquid surface water and sublimation (ice to water vapor) of frozen water, thus moving large amounts of water into the atmosphere as water vapor. Over time, this water vapor condenses into clouds as liquid or frozen droplets and eventually leads to precipitation (rain or snow), which returns water to Earth’s surface. Rain reaching Earth’s surface may evaporate again, flow over the surface, or percolate into the ground. Most easily observed is surface runoff: the flow of fresh water either from rain or melting ice. Runoff can make its way through streams and lakes to the oceans or flow directly to the oceans themselves.
In most natural terrestrial environments rain encounters vegetation before it reaches the soil surface. A significant percentage of water evaporates immediately from the surfaces of plants. What is left reaches the soil and begins to move down. Surface runoff will occur only if the soil becomes saturated with water in a heavy rainfall. Most water in the soil will be taken up by plant roots. The plant will use some of this water for its own metabolism, and some of that will find its way into animals that eat the plants, but much of it will be lost back to the atmosphere through a process known as evapotranspiration. Water enters the vascular system of the plant through the roots and evaporates, or transpires, through the stomata of the leaves. Water in the soil that is not taken up by a plant and that does not evaporate is able to percolate into the subsoil and bedrock. Here it forms groundwater.
Groundwater is a significant reservoir of fresh water. It exists in the pores between particles in sand and gravel, or in the fissures in rocks. Shallow groundwater flows slowly through these pores and fissures and eventually finds its way to a stream or lake where it becomes a part of the surface water again. Streams do not flow because they are replenished from rainwater directly; they flow because there is a constant inflow from groundwater below. Some groundwater is found very deep in the bedrock and can persist there for millennia. Most groundwater reservoirs, or aquifers, are the source of drinking or irrigation water drawn up through wells. In many cases these aquifers are being depleted faster than they are being replenished by water percolating down from above.
Rain and surface runoff are major ways in which minerals, including carbon, nitrogen, phosphorus, and sulfur, are cycled from land to water. The environmental effects of runoff will be discussed later as these cycles are described.
The Carbon Cycle
Carbon is the fourth most abundant element in living organisms. Carbon is present in all organic molecules, and its role in the structure of macromolecules is of primary importance to living organisms. Carbon compounds contain energy, and many of these compounds from plants and algae have remained stored as fossilized carbon, which humans use as fuel. Since the 1800s, the use of fossil fuels has accelerated. As global demand for Earth’s limited fossil fuel supplies has risen since the beginning of the Industrial Revolution, the amount of carbon dioxide in our atmosphere has increased as the fuels are burned. This increase in carbon dioxide has been associated with climate change and is a major environmental concern worldwide.
The carbon cycle is most easily studied as two interconnected subcycles: one dealing with rapid carbon exchange among living organisms and the other dealing with the long-term cycling of carbon through geologic processes. The entire carbon cycle is shown in Figure \(\PageIndex{3}\).
The Biological Carbon Cycle
Living organisms are connected in many ways, even between ecosystems. A good example of this connection is the exchange of carbon between heterotrophs and autotrophs within and between ecosystems by way of atmospheric carbon dioxide. Carbon dioxide is the basic building block that autotrophs use to build multi-carbon, high-energy compounds, such as glucose. The energy harnessed from the Sun is used by these organisms to form the covalent bonds that link carbon atoms together. These chemical bonds store this energy for later use in the process of respiration. Most terrestrial autotrophs obtain their carbon dioxide directly from the atmosphere, while marine autotrophs acquire it in the dissolved form (carbonic acid, HCO 3 – ). However the carbon dioxide is acquired, a byproduct of fixing carbon in organic compounds is oxygen. Photosynthetic organisms are responsible for maintaining approximately 21 percent of the oxygen content of the atmosphere that we observe today.
The partners in biological carbon exchange are the heterotrophs (especially the primary consumers, largely herbivores). Heterotrophs acquire the high-energy carbon compounds from the autotrophs by consuming them and breaking them down by respiration to obtain cellular energy, such as ATP. The most efficient type of respiration, aerobic respiration, requires oxygen obtained from the atmosphere or dissolved in water. Thus, there is a constant exchange of oxygen and carbon dioxide between the autotrophs (which need the carbon) and the heterotrophs (which need the oxygen). Autotrophs also respire and consume the organic molecules they form: using oxygen and releasing carbon dioxide. They release more oxygen gas as a waste product of photosynthesis than they use for their own respiration; therefore, there is excess available for the respiration of other aerobic organisms. Gas exchange through the atmosphere and water is one way that the carbon cycle connects all living organisms on Earth.
The Biogeochemical Carbon Cycle
The movement of carbon through land, water, and air is complex, and, in many cases, it occurs much more slowly geologically than the movement between living organisms. Carbon is stored for long periods in what are known as carbon reservoirs, which include the atmosphere, bodies of liquid water (mostly oceans), ocean sediment, soil, rocks (including fossil fuels), and Earth’s interior.
As stated, the atmosphere is a major reservoir of carbon in the form of carbon dioxide that is essential to the process of photosynthesis. The level of carbon dioxide in the atmosphere is greatly influenced by the reservoir of carbon in the oceans. The exchange of carbon between the atmosphere and water reservoirs influences how much carbon is found in each, and each one affects the other reciprocally. Carbon dioxide (CO 2 ) from the atmosphere dissolves in water and, unlike oxygen and nitrogen gas, reacts with water molecules to form ionic compounds. Some of these ions combine with calcium ions in the seawater to form calcium carbonate (CaCO 3 ), a major component of the shells of marine organisms. These organisms eventually form sediments on the ocean floor. Over geologic time, the calcium carbonate forms limestone, which comprises the largest carbon reservoir on Earth.
On land, carbon is stored in soil as organic carbon as a result of the decomposition of living organisms or from weathering of terrestrial rock and minerals. Deeper under the ground, at land and at sea, are fossil fuels, the anaerobically decomposed remains of plants that take millions of years to form. Fossil fuels are considered a non-renewable resource because their use far exceeds their rate of formation. A non-renewable resource is either regenerated very slowly or not at all. Another way for carbon to enter the atmosphere is from land (including land beneath the surface of the ocean) by the eruption of volcanoes and other geothermal systems. Carbon sediments from the ocean floor are taken deep within Earth by the process of subduction: the movement of one tectonic plate beneath another. Carbon is released as carbon dioxide when a volcano erupts or from volcanic hydrothermal vents.
Carbon dioxide is also added to the atmosphere by the animal husbandry practices of humans. The large number of land animals raised to feed Earth’s growing human population results in increased carbon-dioxide levels in the atmosphere caused by their respiration. This is another example of how human activity indirectly affects biogeochemical cycles in a significant way. Although much of the debate about the future effects of increasing atmospheric carbon on climate change focuses on fossils fuels, scientists take natural processes, such as volcanoes, plant growth, soil carbon levels, and respiration, into account as they model and predict the future impact of this increase.
The Nitrogen Cycle
Getting nitrogen into the living world is difficult. Plants and phytoplankton are not equipped to incorporate nitrogen from the atmosphere (which exists as tightly bonded, triple covalent N 2 ) even though this molecule comprises approximately 78 percent of the atmosphere. Nitrogen enters the living world via free-living and symbiotic bacteria, which incorporate nitrogen into their macromolecules through nitrogen fixation (conversion of N 2 ). Cyanobacteria live in most aquatic ecosystems where sunlight is present; they play a key role in nitrogen fixation. Cyanobacteria are able to use inorganic sources of nitrogen to “fix” nitrogen. Rhizobium bacteria live symbiotically in the root nodules of legumes (such as peas, beans, and peanuts) and provide them with the organic nitrogen they need. Free-living bacteria, such as Azotobacter , are also important nitrogen fixers.
Organic nitrogen is especially important to the study of ecosystem dynamics since many ecosystem processes, such as primary production and decomposition, are limited by the available supply of nitrogen. As shown in Figure \(\PageIndex{4}\), the nitrogen that enters living systems by nitrogen fixation is eventually converted from organic nitrogen back into nitrogen gas by bacteria. This process occurs in three steps in terrestrial systems: ammonification, nitrification, and denitrification. First, the ammonification process converts nitrogenous waste from living animals or from the remains of dead animals into ammonium (NH 4 + ) by certain bacteria and fungi. Second, this ammonium is then converted to nitrites (NO 2 − ) by nitrifying bacteria, such as Nitrosomonas , through nitrification. Subsequently, nitrites are converted to nitrates (NO 3 − ) by similar organisms. Lastly, the process of denitrification occurs, whereby bacteria, such as Pseudomonas and Clostridium , convert the nitrates into nitrogen gas, thus allowing it to re-enter the atmosphere.
ART CONNECTION
Which of the following statements about the nitrogen cycle is false?
- Ammonification converts organic nitrogenous matter from living organisms into ammonium (NH 4 + ).
- Denitrification by bacteria converts nitrates (NO 3 − ) to nitrogen gas (N 2 ).
- Nitrification by bacteria converts nitrates (NO 3 − ) to nitrites (NO 2 − ).
- Nitrogen fixing bacteria convert nitrogen gas (N 2 ) into organic compounds.
Human activity can release nitrogen into the environment by two primary means: the combustion of fossil fuels, which releases different nitrogen oxides, and by the use of artificial fertilizers (which contain nitrogen and phosphorus compounds) in agriculture, which are then washed into lakes, streams, and rivers by surface runoff. Atmospheric nitrogen (other than N 2 ) is associated with several effects on Earth’s ecosystems including the production of acid rain (as nitric acid, HNO 3 ) and greenhouse gas effects (as nitrous oxide, N 2 O ), potentially causing climate change. A major effect from fertilizer runoff is saltwater and freshwater eutrophication, a process whereby nutrient runoff causes the overgrowth of algae and a number of consequential problems.
A similar process occurs in the marine nitrogen cycle, where the ammonification, nitrification, and denitrification processes are performed by marine bacteria and archaea. Some of this nitrogen falls to the ocean floor as sediment, which can then be moved to land in geologic time by uplift of Earth’s surface, and thereby incorporated into terrestrial rock. Although the movement of nitrogen from rock directly into living systems has been traditionally seen as insignificant compared with nitrogen fixed from the atmosphere, a recent study showed that this process may indeed be significant and should be included in any study of the global nitrogen cycle. 1
The Phosphorus Cycle
Phosphorus is an essential nutrient for living processes; it is a major component of nucleic acids and phospholipids, and, as calcium phosphate, makes up the supportive components of our bones. Phosphorus is often the limiting nutrient (necessary for growth) in aquatic, particularly freshwater, ecosystems.
Phosphorus occurs in nature as the phosphate ion (PO 4 3 - ). In addition to phosphate runoff as a result of human activity, natural surface runoff occurs when it is leached from phosphate-containing rock by weathering, thus sending phosphates into rivers, lakes, and the ocean. This rock has its origins in the ocean. Phosphate-containing ocean sediments form primarily from the bodies of ocean organisms and from their excretions. However, volcanic ash, aerosols, and mineral dust may also be significant phosphate sources. This sediment then is moved to land over geologic time by the uplifting of Earth’s surface. (Figure \(\PageIndex{5}\))
Phosphorus is also reciprocally exchanged between phosphate dissolved in the ocean and marine organisms. The movement of phosphate from the ocean to the land and through the soil is extremely slow, with the average phosphate ion having an oceanic residence time between 20,000 and 100,000 years.
Excess phosphorus and nitrogen that enter these ecosystems from fertilizer runoff and from sewage cause excessive growth of algae. The subsequent death and decay of these organisms depletes dissolved oxygen, which leads to the death of aquatic organisms, such as shellfish and finfish. This process is responsible for dead zones in lakes and at the mouths of many major rivers and for massive fish kills, which often occur during the summer months (see Figure \(\PageIndex{6}\)).
A dead zone is an area in lakes and oceans near the mouths of rivers where large areas are periodically depleted of their normal flora and fauna; these zones can be caused by eutrophication, oil spills, dumping toxic chemicals, and other human activities. The number of dead zones has increased for several years, and more than 400 of these zones were present as of 2008. One of the worst dead zones is off the coast of the United States in the Gulf of Mexico: fertilizer runoff from the Mississippi River basin created a dead zone of over 8,463 square miles. Phosphate and nitrate runoff from fertilizers also negatively affect several lake and bay ecosystems including the Chesapeake Bay in the eastern United States.
CAREERS IN ACTION: Chesapeake Bay
The Chesapeake Bay (Figure \(\PageIndex{7}\) a ) is one of the most scenic areas on Earth; it is now in distress and is recognized as a case study of a declining ecosystem. In the 1970s, the Chesapeake Bay was one of the first aquatic ecosystems to have identified dead zones, which continue to kill many fish and bottom-dwelling species such as clams, oysters, and worms. Several species have declined in the Chesapeake Bay because surface water runoff contains excess nutrients from artificial fertilizer use on land. The source of the fertilizers (with high nitrogen and phosphate content) is not limited to agricultural practices. There are many nearby urban areas and more than 150 rivers and streams empty into the bay that are carrying fertilizer runoff from lawns and gardens. Thus, the decline of the Chesapeake Bay is a complex issue and requires the cooperation of industry, agriculture, and individual homeowners.
Of particular interest to conservationists is the oyster population (Figure \(\PageIndex{7}\) b ); it is estimated that more than 200,000 acres of oyster reefs existed in the bay in the 1700s, but that number has now declined to only 36,000 acres. Oyster harvesting was once a major industry for Chesapeake Bay, but it declined 88 percent between 1982 and 2007. This decline was caused not only by fertilizer runoff and dead zones, but also because of overharvesting. Oysters require a certain minimum population density because they must be in close proximity to reproduce. Human activity has altered the oyster population and locations, thus greatly disrupting the ecosystem.
The restoration of the oyster population in the Chesapeake Bay has been ongoing for several years with mixed success. Not only do many people find oysters good to eat, but the oysters also clean up the bay. They are filter feeders, and as they eat, they clean the water around them. Filter feeders eat by pumping a continuous stream of water over finely divided appendages (gills in the case of oysters) and capturing prokaryotes, plankton, and fine organic particles in their mucus. In the 1700s, it was estimated that it took only a few days for the oyster population to filter the entire volume of the bay. Today, with the changed water conditions, it is estimated that the present population would take nearly a year to do the same job.
Restoration efforts have been ongoing for several years by non-profit organizations such as the Chesapeake Bay Foundation. The restoration goal is to find a way to increase population density so the oysters can reproduce more efficiently. Many disease-resistant varieties (developed at the Virginia Institute of Marine Science for the College of William and Mary) are now available and have been used in the construction of experimental oyster reefs. Efforts by Virginia and Delaware to clean and restore the bay have been hampered because much of the pollution entering the bay comes from other states, which emphasizes the need for interstate cooperation to gain successful restoration.
The new, hearty oyster strains have also spawned a new and economically viable industry—oyster aquaculture—which not only supplies oysters for food and profit, but also has the added benefit of cleaning the bay.
The Sulfur Cycle
Sulfur is an essential element for the macromolecules of living things. As part of the amino acid cysteine, it is involved in the formation of proteins. As shown in Figure \(\PageIndex{8}\), sulfur cycles between the oceans, land, and atmosphere. Atmospheric sulfur is found in the form of sulfur dioxide (SO 2 ), which enters the atmosphere in three ways: first, from the decomposition of organic molecules; second, from volcanic activity and geothermal vents; and, third, from the burning of fossil fuels by humans.
On land, sulfur is deposited in four major ways: precipitation, direct fallout from the atmosphere, rock weathering, and geothermal vents (Figure \(\PageIndex{9}\)). Atmospheric sulfur is found in the form of sulfur dioxide (SO 2 ), and as rain falls through the atmosphere, sulfur is dissolved in the form of weak sulfuric acid (H 2 SO 4 ). Sulfur can also fall directly from the atmosphere in a process called fallout. Also, as sulfur-containing rocks weather, sulfur is released into the soil. These rocks originate from ocean sediments that are moved to land by the geologic uplifting of ocean sediments. Terrestrial ecosystems can then make use of these soil sulfates (SO 4 2 - ), which enter the food web by being taken up by plant roots. When these plants decompose and die, sulfur is released back into the atmosphere as hydrogen sulfide (H 2 S) gas.
Sulfur enters the ocean in runoff from land, from atmospheric fallout, and from underwater geothermal vents. Some ecosystems rely on chemoautotrophs using sulfur as a biological energy source. This sulfur then supports marine ecosystems in the form of sulfates.
Human activities have played a major role in altering the balance of the global sulfur cycle. The burning of large quantities of fossil fuels, especially from coal, releases larger amounts of hydrogen sulfide gas into the atmosphere. As rain falls through this gas, it creates the phenomenon known as acid rain, which damages the natural environment by lowering the pH of lakes, thus killing many of the resident plants and animals. Acid rain is corrosive rain caused by rainwater falling to the ground through sulfur dioxide gas, turning it into weak sulfuric acid, which causes damage to aquatic ecosystems. Acid rain also affects the man-made environment through the chemical degradation of buildings. For example, many marble monuments, such as the Lincoln Memorial in Washington, DC, have suffered significant damage from acid rain over the years. These examples show the wide-ranging effects of human activities on our environment and the challenges that remain for our future.
Art Connections
Figure \(\PageIndex{4}\): Which of the following statements about the nitrogen cycle is false?
A. Ammonification converts organic nitrogenous matter from living organisms into ammonium (NH
4
+
).
B. Denitrification by bacteria converts nitrates (NO
3
-
) to nitrogen gas (N
2
).
C. Nitrification by bacteria converts nitrates (NO
3
-
) to nitrites (NO
2
-
).
D. Nitrogen fixing bacteria convert nitrogen gas (N
2
) into organic compounds.
- Answer
-
C: Nitrification by bacteria converts nitrates (NO 3 - ) to nitrites (NO 2 - ).
Footnotes
- 1 Scott L. Morford, Benjamin Z. Houlton, and Randy A. Dahlgren, “Increased Forest Ecosystem Carbon and Nitrogen Storage from Nitrogen Rich Bedrock,” Nature 477, no. 7362 (2011): 78–81.
Contributors and Attributions
Remixed and/or curated from the following works:
Fowler, S., Roush, R., & Wise, J. (2013). 20.2 Biogeochemical Cycles . In Concepts of Biology . OpenStax (CC BY 4.0; Access for free at https://openstax.org/books/concepts-biology/pages/1-introduction ).


1.6: Auxiliary Views
When an object has a slanted or inclined surface, it usually is not possible to show the inclined surface in an orthographic drawing without distortion. To present a more accurate description of any inclined surface, an additional view, known as an auxiliary view, is usually required.
An auxiliary view is simply a “helper” view, which shows the slanted part of the object as it actually is. It turns, or projects, the. object so that the true size and shape of the surf ace (or surfaces) are seen as they actually are.
Auxiliary views are commonly found on many types of industrial drawings.
Front View Auxiliaries
There are three basic type of auxiliary views. In the first type, the auxiliary view is projected from the front view of a three view (orthographic) drawing. In the second and third types of drawings, the auxiliary views are projected from the top and side views.
Here is a front view auxiliary of a simple object with an inclined surface.
Notice that the projection lines are perpendicular to the slanted surface of the first view, and that only the slanted surface of the object is shown in the auxiliary view. · The rest of the object is omitted, however, for clarification portions of the adjacent· surfaces are sometimes shown. Also, notice that the slanted surfaces of the top and side views are shortened because of distortion, whereas the surface of the auxiliary view is true, or actual size.
To sketch an auxiliary view, you begin with orthographic. views of the object and add projection lines perpendicular (90 ◦ ) to the slanted surface, adding a reference line any convenient distance from the view with the slanted surface.
Next, the distance CB on the auxiliary view is made the same length as the related distance in one of the orthographic views; in this example it’s the side view. This completes the auxiliary view.
Top View Auxiliaries
A top view auxiliary is developed in the same way as a front view auxiliary, except that the auxiliary is projected from the top view.
Whether the auxiliary view is to be projected from the front, top, or side view depends on the position of the object, or which surface of the object is slanted. In this example, the top view is slanted. Therefore the auxiliary view must be projected from the top view.
Again, notice how the angled surfaces shown in the front and side views are not shown in true length.
Side View Auxiliary
Side view auxiliaries are drawn in the same way as front and top view auxiliaries. Again, where the auxiliary view is to be projected depends upon the position of the object or which surface of the object is slanted.
Obviously, these are very basic auxiliary view examples and are presented to introduce you to the concept of auxiliary views.
As objects with inclined surfaces become more complex, auxiliary views provide a means of presenting objects in their true size and shape.
Sketching Auxiliary Views
The following problems require and auxiliary view to be complete. Sketch the auxiliary views required in the spaces provided.
Drawing practice 1
Drawing practice 2
In this problem, a round hole is centered on the slanted surface and drilled through the object. The hole appears elliptical in the. front and side views because of distortion. It will appear in its true shape on the auxiliary view. Remember that the auxiliary is developed from the view with the slanted surface. Complete the auxiliary view.
Drawing practice 3
In this problem, a square hole has been cut part way into the object. Complete the auxiliary view.
Quiz
Directions: Complete the auxiliary view in the space provided.


8.4: Concentration of solutions
The concentration of a solution tells the amount of solute dissolved in a given amount of solution.
Making a solution of know concentration
A measured amount of solute is dissolved in enough solvent to make the desired volume of the solution, as illustrated in Fig. 5.4.1. The concentration of the solution can be expressed in different ways using mass, volume, or mole units, as explained in the following.
Concentration in percent (%)
Percentage (%) is a number or ratio that represent a fraction of 100.
For example, 5% means 5:100, where 5 is the part, and 100 is the total. The percentage is calculated as a hundred times of part by total, i.e.,
\begin{equation}
\text { Percentage }(\%)=\frac{\text { part }}{\text { Total }} \times 100 .\nonumber
\end{equation}
A 50.0 g NaCl is dissolved in water to make a 500 g solution. What is the percentage of NaCl in the solution?
Solution
Given part = 50.0 g NaCl, and total = 500 g solution. Desired: %NaCl in the solution?
Formula: \(\text { Percentage }(\%)=\frac{\text { part }}{\text { Total }} \times 100 \text {. }\nonumber\)
Calculations: \(\text { Percentage }(\%)=\frac{50.0 cancel{\mathrm{~g}}}{500 cancel{\mathrm{~g}}} \times 100=10.0 ~\% \mathrm{NaCl}\)
The units cancel in the fraction calculation part, and a % sign is added to the answer to tell that it is a fraction out of a hundred.
Mass percent (m/m)% concentration
The mass percent concentration expresses the mass units of solute in a hundred mass units of the solution.
\begin{equation}
\operatorname{Mass}(\%)=\frac{\text { mass of solute }(g)}{\text { mass of solute }(g)+\text { mass of solvent }(g)} \times 100=\frac{\text { mass of solute }(g)}{\text { mass of solution }(g)} \times 100\nonumber
\end{equation}
Note that the total is solute and solvent added together, i.e., solution.
What is the mass % of NaOH in a solution prepared by dissolving 10.0 g NaOH in 100 g water?
Solution
Given solute = 10.0 g, and solvent = 100 g, Desired: Mass% NaOH?
Formula: \(\text { Mass }(\%)=\frac{\text { mass of solute }(g)}{\text { mass of solute }(g)+\text { mass of solvent }(g)} \times 100\)
Calculations: \(\text { Mass }(\%)=\frac{10.0 \mathrm{~g} \mathrm{NaOH}}{(10.0 \mathrm{~g}+100 \mathrm{~g}) \text { solution }} \times 100=9.09 \% \mathrm{NaOH}\)
Note that the mass% concentration and its reciprocal are two conversion factor: \(\frac{\text { given } g \text { solute }}{100 g \text { solution }}\) and \(\frac{100 g \text { solution }}{\text { given g solute }}\)
Neosporin antibiotic is a 3.5% m/m neomycin solution. How many grams of neomycin are in 50 g of ointment?
Solution
Given: \(3.5 \% \text { neomycin }=\frac{3.5 \mathrm{~g} \text { neomycin }}{100 \mathrm{~g} \text { solution }}\), and Solution amount = 50 g, Desired: ? g neomycin
Calculations: \[50 \cancel{\mathrm{~g} \text { solution }} \times \frac{3.5 \mathrm{~g} \text { neomycin }}{100 \cancel{\mathrm{~g} \text { solution }}}=1.8 \mathrm{~g} \text { neomycin. }\nonumber\]
Volume percent (v/v)% concentration
The volume percent concentration expresses the volume units of solute in a hundred volume units of the solution.
The mathematical form of the v/v % is:
\begin{equation}
\text { Volume }(\%)=\frac{\text { volume of solute }(\mathrm{mL})}{\text { volume of solution }(\mathrm{mL})} \times 100\nonumber
\end{equation}
Fig. 5.4.2 shows the volume percent concentration ranges of different classes of fragrances.
What is the volume % of rose extract in a solution prepared by dissolving 14.0 mL rose extract in a solvent to make 200 mL of solution?
Solution
Given: Solute = 14.0 g, and solution = 200 g, Desired: Volume% rose solution?
Formula: \begin{equation}
\text { Volume }(\%)=\frac{\text { volume of solute }(m L)}{\text { volume of solution }(m L)} \times 100\nonumber
\end{equation}
Calculations: \begin{equation}
\text { Volume }(\%)=\frac{14 \mathrm{~mL} \text { rose extract }}{200 \mathrm{~mL} \text { solution }} \times 100=7.0 \% \text { rose solution }\nonumber
\end{equation}
The two conversion factors for v/v % concentration are: \begin{equation}
\frac{\text { given mL solute }}{100 \mathrm{~mL} \text { solution }} \quad\text {, and }\quad \frac{100 \mathrm{~mL} \text { solution }}{\text { given } \mathrm{~mL} \text { solute }}\nonumber
\end{equation}
What is the volume of bromine (Br 2 ) in 250 mL of 4.8% v/v of Br 2 solution in carbon tetrachloride?
Solution
Given: Concentration 4.8% v/v bromine \(=\frac{4.8 ~m L \text { bromine }}{100 ~m L \text { solution }}\), volume of solution = 250 mL, Desired: Volume of solute, i.e., ? mL bromine.
Calculations: \[
250 \mathrm{~mL} \text { solution } \times \frac{4.8 \mathrm{~mL} \text { bromine }}{100 \mathrm{~mL} \text { solution} .}=12 \mathrm{~mL ~bromine} \text {. }\nonumber\]
Mass/volume percent (m/v)% concentration
The mass/volume percent concentration expresses the mass units of solute in a hundred volume units of solution.
Mathematical form of m/v % is:
\begin{equation}
\text { Mass/volume }(\%)=\frac{\text { mass of solute }(g)}{\text { volume of solution }(m L)} \times 100\nonumber
\end{equation}
What is the mass/volume % of glucose solution prepared by dissolving 50 g glucose in enough water to make 1000 mL of solution?
Solution
Given: Solute = 50.0 g, and Solution = 1000 mL, Desired: Mass/volume % glucose solution?
Formula: \begin{equation}
\text { Mass/volume }(\%)=\frac{\text { mass of solute }(g)}{\text { volume of solution }(m L)} \times 100\nonumber
\end{equation}
Calculations: \begin{equation}
\frac{\text { Mass }}{\text { volume }}(\%)=\frac{50 \mathrm{~g} \text { glucose }}{1000 \mathrm{~mL} \text { solution }} \times 100=5.0 \% \text { glucose solution by } \frac{\mathrm{m}}{\mathrm{v}} .\nonumber
\end{equation}
The two conversion factors from ms/v % concentration are: \begin{equation}
\frac{\text { given } g \text { solute }}{100 \mathrm{~mL} \text { solution }}\quad \text { and }\quad \frac{100 \mathrm{~mL} \text { solution }}{\text { given } \mathrm{g} \text { solute }}\nonumber
\end{equation}
How many grams of clindamycin antibiotics are in a 45 mL capsule of the 1.0% (m/v) clindamycin?
Solution
Given: % m/v concentration: 1.08 % m/v clindamycin \(=\frac{1.0 \mathrm{~g} \text { clindamycin }}{100 \mathrm{~mL} \text { solution }}\), and volume of solution = 45 mL, Desired: ? g clindamycin?
Calculations: \begin{equation}
45 \text { mL solution } \times \frac{1.0 \mathrm{~g} \text { clindamycin }}{100 \mathrm{~mL} \text { solution }}=4.5 \mathrm{~g} \text { clindamycin. }\nonumber
\end{equation}
Parts per million (ppm) and parts per billion (ppb) concentration
Parts per million (ppm) is a number or ratio expressed as a fraction of a million (10 6 ).
For example, 2 ppm means \(\frac{2}{1,000,000}\) or 2:1,000,000, where 2 is the part, and 1,000,000 is the total. The concentration in ppm is calculated as a million times of part by total, i.e.: \begin{equation}
\text { Concentration in ppm }=\frac{p a r t}{\text { Total }} \times 10^{6}\nonumber
\end{equation}
Parts per billion (ppb) is a number or ratio expressed as a fraction of billion (10 9 ).
That is: \begin{equation}
\text { Concentration in ppb }=\frac{\text { part }}{\text { Total }} \times 10^{9}\nonumber
\end{equation}
Like percentage concentration, the ppm and ppb can be mass/mass (m/m), volume/volume (v/v) or mass/volume (m/v).
EPA’s action limit for copper is 1.3 mg/L in drinking water. What is this limit in ppm of copper m/v in the drinking water?
Solution
Given: 1.3 mg copper in 1L solution, Desired: ? ppm m/v of Copper in water
Formula: \(\text { Concentration in ppm }=\frac{\operatorname{solute}(\mathrm{~g})}{\operatorname{solution}(\mathrm{~mL})} \times 10^{6}\)
Calculations: First, convert the given units of mass and volume into the corresponding units that the formula takes, then plug the values in the formula and calculate.
\[\text { Solute }=1.3 \mathrm{~mg} \times \frac{1 \mathrm{~g}}{1000 \mathrm{~mg}}=0.0013 \mathrm{~g}\nonumber\]
\[\text { Solution }=1 \mathrm{~L} \times \frac{1000 \mathrm{~mL}}{1 \mathrm{~L}}=1000 \mathrm{~mL}\nonumber\]
\[\text { Concentration in ppm }=\frac{0.0013 \mathrm{~g}}{1000 \mathrm{~mL}} \times 10^{6}=1.3 \mathrm{~ppm} \text { copper } v / \mathrm{m}\nonumber\]
EPA’s action limit for lead is 0.015 mg/L in drinking water. What is this limit in ppb of lead m/v in the drinking water?
Solution
Given: 0.015 mg in 1L solution, Desired: ? ppb m/v of Lead in water
Formula: \(\text { Concentration in ppb }=\frac{\operatorname{solute}(g)}{\operatorname{solution}(\mathrm{mL})} \times 10^{9}\)
Calculations: First, convert the given units of mass and volume into the corresponding units that the formula takes, then plug the values in the formula and calculate.
\[\text { Solute }=0.015 \mathrm{~mg} \times \frac{1 \mathrm{~g}}{1000 \mathrm{~mg}}=0.000015 \mathrm{~g}\nonumber\]
\[\text { Solution }=1 \mathrm{~L} \times \frac{1000 \mathrm{~mL}}{1 \mathrm{~L}}=1000 \mathrm{~mL}\nonumber\]
\[\text { Concentration in ppb }=\frac{0.000015 \mathrm{~g}}{1000 \mathrm{~mL}} \times 10^{9}=15 \mathrm{~ppb} \text { lead } \mathrm{v} / \mathrm{m}\nonumber\]
Molarity
Molarity (M) expresses the moles of solute in a liter of solution.
The most common solution concentration unit used in chemistry is molarity (M):
\[\operatorname{Molarity}~({M})=\frac{n~(\text {moles of solute })}{V ~\text { (Litters of solution })}\nonumber\]
What is the molarity (M) of a solution prepared by dissolving 50.0 g NaOH in enough water to make 250 mL solution?
Solution
Given: Solute = 50.0 g NaOH, Volume of solution = 250 mL, Desired: ? M NaOH solution?
Formula: \(\text { Molarity }(M)=\frac{n~(\text {moles of solute })}{V~(\text {Litters of solution })}\)
Calculations: First, convert the given units of mass and volume into the corresponding units that the formula takes, then plug the values in the formula and calculate.
\[\text { Solute }=50.0 \mathrm{~g} \mathrm{~NaOH} \times \frac{1 \mathrm{~mol} \mathrm{~NaOH}}{40.00 \mathrm{~g} \mathrm{~NaOH}}=1.25 \mathrm{~mol} \mathrm{~NaOH}\nonumber\]
\[\text { Solution }=250 \mathrm{~mL} \times \frac{1 \mathrm{~L}}{1000 \mathrm{~mL}}=0.250 \mathrm{~L}\nonumber\]
\[\text { Molarity }(M)=\frac{1.25 \mathrm{~mol} \mathrm{~NaOH}}{0.250 \mathrm{~L} \mathrm{~solution}}=5.00 \mathrm{~M} \mathrm{~NaOH}\nonumber\]
The two conversion factor from molarity are the following:
\[\frac{n \text { (moles of solute) }}{V \text { (Litters of solution) }} \quad\text { and }\quad \frac{V \text { (Litters of solution) }}{n \text { (moles of solute })}\nonumber\]
How many litters of 0.211 M HCl solution are needed to provide 0.400 mol of HCl?
Solution
Given: amount of solute = 0.400 mol HCl, Concentration of solute = 0.211M = \(\frac{0.211 \text { mol HCl}}{1 L \text { solution }}\)
Calculations: \[\text { Liters of solution needed }=0.400 \mathrm{~mol} \mathrm{~HCl} \times \frac{1 \mathrm{~L} \text { soluton }}{0.211 \mathrm{~mol} \mathrm{~HCl}}=1.90 \mathrm{~L} \text { solution }\nonumber\]
A 2.50 L of 1.12 M NaOH solution contains how many moles of NaOH?
Solution
Given: Volume of solution = 2.50 L solution, concentration of solution = \(1.12 \mathrm{~M} \mathrm{~NaOH}=\frac{1.12 \mathrm{~mol} \mathrm{~NaOH}}{1 \mathrm{~L} \text { solution }}\), Desired: ? moles of NaOH?
Calculations: \[\text { Moles of } \mathrm{~NaOH} \text { in the solution }=2.50 \text { L solution } \times \frac{1.12 \mathrm{~mol} \mathrm{~NaOH}}{1 \mathrm{~L} \text { solution }}=2.80 \mathrm{~mol} \mathrm{} \mathrm{~NaOH}\nonumber\]
Dilution of solutions
Dilution of a solution is the addition of a solvent to decrease the solute concentration of the solute in the solution.
The product of concentration (C) and volume (V) is the amount of solute, i.e.,
\begin{equation}
\text { Amount of solute }=C \text { in } \frac{\text { amount of solute }}{\text { volume of solution }} \times V \text { in volume of solution. }\nonumber
\end{equation}
The amount of solute does not change by adding solvent. Therefore, the product of concentration and volume, i.e., CV, which is the amount of solute, is a constant, i.e.,
\begin{equation}
C_{1} V_{1}=C_{2} V_{2}=\text { amount of solute }\nonumber
\end{equation}
Fig. 5.4.3 shows that if the initial concentration is C 1 , the initial volume is V 1, and after dilution, the final concentration is C 2 , the final volume is V 2 , then C 1 V 1 = C 2 V 2 = amount of solute that is constant. If three of the four variables in this equation are known, the missing one can be calculated, as explained in the following example.
Keep in mind that the concentrations and volumes should be in the same units on both sides of the equation: C 1 V 1 = C 2 V 2 . If they are not in the same units, convert them to the same units before plunging them in the formula.
how much volume of 11.3 M HCl is needed to prepare 250 mL of 2.00 M HCl?
Solution
Given: C 1 = 11.3 M HCl, C 2 = 2.00 M HCl, V 2 = 250 mL solution, Desired V 1 = ?
Formula: C 1 V 1 = C 2 V 2 , rearrange it to isolate the desired parameter: \(V_{1}=\frac{C_{2} V_{2}}{C_{1}}\)
Calculations: \[V_{1}=\frac{C_{2} V_{2}}{C_{1}}=\frac{2.00 \mathrm{~M~HCl} \times 250 \mathrm{~mL} \text { solution }}{11.3 \mathrm{~M} \mathrm{~HCl}}=44.2 \mathrm{~mL} \text { solution }\nonumber\]
what is the molarity of the NaOH solution prepared by diluting 100 mL of 0.521 M NaOH solution to 500 mL?
Solution
Given C 1 = 0.521 M NaOH, V 1 = 100 mL solution, V 2 = 500 mL solution, Desired: Concentration of the final solution C 2 = ? M NaOH
Formula: C 1 V 1 = C 2 V 2 , rearrange to isolate the desired parameter: \(C_{2}=\frac{C_{1} V_{1}}{V_{2}}\)
Calculations: \[C_{2}=\frac{C_{1} V_{1}}{V_{2}} = \frac{0.521 \mathrm{~M~NaOH} \times 100 \mathrm{~mL} \mathrm{~NaOH}}{500 \mathrm{~mL} \mathrm{~NaOH}}=0.104 \mathrm{~M~NaOH}\nonumber\]
Dopamine is administered intravenously to a patient to increase blood pressure. How many milliliters (mL) of a 4.0% (m/v) dopamine solution is needed to prepare 250 mL of a 0.030% m/v) solution?
Solution
Given: C 1 = 4.0% (m/v), C 2 = 0.030% (m/v), V 2 = 250 mL solution, Desired V 1 = ?
Formula: C 1 V 1 = C 2 V 2 , rearrange to isolate the desired parameter: \(V_{1}=\frac{C_{2} V_{2}}{C_{1}}\)
Calculations: \[V_{1}=\frac{C_{2} V_{2}}{C_{1}}=\frac{0.030 \% \times 250 \mathrm{~mL} \text { solution }}{4.0 \%}=5.0 \mathrm{~mL} \text { of solution }\nonumber\]
Logarithmic dilution
Take a unit volume of a given solution and add enough solvent to increase the volume of the solution 10 times for a logarithmic diluiton.
A logarithmic dilution is ten times dilution, i.e., proven by the following formula: \[C_{2}=\frac{C_{1} V_{1}}{V_{2}}=\frac{1 \mathrm{~mL} \times C_{1}}{10 \mathrm{~mL}}=0.1 \times C_{1}\nonumber\]
Repeating the above step with the diluted solution results in 10x10 = 100-time dilution, and repeating third-time results in 10x10x10 = 1000-time dilution. This dilution of 10 times in each step is called logarithmic dilution. Fig. 5.4.4 shows that five steps of logarithmic dilution on a 10% initial solution results in a concentration of 10 ppm in the final solution.


6.2: Review of the Central Nervous System
To understand how psychotropic medications work, it is important to understand the anatomy and physiology of the central nervous system. The nervous system is divided into the central and peripheral nervous systems. The central nervous system (CNS) is the brain and spinal cord, and the peripheral nervous system includes everything else in the nervous system. See Figure 6.1 [1] for an illustration of the central and peripheral nervous systems.
The peripheral nervous system consists of sensory neurons and motor neurons. Sensory neurons sense the environment and conduct signals to the brain that become a person’s conscious perception of that stimulus. This conscious perception may lead to a motor response that is conducted from the brain to the peripheral nervous system via motor neurons. Motor neurons are part of the somatic nervous system that stimulates voluntary movement of muscles and the autonomic nervous system that controls involuntary responses.
Sympathetic and Parasympathetic Nervous System
The autonomic nervous system is divided into the sympathetic nervous system (SNS) and the parasympathetic nervous system (PNS). Homeostatic mechanisms are regulated by the body through a balance of SNS and PNS stimulation. For example, stimulation of SNS receptors increases the heart rate, increases blood pressure via the constriction of blood vessels, and causes bronchodilation, whereas stimulation of the PNS slows the heart, lowers blood pressure due to vasodilation, and causes bronchoconstriction. Due to these effects, the SNS is associated with the “fight-or-flight” response, and the PNS is often referred to as the “rest and digest” system. See Figure 6.2 [2] to compare the effects of PNS and SNS stimulation on target organs.
SNS Receptors
SNS receptors include Alpha-1, Alpha-2, Beta-1, and Beta-2 receptors that are stimulated by epinephrine and norepinephrine. Medications that stimulate these receptors are referred to as adrenergic agonists because they mimic the effects of the body’s natural SNS stimulation. For example, stimulants like methylphenidate are adrenergic agonists used to treat attention deficit hyperactivity disorder (ADHD). Conversely, adrenergic antagonists block SNS receptors. For example, propranolol is a Beta-2 antagonist used to treat the physical symptoms of severe anxiety (e.g., trembling, rapid heartbeat, and sweating).
PNS Receptors
PNS receptors include nicotinic and muscarinic receptors that are stimulated by acetylcholine (ACh). Drugs that stimulate nicotinic and muscarinic receptors are called cholinergics . For example, nicotine in tobacco products stimulates nicotinic receptors. Stimulation of muscarinic receptors primarily causes smooth muscle contraction. An example of a muscarinic agonist is bethanechol used to treat urinary retention by increasing the tone of the detrusor muscle to increase bladder emptying. [3] Drugs that block the effects of PNS receptors are called anticholinergics. For example, benztropine is an anticholinergic used to treat muscle spasms associated with extrapyramidal symptoms from antipsychotic medications. [4] Many psychotropic medications cause anticholinergic adverse effects that can be especially hazardous for older adults. SLUDGE is a mnemonic for anticholinergic side effects: Salivation decreased, Lacrimation decreased, Urinary retention, Drowsiness/dizziness, GI upset, and Eyes (blurred vision/dry eyes). See Figure 6.3 [5] for an illustration of the “SLUDGE” effects caused by anticholinergics.
Opioid System
The opioid system in the brain controls pain, reward, and addictive behaviors. There are three types of opioid receptors called mu, delta, and kappa receptors. Opioid receptors are stimulated by endogenous peptides released by neurons (such as endorphins) and exogenous opiates. Opiates include powerful analgesics (such as morphine and oxycodone) prescribed to treat moderate to severe pain. Opiates also include illicit drugs (such as heroin). Chronic use of prescribed and illicit opiates can be highly addictive because of their actions on the reward system of the brain. [6] Read more about the addictive cycle in the “ Substance Use Disorders ” chapter.
Neurotransmitters
Neurotransmitters are chemical substances released at the end of a neuron by the arrival of an electrical impulse. They diffuse across the synapse and cause the transfer of the impulse to another nerve fiber, a muscle fiber, or other structure. Neurotransmitters interact with specific receptors like a key and a lock. See Figure 6.4 [7] for an illustration of neuron communication with neurotransmitters and receptors.
There are several types of neurotransmitters associated with mental health disorders and psychoactive medications, including acetylcholine, glutamate, GABA, glycine, dopamine, serotonin, norepinephrine, and histamine [8] , [9] :
- Acetylcholine: Acetylcholine stimulates nicotinic and muscarinic receptors in the parasympathetic nervous system. Other substances also bind to these receptors. For instance, nicotine (in tobacco products) binds to nicotinic receptors, and muscarine (products of specific mushrooms used as a hallucinogenic) binds to muscarinic receptors.
- Glutamate: Glutamate is an excitatory neurotransmitter. Elevated levels of glutamate are associated with psychosis symptoms that can occur with schizophrenia, as well as with illicit drug use such as methamphetamines. Conversely, lamotrigine, a medication used to treat bipolar disorder, inhibits glutamate.
 Low levels of GABA are associated with seizures, anxiety, mania, and impulse control. Pregabalin is an anticonvulsant that mimics the effects of GABA and is used to treat generalized anxiety disorder.
- Dopamine: Dopamine plays an essential role in several brain functions, including learning, motor control, reward, emotion, and executive functions. It is associated with several mental health disorders and is targeted by many psychotropic medications. For example, bupropion is an antidepressant that inhibits dopamine reuptake, leading to increased dopamine levels in the synapse and relieving the symptoms of depression. Conversely, chlorpromazine blocks dopamine receptors and is used to treat psychosis, but this blockade can cause extrapyramidal side effects (involuntary and uncontrolled muscle movements).
- Serotonin: Serotonin modulates multiple neuropsychological processes such as mood, sleep, libido, and temperature regulation. Abnormal levels of serotonin have been linked to many mental health disorders such as depression, bipolar disorder, and anxiety. Many psychotropic medications target serotonin. For example, fluoxetine belongs to a class of antidepressants called selective serotonin reuptake inhibitors (SSRIs). SSRIs prevent the reuptake of serotonin at the synapse, making more of the chemical available in the brain and relieving depression.
- Norepinephrine and Epinephrine: Norepinephrine and epinephrine stimulate alpha- and beta-receptors in the sympathetic nervous system. Their release exerts effects on a variety of body processes, including stress, sleep, attention, and focus. Many psychotropic medications target these neurotransmitters. For example, venlafaxine belongs to a class of antidepressants called norepinephrine reuptake inhibitors (NRIs). NRIs are prescribed to treat depression by preventing the reuptake of norepinephrine at the synapse and boosting levels of norepinephrine in the brain.
- Histamine: Histamine mediates homeostatic functions in the body, promotes wakefulness, modulates feeding behavior, and controls motivational behavior. For example, diphenhydramine, a histamine antagonist, causes drowsiness and is also used to treat extrapyramidal symptoms.
View a YouTube [10] video called the Receptor Debate that compares the effects of neurotransmitters.
- “ 1201 Overview of Nervous System.jpg” by OpenStax is licensed under CC BY 4.0. Access for free at https://openstax.org/books/anatomy-and-physiology/pages/12-1-basic-structure-and-function-of-the-nervous-system ↵
- “ Updated SNS-PNS image.png ” by Meredith Pomietlo for Open RN is licensed under CC BY 4.0 ↵
- This work is a derivative of StatPearls by Padda and Derian and is licensed under CC BY 4.0 ↵
- This work is a derivative of StatPearls by Ahuja and Abdijadid and is licensed under CC BY 4.0 ↵
- “SLUDGE effects of Anticholinergics” by Dominic Slausen at Chippewa Valley Technical College is licensed under CC BY 4.0 ↵
- This work is a derivative of StatPearls by Dhaliwal and Gupta and is licensed under CC BY 4.0 ↵
- “ Chemical synapse schema cropped.jpg” by Looie496 is licensed under Public Domain. Access for free at https://med.libretexts.org/Bookshelves/Anatomy_and_Physiology/Book%3A_Anatomy_and_Physiology_(Boundless)/10%3A_Overview_of_the_Nervous_System/10.1%3A_Introduction_to_the_Nervous_System/10.1A%3A_Organization_of_the_Nervous_System ↵
- This work is a derivative of Anatomy and Physiology by OpenStax and is licensed under CC BY 4.0 . Access for free at https://openstax.org/books/anatomy-and-physiology/pages/1-introduction ↵
- This work is a derivative of StatPearls by Sheffler, Reddy, and Pillarisetty and is licensed under CC BY 4.0 ↵
- NEI Psychopharm. (2016, November 3). Receptor Debate. [Video]. YouTube. All rights reserved. https://youtu.be/GqX_J5h4aBw ↵


 In the preceding two chapters, we followed the life story of stars, from the process of birth to the brink of death. Now we are ready to explore the ways that stars end their lives. Sooner or later, each star exhausts its store of nuclear energy. Without a source of internal pressure to balance the weight of the overlying layers, every star eventually gives way to the inexorable pull of gravity and collapses under its own weight. Following the rough distinction made in the last chapter, we will discuss the end-of-life evolution of stars of lower and higher mass separately. What determines the outcome—bang or whimper—is the mass of the star when it is ready to die , not the mass it was born with. As we noted in the last chapter, stars can lose a significant amount of mass in their middle and old age.
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- 23.1: The Death of Low-Mass Stars
- During the course of their evolution, stars shed their outer layers and lose a significant fraction of their initial mass. Stars with masses of 8 MSun or less can lose enough mass to become white dwarfs, which have masses less than the Chandrasekhar limit (about 1.4 MSun). The pressure exerted by degenerate electrons keeps white dwarfs from contracting to still-smaller diameters. Eventually, white dwarfs cool off to become black dwarfs, stellar remnants made mainly of carbon, oxygen, and neon.
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- 23.2: Evolution of Massive Stars- An Explosive Finish
- In a massive star, hydrogen fusion in the core is followed by several other fusion reactions involving heavier elements. Just before it exhausts all sources of energy, a massive star has an iron core surrounded by shells of silicon, sulfur, oxygen, neon, carbon, helium, and hydrogen. The fusion of iron requires energy (rather than releasing it). If the mass of a star’s iron core exceeds the Chandrasekhar limit (but is less than 3 MSun), the core collapses until its density exceeds that of an ato
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- 23.3: Supernova Observations
- A supernova occurs on average once every 25 to 100 years in the Milky Way Galaxy. Despite the odds, no supernova in our Galaxy has been observed from Earth since the invention of the telescope. However, one nearby supernova (SN 1987A) has been observed in a neighboring galaxy, the Large Magellanic Cloud. The star that evolved to become SN 1987A began its life as a blue supergiant, evolved to become a red supergiant, and returned to being a blue supergiant at the time it exploded. Studies of SN 1
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- 23.4: Pulsars and the Discovery of Neutron Stars
- At least some supernovae leave behind a highly magnetic, rapidly rotating neutron star, which can be observed as a pulsar if its beam of escaping particles and focused radiation is pointing toward us. Pulsars emit rapid pulses of radiation at regular intervals; their periods are in the range of 0.001 to 10 seconds. The rotating neutron star acts like a lighthouse, sweeping its beam in a circle and giving us a pulse of radiation when the beam sweeps over Earth. As pulsars age, they lose energy, t
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- 23.5: The Evolution of Binary Star Systems
- When a white dwarf or neutron star is a member of a close binary star system, its companion star can transfer mass to it. Material falling gradually onto a white dwarf can explode in a sudden burst of fusion and make a nova. If material falls rapidly onto a white dwarf, it can push it over the Chandrasekhar limit and cause it to explode completely as a type Ia supernova. Another possible mechanism for a type Ia supernova is the merger of two white dwarfs. Material falling onto a neutron star can
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- 23.6: The Mystery of the Gamma-Ray Bursts
- Gamma-ray bursts last from a fraction of a second to a few minutes. They come from all directions and are now known to be associated with very distant objects. The energy is most likely beamed, and, for the ones we can detect, Earth lies in the direction of the beam. Long-duration bursts (lasting more than a few seconds) come from massive stars with their outer hydrogen layers missing that explode as supernovae. Short-duration bursts are believed to be mergers of stellar corpses (neutron stars o
Thumbnail: This remarkable picture of NGC 3603, a nebula in the Milky Way Galaxy, was taken with the Hubble Space Telescope. This image illustrates the life cycle of stars. In the bottom half of the image, we see clouds of dust and gas, where it is likely that star formation will take place in the near future. Near the center, there is a cluster of massive, hot young stars that are only a few million years old. Above and to the right of the cluster, there is an isolated star surrounded by a ring of gas. Perpendicular to the ring and on either side of it, there are two bluish blobs of gas. The ring and the blobs were ejected by the star, which is nearing the end of its life (credit: modification of work by NASA, Wolfgang Brandner (JPL/IPAC), Eva K. Grebel (University of Washington), You-Hua Chu (University of Illinois Urbana-Champaign)).


11.1: Interpersonal Conflict
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In this section, we will define interpersonal conflict and explain the importance of managing it constructively.
Conflict occurs due to real or perceived incompatible goals, scarce resources, or opposing viewpoints. It can be expressed both verbally and/or nonverbally, explicated stated or passively conveyed, and ranges on a continuum from nearly imperceptible (e.g., giving someone the ‘cold shoulder’) to very obvious (e.g., verbally yelling).
Conflict is an inevitable part of close relationships and can take a negative emotional toll. It takes effort to ignore someone or to be passive aggressive, and the negative feelings of anger or guilt we may feel after blowing up at someone are valid. However, conflict isn’t always negative or unproductive. In fact, numerous research studies have shown that the number of conflicts in a relationship is not as important as how the conflict is handled (Markman et al., 1993).
Improving your competence in dealing with conflict can yield positive effects in the real world. Since conflict is inevitable in our personal and professional lives, the ability to manage conflict and negotiate desirable outcomes can help us be more successful. Whether you are trying to decide what brand of flat-screen television to buy with your partner or discussing the upcoming political election with your mother, the potential for conflict is present.
Being able to manage conflict situations can make life more pleasant as opposed to what we may feel if we let a situation stagnate or escalate. Additionally, when conflict is well managed, it has the potential to lead to more rewarding and satisfactory relationships (Canary & Messman, 2000). The negative effects of poorly handled conflict could range from an awkward last few weeks of a semester with a college roommate to violence or divorce.


6.1: Building and Maintaining Positive Relationships with Families
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Honest, caring, understanding, and respectful exchanges with family members lead to their sharing important information with teachers that help to inform how to care and support each child’s learning and development. Taking the time to find out from family members about their child’s unique characteristics and needs plays an important role in providing teachers with the information needed to set up developmentally appropriate learning environments, curriculum, and guidance strategies for individual children in their early learning programs. Establishing positive relationships with families helps to bridge children’s experiences between the program and home, and it fosters children’s sense of belonging in the early education setting.
Teachers view families as children’s first teachers and seek their assessments of a child’s needs, interests, and abilities. Different families and communities have different views and expectations of preschool aged children. The effective early childhood educator recognizes, understands, and respects the values of children’s families and communities and attempts to make the environment as congruent with those values as possible. In high-quality early childhood programs, the teacher speaks frequently with family members and, whenever appropriate, strengthens the links between the home and program. Frequent communication between program staff and family members is important, especially in the case of children with disabilities or other special needs. Through collaboration with families, preschool teachers can gain insight into ways in which they can be important contributors to the child’s learning and development. To support children’s learning across home and school contexts, the program can encourage family participation in activities at the early care and education program. [2]
“Family engagement with schools has been linked to important outcomes for children of all families, including families with children who are dual language learners . . .
Source: State Advisory Council on Early Learning and Care 2013, Paper 4, Family Engagement, 121.
Programs convey an important message to families when they seek their views and collaborate with them in the care of their children. This message helps family members understand that their preferences and their concerns about the learning and development of their child are important to teachers and program leaders. When a teacher has open, honest, and understanding relationships with family members, the resulting links between home and the early care education setting often helps their child feel safe and comfortable.


3.5: The Gaussian Integral
Here’s a famous integral: \[\int_{-\infty}^\infty \; e^{-\gamma x^2} \; dx.\] The integrand is called a Gaussian , or bell curve , and is plotted below. The larger the value of \(\gamma\) , the more narrowly-peaked the curve.
The integral was solved by Gauss in a brilliant way. Let \(I(\gamma)\) denote the value of the integral. Then \(I^2\) is just two independent copies of the integral, multiplied together: \[I^2(\gamma) = \left[\int_{-\infty}^\infty dx\; e^{-\gamma x^2}\right] \times \left[\int_{-\infty}^\infty dy\; e^{-\gamma y^2}\right].\] Note that in the second copy of the integral, we have changed the “dummy” label \(x\) (the integration variable) into \(y\) , to avoid ambiguity.  Next, change from Cartesian to polar coordinates: \[I^2(\gamma) = \int_{0}^\infty dr\, r \int_{0}^{2\pi} d\phi \; e^{-\gamma r^2} = \left[ \int_{0}^\infty dr\, r \, e^{-\gamma r^2}\right] \times \left[\int_{0}^{2\pi} d\phi \right] = \frac{1}{2\gamma} \cdot 2\pi.\] By taking the square root, we arrive at the result \[I(\gamma) = \int_{-\infty}^\infty dx \; e^{-\gamma x^2} = \sqrt{\frac{\pi}{\gamma}}.\]


10.4: Surfaces
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We should also recognise that writing is deployed on a vast range of preserved materials, with no exceptions known to me, except obsidian and amber; even one lead architectural clamp from the Agora excavations has a text, albeit very difficult to read, cut on it (David Jordan pers. comm.). The full extent of painted texts will never be known to us; it would be a nice pipe-dream to think that in, say, 2030, somebody will write “people made the claim only two decades ago that we would never read such texts”. In the British Museum is a remarkable early marble monument, of c. 600 bc ( Figure 10 ), where both angular and curvy sigmas are still discernible — Phanodikos’ stele, an epigraphic colossus to place beside contemporary sculptural tours de force up to four times life size (Jeffery 1990: 371, no. 43, pl. 71). It was removed by Elgin from near the site of ancient Sigeion in the Troad. The cutting on it of a similar text in two different Greek dialects and scripts, Attic and Ionic, says much about the independence of the small Greek states of the period and their local pride, but also something about locally-driven writing habits. Ann Jeffery noted that in the area of Ionia there is much scruffy looking writing on stone dated to the 6th century, and she wondered whether this may have been the result of the reported flowering here of many branches of written literature, presumably produced in ink, at this time (Jeffery 1990: 57). It is certainly a tendency far different from that of Athens later, in the 5th century, where we see a new ‘aesthetic’, I use the word deliberately, of formally patterned chessboards of letters. Ironically, however, that stoichedon system may have been initiated in Ionia, an early example being the scruffy lettering, but also patterned, text on the side of the throne dedicated on Samos by Aiakes ( Figure 11 ), a piece, whether sculpture or text, of much disputed date — 540 or 500? BC — (see Immerwahr 1990: 96–97 for an assessment, even if he tends towards an Athenian origin for the system).
Unfortunately we have little substantial evidence to support Jeffery’s suggestion; while we can now point to an expanding series of personal letters written mostly on lead from the broad Ionian world, which are of high interest in other respects — especially for the fact that financial problems seem to be the sole topic of epistolary intercourse — they add little regarding the written word. The grammar sometimes fails to reach A-level standards but that again is by the way. More useful is the reference in one such text ( Figure 12 ) to documents written on skins (see Avram 2007: 239 for general bibliography; diphtheria are mentioned in the text from Olbia, Dana 2007: 75–76, with n. 16).
A recent suggestion that this part of the world did see wide use of cursive writing in the period under consideration has been put forward by Adiego (1998: especially 57–79; 2007: 230–233), who finds the oddities of letter shapes in Carian texts best explained by positing that the forms we have in inscriptions from the later 7 th century onward are petrifications of unattested cursive forms used in the area in an earlier period. Much as one would like to see a rational explanation of the Carian alphabet, on all analogy this one seems highly improbable.