6.20: Skeleton Worksheet
2. Add the following labels to the diagram of the vertebra shown below:
- h) Dorsal (neural) spine
- i) Transverse process
- j) Body
- k) Neural (central) canal
3. Add the following labels to the diagram of the dog skeleton shown below:
- l) Atlas vertebra
- m) Cervical vertebrae
- n) Lumbar vertebrae
- o) Sacrum
- p) Thoracic vertebrae
- q) Scapula
- r) Mandible
- s) Tibia
- t) Fibula
- u) Femur
- v) Carpals
- w) Metacarpals
- x) Tarsals
- y) Metatarsals
- z) Hip bone or pelvis
- aa) Humerus
- bb) Radius
- cc) Ulna
- dd) Ribs
- ee) Sternum
4. Cross out the statement(s) that are NOT true.
- The skeleton:
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- supports and protects the organs of the body
- provides a means of locomotion
- grows throughout the life of the animal
- helps keep the level of calcium ions in the body constant
- develops from the cartilage laid down in the fetus
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5. True or False. If false indicate the correct answer.
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- The elbow joint is a synovial joint
- The patella is a compact bone
- The joints in the skull are fixed (immovable joints)
- Unguligrade locomotion is walking on the toenails or hoofs
- Flexion means increasing the angle between two bones
- The joint between the axis and the atlas is a hinge joint
- The articular surface of a joint is covered with spongy bone
- Ligaments join two bones together at a joint
- Plantigrade locomotion is walking on the digits only.
- The hip joint is a hinge joint.


3.3.5: Glossary
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Affect Dealing with a person’s feelings toward the person or object.
Attitude A predisposition to respond in a favorable or unfavorable way to objects or persons in one’s environment.
Attribution biases Covers both the fundamental attribution error and the self-serving bias.
Attribution theory Concerns the process by which an individual interprets events as being caused by a particular part of a relatively stable environment.
Behavioral justification The need to ensure that one’s behaviors are consistent with their attitudes toward the event.
Body language The manner in which people express their inner feelings subconsciously through physical actions such as sitting up straight versus being relaxed or looking people straight in the eye versus looking away from people.
Cognitive consistency The need for behavioral justification to ensure that a person’s behaviors are consistent with their attitudes toward an event.
Cognitive dissonance Finding one’s self acting in a fashion that is inconsistent with their attitudes and experiencing tension and attempting to reduce this tension and return to a state of cognitive consistency.
Dispositional approach Argues that attitudes represent relatively stable predispositions to respond to people or situations around them.
Fundamental attribution error The tendency to underestimate the effects of external or situational causes of behavior and to overestimate the effects of internal or personal causes.
Halo effect The influence of positive arbitrary biases.
Job involvement Refers to the extent to which a person is interested in and committed to assigned tasks.
Job satisfaction A pleasurable or positive emotional state resulting from the appraisal of one’s job or job experience.
Organizational commitment Represents the relative strength of an individual’s identification with and involvement in an organization.
Perception The process by which one screens, selects, organizes, and interprets stimuli to give them meaning.
Perceptual defense A defense that perceives emotionally disturbing or threatening stimuli as having a higher recognition threshold than neutral stimuli. Such stimuli are likely to elicit substitute perceptions that are radically altered so as to prevent recognition of the presented stimuli that arouse emotional reactions even though the stimuli are not recognized.
Perceptual organization When meaning has been attached to an object, individuals are in a position to determine an appropriate response or reaction to it.
Perceptual selectivity Refers to the process by which individuals select objects in the environment for attention.
Response disposition The tendency to recognize familiar objects more quickly than unfamiliar ones.
Response salience The tendency to focus on objects that relate to our immediate needs or wants.
Selective perception The process by which we systematically screen out information we don’t wish to hear, focusing instead on more salient information.
Self-serving bias The tendency for individuals to attribute success on an event or project to their own actions while attributing failure to others.
Situational approach This approach argues that attitudes emerge as a result of the uniqueness of a given situation.
Social perception Consists of those processes by which we perceive other people. Social-information-processing approach Asserts that attitudes result from “socially constructed realities” as perceived by the individual.
Stereotyping A tendency to assign attributes to people solely on the basis of their class or category.


15.8: Perception vs. Expectation
- Define customer perception and customer expectation
A person’s perceptions, along with their beliefs, attitudes, and values can substantially influence his or her experience and involvement with products.
Perception
Perception can have various meanings but in marketing, it is often described as a process by which a consumer identifies, organizes, and interprets information to create meaning. A consumer will selectively perceive what they will ultimately classify as their needs and wants.
Perception is a psychological variable involved in the purchase decision process that is known to influence consumer behavior. Other variables included in this consumer process include: motivation, learning, attitude, personality, and lifestyle. All of these concepts are crucial in interpreting the consumer buying process and can also help guide marketing efforts.
In order to understand the subjectivity of one’s perception, we might consider optical illusions where one image can look like two things at once.
For example, some people may see an image as a candlestick while another may see the same image as two people facing one another. Another example in advertising is known as Selective Perception, which is the process by which individuals perceive what they want to from media messages and they may disregard the rest.
Seymor Smith, a prominent advertising researcher, found evidence for Selective Perception in advertising research in the early 1960s, and he defined it as “a procedure by which people let in, or screen out, advertising material they have an opportunity to see or hear. They do so because of their attitudes, beliefs, usage preferences and habits, conditioning, etc.” People who like, buy, or are considering buying a brand are more likely to notice advertising than are those who are neutral toward the brand. This fact has repercussions within the field of advertising research because any post-advertising analysis that examines the differences in attitudes or buying behavior among those aware versus those unaware of advertising is flawed unless pre-existing differences are controlled for. In other words, understanding a person’s preference for brands will influence their decisions.
Selective Perceptions are categorized under two types: a low level of perception, known as perceptual vigilance, and a higher level of perception, known as perceptual defense.
Customer Experience
In general, four main factors influence a consumers’s experience, involvement, and satisfaction with a product:
- Personal: A person’s perceptions, beliefs, attitudes, and values can substantially influence his or her experience and involvement with products. For example, certain cultures highly discourage women from exposing some of their body parts as part of their religious beliefs, which inevitably affects their consumption of clothing. Other examples of cultural influences include language, myths, customs, rituals, and laws. Consumers tend to be more involved with products that they believe can fill their own needs, which in turn are regarded as holding importance and relevance in their lives. Personal or individual factors can also serve as strong influences, including gender, age, income level or social class, ethnicity, and sexual orientation.
- Object: The degree of information that a consumers have about a product, including how well they can distinguish its characteristics, can also effect their experience, involvement, and satisfaction. Typically, the higher a consumer’s product knowledge, the more involved with it he or she will be. Deeper knowledge about a product also translates into higher involvement because the consumer perceives it as more important, especially if some of that knowledge pertains to characteristics that hold personal meaning.
- Situational: Products that can easily conform to and enrich a consumer’s lifestyle tend to be consumed with more frequency and involvement. For example, a busy working mother might rely heavily on her smart phone to keep her organized and effective in an effortless manner.
- Social: Social influence can deeply affect consumer behavior, especially as related to the products they consider and consume. A consumer’s social network has a strong influence on the products he or she uses, since individuals tend to rely on the opinions and advice of friends and family. Other social influences can include opinion leaders and reference groups.
Consumer Involvement
Consumer involvement tends to vary dramatically depending on the type of product and its relationship to the consumer. In general, consumer involvement tends to be higher for products that are very expensive (e.g., a home, a car) or are considered highly significant in the consumer’s life (e.g., a newborn baby product).
Marketing strategy should take into account the level of involvement that a consumer has with a specific product, as this also dictates the type of information that the consumer needs to process in order to make a purchase decision.
The following levels of information processing are required, which can help dictate the marketing approach that should be used:
- Low-Involvement purchases tend to be made by habitual decisions (e.g., dish washing liquid, toothbrush). These require minimal information processing.
- Moderate-Involvement purchases tend to be made by simple decisions (e.g., orange juice, snacks). These often may require some evaluation of alternatives.
- High-Involvement purchases tend to be made by lengthy or more involved decisions (e.g., a car or a house). These are usually considered highly important to consumers and require extensive information processing.
Print advertising is considered high-involvement because newspapers and magazines provide information that can be processed clearly and can help shape attitudes and influence decisions. Television advertising is considered low-involvement because it presents information that is considered passive.
The four main types of buying behavior in consumer marketing depend on the level of consumer involvement:
High involvement & significant differences between brands (complex buying behavior):
- Example: Houses, kitchen renovation
- One-time sale
- Consumers need evaluation and pre-sale learning
- Selling activities are key
Low involvement & significant differences between brands (variety-seeking buying behavior):
- Example: Retail food stuff
- Consumers have added buying triggers
- Consumers want free samples, special deals
High involvement & few differences between brands (dissonance-reducing buying behavior):
- Example: Consumer electronics, top-line sport equipment
- Decision making is difficult both pre- and post-purchase
Low involvement & few differences between brands (habitual buying behavior):
- Example: Food, personal care products
- Brand familiarity and promotion with convenience is key
- Consumers look for price/sales promotions
Contributors and Attributions
- Boundless Marketing. Provided by : Boundless. Located at : https://courses.lumenlearning.com/boundless-marketing/ . License : CC BY-SA: Attribution-ShareAlike


7.1.1: Graph Linear Inequalities in Two Variables
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SUMMARY
By the end of this section, you will be able to:
- Verify solutions to an inequality in two variables.
- Recognize the relation between the solutions of an inequality and its graph.
- Graph linear inequalities in two variables
- Solve applications using linear inequalities in two variables
Before you get started, take this readiness quiz.
Verify Solutions to an Inequality in Two Variables
Previously we learned to solve inequalities with only one variable. We will now learn about inequalities containing two variables. In particular we will look at linear inequalities in two variables which are very similar to linear equations in two variables.
Linear inequalities in two variables have many applications. If you ran a business, for example, you would want your revenue to be greater than your costs—so that your business made a profit.
LINEAR INEQUALITY
A linear inequality is an inequality that can be written in one of the following forms:
\( \begin{array} {l} { }& {Ax+By>C} &{Ax+By\geq C} &{Ax+By<C} &{Ax+By\leq C} \\ \end{array} \)
Where A and B are not both zero.
Recall that an inequality with one variable had many solutions. For example, the solution to the inequality x>3x>3 is any number greater than 3. We showed this on the number line by shading in the number line to the right of 3, and putting an open parenthesis at 3. See Figure .
Similarly, linear inequalities in two variables have many solutions. Any ordered pair (x,y)(x,y) that makes an inequality true when we substitute in the values is a solution to a linear inequality .
SOLUTION TO A LINEAR INEQUALITY
An ordered pair \((x,y)\) is a solution to a linear inequality if the inequality is true when we substitute the values of x and y .
Example \(\PageIndex{1}\)
Determine whether each ordered pair is a solution to the inequality y>x+4:y>x+4:
ⓐ (0,0)(0,0) ⓑ (1,6)(1,6) ⓒ (2,6)(2,6) ⓓ (−5,−15)(−5,−15) ⓔ (−8,12)(−8,12)
- Answer
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ⓐ
\((0,0)\) Simplify. So, \((0,0)\) is not a solution to \(y>x+4\).
ⓑ
\((1,6)\) Simplify. So, \((1,6)\) is a solution to \(y>x+4\). ⓒ
\((2,6)\) Simplify. So, \((2,6)\) is not a solution to \(y>x+4\). ⓓ
\((−5,−15)\) Simplify. So, \((−5,−15)\) is not a solution to \(y>x+4\). ⓔ
\((−8,12)\) Simplify. So, \((−8,12)\) is a solution to \(y>x+4\).
Determine whether each ordered pair is a solution to the inequality \(y>x−3\):
ⓐ \((0,0)\) ⓑ \((4,9)\) ⓒ \((−2,1)\) ⓓ \((−5,−3)\) ⓔ \((5,1)\)
- Answer
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ⓐ yes ⓑ yes ⓒ yes ⓓ yes ⓔ no
Example \(\PageIndex{3}\)
Determine whether each ordered pair is a solution to the inequality \(y<x+1\):
ⓐ \((0,0)\) ⓑ \((8,6)\) ⓒ \((−2,−1)\) ⓓ \((3,4)\) ⓔ \((−1,−4)\)
- Answer
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ⓐ yes ⓑ yes ⓒ no ⓓ no ⓔ yes
Recognize the Relation Between the Solutions of an Inequality and its Graph
Now, we will look at how the solutions of an inequality relate to its graph.
Let’s think about the number line in shown previously again. The point \(x=3\) separated that number line into two parts. On one side of 3 are all the numbers less than 3. On the other side of 3 all the numbers are greater than 3. See Figure .
Similarly, the line \(y=x+4\) separates the plane into two regions. On one side of the line are points with \(y<x+4\). On the other side of the line are the points with \(y>x+4\). We call the line \(y=x+4\) a boundary line .
BOUNDARY LINE
The line with equation \(Ax+By=C\) is the boundary line that separates the region where \(Ax+By>C\) from the region where \(Ax+By<C\).
For an inequality in one variable, the endpoint is shown with a parenthesis or a bracket depending on whether or not a is included in the solution:
Similarly, for an inequality in two variables, the boundary line is shown with a solid or dashed line to show whether or not it the line is included in the solution.
\[ \begin{array} {ll} {Ax+By<C} &{Ax+By\leq C} \\ {Ax+By>C} &{Ax+By\geq C} \\ {\text{Boundary line is }Ax+By=C.} &{\text{Boundary line is }Ax+By=C.} \\ {\text{Boundary line is not included in solution.}} &{\text{Boundary line is included in solution.}} \\ {\textbf{Boundary line is dashed.}} &{\textbf{Boundary line is solid.}} \\ \nonumber \end{array} \]
Now, let’s take a look at what we found in Example. We’ll start by graphing the line \(y=x+4\), and then we’ll plot the five points we tested, as shown in the graph. See Figure .
In Example we found that some of the points were solutions to the inequality \(y>x+4\) and some were not.
Which of the points we plotted are solutions to the inequality \(y>x+4\)?
The points \((1,6)\) and \((−8,12)\) are solutions to the inequality \(y>x+4\). Notice that they are both on the same side of the boundary line \(y=x+4\).
The two points \((0,0)\) and \((−5,−15)\) are on the other side of the boundary line \(y=x+4\), and they are not solutions to the inequality \(y>x+4\). For those two points, \(y<x+4\).
What about the point \((2,6)\)? Because \(6=2+4\), the point is a solution to the equation \(y=x+4\), but not a solution to the inequality \(y>x+4\). So the point \((2,6)\) is on the boundary line.
Let’s take another point above the boundary line and test whether or not it is a solution to the inequality \(y>x+4\). The point \((0,10)\)clearly looks to above the boundary line, doesn’t it? Is it a solution to the inequality?
\[\begin{array} {lll} {y} &{>} &{x+4} \\ {10} &{\overset{?}{>}} &{0+4} \\ {10} &{>} &{4} \\ \nonumber \end{array}\]
So, \((0,10)\) is a solution to \(y>x+4\).
Any point you choose above the boundary line is a solution to the inequality \(y>x+4\). All points above the boundary line are solutions.
Similarly, all points below the boundary line, the side with \((0,0)\) and \((−5,−15)\), are not solutions to \(y>x+4\), as shown in Figure .
The graph of the inequality \(y>x+4\) is shown in below.
The line \(y=x+4\) divides the plane into two regions. The shaded side shows the solutions to the inequality \(y>x+4\).
The points on the boundary line, those where \(y=x+4\), are not solutions to the inequality \(y>x+4\), so the line itself is not part of the solution. We show that by making the line dashed, not solid.
Example \(\PageIndex{4}\)
The boundary line shown in this graph is \(y=2x−1\). Write the inequality shown by the graph.
- Answer
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The line \(y=2x−1\) is the boundary line. On one side of the line are the points with \(y>2x−1\) and on the other side of the line are the points with \(y<2x−1\).
Let’s test the point \((0,0)\) and see which inequality describes its position relative to the boundary line.
At \((0,0)\), which inequality is true: \(y>2x−1\) or \(y<2x−1\)?
\[\begin{array} {ll} {y>2x−1} &{y<2x−1} \\ {0\overset{?}{>}2·0−1} &{0\overset{?}{<}2·0−1} \\ {0>−1\text{ True}} &{0<−1\text{ False}} \\ \nonumber \end{array}\]
Since, \(y>2x−1\) is true, the side of the line with \((0,0)\), is the solution. The shaded region shows the solution of the inequality \(y>2x−1\).
Since the boundary line is graphed with a solid line, the inequality includes the equal sign.
The graph shows the inequality \(y\geq 2x−1\).
We could use any point as a test point, provided it is not on the line. Why did we choose \((0,0)\)? Because it’s the easiest to evaluate. You may want to pick a point on the other side of the boundary line and check that \(y<2x−1\).
Example \(\PageIndex{5}\)
Write the inequality shown by the graph with the boundary line \(y=−2x+3\).
- Answer
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\(y\geq −2x+3\)
Example \(\PageIndex{6}\)
Write the inequality shown by the graph with the boundary line \(y=\frac{1}{2}x−4\).
- Answer
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\(y\leq \frac{1}{2}x−4\)
Example \(\PageIndex{7}\)
The boundary line shown in this graph is \(2x+3y=6\). Write the inequality shown by the graph.
- Answer
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The line \(2x+3y=6\) is the boundary line. On one side of the line are the points with \(2x+3y>6\) and on the other side of the line are the points with \(2x+3y<6\).
Let’s test the point \((0,0)\) and see which inequality describes its side of the boundary line.
At \((0,0)\), which inequality is true: \(2x+3y>6\) or \(2x+3y<6\)?
\[\begin{array} {ll} {2x+3y>6} &{2x+3y<6} \\ {2(0)+3(0)\overset{?}{>}6} &{2(0)+3(0)\overset{?}{<}6} \\ {0>6\text{ False}} &{0<6\text{ True}} \\ \nonumber \end{array}\]
So the side with \((0,0)\) is the side where \(2x+3y<6\).
(You may want to pick a point on the other side of the boundary line and check that \(2x+3y>6\).)
Since the boundary line is graphed as a dashed line, the inequality does not include an equal sign.
The shaded region shows the solution to the inequality \(2x+3y<6\).
Example \(\PageIndex{8}\)
Write the inequality shown by the shaded region in the graph with the boundary line \(x−4y=8\).
- Answer
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\(x−4y\leq 8\)
Example \(\PageIndex{9}\)
Write the inequality shown by the shaded region in the graph with the boundary line \(3x−y=6\).
- Answer
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\(3x−y\geq 6\)
Graph Linear Inequalities in Two Variables
Now that we know what the graph of a linear inequality looks like and how it relates to a boundary equation we can use this knowledge to graph a given linear inequality.
Example \(\PageIndex{10}\): How to Graph a Linear Equation in Two Variables
Graph the linear inequality \(y\geq \frac{3}{4}x−2\).
- Answer
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Example \(\PageIndex{11}\)
Graph the linear inequality \(y>\frac{5}{2}x−4\).
- Answer
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All points in the shaded region and on the boundary line, represent the solutions to \(y>\frac{5}{2}x−4\).
Example \(\PageIndex{12}\)
Graph the linear inequality \(y<\frac{2}{3}x−5\).
- Answer
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All points in the shaded region, but not those on the boundary line, represent the solutions to \(y<\frac{2}{3}x−5\).
The steps we take to graph a linear inequality are summarized here.
GRAPH A LINEAR INEQUALITY IN TWO VARIABLES.
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Identify and graph the boundary line.
- If the inequality is \leq or\geq ,\leq or\geq , the boundary line is solid.
- If the inequality is <or>,<or>, the boundary line is dashed.
- Test a point that is not on the boundary line. Is it a solution of the inequality?
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Shade in one side of the boundary line.
- If the test point is a solution, shade in the side that includes the point.
- If the test point is not a solution, shade in the opposite side.
Example \(\PageIndex{13}\)
Graph the linear inequality \(x−2y<5\).
- Answer
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First, we graph the boundary line \(x−2y=5\). The inequality is \(<\) so we draw a dashed line.
Then, we test a point. We’ll use \((0,0)\) again because it is easy to evaluate and it is not on the boundary line.
Is \((0,0)\) a solution of \(x−2y<5\)?
The point \((0,0)\) is a solution of \(x−2y<5\), so we shade in that side of the boundary line.
All points in the shaded region, but not those on the boundary line, represent the solutions to \(x−2y<5\).
Example \(\PageIndex{14}\)
Graph the linear inequality: \(2x−3y<6\).
- Answer
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All points in the shaded region, but not those on the boundary line, represent the solutions to \(2x−3y<6\).
Example \(\PageIndex{15}\)
Graph the linear inequality: \(2x−y>3\).
- Answer
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All points in the shaded region, but not those on the boundary line, represent the solutions to \(2x−y>3\).
What if the boundary line goes through the origin? Then, we won’t be able to use \((0,0)\) as a test point. No problem—we’ll just choose some other point that is not on the boundary line.
Example \(\PageIndex{16}\)
Graph the linear inequality: \(y\leq −4x\).
- Answer
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First, we graph the boundary line \(y=−4x\). It is in slope–intercept form, with \(m=−4\) and \(b=0\). The inequality is \(\leq\) so we draw a solid line.
Now we need a test point. We can see that the point (1,0)(1,0) is not on the boundary line.
Is \((1,0)\) a solution of \(y\leq −4x\)?
The point \((1,0)\) is not a solution to \(y\leq −4x\), so we shade in the opposite side of the boundary line.
All points in the shaded region and on the boundary line represent the solutions to \(y\leq −4x\).
Example \(\PageIndex{17}\)
Graph the linear inequality: \(y>−3x\).
- Answer
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All points in the shaded region, but not those on the boundary line, represent the solutions to \(y>−3x\).
Example \(\PageIndex{18}\)
Graph the linear inequality: \(y\geq −2x\).
- Answer
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All points in the shaded region and on the boundary line, represent the solutions to \(y\geq −2x\).
Some linear inequalities have only one variable. They may have an x but no y , or a y but no x . In these cases, the boundary line will be either a vertical or a horizontal line.
Recall that:
\[\begin{array} {ll} {x=a} &{\text{vertical line}} \\ {y=b} &{\text{horizontal line}} \\ \nonumber \end{array}\]
Example \(\PageIndex{19}\)
Graph the linear inequality: \(y>3\).
- Answer
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First, we graph the boundary line \(y=3\). It is a horizontal line. The inequality is \(>\) so we draw a dashed line.
We test the point \((0,0)\).
\[y>3\nonumber\]\[0\slashed{>}3\nonumber\]
So, \((0,0)\) is not a solution to \(y>3\).
So we shade the side that does not include \((0,0)\) as shown in this graph.
All points in the shaded region, but not those on the boundary line, represent the solutions to \(y>3\).
Example \(\PageIndex{20}\)
Graph the linear inequality: \(y<5\).
- Answer
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All points in the shaded region, but not those on the boundary line, represent the solutions to \(y<5\).
Example \(\PageIndex{21}\)
Graph the linear inequality: \(y\leq −1\).
- Answer
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All points in the shaded region and on the boundary line represent the solutions to \(y\leq −1\).
Solve Applications using Linear Inequalities in Two Variables
Many fields use linear inequalities to model a problem. While our examples may be about simple situations, they give us an opportunity to build our skills and to get a feel for how thay might be used.
Example \(\PageIndex{22}\)
Hilaria works two part time jobs in order to earn enough money to meet her obligations of at least $240 a week. Her job in food service pays $10 an hour and her tutoring job on campus pays $15 an hour. How many hours does Hilaria need to work at each job to earn at least $240?
ⓐ Let xx be the number of hours she works at the job in food service and let y be the number of hours she works tutoring. Write an inequality that would model this situation.
ⓑ Graph the inequality.
ⓒ Find three ordered pairs \((x,y)\) that would be solutions to the inequality. Then, explain what that means for Hilaria.
- Answer
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ⓐ We let x be the number of hours she works at the job in food service and let y be the number of hours she works tutoring.
She earns $10 per hour at the job in food service and $15 an hour tutoring. At each job, the number of hours multiplied by the hourly wage will gives the amount earned at that job.
ⓑ To graph the inequality, we put it in slope–intercept form.
\[\begin{align} {10x+15y} &\geq 240 \\ 15y &\geq -10x+240 \\ y &\geq {−\frac{2}{3}x+16} \\ \nonumber \end{align}\]
ⓒ From the graph, we see that the ordered pairs \((15,10)\), \((0,16)\), \((24,0)\) represent three of infinitely many solutions. Check the values in the inequality.
For Hilaria, it means that to earn at least $240, she can work 15 hours tutoring and 10 hours at her fast-food job, earn all her money tutoring for 16 hours, or earn all her money while working 24 hours at the job in food service.
Example \(\PageIndex{23}\)
Hugh works two part time jobs. One at a grocery store that pays $10 an hour and the other is babysitting for $13 hour. Between the two jobs, Hugh wants to earn at least $260 a week. How many hours does Hugh need to work at each job to earn at least $260?
ⓐ Let x be the number of hours he works at the grocery store and let y be the number of hours he works babysitting. Write an inequality that would model this situation.
ⓑ Graph the inequality.
ⓒ Find three ordered pairs ( x , y ) that would be solutions to the inequality. Then, explain what that means for Hugh.
- Answer
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ⓐ \(10x+13y\geq 260\)
ⓑⓒ Answers will vary..
Example \(\PageIndex{24}\)
Veronica works two part time jobs in order to earn enough money to meet her obligations of at least $280 a week. Her job at the day spa pays $10 an hour and her administrative assistant job on campus pays $17.50 an hour. How many hours does Veronica need to work at each job to earn at least $280?
ⓐ Let x be the number of hours she works at the day spa and let y be the number of hours she works as administrative assistant. Write an inequality that would model this situation.
ⓑ Graph the inequality.
ⓒ Find three ordered pairs ( x , y ) that would be solutions to the inequality. Then, explain what that means for Veronica
- Answer
-
ⓐ \(10x+17.5y\geq 280\)
ⓑⓒ Answers will vary.
Access this online resource for additional instruction and practice with graphing linear inequalities in two variables.
Key Concepts
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How to graph a linear inequality in two variables.
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Identify and graph the boundary line.
If the inequality is \(\leq\) or \(\geq\), the boundary line is solid.
If the inequality is \(<\) or \(>\), the boundary line is dashed. - Test a point that is not on the boundary line. Is it a solution of the inequality?
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Shade in one side of the boundary line.
If the test point is a solution, shade in the side that includes the point.
If the test point is not a solution, shade in the opposite side.
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Identify and graph the boundary line.
Glossary
- boundary line
- The line with equation \(Ax+By=C\) is the boundary line that separates the region where \(Ax+By>C\) from the region where \(Ax+By<C\).
- linear inequality
- A linear inequality is an inequality that can be written in one of the following forms: \(Ax+By>C\), \(Ax+By\geq C\), \(Ax+By<C\), or \(Ax+By\leq C\), where A and B are not both zero.
- solution to a linear inequality
- An ordered pair \((x,y)\) is a solution to a linear inequality if the inequality is true when we substitute the values of x and y .


10.12.2: Thought Questions
Thought Questions
What are the advantages of using radar imaging rather than ordinary cameras to study the topography of Venus? What are the relative advantages of these two approaches to mapping Earth or Mars?
14.
Venus and Earth are nearly the same size and distance from the Sun. What are the main differences in the geology of the two planets? What might be some of the reasons for these differences?
15.
Why is there so much more carbon dioxide in the atmosphere of Venus than in that of Earth? Why so much more carbon dioxide than on Mars?
16.
If the Viking missions were such a rich source of information about Mars, why have we sent the Pathfinder, Global Surveyor , and other more recent spacecraft to Mars? Make a list of questions about Mars that still puzzle astronomers.
17.
Compare Mars with Mercury and the Moon in terms of overall properties. What are the main similarities and differences?
18.
Contrast the mountains on Mars and Venus with those on Earth and the Moon.
19.
We believe that all of the terrestrial planets had similar histories when it comes to impacts from space. Explain how this idea can be used to date the formation of the martian highlands, the martian basins, and the Tharsis volcanoes. How certain are the ages derived for these features (in other words, how do we check the ages we derive from this method)?
20.
Is it likely that life ever existed on either Venus or Mars? Justify your answer in each case.
21.
Suppose that, decades from now, NASA is considering sending astronauts to Mars and Venus. In each case, describe what kind of protective gear they would have to carry, and what their chances for survival would be if their spacesuits ruptured.
22.
We believe that Venus, Earth, and Mars all started with a significant supply of water. Explain where that water is now for each planet.
23.
One source of information about Mars has been the analysis of meteorites from Mars. Since no samples from Mars have ever been returned to Earth from any of the missions we sent there, how do we know these meteorites are from Mars? What information have they revealed about Mars?
24.
The runaway greenhouse effect and its inverse, the runaway refrigerator effect, have led to harsh, uninhabitable conditions on Venus and Mars. Does the greenhouse effect always cause climate changes leading to loss of water and life? Give a reason for your answer.
25.
In what way is the high surface temperature of Venus relevant to concerns about global warming on Earth today?
26.
What is a dust devil? Would you expect to feel more of a breeze from a dust devil on Mars or on Earth? Explain.
27.
Near the martian equator, temperatures at the same spot can vary from an average of –135 °C at night to an average of 30 °C during the day. How can you explain such a wide difference in temperature compared to that on Earth?


2.2.11: Gustave Flaubert (1821-1880)
A Simple Soul French Realism Gustave Flaubert was born on Dec. 12, 1821 in Rouen, France. He grew up in an affluent middle class family; his father was a respected surgeon. As a young man, Flaubert became friends in college with other students who despised the bourgeoisie, and began writing short stories and, eventually, novels that were critical of middle class values. Flaubert’s health problems (he suffered from epilepsy) forced him to give up plans to study the law, so he devoted his energies to writing literature. After his father died, he retired to a country house near Rouen, where he would spend the rest of his life. His masterpiece, Madame Bovary , is a psychological study of a woman desperate to escape a banal middle-class life. Flaubert is considered to be one of the greatest practitioners of literary realism in France. "A Simple Soul" is the study of the life of Felicite, a servant of Madame Aubain. Over the course of 50 years, she loses many people for whom she cares, and she ends her life caring for a rather difficult parrot named Loulou. Consider while reading:
- What characteristics of realism do you see in this story?
- Analyze the character of Felicite. What kind of suffering and loss does she undergo in her life?
- What do you think Flaubert is saying about life through this character. How do you respond to her?
- What is the significance of the title of the short story?
Written by Anita Turlington


6.2: Orchestral Instruments
Introduction
The modern Western orchestra first developed in Europe over a period of several centuries, but in modern times it has become widely adopted all over the world. Various types of bands and smaller ensembles composed mainly of orchestral instruments are also very popular. So many people are familiar with the “orchestra section” method of classifying musical instruments. Here are the sections of the orchestra and the instruments commonly found in them.
The Sections of the Orchestra
The typical orchestra is divided into four groups of instruments: strings, woodwinds, brass, and percussion. The typical Western marching band, school band, or wind ensemble (woodwinds and brass together are winds) leaves out the strings, but otherwise uses most of the same instruments as the orchestra.
Strings
There are four stringed instruments commonly used in the modern orchestra: the violin, viola, cello, and bass. All are made of wood and have four strings. All are usually played by drawing a bow across the strings, but are also sometimes played by plucking the strings.
The violin is smallest, has the highest sound, and is most numerous; there are normally two violin sections (the first violins and second violins), but only one section of each of the other strings.
The viola is only a little bit bigger than a violin, with a slightly deeper and mellower tone. A nonmusician can have trouble telling a viola from a violin without a side-by-side comparison.
The cello is technically the “violoncello,” but few people call it that anymore. There is no mistaking it for a violin or viola; it is much bigger, with a much lower, deeper sound. Whereas violins and violas are held up under the chin to be played, cellos and basses have to rest on the floor to be played.
The bass, also called the “double bass” (its official name), “standing bass” or “string bass,” is so big that the player must sit on a high stool or stand up to play it. It has a very low sound.
Woodwinds
The woodwind members of the orchestra are the flute, oboe, clarinet, and bassoon. There can be two, three, or four, of any of these woodwinds in an orchestra, depending on the size of the orchestra and the piece being played. All of the modern orchestral woodwinds are played by blowing into them and fingering different notes using keys that cover various holes. Most, but not all, are made of wood and have at least one piece of reed in the mouthpiece.
You may be surprised that the saxophone is not here. This is the one instrument that is always found in bands and wind ensembles, but only very rarely plays in the orchestra.
Although flutes may be made of wood, the orchestral flute is usually made of metal. It also does not have a reed. It is grouped with the woodwinds partly because it is in fact more closely related to those instruments than to the brass (please see Wind Instruments: Some Basics), but also because the color of its sound fits in the woodwind section. The sound is produced when the player blows across a hole in the side (not the end) of the instrument. It has a clear, high sound that can be either gentle or piercing. An even higher-sounding instrument is the piccolo, a very small flute that is much more common in bands than in orchestras.
The oboe is the instrument that traditionally sounds the first “A” that the orchestra tunes to. It is black, made of wood, and at sight can be mistaken by the nonmusician for a clarinet. But its sound is produced when the player blows in between two small reeds, and its high “double-reed” sound is not easily mistaken for any other instrument. The cor anglais, or English horn, is a slightly larger double reed instrument with a deeper, gentler tone, that is sometimes called for in orchestral music.
The clarinet is also black and normally made of wood, although good plastic clarinets are also made. It uses only a single reed. It is a versatile instrument, with a very wide range of notes from low to high, and also a wide range of different sound colors available to it. In the orchestra, clarinets are no more numerous than the other woodwinds, but it is usually the most numerous instrument in bands and wind ensembles because of its useful versatility. There are many sizes of clarinet available, including bass and contrabass clarinets, but the most common is the B flat clarinet. The clarinet is the only common orchestral woodwind that is usually a transposing instrument, although there are less common woodwinds, such as English horn, that are also transposing instruments.
The bassoon is the largest and lowest-sounding standard orchestral woodwind. (Bass clarinet and contrabassoon are used only occasionally.) It is a long hollow tube of wood; you can often see the tops of the bassoons over the rest of the orchestra. Like the oboe, the bassoon is a double reed – the player blows between two reeds – but the player does not blow into the end of the bassoon. The air from the reeds goes through a thin metal tube into the middle of the instrument.
Brass
The orchestral brass are all made of metal, although the metal can be a silvery alloy instead of brass. The sound is actually produced by “buzzing” the lips against the mouthpiece; the rest of the instrument just amplifies and refines the sound from the lips so that it is a pretty, musical sound by the time it comes out of the bell at the other end of the instrument. A slide, or three or four valves, help the instruments get different notes, but players rely heavily on the harmonic series of their instruments to get the full range of notes. (Please see Wind Instruments: Some Basics for more on the subject.) The orchestral brass instruments are the trumpet, French horn, trombone, and tuba. As with the woodwinds, the number of each of these instruments varies depending on the size of the orchestra and the piece being played. There are usually two to five each of trumpets, horns, and trombones, and one or two tubas.
The trumpet is the smallest, highest-sounding orchestral brass instrument. Its shape is quite cylindrical (it doesn’t flare much until the very end), giving it a very clear, direct sound. Trumpets may read in C or may be B flat transposing instruments. The cornet, which is more common in bands than in orchestras, is very similar to the trumpet and the two instruments are often considered interchangeable. The cornet has a more conical, gently-flaring shape and a slightly mellower sound.
The French horn, or horn, is much more conical than the trumpet and has a much mellower, more distant sound. It has a wide range that overlaps both the trumpet and trombone ranges, and in the orchestra is often used to fill in the middle of the brass sound. Its long length of tubing is wrapped into a circular shape and the bell faces backward and is normally rested on the player’s leg. It is a transposing instrument that usually reads music in F.
The trombone is the only valveless brass instrument in the modern orchestra. One section of its tubing – the slide – slides in and out to specific positions to get higher and lower pitches, but, as with the other brass, it uses the harmonic series to get all the notes in its range. Its range is quite a bit lower than the trumpet, but it also has a brassy, direct (cylindrical-shape) sound.
There are a few instruments in the middle and low range of the brass section that are commonly found in bands, but very rare in the orchestra. The baritone and euphonium play in the same range as the trombone, but have the more cylindrical shape and a very mellow, sweet sound. In marching bands, the horn players often play mellophone and the tuba players play the sousaphone. The mellophone is an E flat or F transposing instrument with a forward-facing bell that is more suitable for marching bands than the French horn. The sousaphone was also invented for use in a marching band; its tubing is wrapped so that the player can carry it on the shoulders.
The tuba is the largest, lowest-sounding orchestral brass instrument. It is a conical brass instrument, with a much mellower, distant sound than the trombone. Its bell (and the bell of the baritone and euphonium) may either point straight up or upward and forward.
Percussion
In a Western orchestra or band, anything that is not classified as strings, woodwinds, or brass goes in the percussion section, including whistles. Most of the instruments in this section, though, are various drums and other instruments that are hit with drumsticks or beaters. Here are some of the more common instruments found in an orchestra percussion section.
Timpani are large kettledrums (drums with a rounded bottom) that can be tuned to play specific pitches. An orchestra or wind ensemble will usually have a few tympani of various sizes.
Other common drums do not have a particular pitch. They are usually cylindrical, sometimes with a drum head on each end of the cylinder. They include the small side drum, which often has a snare that can be engaged to give the drum an extra rattling sound, the medium-sized tenor drum, and the large bass drum. All orchestral drums (including tympani) are played using hard drum sticks or softer beaters. Drums that are played with the hands, like bongos, are rare in traditional orchestras and bands.
Cymbals can be clashed together, hit with a beater, or slapped together in “hi-hat” fashion. For smaller ensembles, various cymbals and drums may be grouped into a drum set so that one player can play all of them. Gongs are usually larger and thicker than cymbals and are usually hit with a soft beater.
There is only one group of common percussion instruments on which it is easy to play a melody. In these instruments, bars, blocks or tubes are arranged in two rows like the black and white keys of a piano keyboard. Orchestral xylophones and marimbas use wooden bars arranged over hollow tubes that help amplify their sound. The glockenspiel uses metal bars (like the familiar children’s xylophone), and tubular bells use long, hollow, metal tubes.
Common percussion extras that add special color and effects to the music include the tambourine, triangle, maracas and other shakers, castanets, claves and various wood blocks, and various bells and scrapers.
Contributors and Attributions
- Orchestral Instruments. Authored by : Catherine Schmidt-Jones. Located at : http://cnx.org/contents/d83ffcf4-a12d-4b41-b182-3035c1f7403e@4/Orchestral-Instruments . License : CC BY: Attribution
- French Horn. Authored by : Wolfgang Lonien. Located at : https://www.flickr.com/photos/wjlonien/15776903112/ . License : CC BY-SA: Attribution-ShareAlike
- Classical Oboe. Authored by : OboeCrack. Provided by : Wikimedia. Located at : https://commons.wikimedia.org/wiki/File:ClassicalOboe.jpg . License : CC BY-SA: Attribution-ShareAlike
- Praetorius Trombones. Provided by : Wikimedia. Located at : https://en.Wikipedia.org/wiki/File:Praetorius_Trombones_1614-1620_Syntagma_Musicum.png#/media/File:Praetorius_Trombones_1614-1620_Syntagma_Musicum.png . License : Public Domain: No Known Copyright


11.1.4E: Pluralism
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Multiculturalism is an ideology that promotes the institutionalization of communities containing multiple cultures.
Learning Objectives
- Reconstruct the crux of the debate about multiculturalism, including its different forms and opposition to it
Key Points
- Multiculturalism is seen by its supporters as a fairer system that allows people to truly express who they are within a society, that is more tolerant, and that adapts better to social issues.
- Critics of multiculturalism often debate whether the multicultural ideal of benignly co-existing cultures that interrelate and influence one another, and yet remain distinct, is sustainable, paradoxical, or even desirable.
- Multiculturalism is often contrasted with the concepts of assimilationism and has been described as a “salad bowl” or “cultural mosaic” rather than an assimilationist “melting pot”.
Key Terms
- multiculturalism : A characteristic of a society that has many different ethnic or national cultures mingling freely. It can also refer to political or social policies which support or encourage such a coexistence. Important in this is the idea that cultural practices, no matter how unusual, should be tolerated as a measure of respect.
Multiculturalism is an ideology that promotes the institutionalization of communities containing multiple cultures. It is generally applied to the demographic make-up of a specific place, usually at the organizational level (e.g., schools, businesses, neighborhoods, cities, or nations).
In a political context, the term is used for a wide variety of meanings. These can range from the advocacy of equal respect for the various cultures in a society, to a policy of promoting the maintenance of cultural diversity, to policies in which people of various ethnic and religious groups are addressed by the authorities according to the definition of the group to which they belong. A common aspect of many such policies is that they avoid presenting any specific ethnic, religious, or cultural community values as central.
Multiculturalism is often contrasted with the concepts of assimilationism and has been described as a “salad bowl” or “cultural mosaic,” rather than an assimilationist “melting pot.”
Definition
There is no single, agreed-upon definition for multiculturalism and different countries approach the issue in a variety of manners. However two main different and seemingly inconsistent strategies have developed through varied government policies and strategies.
- The first focuses on interaction and communication between different cultures. By encouraging different cultures to interact, hopefully, cultural differences can be recognized and accepted rather than suppressed or ignored, thus promoting a sense of multiculturalism.
- The second centers on diversity and cultural uniqueness. Cultural isolation can protect the uniqueness of the local culture of a nation or area and also contribute to global cultural diversity.
Political scholar Andrew Heywood distinguishes between two forms of multiculturalism: descriptive and normative:
- As a descriptive term, it refers to general cultural diversity.
- As a normative term, multiculturalism “implies a positive endorsement, even celebration, of communal diversity, typically based on either the right of different groups to respect and recognition, or to the alleged benefits to the larger society of moral and cultural diversity”.
Multiculturalism as Government Policy
Multiculturalism has been an official policy in several Western nations since the 1970s, for reasons that vary from country to country, including the fact that many of the great cities of the Western world are increasingly made of a mosaic of cultures. The Canadian government has often been described as the instigator of multicultural ideology because of its public emphasis on the social importance of immigration. The Canadian Royal Commission on Bilingualism and Biculturalism is often refered to as the origins of modern political awareness of multiculturalism.
Support for Multiculturalism
Multiculturalism is seen by its supporters as a fairer system that allows people to truly express who they are within a society, that is more tolerant, and adapts better to social issues. They argue that culture is not one definable thing based on one race or religion, but rather the result of multiple factors that change as the world changes.
Multiculturalism in Western countries was seen as a useful set of strategies to combat racism, protect minority communities of all types, and to undo policies that had prevented minorities from having full access to the opportunities for freedom and equality promised by the liberalism that have been the hallmark of Western societies since the Age of Enlightenment.
Opposition to Multiculturalism
Critics of multiculturalism often debate whether or not the multicultural ideal of benignly co-existing cultures that interrelate and influence one another, and yet remain distinct, is sustainable, paradoxical, or even desirable. It is argued that nation states, which would previously have been synonymous with a distinctive cultural identity of their own, lose out to enforced multiculturalism and that this ultimately erodes the host nations’ distinct culture.
Harvard professor of political science Robert D. Putnam conducted a nearly decade-long study of how multiculturalism affects social trust. He surveyed 26,200 people in 40 American communities, finding that when the data were adjusted for class, income, and other factors, the more racially diverse a community is, the greater the loss of trust. People in diverse communities “don’t trust the local mayor, they don’t trust the local paper, they don’t trust other people and they don’t trust institutions,” writes Putnam.


5.1: Standards and Competencies
“Babies are such a nice way to start people.” – Don Herald
NAEYC Standards
The following NAEYC Standard for Early Childhood Professional Preparation addressed in this chapter:
- Promoting Child Development and Learning
- Building Family and Community Relationships
- Observing, Documenting, and Assessing to Support Young Children and Families
- Using Developmentally Effective Approaches to Connect with Children and Families
- Using Content Knowledge to Build Meaningful Curriculum
- Becoming a professional
California Early Childhood Educator Competencies
- Child Development and Learning
- Culture, Diversity, and Equity
- Dual-Language Development
- Family and Community Engagement
- Learning Environments and Curriculum
- Observation, Screening, Assessment, and Documentation
- Professionalism
- Relationships, Interaction, and Guidance
- Special Needs and Inclusion
National Association for the Education of Young Children (NAEYC) Code of Ethical Conduct (May 2011)
The following elements of the code are touched upon in this chapter:
Section I: Ethical Responsibilities to Children
Ideals: 1.1 – 1.4, 1.10, 1.11
Principles 1.1, 1.2, 1.7
Section II: Ethical Responsibilities to Families
Ideals: 2.2, 2.4, 2.6, 2.7
Principles: 2.6


5.2: Anticholinergics
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Ipratropium is an example of a short-acting anticholinergic. Tiotropium is an example of a long-acting anticholinergic. Additional information regarding anticholinergics can be found in the “Autonomic Nervous System” chapter. (See Figure 5.13 [1] for an image of tiotropium.)
Mechanism of Action
Anticholinergics block the action of acetylcholine in bronchial smooth muscle, which reduces bronchoconstrictive substance release.
Indications for Use
Anticholinergics are used for maintenance therapy of bronchoconstriction associated with asthma, chronic bronchitis, and emphysema.
Adverse/Side Effects
Anticholinergics should be used with caution with the elderly and can cause cough, drying of the nasal mucosa, nervousness, nausea, GI upset, headaches, and dizziness. [2]
Patient Teaching & Education
Patients should be instructed to use the inhaler as directed and be careful not to exceed dosage recommendations. They should receive education regarding the onset of medication and differences in usage for short- and long-acting anticholinergics. Some long-acting anticholinergics may cause signs of angioedema and the healthcare provider should be notified if this occurs. [3]
Now let’s take a closer look at the medication grid for ipratropium and tiotropium in Table 5.11. [4] , [5] , [6] , [7]
Class/Subclass |
Prototype/Generic |
Administration Considerations |
Therapeutic Effects |
Adverse/Side Effects |
|---|---|---|---|---|
| Anticholinergics (short acting) | ipratropium |
Long-term management of pulmonary disease
Slower onset of action |
Rapid bronchodilation | Cough and drying of the nasal mucosa |
| Anticholinergics (long acting) | tiotropium |
Long-term management of pulmonary disease
Slower onset of action |
Prevention of bronchospasm and reduces exacerbations in COPD patients | Cough and drying of the nasal mucosa |
- "Spiriva HandiHaler"-brand dry powder inhaler (open).png" by RonEJ at English Wikipedia is licensed under CC0 1.0 ↵
- Frandsen, G. & Pennington, S. (2018). Abrams’ clinical drug: Rationales for nursing practice (11th ed.). Wolters Kluwer. ↵
- uCentral from Unbound Medicine. https://www.unboundmedicine.com/ucentral ↵
- This work is a derivative of Pharmacology Notes: Nursing Implications for Clinical Practice by Gloria Velarde licensed under CC BY-NC-SA 4.0 . ↵
- Frandsen, G. & Pennington, S. (2018). Abrams’ clinical drug: Rationales for nursing practice (11th ed.). Wolters Kluwer. ↵
- This work is a derivative of Daily Med by U.S. National Library of Medicine in the public domain . ↵
- Adams, M., Holland, N., & Urban, C. (2020). Pharmacology for nurses: A pathophysiologic approach (6th ed.). pp. 622-63 & 626. Pearson. ↵


4.2: Beta-1 Agonists
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Dobutamine is a Beta-1 agonist.
Mechanism of Action: Dobutamine stimulates Beta-1 receptors to increase heart rate, force of contraction, and conduction velocity.
Indications: Dobutamine is used to treat cardiogenic shock and severe heart failure to increase contractility and cardiac output.
Nursing Considerations: In IV administration, dilute concentration before administering. Continuously monitor electrocardiogram (ECG), blood pressure, cardiac output, and urine output during therapy. This drug can cause a marked increase in heart rate and blood pressure. Report all adverse reactions promptly, especially labored breathing, angina, palpitations, and dizziness.
Patient Teaching & Education: The patient should be instructed to inform the nurse immediately if they notice chest pain, shortness of breath, or numbness or tingling in the extremities. [1]
Now let’s take a closer look at the dobutamine medication grid in Table 4.11. [2]
|
Class/Subclass |
Prototype/Generic |
Administration Considerations |
Therapeutic Effects |
Side/Adverse Effects |
|---|---|---|---|---|
| Beta-1 agonist | dobutamine | Continuously monitor ECG, blood pressure, cardiac output, and urine output during therapy | Increases heart rate, force of heart contraction, and speed of conduction between SA to AV nodes |
Marked increase in heart rate and blood pressure
Report all adverse reactions promptly, especially labored breathing, angina, palpitations, and dizziness |
- uCentral from Unbound Medicine. https://www.unboundmedicine.com/ucentral ↵
- This work is a derivative of Daily Med by U.S. National Library of Medicine in the public domain . ↵


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5.4.11: Managerial Skills Application Exercise
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Do you agree that diversity can be a source of greater benefit than harm to organizations? Why or why not?
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Have you ever worked in a diverse team setting before? If so, did you encounter any attitudes or behaviors that could potentially cause conflict? If not, how would you manage conflict stemming from diversity?
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List three organizational goals you would implement to create an organizational culture of diversity and inclusion.
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Have you or has someone you know experienced discrimination? How did that affect you or that person emotionally, physically, or financially?
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Pick an identity group (e.g., gay, Black, or woman) other than your own. Imagine and list the negative experiences and interactions you believe you might encounter at work. What policies or strategies could an organization implement to prevent those negative experiences from occurring?
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Provide a concrete example of how different perspectives stemming from diversity can positively impact an organization or work group. You may use a real-life personal example or make one up.


11.24: Summary Comparison of 15- and 30-Year Mortgages
The following table presents a comparison of the $100,000 annual pay mortgage (above) at 6% interest for 15- and 30-years.
Notes and Questions :
- The shorter-term mortgage presents a higher periodic payment requirement but entails less overall interest payments over time.
- The longer-term mortgage presents a much higher total interest payment requirement but requires a lower periodic outlay.
- Question : Under what conditions does it pay to take out the shorter-term mortgage?
- Answer : It pays if the mortgagee has sufficient cash flow, and wishes to minimize total payments, especially interest, over time.
- Question : Under what conditions does it pay to take out the longer-term mortgage?
- Answer : It pays if one does not have sufficient cash flow, is unwilling to settle for a less-costly home, and is relatively unconcerned about the long-term, larger amount to be paid; perhaps he does not intend to stay for the full thirty years.
- In most circumstances, a 15-year mortgage will bear a lower rate than a 30-year mortgage – unlike this illustration. Here we focused on a single variable – time – which greatly impacts the scenario depicted relative to the minimal impact that a small premium interest rate would have for the increased term to maturity.
- Taxation will also have an effect. Recall that interest payments on mortgages are, under current law, tax-deductible.
The mortgage formula is important to master as it will be used again in three additional contexts: 1. Leasing; 2. Bond Accounting; and 3. Capital Budgeting: The Annual Annuity Approach.
Mortgages in the New Millennium
Innovation has brought about a multitude of new products, such as sub-prime loans and niche credit programs for immigrants… Unquestionably, innovation and deregulation have vastly expanded credit availability to virtually all income classes. Access to credit has enabled families to purchase homes, deal with emergencies, and obtain goods and services. Home ownership is at a record high, and the number of home mortgage loans to low- and moderate-income and minority families has risen rapidly over the past five years.
-Dr. Alan Greenspan (2005)
Chairman of the Federal Reserve Bank
http://www.federalreserve.gov/BOARDDOCS/Speeches/2005/20050408/default.htm
Following an extended boom in construction driven in large part by overly loose mortgage lending standards and unrealistic expectations for future home price increases, the housing market collapsed – sales and prices plunged and mortgage credit was sharply curtailed. Tight mortgage credit conditions are continuing to make it difficult for many families to buy homes, despite record-low mortgage interest rates that have helped make housing very affordable… the contribution of housing investment to overall economic activity remains considerably below the average seen in past recoveries.
-Dr. Janet Yellin (2013)
Chairman of the Federal Reserve
http://www.federalreserve.gov/newsevents/speech/yellen20130211a.htm


11.1.4D: Assimilation
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Assimilation describes the process of social, cultural, and political integration of a minority into a dominant culture and society.
Learning Objectives
- Give a real life example for each of the four benchmarks of immigrant assimilation
Key Points
- Immigrant assimilation is one of the most common forms of assimilation, and is a very complex process.
- Social scientists rely on four primary benchmarks to assess immigrant assimilation: socioeconomic status, geographic distribution, second language attainment, and intermarriage.
- Socioeconomic status is defined by educational attainment, occupation, and income. Spatial concentration is defined by geography or residential patterns.
- Language attainment refers to the ability to speak English and the loss of the individual’s mother tongue. Intermarriage involves marriage across racial, ethnic, or, occasionally, generational lines.
- Segmented assimilation states that there are three main paths of assimilation for second generation immigrants: some assimilate smoothly, others experience downward assimilation, and others experience rapid economic success while preserving the values of their immigrant community.
- Intermarriage involves marriage across racial, ethnic, or, occasionally, generational lines.
Key Terms
- intermarriage : a marriage between people belonging to different groups, ethnic, religious or otherwise.
- spatial concentration : A measure of how densely particular ethnic groups are situated in a geographic location.
- socioeconomic status : One’s social position as determined by income, wealth, occupational prestige, and educational attainment.
Assimilation describes the process by which a minority integrates socially, culturally, and/or politically into a larger, dominant culture and society. The term assimilation is often used in reference to immigrants and ethnic groups settling in a new land. Immigrants acquire new customs and attitudes through contact and communication with a new society, while they also introduce some of their own cultural traits to that society.
Assimilation usually involves a gradual change of varying degree. Full assimilation occurs when new members of a society become indistinguishable from native members.
Any group (such as a state, immigrant population, or ethnicity) may choose to adopt a different culture for a variety of reasons such as political relevance or perceived advantage. However, a group may also be forced or feel compelled to do so as a result of imperialistic conquest, immigration, or drastic changes in population.
Assimilation of Immigrants
Immigrant assimilation is one of the most common forms of assimilation. It is a complex process through which an immigrant integrates themselves into a new country. Geography professor and human migration specialist William A. V. Clark says that immigrant assimilation is “a way of understanding the social dynamics of American society” and defines it as “the process that occurs spontaneously and often unintended in the course of interaction between majority and minority groups. ”
Social scientists rely on four benchmarks, initially formulated when studying European immigrants in the U.S., to assess immigrant assimilation:
- Socioeconomic status is defined by educational attainment, occupation, and income. By measuring socioeconomic status, researchers seek to determine whether immigrants eventually catch up to native-born people in matters of capital.
- Spatial concentration is defined by geography or residential patterns. The spatial residential model states that increasing socioeconomic attainment, longer residence in the U.S, and higher generational status lead to decreasing residential concentration for a particular ethnic group.
- Language attainment is defined as the ability to speak English and the loss of the individual’s mother tongue. The three-generation model of language assimilation states that the first generation makes some progress in language assimilation but retains primary fluency in their native tongue, while the second generation is bilingual and the third generation speaks only English.
- Intermarriage refers to marriage across racial, ethnic, or, occasionally, generational lines. High rates of intermarriage are considered to be an indication of social integration, as they suggest intimate and profound relations between people of different groups. Intermarriage reduces the ability of families to pass on to their children a consistent ethnic culture and thus is an agent of assimilation.
Naturalization and Immigrant Assimilation
Other than marriage, citizenship is one of the most significant factors in assimilation. Thus, immigration debates focus not only on the number of immigrants that should be admitted into a country and the processes of incorporation, but also on how citizenship should be extended and to whom. Proponents of immigration often argue that new residents will help to build and enrich American democracy, while opponents counter that the identity and legitimacy of the nation may be challenged and perhaps even threatened by immigrants. Questions of citizenship in relation to illegal immigration is a particularly controversial issue and a common source of political tension.
New Immigrant Gateways and Immigrant Assimilation
The majority of immigrants have tended to settle in traditional gateway states such as Florida, New York, California, Illinois, Texas, and Massachusetts, where immigrants find large existing populations of foreign-born people. Recently, however, immigrants have increasingly been settling in areas outside these gateway states. Sociologists Mary Waters and Tomas R. Jimenez have suggested that these geographical shifts may change the way researchers assess immigrant assimilation, as immigrants settling in new areas may encounter different experiences than immigrants settling in more traditional gateways. Specifically, Waters and Jimenez identify three distinguishing characteristics in more recent, less traditional, immigration patterns: less established social hierarchies, smaller immigrant population size, and different institutional arrangements.
Segmented Assimilation
The theory of segmented assimilation for second generation immigrants is highly researched in the sociological arena. Segmented assimilation, researched by Min Zhou and Alejandro Portes, focuses on the notion that people take different paths in how they adapt to life in the United States. This theory states that there are three main different paths of assimilation for second generation immigrants. Some immigrants assimilate smoothly into the white middle class of America, others experience downward assimilation, and others experience rapid economic success while preserving the values of their immigrant community.
This theory also includes the concept of modes of incorporation, which are the external factors within the host community that affect assimilation. These factors are created by the underlying policies of the government, the strength of prejudice in the society, and the makeup of coethnic communities within the society. These modes of incorporation affect how a child will assimilate into U.S. society, and determine how vulnerable the child will be towards downward assimilation. Factors that enhance such vulnerability include racial discrimination, location, and changes in the economy that have made it harder for intergenerational mobility.
In addition, differing modes of incorporation make available certain resources that second generation immigrants can use to overcome challenges to the process of assimilation. If the child belongs to a group that has been exempt from the prejudice experienced by most immigrants, such as European immigrants, they will experience a smoother process of assimilation. A second generation immigrant can also make use of established networks in the coethnic community. These networks provide these children with additional resources beyond those offered by the government, such as gateways into well paying jobs in businesses established by the ethnic community. Children of middle class immigrants have a greater likelihood of moving up the social ladder and joining American mainstream society than children of lower class immigrants, as they have access to both the resources provided by their parents and to the educational opportunities afforded to the middle class in the U.S.


11.12C: Artificial Immunity
- Describe artificially acquired immunity and how it is obtained
Immunity is the state of protection against infectious disease conferred either through an immune response generated by immunization or by previous infection or other non-immunological factors.
Artificial immunity can be active or passive.
Artificially-acquired passive immunity is an immediate, but short-term immunization provided by the injection of antibodies, such as gamma globulin, that are not produced by the recipient’s cells. These antibodies are developed in another individual or animal and then injected into another individual. Antiserum is the general term used for preparations that contains antibodies.
Artificial active immunization is where the microbe, or parts of it, are injected into the person before they are able to take it in naturally. If whole microbes are used, they are pre-treated, attenuated vaccines. This vaccine stimulates a primary response against the antigen in the recipient without causing symptoms of the disease.
Artificial passive immunization is normally administered by injection and is used if there has been a recent outbreak of a particular disease or as an emergency treatment for toxicity, as in for tetanus. The antibodies can be produced in animals, called ” serum therapy,” although there is a high chance of anaphylactic shock because of immunity against animal serum itself. Thus, humanized antibodies produced in vitro by cell culture are used instead if available.
The first record of artificial immunity was in relation to a disease known as smallpox. Individuals were exposed to a minor strain of smallpox in a controlled environment. Once their bodies built up a natural immunity or resistance to the weakened strain of smallpox, they became much less likely to become infected with the more deadly strains of the disease. In essence, patients were given the disease in order to help fight it later in life. Although this method was an effective one, the scientists of the time had no real scientific knowledge of why it worked.
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Key Points
- The most common form of artificial immunity is classified as active and comes in the form of vaccinations, typically given to children and young adults.
- The passive form of artificial immunity involves introducing an antibody into the system once a person has already been infected with a disease, ultimately relieving the present symptoms of the sickness and preventing re-occurrence.
- Once the body has successfully rid itself of a disease caused by a certain pathogen, a second infection with the same pathogen would prove harmless.
Key Terms
- gamma globulin : a class of proteins in the blood, identified by their position after serum protein electrophoresis, such as antibodies
- anaphylactic shock : A severe and rapid systemic allergic reaction to an allergen, constricting the trachea and preventing breathing.
- herd immunity : the protection given to a community against an epidemic of a contagious disease when a sufficient number of the population are immunised or otherwise develop immunity to it


36.3: Somatosensation - Somatosensory Receptors
- Describe the structure and function of mechanoreceptors
Somatosensory Receptors
Sensory receptors are classified into five categories: mechanoreceptors, thermoreceptors, proprioceptors, pain receptors, and chemoreceptors. These categories are based on the nature of the stimuli that each receptor class transduces. Mechanoreceptors in the skin are described as encapsulated or unencapsulated. A free nerve ending is an unencapsulated dendrite of a sensory neuron; they are the most common nerve endings in skin. Free nerve endings are sensitive to painful stimuli, to hot and cold, and to light touch. They are slow to adjust to a stimulus and so are less sensitive to abrupt changes in stimulation.
Mechanoreceptors
There are three classes of mechanoreceptors: tactile, proprioceptors, and baroreceptors. Mechanoreceptors sense stimuli due to physical deformation of their plasma membranes. They contain mechanically-gated ion channels whose gates open or close in response to pressure, touch, stretching, and sound. There are four primary tactile mechanoreceptors in human skin: Merkel’s disks, Meissner’s corpuscles, Ruffini endings, and Pacinian corpuscle; two are located toward the surface of the skin and two are located deeper. A fifth type of mechanoreceptor, Krause end bulbs, are found only in specialized regions.
Merkel’s disks are found in the upper layers of skin near the base of the epidermis, both in skin that has hair and on glabrous skin; that is, the hairless skin found on the palms and fingers, the soles of the feet, and the lips of humans and other primates. Merkel’s disks are densely distributed in the fingertips and lips. They are slow-adapting, unencapsulated nerve endings, which respond to light touch. Light touch, also known as discriminative touch, is a light pressure that allows the location of a stimulus to be pinpointed. The receptive fields of Merkel’s disks are small, with well-defined borders. That makes them very sensitive to edges; they come into use in tasks such as typing on a keyboard.
Meissner’s corpuscles, also known as tactile corpuscles, are found in the upper dermis, but they project into the epidermis. They are found primarily in the glabrous skin on the fingertips and eyelids. They respond to fine touch and pressure, but they also respond to low-frequency vibration or flutter. They are rapidly- adapting, fluid-filled, encapsulated neurons with small, well-defined borders which are responsive to fine details. Merkel’s disks and Meissner’s corpuscles are not as plentiful in the palms as they are in the fingertips.
Deeper in the dermis, near the base, are Ruffini endings, which are also known as bulbous corpuscles. They are found in both glabrous and hairy skin. These are slow-adapting, encapsulated mechanoreceptors that detect skin stretch and deformations within joints; they provide valuable feedback for gripping objects and controlling finger position and movement. Thus, they also contribute to proprioception and kinesthesia. Ruffini endings also detect warmth. Note that these warmth detectors are situated deeper in the skin than are the cold detectors. It is not surprising, then, that humans detect cold stimuli before they detect warm stimuli.
Pacinian corpuscles, located deep in the dermis of both glabrous and hairy skin, are structurally similar to Meissner’s corpuscles. They are found in the bone periosteum, joint capsules, pancreas and other viscera, breast, and genitals. They are rapidly-adapting mechanoreceptors that sense deep, transient (not prolonged) pressure, and high-frequency vibration. Pacinian receptors detect pressure and vibration by being compressed which stimulates their internal dendrites. There are fewer Pacinian corpuscles and Ruffini endings in skin than there are Merkel’s disks and Meissner’s corpuscles.
Key Points
- The four major types of tactile mechanoreceptors include: Merkel’s disks, Meissner’s corpuscles, Ruffini endings, and Pacinian corpuscles.
- Merkel’s disk are slow-adapting, unencapsulated nerve endings that respond to light touch; they are present in the upper layers of skin that has hair or is glabrous.
- Meissner’s corpuscles are rapidly-adapting, encapsulated neurons that responds to low-frequency vibrations and fine touch; they are located in the glabrous skin on fingertips and eyelids.
- Ruffini endings are slow adapting, encapsulated receptors that respond to skin stretch and are present in both the glabrous and hairy skin.
- -Pacinian corpuscles are rapidly-adapting, deep receptors that respond to deep pressure and high-frequency vibration.
Key Terms
- dendrite : branched projections of a neuron that conduct the impulses received from other neural cells to the cell body
- glabrous : smooth, hairless, bald


6: Sexual Orientation Last updated Save as PDF Page ID 167191 Susan Rahman with Nathan Bowman, Dahmitra Jackson, Lushtak, Remi Newman, & Prateek Sunder California Consortium for Equitable Change in Hispanic Serving Institutions Open Educational Resources (CC ECHO) 6.1: Introduction to Sexual Orientation 6.2: Sexual Orientation 6.3: Identity Formation 6.4: Sexual Fluidity 6.5: Heteronormativity and the Sexual Hierarchy 6.6: Different Types of Sexualities 6.7: Sexual Essentialism and the Compulsory Sexuality 6.8: The Kinsey Scale 6.9: The Lavender Scare 6.10: Stonewall 6.11: Homosexuality and Psychology 6.12: The HIV/AIDS Pandemic 6.13: Marriage Equality and Current Social Movements 6.14: Don't say Gay Bill in Florida 6.15: Unveiling the Truth - Heteronormativity and Cisnormativity 6.16: Sex Education and LGBTQIA+ Young People 6.17: Conclusion 6.18: Discussion Questions 6.19: For Further Exploration 6.20: Glossary 6.21: References Thumbnail: “I’m not missing a minute of this. It’s the revolution!” Sylvia Rivera


6.4: Power Screws
A power screw (also sometimes called a lead screw) is another simple machine that can be used to create very large forces. The screw can be thought of as a wedge or a ramp that has been wound around a shaft. By holding a nut stationary and rotating the shaft, we can have the nut sliding either up or down the wedge in the shaft. In this way, a relatively small moment on the shaft can cause very large forces on the nut.
Static Analysis of Power Screws:
The easiest way to analyze a power screw system is to turn the problem into a 2D problem by "unwrapping" the ramp from around the shaft. To do this we will need two numbers. First we will need the diameter of the shaft, and second we will need either the threads-per-inch/centimeter or the pitch of the screw. The threads-per-inch tells you how many threads you have per inch/centimeter of screw. With a single thread design (most screws) this will also be the number of times the thread wraps around the screw in one inch/centimeter. The pitch, on the other hand, gives you the distance between two adjacent threads. Either of these numbers can be used to find the other.
Once we have these numbers, we can imagine unwrapping the ramp from around the screw and ending up with a ramp in one of the two situations below. In either case, we can use the inverse tangent function to find the lead angle , which can be thought of as the angle of the thread that the nut is climbing up. Finding the lead angle is the first step in analyzing a power screw system.
Once we find the lead angle, we can draw a free body diagram of the "nut" in our unwrapped system. Here we include the pushing force which is pushing our nut up the incline, the load force which is the force the nut exerts on some external body, the normal force between the nut and screw, and the friction force between the nut and the screw.
If our screw is pushing a load at some constant rate, then we can assume two things: First, the nut is in equilibrium, so we can write out the equilibrium equations for the nut. Second, the nut is sliding, indicating that the friction force will be equal to the normal force times the kinetic coefficient of friction.
\[ F_f = \mu_k * F_N \]
\[ \sum F_x = F_{push} - F_N * \sin (\theta) - \mu_k * F_N * \cos (\theta) = 0 \]\[ \sum F_y = F_{push} - F_N * \cos (\theta) - \mu_k * F_N * \sin (\theta) = 0 \]
We can then simplify the equations above into a single equation relating the load force and the pushing force.
\[ F_{push} = \frac{\sin (\theta) + \mu_k * \cos (\theta)}{\cos (\theta) - \mu_k * \sin (\theta)} * F_{load} \]
In reality, the pushing force is not a single force at all. It is the forces preventing the nut from rotating with the screw. The cumulative pushing force will really cause an equal and opposite moment to the input moment that is spinning the shaft.
Finally, if we replace the pushing force with the moment that is driving the screw in our system (in this case the torque \(T\)), we can relate the input torque that is driving our screw to the force that the nut on the screw is pressing forward with.
\[ T = \frac{\sin (\theta) + \mu_k \cos (\theta)}{\cos (\theta) - \mu_k \sin (\theta)} * F_{load} * r_{shaft} \]
Self-Locking Screws
Imagine that we apply a torque to a power screw to lift a body; then when we get the load to the desired height we stop applying that torque to let the body sit where it is. If we were to redraw our free body diagram from earlier for the new situation, we would find two things.
- The pushing force is missing (since a torque is no longer applied to the shaft).
- The friction is now fighting against the nut sliding back down the ramp.
With this new free body diagram, there are two possible scenarios that could occur:
- The friction force is large enough to keep the nut from sliding down the ramp, meaning everything will remain in static equilibrium if released.
- The friction force will not be sufficient to keep the nut from sliding down the ramp, meaning that the load would begin to fall as soon as the torque is removed from the shaft.
With power screw applications such as a car jack, the second option could be very dangerous. It is therefore important to know if a power screw system is self-locking (scenario 1 above) or not self-locking (scenario 2 above).
To define the boundary between self-locking systems and non-self-locking systems, we use something called the self-locking angle . As intuition would tell us, slipping does not occur on very gentle slopes (small lead angles) while it does occur on very steep slopes (large lead angles). The angle at which the nut would begin to slip is known as the self-locking angle.
To find the self-locking angle, we will assume impending motion (relating the friction force to the normal force) and leave the lead angle as an unknown. This lets us create the free body diagram as shown below and gives us the equilibrium equations below.
\[ \sum F_x = - F_N * \sin (\theta) + \mu_s * F_N * \cos (\theta) = 0 \] \[ \sum F_y = -F_{load} + F_N * \cos (\theta) + \mu_s * F_N * \sin (\theta) = 0 \]
Using the \(x\) equilibrium equation as a starting point, we can solve for the angle \(\theta\) (eliminating the normal force all together in the process). This new equation shown below gives us the self-locking angle. \[ \theta_{locking} = \tan ^{-1} (\mu_s) \]
Systems with lead angles smaller than this will be self-locking, while systems with lead angles larger than this will not be self-locking.
Example \(\PageIndex{1}\)
The power screw below is being used to lift a platform with a weight of 12 pounds. Based on the information below...
- What is the required torque on the shaft to lift the load?
- Would the load fall if the toque was removed from the shaft?
- Solution


3.3: Harmonic Syntax - The Idealized Phrase
Harmonic syntax concerns the norms or principles according to which harmonies (chords) are placed into meaningful successions. These norms include progressions that are more or less common than others. Those norms generate expectations for listeners familiar with the style: if IV–V is more common than IV–VI , the appearance of a IV chord generates an expectation that the next chord is more likely to be V than it is to be VI .
In Western classical music, harmonies generally group into three harmonic functions — tonic (T), subdominant (S), and dominant (D) — and these functions group together chords that progress to and from other chords in similar ways. For example, since II and IV are both subdominant chords, they will participate in many of the same kinds of chord progressions, and at times can be substituted for each other with only a minimal change to the musical effect.
On a local level (chord-to-chord progressions), we can summarize the tendencies of these functions with the cycle T–S–D–T . That is, harmonies tend to progress through a cyclical progression of those three functions:
T → S → D → T → and so on . . .
That does not rule out T progressing to D, D progressing to S, etc. But it does mean that those progressions tend to be less common, at least in classical music.
Higher-level musical structures also impact the norms according to which these harmonic functions progress. For now, we will consider one higher-level structure that influences chord-progression tendencies — the phrase — and we will limit our study to isolated, complete, self-sufficient phrases. This is an idealized, oversimplified setting — like strict voice-leading — that is useful for learning the basics. Some such phrases even exist in real music! But most of the time there are a number of competing factors that influence the chord-progression strategies employed by a composer at any given moment. However, the idealized phrase is a helpful starting point. Future study will explore how classical composers employ harmonic progressions in larger musical works that combine multiple phrases (which are not self-sufficient) into larger themes and movements.
The idealized phrase
The idealized phrase (also called the phrase model ) is a single musical phrase that progresses through an entire cycle of harmonic functions, beginning and ending on tonic. (Strict voice-leading exercises are such phrases.) These phrases begin with a point of stability (tonic), move away from that stable point, and then eventually lead to a point of high tension and resolution (an authentic cadence ). This pattern of stability–instability–stability, or rest–motion–rest, with a single goal at the end, should be familiar both from species counterpoint and from strict keyboard-style voice-leading. (This pattern also governs large-scale formal structures in classical music.)
The simplest phrase that exhibits this complete harmonic cycle is a tonic-dominant-tonic progression: I–V–I. This phrase begins and ends with the most stable harmony ( I ), and includes an authentic cadence ( V–I ). The V is the high point of instability, containing the tendency tone ( ti ) that most strongly points to the final point of arrival ( do , or tonic).
This harmonic cycle can be expanded by inserting a subdominant chord, a destabilized tonic chord, or both, as in the following examples:
I IV V I
I II V I
I VI V I
I VI II V I
In functional bass terms, any harmonic progression that follows the pattern
T1 → (S_) → D5 → T1
can serve as the basis for a complete idealized phrase. (Harmonies in parentheses are optional.)
Phrases are seldom 3–5 chords long, however, and a harmonic function can be expressed by more than a single chord. Thus we can understand the harmonic functions not simply as chords, but as zones of varying length in a phrase, which can be created by a number of chords or short chord progressions. More generally, then, our idealized musical phrase contains a single progression of functional zones T → (S) → D → T , begins with T1 , and ends with an authentic cadence ( D5–T1 ), as seen in the example below.
Triggering and prolonging harmonic functions in an idealized phrase
To establish, or trigger, a harmonic functional zone, composers tend to use a fixed scale degree in the bass . In other words, tonic tends to be triggered by T1 (always I ), subdominant by S2 or S4 (including a variety of II and IV chords, in in root position or inversions, with and without sevenths), and dominant by D5 ( V , with or without a seventh, or a compound cadence ). These four categories of chords — T1 , S2 , S4 , and D5 — are called functional chords (because they trigger the function) or cadential chords (because they can participate in a cadence).
Other chords are often called contrapuntal chords or embellishing chords , and are typically used to prolong a function throughout the zone.
Functional prolongations are shown in a harmonic analysis by writing/typing T, S, or D underneath the individual chord labels (Roman numerals or functional bass) and extending a line from the beginning of the functional zone to the end.
The following excerpt is from Mozart’s Piano Sonata in A Major, K. 331, I., mm. 1–4, with a harmonic reduction and analysis provided below the original score. Such an analysis is called an interpreted harmonic analysis, because the harmonies are interpreted according to the way they behave in the phrase, rather than merely labeled. In this phrase, note the following:
- The tonic zone is triggered by a root-position tonic triad ( I or T1 ).
- Contrapuntal dominant chords ( D7 — first-inversion dominant chords) create a passing bass motion between the opening I chord, the vi in m. 3, and the return of I in m. 4.
- The cadential progression begins in m. 4 with the move from I to ii 6 ( S4 ) and then to the cadential six-four and dominant triad ( D5 ). Note that the entirety of the cadential progression in m. 4 is made up of cadential chords — chords with fixed scale degrees in the bass.
- In contrast, the entire tonic-prolongation zone is made up of contrapuntal chords — variable scale degrees in the bass — with the exception of the I chord that triggered the tonic function.
- The vi chord is a root-position chord, but still an embellishing chord, while the ii 6 is an inverted chord, but still a functional/cadential chord. The difference is not the inversion, but the scale degree of the bass.
Not all classical phrases as neatly fit the general trends outlined in this resource. As discussed in Style and tendency , the principles of harmonic syntax are both reliable and bendable/breakable, and it is often the music that bends/breaks the “rules” in interesting ways that we care about the most. So in your own analyses, keep these principles in mind as general principles, and simultaneously look for where composers meet these expectations as well as where they break them.
For more details on the triggering and prolonging of harmonic functions in a classical phrase, see Harmonic syntax – prolongation .