7.4: Problems
1 . The musical note middle C has a frequency of 262 Hz. What are its period and wavelength?
2 . The following is a graph of the height of a water wave as a function of position , at a certain moment in time.
Trace this graph onto another piece of paper, and then sketch below it the corresponding graphs that would be obtained if
(a) the amplitude and frequency were doubled while the velocity remained the same;
(b) the frequency and velocity were both doubled while the amplitude remained unchanged;
(c) the wavelength and amplitude were reduced by a factor of three while the velocity was doubled.
Explain all your answers. [Problem by Arnold Arons.]
3
. (a) The graph shows the height of a water wave pulse as a function of position. Draw a graph of height as a function of time for a specific point on the water. Assume the pulse is traveling to the right.
(b) Repeat part a, but assume the pulse is traveling to the left.
(c) Now assume the original graph was of height as a function of time, and draw a graph of height as a function of position, assuming the pulse is traveling to the right.
(d) Repeat part c, but assume the pulse is traveling to the left.
Explain all your answers. [Problem by Arnold Arons.]
4
. At a particular moment in time, a wave on a string has a shape described by \(y=3.5\cos (0.73\pi x+0.45\pi t+0.37\pi)\). The stuff inside the cosine is in radians. Assume that the units of the numerical constants are such that \(x\), \(y\), and \(t\) are in SI units.\hwhint{hwhint:sinwavekinem}
(a) Is the wave moving in the positive \(x\) or the negative \(x\) direction?
(b) Find the wave's period, frequency, wavelength.
(c) Find the wave's velocity.
(d) Find the maximum velocity of any point on the string, and compare with the magnitude and direction of the wave's velocity. (answer check available at lightandmatter.com)
5 . The figure shows one wavelength of a steady sinusoidal wave traveling to the right along a string. Define a coordinate system in which the positive \(x\) axis points to the right and the positive \(y\) axis up, such that the flattened string would have \(y=0\). Copy the figure, and label with \(y=0\) all the appropriate parts of the string. Similarly, label with \(v=0\) all parts of the string whose velocities are zero, and with \(a=0\) all parts whose accelerations are zero. There is more than one point whose velocity is of the greatest magnitude. Pick one of these, and indicate the direction of its velocity vector. Do the same for a point having the maximum magnitude of acceleration. Explain all your answers.
[Problem by Arnold Arons.]
6 . Find an equation for the relationship between the Doppler-shifted frequency of a wave and the frequency of the original wave, for the case of a stationary observer and a source moving directly toward or away from the observer.
7 . Suggest a quantitative experiment to look for any deviation from the principle of superposition for surface waves in water. Try to make your experiment simple and practical.
8
. The simplest trick with a lasso is to spin a flat loop in a horizontal plane. The whirling loop of a lasso is kept under tension mainly due to its own rotation. Although the spoke's force on the loop has an inward component, we'll ignore it. The purpose of this problem, which is based on one by A.P. French, is to prove a cute fact about wave disturbances moving around the loop. As far as I know, this fact has no practical implications for trick roping! Let the loop have radius \(r\) and mass per unit length \(\mu\), and let its angular velocity be \(\omega\).
(a) Find the tension, \(T\), in the loop in terms of \(r\), \(\mu\), and \(\omega\). Assume the loop is a perfect circle, with no wave disturbances on it yet. \hwhint{hwhint:lasso} \hwans{hwans:lasso}
(b) Find the velocity of a wave pulse traveling around the loop. Discuss what happens when the pulse moves is in the same direction as the rotation, and when it travels contrary to the rotation.
9
. A string hangs vertically, free at the bottom and attached at the top.
(a) Find the velocity of waves on the string as a function of the distance from the bottom
(b) Find the acceleration of waves on the string.\hwans{hwans:wave-on-hanging-string}
(c) Interpret your answers to parts a and b for the case where a pulse comes down and reaches the end of the string. What happens next? Check your answer against experiment and conservation of energy.
10 . Singing that is off-pitch by more than about 1% sounds bad. How fast would a singer have to be moving relative to a the rest of a band to make this much of a change in pitch due to the Doppler effect?
11 . Light travels faster in warmer air. Use this fact to explain the formation of a mirage appearing like the shiny surface of a pool of water when there is a layer of hot air above a road.
12
. (a) Compute the amplitude of light that is reflected back into air at an air-water interface, relative to the amplitude of the incident wave. Assume that the light arrives in the direction directly perpendicular to the surface.The speeds of light in air and water are \(3.0\times10^8\) and \(2.2\times10^8\) m/s, respectively.
(b) Find the energy of the reflected wave as a fraction of the incident energy. \hwhint{hwhint:airwaterrefl}(answer check available at lightandmatter.com)
13 . A concert flute produces its lowest note, at about 262 Hz, when half of a wavelength fits inside its tube. Compute the length of the flute. \hwans{hwans:flute}
14
. (a) A good tenor saxophone player can play all of the following notes without changing her fingering, simply by altering the tightness of her lips: E\(\flat\) (150 Hz), E\(\flat\) (300 Hz), B\(\flat\) (450 Hz), and E\(\flat\) (600 Hz). How is this possible? (I'm not asking you to analyze the coupling between the lips, the reed, the mouthpiece, and the air column, which is very complicated.)
(b) Some saxophone players are known for their ability to use this technique to play “freak notes,” i.e., notes above the normal range of the instrument. Why isn't it possible to play notes below the normal range using this technique?
| C | 261.6 Hz |
| D | 293.7 |
| E | 329.6 |
| F | 349.2 |
| G | 392.0 |
| A | 440.0 |
| flat | 466.2 |
Problem 15 .
15
. The table gives the frequencies of the notes that make up the key of F major, starting from middle C and going up through all seven notes.
(a) Calculate the first four or five harmonics of C and G, and determine whether these two notes will be consonant or dissonant. (Recall that harmonics that differ by about 1-10% cause dissonance.)
(b) Do the same for C and B\(\flat\).
16
. A Fabry-Perot interferometer, shown in the figure being used to measure the diameter of a thin filament, consists of two glass plates with an air gap between them. As the top plate is moved up or down with a screw, the light passing through the plates goes through a cycle of constructive and destructive interference, which is mainly due to interference between rays that pass straight through and those that are reflected twice back into the air gap. (Although the dimensions in this drawing are distorted for legibility, the glass plates would really be much thicker than the length of the wave-trains of light, so no interference effects would be observed due to reflections within the glass.)
(a) If the top plate is cranked down so that the thickness, \(d\), of the air gap is much less than the wavelength \(\lambda\) of the light, i.e., in the limit \(d \rightarrow 0\), what is the phase relationship between the two rays? (Recall that the phase can be inverted by a reflection.) Is the interference constructive, or destructive?
(b) If \(d\) is now slowly increased, what is the first value of \(d\) for which the interference is the same as at \(d\rightarrow 0\)? Express your answer in terms of \(\lambda\).
(c) Suppose the apparatus is first set up as shown in the figure. The filament is then removed, and \(n\) cycles of brightening and dimming are counted while the top plate is brought down to \(d=0\). What is the thickness of the filament, in terms of \(n\) and \(\lambda\)?
Based on a problem by D.J. Raymond.
17
. (a) A wave pulse moves into a new medium, where its velocity is greater by a factor \(\alpha\). Find an expression for the fraction, \(f\), of the wave energy that is transmitted, in terms of \(\alpha\). Note that, as discussed in the text, you cannot simply find \(f\) by squaring the amplitude of the transmitted wave. \hwans{hwans:maxtransmission}
(b) Suppose we wish to transmit a pulse from one medium to another, maximizing the fraction of the wave energy transmitted. To do so, we sandwich another layer in between them, so that the wave moves from the initial medium, where its velocity is \(v_1\), through the intermediate layer, where it is \(v_2\), and on into the final layer, where it becomes \(v_3\). What is the optimal value of \(v_2\)? (Assume that the middle layer is thicker than the length of the pulse, so there are no interference effects. Also, although there will be later echoes that are transmitted after multiple reflections back and forth across the middle layer, you are only to optimize the strength of the transmitted pulse that is first to emerge. In other words, it's simply a matter of applying your answer from part a twice to find the amount that finally gets through.) \hwans{hwans:maxtransmission}
(c) 1998-2013 Benjamin Crowell, licensed under the Creative Commons Attribution-ShareAlike license . Photo credits are given at the end of the Adobe Acrobat version.
Contributors and Attributions
Benjamin Crowell (Fullerton College). Conceptual Physics is copyrighted with a CC-BY-SA license.


11.8: Primary Sources
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Migrant Farmers and Immigrant Labor (1952)
During the labor shortages of World War II, the United States’ launched the Bracero (“laborer”) program to bring Mexican laborers into the United States. The program continued into the 1960s and brought more than a million workers into the United States on short-term contracts. Undocumented immigration continued, however. Congress held hearings and, in the selection below, a migrant worker named Juanita Garcia testifies to Congress about the state of affairs in California’s Imperial Valley. Beginning in 1954, Dwight Eisenhower’s administration oversaw, with the cooperation of the Mexican government, “Operation Wetback,” which empowered to the Border Patrol to crack down upon illegal immigration.
Pete Hernandez, a migrant worker, was tried for the murder of his employer, Joe Espinosa, in Edna, Texas, in 1950. Hernandez was convicted by an all-white jury. His lawyers appealed. They argued that Hernandez was entitled to a jury “of his peers” and that systematic exclusion of Mexican Americans violated constitutional law. In a unanimous decision, the United States Supreme Court ruled that Mexican Americans—and all “classes”—were entitled to the “equal protection” articulated in the Fourteenth Amendment.
Brown v. Board of Education of Topeka (1954)
In 1896 [confirm date], the United States Supreme Court declared in Plessy v. Ferguson that the doctrine of “separate but equal” was constitutional. In 1954, the United States Supreme Court overturned that decision and
Richard Nixon on the American Standard of Living (1959)
As Cold War tensions eased, exhibitions allowed for Americans and Soviets to survey the other’s culture and way of life. In 1959, the Russians held an exhibition in New York, and the Americans in Moscow. A videotaped discussion between Vice President Richard Nixon and Soviet Premier Nikita Kruschev, the so-called “Kitchen Debate,” won Richard Nixon acclaim at home for his articulate defense of the American standard of living. In the following extract from July 24, 1959, Nixon opened the American Exhibition in Moscow.
John F. Kennedy on the Separation of Church and State (1960)
American Anti-Catholicism had softened in the aftermath of World War II, but no Catholic had ever been elected president and Protestant Americans had long been suspicious of Catholic politicians when John F. Kennedy ran for the presidency in 1960. (Al Smith, the first Catholic presidential candidate, was roundly defeated in 1928 owing in large part to popular anti-Catholic prejudice). On September 12, 1960, Kennedy addressed the Greater Houston Ministerial Association and he not only allayed popular fears of his Catholic faith, he delivered a seminal statement on the separation of church and state.
In 1959, photographer John Bledsoe captured this image of the crowd on the steps of the Arkansas state capitol building, protesting the federally mandated integration of Little Rock’s Central High School. This image shows how worries about desegregation were bound up with other concerns, such as the reach of communism and government power.
Redbook made this film to convince advertisers that the magazine would help them attract the white suburban consumers they desired. The “happy go spending, buy it now, young adults of today” are depicted by the film as flocking to the suburbs to escape global and urban turmoil. Redbook Magazine, “In The Suburbs” (1957). Via The Internet Archive .


1.3: Principles of Communication
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In this section, we will be discussing how communication is used to meet needs; exists on multiple levels; is a transactional process; is situated; can be either face-to-face, mediated, or both; is continuous, intentional, and unintentional; and is irreversible.
In addition to using communication to exchange messages and create shared meaning, we also use it to meet the various needs we have as human beings. Communication meets four needs: physical, instrumental, relational, and identity.
Physical needs include needs that keep our bodies and minds functioning. Communication, which we most often associate with our brain, mouth, eyes, and ears, actually has many more connections to and effects on our physical body and well-being. At the most basic level, communication can alert others that our physical needs are not being met. Human beings are social creatures, which makes communication important for our survival.
Instrumental needs include needs that help us ‘get things done’ in our day-to-day lives and achieve short- and long-term goals. We all work towards short- and long-term goals every day. Fulfilling these goals is an ongoing communicative task, which means we spend much of our time communicating for instrumental needs. Some common instrumental needs include influencing others, getting information we need, or getting support (Burleson, Metts, & Kirch, 2000).
Communication meets our relational needs because it is through communication that we begin, develop, maintain, and end relationships. In order to develop a relationship, we may use nonverbal communication to assess whether someone is interested in talking to us or not, then use verbal communication to strike up a conversation. Then, through the mutual process of self-disclosure, a relationship forms over time. Once formed, we need to maintain a relationship, so we use communication to express our continued liking of someone. We can verbally say things like “You’re such a great friend.” Finally, communication or the lack of it helps us end relationships. We may communicate our deteriorating commitment to a relationship by avoiding communication with someone, verbally criticizing him or her, or explicitly ending a relationship. From checking in with relational partners by text, social media, or face-to-face, to celebrating accomplishments, communication forms the building blocks of our relationships.
Identity needs include our need to present ourselves to others and be thought of in particular ways. Our identity changes as we progress through life, but communication is the primary means of establishing our identity and fulfilling our identity needs. Communication allows us to present ourselves to others in particular ways. Just as many companies, celebrities, and politicians create a public image, we present different faces in different contexts. The influential scholar Erving Goffman compared self-presentation to a performance and suggested we all perform different roles in different contexts (Goffman, 1959). For example, you may perform the role of a parent when at home with your child, but the role of supervisor when at work.
Communication operates on two distinct levels: there is a content dimension and a relational dimension. The content dimension is the meaning of the actual message itself, whereas the relational dimension expresses “how you feel about the other person: whether you like or dislike the other person, feel in control or subordinate, feel comfortable or anxious, and so on” (Adler, 2017, p. 18). For example, consider the difference between someone saying “I’m busy tonight” in an annoyed tone versus “Sorry babe, I’m busy tonight” in an apologetic tone. Both messages mean the same thing on the content dimension, but express different feelings on the relational dimension. There may be times when the content dimension is all that matters; likewise, there are other times where more importance is placed on the relational dimension (Adler & Proctor, 2017).
Communication is also a transactional process, this means that: 1) Each communicator is simultaneously a sender and receiver of messages. 2) Meaning is co-created in the interaction by both communicators. 3) Communication is an ongoing process and previous interactions between communicators influence current interactions. And since communication is ongoing, 4) current interactions likewise will influence future interactions and will either affirm or modify perceptions of the other and the relationship (Alberts, Nakayama, & Martin, 2016).
Communicative interactions can take place face-to-face using verbal symbols, such as words, and nonverbal symbols, such as gestures. They can also take place through a mediated platform, such as a smoke signal, email, or text message. Sometimes, it can even be a combination of face-to-face and mediated, such as when a speaker is presenting to an audience with a microphone. How the interaction takes place will affect how messages are produced, interpreted, and coordinated.
All communication is situated, which means that communication occurs within a specific setting “that affects how the messages are produced, interpreted, and coordinated” (Verderber, MacGeorge, & Verderber, 2016, p. 16). Not only do the contextual factors mentioned in Section 2 influence communication, but communication is also situated historically, economically, socially, and politically. For example, some current political rhetoric surrounding Mexican immigrants paints them as criminals and rapists; this can affect how others perceive and communicate (or avoid communicating) with people that fall into this group.
In all communicative interactions, we are continuously sending messages, whether they are verbal or nonverbal, and whether it is intentional (conscious), or unintentional (unconscious). Although communication may seem like a perceptible and deliberate process, we often send messages without conscious thought. In fact, there are so many messages being sent at one time that many of them may not even be received.
Additionally, not all behavior is consciously encoded. For example, we might have had a rough night with little sleep, which us yawn more often than we normally would. We are not deliberately and consciously encoding the yawn, rather our body does it without forethought. However, our yawn may unintentionally communicate “boredom” to the other person in the interaction. In contrast, a we may consciously decide to communicate a particular message (encoding) to another person if their story has gone on a very long time and we have somewhere else to go. We may decide in our heads that we need a way out of the conversation and consider a yawn and a glance toward the door to be an effective way to hint that we have to leave.
Once something is communicated, it is irreversible and cannot be un-communicated. While we “may try to qualify, negate, or somehow reduce the effects… once it has been sent and received, the message itself cannot be reversed” (DeVito, 2014, p. 25).  You may have even quickly said “I take it back,” but the impression created in the mind of the other cannot be erased. While we can apologize, there can still be consequences of the original message. This principle is also important to note in mediated-communication that takes place through platforms such as email or a text message, as your interactions can also be saved and shared with others.


1.5: Functional Areas
What you’ll learn to do: identify the primary functional areas within a business and describe their contribution to the organization
The decisions about how best to use the factors of production to provide the goods or services of the business require a team of people working in a variety of jobs. As businesses grow larger and their products and services become more complex, the number of functional areas within a business grows. Each functional area makes specific and valuable contributions to the organization as a whole. In this section we will explore some of the most common functional areas in a business and how each contributes to the overall success of the business.
Learning Objectives
- Identify key people and explain the activities within each functional area
Functional Areas of Business
Just as different functions in the human body are performed and regulated by different organs, different functions within a business are performed and controlled by different parts of the business. One of the reasons for separating business operations into functional areas is to allow each to operate within its area of expertise, thus building efficiency and effectiveness across the business as a whole. The key functional areas of a business are the following:
- Management
- Operations
- Marketing
- Accounting
- Finance
Management
The primary role of managers in business is to supervise other people’s performance. Most management activities fall into the following categories:
- Planning : Managers plan by setting long-term goals for the business, as well short-term strategies needed to execute against those goals.
- Organizing : Managers are responsible for organizing the operations of a business in the most efficient way, enabling the business to use its resources effectively.
- Controlling : A large percentage of a manager’s time is spent controlling the activities within the business to ensure that it’s on track to achieve its goals. When people or processes stray from the path, managers are often the first ones to notice and take corrective action.
- Leading : Managers serve as leaders for the organization, in practical as well as symbolic ways. The manager may lead work teams or groups through a new process or the development of a new product. The manager may also be seen as the leader of the organization when it interacts with the community, customers, and suppliers.
Operations
Operations is where inputs (factors of production) are converted to outputs (goods and services). Operations is like the heart of a business, pumping out goods and services in a quantity and of a quality that meets the needs of the customers. The operations manager is responsible for overseeing the day-to-day business operations, which can encompass everything from ordering raw materials to scheduling workers to produce tangible goods.
Marketing
Marketing consists of all that a company does to identify customers’ needs and design products and services that meet those needs. The marketing function also includes promoting goods and services, determining how the goods and services will be delivered, and developing a pricing strategy to capture market share while remaining competitive. In day’s technology-driven business environment, marketing is also responsible for building and overseeing a company’s Internet presence (e.g., the company Web site, blogs, social media campaigns, etc.). Today, social media marketing is one of the fastest growing sectors within the marketing function.
Accounting
Accountants provide managers with information needed to make decisions about the allocation of company resources. This area is ultimately responsible for accurately representing the financial transactions of a business to internal and external parties, government agencies, and owners/investors. Financial Accountants are primarily responsible for the preparation of financial statements to help entities both inside and outside the organization assess the financial strength of the company. Managerial accountants provide information regarding costs, budgets, asset allocation, and performance appraisal for internal use by management for the purpose of decision-making.
Finance
Although related to accounting, the finance function involves planning for, obtaining, and managing a company’s funds. Finance managers plan for both short- and long-term financial capital needs and analyze the impact that borrowing will have on the financial well-being of the business. A company’s finance department answers questions about how funds should be raised (loans vs. stocks), the long-term cost of borrowing funds, and the implications of financing decisions for the long-term health of the business.


5.3: End Punctuation
- Demonstrate the proper use of periods, question marks, and exclamation points
There are three punctuation marks that come at the end of a sentence: the period ( . ), the question mark ( ? ), and the exclamation point ( ! ). A sentence is always followed by a single space, no matter what the concluding punctuation is.
Periods
Periods indicate a neutral sentence, and as such are by far the most common ending punctuation mark. They’re at the end of every sentence on this page so far. They occur at the end of statements. While two spaces after periods used to be the norm, now just one space is standard.
Question Marks
A question mark comes at the end of a question (How was class today?). A rhetorical question is asked to make a point, and an answer is not expected (Why does it always have to rain on the first day of class?). Some questions are used principally as polite requests (Would you pass the salt?).
All of these questions can be categorized as direct questions, and all of these questions require a question mark at their ends.
Indirect Questions
Indirect questions do not have question marks at their ends. They can be used in many of the same ways as declarative ones, but they often emphasize uncertainty or lack of knowledge:
- I can’t guess how Tamika managed it .
- I wonder whether I looked that bad .
- Cecil asked where the reports were .
Notice that different word order is used in direct and indirect questions: in direct questions, the verb usually comes before the subject, while in indirect questions, the verb appears second.
What about when you have a sentence that is part statement and part question? What do you do then? You have a couple of options, depending upon the situation. You might have a sentence like this:
- The question I have is, how are we going to get out of here?
In this case, the statement before the question isn’t complete, so you can simply use a comma to separate the statement from the question.
Of course, the sample sentence is a bit awkward, so it might be preferable to rewrite the sentence. You could change the sentence so the first part, the statement part, is a complete sentence. In this situation, you might have a sentence like the following:
- One question remains: How are we going to get out of here?
Exclamation Points
The exclamation point is a punctuation mark usually used after an interjection or exclamation to indicate strong feelings or high volume, and it often marks the end of a sentence. You’ve likely seen it overused on the internet.
While this kind of statement is excessive, there are appropriate ways to use exclamation points. A sentence ending in an exclamation mark may be an exclamation (such as “Wow!” or “Boo!”), or an imperative (“Stop!”), or it may indicate astonishment: “They were the footprints of a gigantic duck!”
The exclamation point is sometimes used in conjunction with the question mark to convey protest or astonishment (“Of all the coffee shops, you want to meet at the Pied Cow?!”).
Exclamation points may be repeated for additional emphasis (“That’s great!!!”), but this practice is generally appropriate only in casual or informal writing, such as text messaging or online communication with friends and family.
In most cases, you should be careful with exclamation marks and make sure the situation calls for them. They are generally considered pretty informal, and a particularly famous writer had this to say about them:
Cut out all these exclamation points. An exclamation point is like laughing at your own joke.
— F. Scott Fitzgerald, author of The Great Gatsby
Punctuation Clusters
Occasionally, you’ll encounter cases that seem to require multiple punctuation marks right next to each other. Sometimes you need to keep all the marks, but other times, you should leave some out.
In general, you should not use more than one ending punctuation mark (period, question mark, exclamation point) in a row. If you are quoting a question, it should end with a question mark, not a question mark and a period. If an abbreviation, like etc ., ends a sentence, you should use only one period.
- Carlos leaned forward and asked, “Did you get the answer to number six?”
- I think we’ll have enough food. Mary bought the whole store: chips, soda, candy, cereal, etc.
However, you can place a comma immediately after a period, as you can see in the paragraph above with etc. This rule also applies to the abbreviations e.g. and i.e.
Note: e.g . is an abbreviation for the Latin phrase exempli gratia , which means “for example,” and i.e. stands for id est , which is Latin for “that is.”Periods and parentheses can also appear right next to each other. Sometimes the period comes after the closing parenthesis, but sometimes it appears inside the parentheses. This depends on how much of the sentence is explaining or qualifying the rest of the sentence.
- I have always wanted to travel to Cuba (although the only city I know of is Havana).
- I am going on a trip to Cuba next week. (I have always wanted to go there.)
Contributors and Attributions
- Text: Periods, Text: Punctuation Clusters. Authored by : Lumen Learning. License : CC BY: Attribution
- Original Icons. Provided by : Lumen Learning. License : CC BY: Attribution
- Revision and Adaptation of Wikipedia content. Provided by : Lumen Learning. License : CC BY-SA: Attribution-ShareAlike
- Question. Provided by : Wikipedia. Located at : https://en.Wikipedia.org/wiki/Question . License : CC BY-SA: Attribution-ShareAlike
- Content clause. Provided by : Wikipedia. Located at : https://en.Wikipedia.org/wiki/Content_clause#Interrogative_content_clauses . License : CC BY-NC-SA: Attribution-NonCommercial-ShareAlike
- Exclamation mark. Provided by : Wikipedia. Located at : https://en.Wikipedia.org/wiki/Exclamation_mark . License : CC BY-SA: Attribution-ShareAlike
- Modification of Potoooooooo (errors added). Provided by : Wikipedia. Located at : https://en.Wikipedia.org/wiki/Potoooooooo . License : CC BY-SA: Attribution-ShareAlike
- Part questions. Authored by : Excelsior OWL. Located at : https://owl.excelsior.edu/grammar-essentials/punctuation/question-marks/ . License : CC BY: Attribution
- Exclamation Marks. Authored by : Excelsior OWL. Located at : https://owl.excelsior.edu/grammar-essentials/punctuation/exclamation-marks/ . License : CC BY: Attribution


6.2E: Exercises
Practice Makes Perfect
Find the Greatest Common Factor of Two or More Expressions
In the following exercises, find the greatest common factor.
1. \(10p^3q,12pq^2\)
- Answer
-
\(2pq\)
2. \(8a^2b^3,10ab^2\)
3. \(12m^2n^3,30m^5n^3\)
- Answer
-
\(6m^2n^3\)
4. \(28x^2y^4,42x^4y^4\)
5. \(10a^3,12a^2,14a\)
- Answer
-
\(2a\)
6. \(20y^3,28y^2,40y\)
7. \(35x^3y^2,10x^4y,5x^5y^3\)
- Answer
-
\(5x^3y\)
8. \(27p^2q^3,45p^3q^4,9p^4q^3\)
Factor the Greatest Common Factor from a Polynomial
In the following exercises, factor the greatest common factor from each polynomial.
9. \(6m+9\)
- Answer
-
\(3(2m+3)\)
10. \(14p+35\)
11. \(9n−63\)
- Answer
-
\(9(n−7)\)
12. \(45b−18\)
13. \(3x^2+6x−9\)
- Answer
-
\(3(x^2+2x−3)\)
14. \(4y^2+8y−4\)
15. \(8p^2+4p+2\)
- Answer
-
\(2(4p^2+2p+1)\)
16. \(10q^2+14q+20\)
17. \(8y^3+16y^2\)
- Answer
-
\(8y^2(y+2)\)
18. \(12x^3−10x\)
19. \(5x^3−15x^2+20x\)
- Answer
-
\(5x(x^2−3x+4)\)
20. \(8m^2−40m+16\)
21. \(24x^3−12x^2+15x\)
- Answer
-
\(3x(8x^2−4x+5)\)
22. \(24y^3−18y^2−30y\)
23. \(12xy^2+18x^2y^2−30y^3\)
- Answer
-
\(6y^2(2x+3x^2−5y)\)
24. \(21pq^2+35p^2q^2−28q^3\)
25. \(20x^3y−4x^2y^2+12xy^3\)
- Answer
-
\(4xy(5x^2−xy+3y^2)\)
26. \(24a^3b+6a^2b^2−18ab^3\)
27. \(−2x−4\)
- Answer
-
\(−2(x+4)\)
28. \(−3b+12\)
29. \(−2x^3+18x^2−8x\)
- Answer
-
\(−2x(x^2−9x+4)\)
30. \(−5y^3+35y^2−15y\)
31. \(−4p^3q−12p^2q^2+16pq^2\)
- Answer
-
\(−4pq(p^2+3pq−4q)\)
32. \(−6a^3b−12a^2b^2+18ab^2\)
33. \(5x(x+1)+3(x+1)\)
- Answer
-
\((x+1)(5x+3)\)
34. \(2x(x−1)+9(x−1)\)
35. \(3b(b−2)−13(b−2)\)
- Answer
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\((b−2)(3b−13)\)
36. \(6m(m−5)−7(m−5)\)
Factor by Grouping
In the following exercises, factor by grouping.
37. \(ab+5a+3b+15\)
- Answer
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\((b+5)(a+3)\)
38. \(cd+6c+4d+24\)
39. \(8y^2+y+40y+5\)
- Answer
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\((y+5)(8y+1)\)
40. \(6y^2+7y+24y+28\)
41. \(uv−9u+2v−18\)
- Answer
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\((u+2)(v−9)\)
42. \(pq−10p+8q−80\)
43. \(u^2−u+6u−6\)
- Answer
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\((u−1)(u+6)\)
44. \(x^2−x+4x−4\)
45. \(9p^2−15p+12p−20\)
- Answer
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\((3p−5)(3p+4)\)
46. \(16q^2+20q−28q−35\)
47. \(mn−6m−4n+24\)
- Answer
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\((n−6)(m−4)\)
48. \(r^2−3r−r+3\)
49. \(2x^2−14x−5x+35\)
- Answer
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\((x−7)(2x−5)\)
50. \(4x^2−36x−3x+27\)
Mixed Practice
In the following exercises, factor.
51. \(−18xy^2−27x^2y\)
- Answer
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\(−9xy(3x+2y)\)
52. \(−4x^3y^5−x^2y^3+12xy^4\)
53. \(3x^3−7x^2+6x−14\)
- Answer
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\((x^2+2)(3x−7)\)
54. \(x^3+x^2−x−1\)
55. \(x^2+xy+5x+5y\)
- Answer
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\((x+y)(x+5)\)
56. \(5x^3−3x^2+5x−3\)
Writing Exercises
57. What does it mean to say a polynomial is in factored form?
- Answer
-
Answers will vary.
58. How do you check result after factoring a polynomial?
59. The greatest common factor of \(36\) and \(60\) is \(12\). Explain what this means.
- Answer
-
Answers will vary.
60. What is the GCF of \(y^4,\space y^5\), and \(y^{10}\)? Write a general rule that tells you how to find the GCF of \(y^a,\space y^b\), and \(y^c\).
Self Check
ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.
ⓑ If most of your checks were:
…confidently. Congratulations! You have achieved your goals in this section! Reflect on the study skills you used so that you can continue to use them. What did you do to become confident of your ability to do these things? Be specific!
…with some help. This must be addressed quickly as topics you do not master become potholes in your road to success. Math is sequential - every topic builds upon previous work. It is important to make sure you have a strong foundation before you move on. Who can you ask for help? Your fellow classmates and instructor are good resources. Is there a place on campus where math tutors are available? Can your study skills be improved?
…no - I don’t get it! This is critical and you must not ignore it. You need to get help immediately or you will quickly be overwhelmed. See your instructor as soon as possible to discuss your situation. Together you can come up with a plan to get you the help you need.


6.1: Poverty
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“Poverty is hunger. Poverty is lack of shelter. Poverty is being sick and not being able to see a doctor. Poverty is not having access to school and not knowing how to read. Poverty is not having a job, is fear for the future, living one day at a time.
Poverty has many faces, changing from place to place and across time, and has been described in many ways . Most often, poverty is a situation people want to escape. So poverty is a call to action — for the poor and the wealthy alike — a call to change the world so that many more may have enough to eat, adequate shelter, access to education and health, protection from violence, and a voice in what happens in their communities.” – The World Bank Organization
Introduction to Poverty
Although poverty is one of the most familiar and enduring conditions known to humanity, it is a highly complicated concept to understand fully. Above is a definition of poverty given by The World Bank Organization. To date there is no one standard definition of poverty, but numerous definitions and descriptions. All current definitions and descriptions agree that poverty is a complex societal problem.
Regardless as to how poverty is defined, it can be agreed that it is a problem requiring everyone’s attention. It is important that all members of our society work together to provide opportunities for all members to reach their full potential. It helps all of us to help one another.
Povery wordart
Poverty looks different across the world. Commonly when we think of poverty, we relate it to the images we see on television of malnourished children living in developing countries. However, poverty is all around us. Even in the wealthiest of countries poverty still exists. Individuals who are living in poverty are made up of all races, ethnicities, ages, backgrounds, and geographic locations (Rodgers, 2015). For many individuals living in poverty, their lives are characterized by low wages, unemployment, underemployment, little property ownership, no savings, and lack of food reserves. The ability to meet even the most basic needs is in constant jeopardy. Feelings of helplessness, dependence, and inferiority develop easily under these circumstances (Sue, Rasheed, & Rasheed, 2012).
Absolute and Relative Poverty
When discussing poverty the terms absolute poverty and relative poverty are often used (Iceland, 2013). Absolute and relative are the two most common forms of poverty delineated in our society and around the world (Pierson & Thomas, 2010).
Absolute poverty
Absolute poverty refers to the amount of money necessary to meet basic needs such as food, clothing, and shelter. The concept of absolute poverty is not concerned with the broader quality of life issues or with the overall level of inequality in society but is based strictly on whether or not basic needs are being met (UNESCO, 2017). Examples of absolute poverty would include not knowing when or where your next meal will come from, not having access to clean drinking water, and not having an adequate place to sleep each night.
Relative poverty
Relative poverty refers to the lack of resources to obtain the types of diet, participate in the activities, and have the living conditions and amenities that are customary to maintain the average standard of living in society (Pierson, & Thomas, 2010; Poverty eradication, 2012). Relative poverty defines poverty in relation to the economic status of other members of the society, therefore determining if people are poor by gauging if they fall below normal standards of living in a given society (UNESCO, 2017). Examples of relative poverty would include not being able to have your children participate in after school activities, not being able to afford to dine out, or not being able to take vacations.
Three degrees of poverty
Evaluating poverty can be broken down into three different levels; the first and most severe is extreme poverty, the second is moderate poverty, and the third is relative poverty.
Extreme poverty
Extreme poverty is the most extensively discussed and researched degree of poverty due to its widespread effect around the world. Those living in extreme poverty are considered the poorest in the world (Harack, 2010). Individuals and families who live in extreme poverty cannot meet their basic needs for survival. These individuals frequently may not have access to food, safe drinking water, shelter, medical care, clothing, and educational opportunities, making everyday life a challenge (Poverty eradication, 2012, The World Bank, 2015).
Moderate poverty
Moderate poverty can be characterized when individuals and families can usually meet their basic needs but commonly face struggles in doing so (Poverty eradication, 2012). Individuals living in moderate poverty are in less danger than those living in extreme poverty. These individuals usually lack much, if any disposable income, but the majority, if not all of their basic needs are being met. Those living in moderate poverty may not be struggling to survive, but this type of poverty does make it difficult for individuals to progress in society and escape poverty completely (Harack, 2010).
Relative poverty : refer to the section above.
Measuring poverty in the United States
In the United States, there are two official poverty measures. Poverty thresholds are the primary version of the federal poverty measure and the second measure being poverty guidelines.
Poverty thresholds
Poverty thresholds were developed in the mid-1960s by Mollie Orshansky, a staff economist at the Social Security Administration. Orshansky created the poverty threshold by determining the cost of a minimum food diet and then multiplied the cost by three to account for other family expenses (United States Census Bureau, 2016). The U.S Census Bureau updates the threshold annually to account for inflation using the Consumer Price Index (Institute for Research on Poverty, 2016).
The U.S. Census Bureau determines poverty status by comparing pre-tax cash income against the threshold that has been set for that year (Institute for Research on Poverty, 2016). If the family’s total income is less than the family’s threshold, then that family and every individual in it is considered to be living in poverty (United States Census Bureau, 2016). According to the U.S Census Bureau in 2015, the most recent year for which data is available, the poverty threshold for a family of four was $24,257, and the official poverty rate was 13.5 percent (Institute for Research on Poverty, 2016). Based on the poverty threshold data it was concluded there were 43.1 million people in the United States living in poverty in 2015 (Institute for Research on Poverty, 2016; Proctor, Semega, & Kollar, 2016).
Money income: Income used to compute poverty status
The poverty thresholds are primarily used for statistical purposes which include tracking poverty over time, poverty rates, and comparing poverty across different demographic groups. Furthermore, the data obtained from the poverty thresholds is used to create and develop annual poverty guidelines. (United States Census Bureau, 2016; Institute for Research on Poverty, 2016)
U.S. Census Bureau Poverty Thresholds, 2015, released September 2016
Poverty guidelines are the other official federal poverty measure used in the United States. The poverty guidelines are a simplification of the poverty thresholds utilized by the federal government to determine an individual’s eligibility for select federal programs (DHHS, 2017).
Updated poverty guidelines are issued every year by the U.S. Department of Health and Human Services (DHHS) (Institute for Research on Poverty, 2016). The 2017 poverty guidelines were determined using data taken from the 2015 poverty thresholds; the updated guidelines take economic changes taken into account.
Examples of federal programs that use poverty guidelines to determine eligibility include the following:
- Department of Health and Human Services: Community Services Block Grant, Head Start, Low-Income Home Energy Assistance
- Department of Agriculture: Supplemental Nutrition Assistance Program (SNAP, formerly Food Stamp Program), National School Lunch Program, Child and Adult Care Food Program
- Department of Energy: Weatherization Assistance for Low-Income Persons
- Department of Labor: Job Corps, National Farmworker Jobs Program, Workforce Investment Act Youth Activities
(Institute for Research on Poverty, 2016)
2017 Povery Guidelines for the 48 Contiguous States and the District of Columbia
Even though the current official poverty measures have been used consistently since the 1960s, there are widespread concerns that the federal poverty measure is flawed. There is an overarching agreement that the Census Bureau does not identify all individuals living in poverty. The Census Bureau is unable to obtain exact numbers because many low-income individuals live with others or are frequently moving, and are in many cases homeless; furthermore, those residing in psychiatric hospitals, college dorms, nursing homes, serving in the military, and/or in jails or prisons are not counted. It is estimated that several million individuals who likely would fall below the poverty threshold and poverty guidelines are not counted each year (Rodgers, 2015).
For annual updates on poverty thresholds and poverty guidelines and further information on measuring poverty, please visit:
- United States Census Bureau at https://www.census.gov/topics/income-poverty.html
- The U.S Department of Health and Human Services at https://aspe.hhs.gov/poverty-guidelines
Measuring Global Poverty
International poverty line
Currently, global poverty is measured by the international poverty line . The international poverty line is a monetary threshold under which an individual is considered to be living in extreme poverty. It is calculated by taking the poverty threshold from each country, given the value of the goods needed to sustain one adult, and converting it to dollars (The World Bank, 2015).
The international poverty line was developed by The World Bank Organization and a team of independent researchers in order to gauge the number of individuals living in poverty around the world. The researchers examined national poverty lines from most impoverished countries around the world and converted the lines into a common currency by using purchasing power parity (PPP) exchange rates. The PPP exchange rates warrant that the same amount of goods or services are priced equivalently across the nation. Once converted into common currency, it was determined that the value of the national poverty line was $1 per day per person in the 1990s (The World Bank, 2015).
Since the first national poverty line was developed, it has been revised twice, first in the mid-2000s when the line rose to $1.25 per person per day after the collection of additional countries’ poverty lines and further data on internationally comparable prices were collected. The second and most recent revision was released in 2015 when the international poverty line rose again to $1.90 per person per day (The World Bank, 2015). Unlike the United States, official poverty measures for the international poverty line does not have a set schedule as to when or how often the line is revised.
For further information on global poverty and how it is measured please visit: The World Bank http://www.worldbank.org/
Poverty in America
Poverty in America is much different than the poverty in third world countries. The standard of what constitutes poverty in the United States is much different than the global standard of poverty (Iceland, 2013). Even though the United States is one of the wealthiest countries in the world, the effects of poverty are crippling.
An example of what living in poverty looks like in America is a single parent who works full time, but still can’t afford to pay for food, rent, child care, medical bills, and the costs of transportation to work (Results, 2017).
Each year millions of Americans live in poverty. The United Sates Census Bureau reports that in 2015, there were 43.1 million people in poverty (Proctor, Semega, & Kollar, 2016). A wide array of Americans from all races, ethnicities, ages, backgrounds, and geographic locations make up the 43.1 million people currently living in poverty. Some groups are more vulnerable to poverty. The most vulnerable groups make up most of the impoverished population (Rodgers, 2015). The groups that are more susceptible to suffer poverty include single parent families (especially those headed by women), minorities, unemployed or under-employed adults, individuals with mental illness or disabilities, and the elderly (Rodgers, 2015).
Poverty is said to be America’s most serious and costly social problem (Rodgers, 2015). High levels of poverty result in many serious social and political consequences. Individuals living in poverty frequently feel alienated from a conventional society which can provoke social disorder. Individuals living in poverty also often feel overlooked in the political realm, further reducing the individual’s confidence in democratic institutions (Iceland, 2013).
Each year hundreds of billions of public and private dollars are spent on efforts to prevent poverty and assist those living in poverty (Rodgers, 2015). To many, it may seem that the efforts put forth to end poverty have not made an impact. However, the most up to date data attainable from the United States Census Bureau shows that there have been improvements. In 2015, for the first time in five years, the number of individuals living in poverty had decreased. The official poverty rate was down to 13.5%, 1.2% lower than in 2014, equaling 3.5 million fewer people living in poverty (Proctor, Semega, & Kollar, 2016). Although we may never see poverty completely eradicated in our lifetime, it is hopeful that poverty will continue to decrease in the coming years.
Find a Place to Live Simulation
Online poverty simulation game; click link to play: http://playspent.org/html/
Homelessness
Similar to the term poverty, there are numerous definitions for the term homeless or homelessness. We have chosen to use the definition of homeless used by the Department of Health and Human Services (DHHS) that was created by, and in conjunction with, the Health Resource and Service Administration (HRSA). It is as follows:
“A homeless individual is defined in section 330(h)(5)(A) as ‘an individual who lacks housing (without regard to whether the individual is a member of a family), including an individual whose primary residence during the night is a supervised public or private facility (e.g., shelters) that provides temporary living accommodations, and an individual who is a resident in transitional housing.” A homeless person is an individual without permanent housing who may live on the streets; stay in a shelter, mission, single room occupancy facilities, abandoned building or vehicle; or in any other unstable or non-permanent situation’ (National Health Care for Homeless Council, 2017, para. 2).
Who is experiencing homelessness?
The current 2016 statistics on homelessness in the United States are derived from The 2016 Annual Homeless Assessment Report (AHAR) to Congress.
- According to the AHAR the number of individuals experiencing homelessness on any given night in 2016 was 549,928.
- Among the 549,928 individuals who experience homelessness each night in the United States vary by age, race, sex, and other classifiable characteristics.
- According to AHAR, 69% of homeless individuals were over the age of 24, 22% were children and adolescents under the age of 18, and 9% were between the ages of 18 and 24.
- The AHAR reports that 60% of the individuals experiencing homelessness were men, 40% were women, and less than 1% were transgender.
- As for race, the AHAR reports that nearly half of all people experiencing homelessness were white totaling 48%, African Americans 39%, multiracial individuals 7%, and Native Americans, Asians, and Pacific Islanders made up the remaining 6%.
The data collected from the 2016 AHAR to Congress further concluded that homelessness and poverty affects all individuals regardless of age, sex, or race.
Picture of homelessness
Sheltering the Homeless
All information below is from The 2016 Annual Homeless Assessment Report (AHAR) .
There are various resources for homeless individuals within the United States to gain safe shelter overnight or for temporary amounts of time. The following are some of the well-known homeless resources in the United States:
Emergency Shelter is a facility with the primary purpose of providing temporary shelter for homeless people
Rapid Rehousing is a housing model designed to provide temporary housing assistance to people experiencing homelessness, moving them quickly out of homelessness and into permanent housing.
S afe Havens are projects that provide private or semi-private long-term housing for people with severe mental illness and are limited to serving no more than 25 people within a facility.
Transitional Housing Programs provide people experiencing homelessness a place to stay combined with supportive services for up to 24 months.
Even with the implementation of the programs listed above, many homeless individuals remain unsheltered on any given night within the United States. Statistics show that 68% (373,571 people) were staying in emergency shelters, transitional housing programs, or safe havens, while 32% (176,357 people) were staying in unsheltered locations.
Rural vs Urban Homelessness
In our society, homelessness is often depicted as an urban problem. Urban areas are known to have a higher population of homeless individuals than in rural areas of the county. However, there is an increasing number of homeless individuals in rural America (National Alliance to End Homelessness, 2010). Geographical location makes a difference to the resources available for those experiencing homelessness, and sadly those living in rural America are often overlooked.
Rural areas face different barriers than urban areas when it comes to serving individuals experiencing homelessness. These barriers include lack of available, affordable housing, limited transportation methods and limited employment opportunities; federal grants and programs also tend to be dispersed in more urban areas (National Alliance to End Homelessness, 2010). The lack of federal funding in rural areas causes a problem when trying to house the homeless. Due to this lack of funding there typically are not homeless shelters in rural areas, causing individuals experiencing homelessness in these areas to sleep in cars, campers, tents because shelter is not available.
Affordable Housing :
There are countless reasons as to why or how an individual becomes homeless, but research shows the key reason as to why he or she cannot escape homelessness is because the individual cannot afford housing. The United States is currently experiencing an extreme shortage of affordable housing (National Alliance to End Homelessness, 2017). The two main types of affordable housing are Public Housing and the Housing Choice Voucher Program (HCVP) which was formerly known as Section 8. It is not uncommon for Public Housing programs and the HCVP to have wait lists that are several years out.
Housing Voucher Program : This program provides vouchers to low-income households to help them pay for housing in the private market and has been found to sharply reduce homelessness (National Alliance to End Homelessness, 2017).
Public Housing : Federally-funded housing that is rented at subsidized rates to eligible low-income families, the elderly, and persons with disabilities.
Federal Government Response to Poverty: Welfare
The United States laid its foundation for a national welfare system in response to the Great Depression that started in 1929 and went through most of the 1930s. The Social Security Act of 1935 was the first of many government policies and welfare programs created to combat poverty and economic hardships (Rodgers, 2015).
The welfare system in the United States consists of government programs which provide financial assistance to individuals and families who cannot support themselves. Welfare programs are funded by taxpayers and allow people to cope with financial stress during challenging periods of their lives. The goals of welfare include the attainment of work, education, and an overall better standard of living and decrease in economic hardship and poverty.
Welfare programs
Since the establishment of Social Security Act of 1935, the federal government has continued to develop numerous welfare programs to attempts to eradicate poverty and the economic hardships faced by millions of Americans.
Key programs to combat poverty include but are not limited to the following:
All information below is from the Center for Poverty Research
1935: The Social Security Act
Part of President Franklin Roosevelt’s New Deal legislation, the original act included grants to states for unemployment compensation, aid to dependent children and public health. Today, Social Security is the largest safety net program in the U.S.
1935: Unemployment Insurance
Unemployment insurance was a part of President Franklin Roosevelt’s 1935 Social Security Act. Today’s U.S. Department of Labor Unemployment Insurance (UI) programs provides benefits to eligible workers who become unemployed through no fault of their own and who meet certain requirements.
1964: Head Start
This pre-school education program was a part of the 1964 Economic Opportunity Act that was designed to reduce disparities among young children. The 1994 Head Start Act Amendments established the Early Head Start program, which expanded the benefits of early childhood development to low-income families with children under three years old.
1964: Supplemental Nutrition Assistance Program (SNAP)
The first Food Stamp program ran from 1939-43, but the program we know today was established with the 1964 Food Stamp Act. The program is now known as the Supplemental Nutrition Assistance Program.
1965: Medicare/Medicaid
These health programs were established with amendments to the Social Security Act in 1965. Today, Medicare provides health insurance for people over 65 years of age and some younger than that but who have certain disabilities or diseases. Medicaid is a Federal and state partnership that provides health coverage for people with low income.
1972: Supplemental Security Income Program (SSI)
SSI is a Federal program that provides income people 65 or older as well as to blind or disabled adults and children.
1972: Women, Infants, and Children (WIC)
WIC is a nutrition program that benefits pregnant women, new mothers and young children who live near poverty and who are at nutritional risk. WIC is not an entitlement program, so the number of people who receive the benefits depends on the amount Congress allots for the program from year to year.
1972: Federal Pell Grant Program
Pell Grants help pay for tuition and other expenses for low-income college students.
1975: The Earned Income Tax Credit (EITC)
The EITC is a tax credit that benefits working people who have low to moderate income, especially families.
1996: Temporary Assistance for Needy Families (TANF)
TANF issues federal grants to states for programs that provide temporary benefits to families with children when the income does not provide for the family’s basic needs. Programs include job preparation, family planning, and other benefits as well as cash assistance.
1997: Children’s Health Insurance Program (CHIP)
CHIP provides health coverage to nearly eight million children in families who cannot afford private health insurance but who have incomes that are too high to qualify for Medicaid.
According to the United States Census Bureau in 2012, there were approximately 52.2 million (or 21.3 %) people in the United States receiving some sort of assistance through government funded welfare programs (United States Census Bureau, 2016). To receive assistance from government funded programs individuals must meet a certain criteria to be eligible; each program has their own distinct criteria. To apply to these programs individuals must go through state Departments of Health and Human Services (DHHS).
For further information on government funded assistance programs please visit:
- The U.S. Department of Health and Human Services, at https://www.hhs.gov/programs/social-services/index.html
- Benefits. Gov Your Path to Government Benefits, at https://www.benefits.gov/
Poverty Stigmas and Stereotypes
Stigmas
In the United States individuals living in poverty are not only faced with their day to day hardships but also with the harsh stigmas that society has surrounding poverty. When evaluating stigmas surrounding poverty, they typically fall into three categories: institutional, social, and personal stigmas (Bell, 2012; Inglis, 2016):
Institutional Stigmas : institutional level stigma can be seen in laws, policies and institutional practices that discriminate against, or shame individuals living in poverty (Inglis, 2016). Institutional stigma is that which arises from the process of claiming benefits (Bell, 2012)
Social Stigmas : Social stigma includes public attitudes toward poverty and welfare, and are typically measured through national surveys (Inglis, 2016). Social stigma is the feeling that other people judge claiming benefits to be shameful (Bell, 2012)
Personal Stigmas : Personal stigma occurs when individuals internalize the various forms of stigma and discrimination that they experience or perceive from others (Inglis, 2016). Personal stigma is a person’s own feeling that claiming benefits is shameful (Bell, 2012).
Stereotypes
Furthermore, society holds many stereotypes about individuals living in poverty. A stereotype can be defined as an often unfair and untrue belief that many people have about all people with a specific characteristic (Stereotype, 2017). The stereotypes that society has labeled individuals living in poverty are usually false. Some of the most common stereotypes and misconceptions of individuals living in poverty include:
- Individuals living in poverty are lazy and have weak work ethics
In reality, there is no suggestion that individuals living in poverty are lazier or have weaker work ethics than individuals from other/higher socioeconomic groups. In fact, poor working adults work, on average, 2,500 hours per year, the rough equivalent of 1.2 full-time jobs often patching together several part-time jobs in order to support their families (Gorski, 2013)
- Individuals living in poverty have problems with substance use
In reality, research has shown that low-income individuals are less likely to use or abuse substances than their wealthier counterparts (Gorski, 2013).
Stigmatizing and stereotyping individuals living in poverty only further creates a divide between low-income people who are living in poverty and those who are not (Inglis, 2016). Society’s harsh views on poverty cause impoverished individuals to further feel socially excluded and ashamed of the situation they are in. Research has shown negative effects on an individual’s self-esteem, self-concept, and mental and physical health due to being stigmatized and stereotyped so severely by society (Inglis, 2016).
Theories and Explanations of Poverty
There are many theories that attempt to explain poverty and why it exists. A theory in simple terms can be defined as idea or a structure of ideas intended to explain something (Theory, 2017). You will learn more about theories in-depth in higher level social work courses.
The following are some of the most commonly used theories to explain the existence of poverty.
The Culture of Poverty
The culture of poverty theory was created by the anthropologist Oscar Lewis in 1959. The culture of poverty is the theory that certain groups and individuals persist in a state of poverty because they have distinct beliefs, values, behavior, and attitudes that are incompatible with economic success (Pierson, & Thomas, 2010). Therefore, the individuals are unable to get out of poverty.
The Cycle of Poverty
The cycle of poverty is also commonly known as the cycle of deprivation. The cycle of deprivation is a theoretical explanation for the persistence of poverty. The theory focuses on how attitudes, values, and behaviors are passed on from one generation to the next, further explaining the ongoing cycle of low educational attainment, unemployment, poor housing and so on within families and communities (Pierson & Thomas, 2010).
As discussed in the explanation of the cycle, poverty is passed down generationally, meaning that children and adolescents are targeted victims falling into the cycle of poverty and not getting out of it. There is much research that indicates that children and adolescents who grow up in poverty suffer significant disadvantages, not just as children but throughout their lifespan. Alarming statistics report that children who grow up in poverty are twice as likely to drop out of school and are one and half times more likely to be unemployed (Rodgers, 2015), further contributing to the ongoing cycle of poverty.
Structural/ Environmental Explanation:
Structural explanations propose that poverty is based on the social structure of society (Kirst-Ashman, 2013). To put it simply, the structural explanation suggests that poverty and its ongoing existence results from problems in society that lead to a lack of opportunity and a lack of jobs (University of Minnesota, 2010). Structural and environmental factors that play a role in this explanation include fluctuations in the economy, not having enough jobs in the job market, low paying jobs or jobs with no benefits, lack of affordable housing, and discrimination (Ritter, 2014). An example of this would be: poverty occurs when wages are too low and that there are not enough adequate paying jobs (Kirst-Ashman, 2013).
Individualistic Explanation :
Similar to the culture of poverty theory, the individualistic explanation of poverty suggests that poverty results from the fact that poor people lack the motivation to work and have certain beliefs and values that contribute to their poverty (University of Minnesota, 2010). Individual factors that contribute to a person living in poverty may include lack of job skills, educational deficits, mental illness, declining health or disabilities, substance use, single parenting, lack of childcare, and lack of reliable transportation (Ritter, 2014). An example of this would be: a person who lost their job due to being late so many days in a row and now he or she cannot afford rent and may be at risk of becoming homeless.
Poverty and Social Work
National Association of Social Work
As discussed in chapter two, social workers abide by the National Association of Social Work (NASW) Code of Ethics. One of the six values in the NASW code of ethics is social justice. The definition of the ethical principle from the NASW states, “Social workers’ social change efforts are focused primarily on issues of poverty, unemployment, discrimination, and other forms of social injustice,” (NASW, 2008). With the NASW Code of Ethics acting as the professions guiding light it is highly important for social workers to have knowledge and understanding of poverty and its severity within our society and around the world.
Social work’s role
The social work profession has an extensive history of working to assist poverty at the micro, mezzo, and macro levels (National Association of Social Workers, 2017). The following are examples of social work roles on each of the three levels.
Micro
Case Study: Micro Level Social Work
“A social worker has an intervention with a young woman living in a poor urban community. When she first appeared for social services, the young woman was pregnant, depressed and unable to pay her rent. However, she was determined to improve her life circumstances and those for her unborn child. She couldn’t save money because she had another child to support. Although he was emotionally supportive, her partner was unable to financially contribute to her support. During their work together, the social worker was able to develop a plan of action with her client. By following up on leads, the young woman was connected with several sources of tangible help in her community. Over the next few months, she was able to identify subsidized housing, obtain prenatal care, and receive treatment for her depression and to enroll in a part-time job training program. Her partner was also able to find employment through a community job bank. By the time her baby was born, the young woman’s outlook on life was brighter.” (NASW, 2017)
Micro level practice works with an individual or a family on a one-on-one basis (Giffords, & Garber, 2014). Micro level social workers are the clinicians who often work most hands- on with individuals who are living in poverty. Micro practice, as it relates to poverty, may include linking a client to unemployment resources, housing resources, assisting individuals in applying for welfare programs, and helping the individual cope with the hardships of living in poverty.
Mezzo
Intervening at the group level constitutes mezzo practice (Giffords, & Garber, 2014). Some focuses on mezzo level social work practice in regards to poverty include facilitating groups that focus on employment skills, working in schools to help low-income children learn to read and write better, and working with community organizations and agencies that assist with poverty and homelessness.
Macro
At the Macro level social workers focus on effecting systematic change that can benefit individuals at a societal level (MSW careers, 2017). In regards to poverty some of the ways macro level social workers can assist include advocating for laws that affect those living in poverty, developing programs to assist individuals and families living in poverty, and educating the community on the need for social change.
For further information on micro, mezzo, and macro social work please refer back to Chapter 4.
Summary
After reading this chapter it is my hope that you have expanded your knowledge and understanding of poverty and how it closely relates to the social work profession. As previously stated social works focus on poverty stems back the NASW Code of Ethics which acts as the professions guiding light.
Regardless as to what career path you take in the field of social work it is anticipated that you will serve individuals and families who fall below the poverty line and face financial hardships. Therefore, as future social workers it is important that you have an adequate understanding of what poverty is and the effects it has on individuals and society as a whole.
References
- Bell, Kate. (n.d.). Poverty, social security, and stigma. Poverty, 144, 10-13. Retrieved from http://www.cpag.org.uk/sites/default/files/CPAG-Povertyarticle-stigma-0213.pdf
- Center for Poverty Research, University of California, Davis. (2017). What are the major federal safety net programs in the U.S. ? Retrieved from https://poverty.ucdavis.edu/article/war-poverty-and-todays-safety-net-0
- Giffords, E. D., & Garber, K. R. (2014). New Perspectives on poverty: P olicies programs and practice . Chicago: Lyceum Books.
- Gorski, P. C. (2013). Reaching and teaching students in poverty : S trategies for erasing the opportunity gap . New York: Teachers College Press.
- Harack, B. (2010, October 5). How do we define poverty? Vision of earth . Retrieved from https://www.visionofearth.org/news/how-do-we-define-poverty/
- Health Resource & Service Administration. (2017). Health center program terms and definitions. Retrieved from https://www.hrsa.gov/grants/apply/assistance/Buckets/definitions.pdf
- Henry, M., Watt, R., Rosenthal, L., & Shivji, A. (2016, November). The 2016 annual homeless assessment report (AHAR) to C ongress. Washington, DC: U.S Department of Housing and Urban Development. Retrieved from https://www.va.gov/homeless/docs/2016-AHAR-Part-1.pdf
- Iceland, J. (2013). Poverty in America . Berkeley: University of California Press.
- Inglis, G. (2016, October 19). The stigma of poverty. T h e P overty A lliance. Retrieved from https://povertyalliance.wordpress.com/2016/10/19/the-stigma-of-poverty/
- Institute for Research on Poverty, University of Wisconsin. (2016). What are poverty thr esholds and poverty guidelines? Retrieved from www.irp.wisc.edu/faqs/faq1.htm
- International Federation of Social Workers. (2012, February 23). Poverty eradication and the role for social workers. Retrieved from http://ifsw.org/policies/poverty-eradication-and-the-role-for-social-workers/
- Kirst-Ashman, K. (2012). Introduction to social work and social welfare [4th ed.]. Pacific Grove, CA: Brooks Cole.
- MSW Careers. (2017). Micro, mezzo and macro: The 3 key areas of social work practice. Retrieved from https://mswcareers.com/careers/micro-mezzo-macro/
- National Alliance to End Homelessness. (2010, January 17). Rural homelessness. Retrieved from http://endhomelessness.org/resource/rural-homelessness/
- National Alliance to End Homelessness. (2016). Housing. Retrieved from http://endhomelessness.org/homelessness-in-america/what-causes-homelessness/housing/
- National Association of Social Workers (NASW). (2008). Code of Ethics of the N ational A ssociation of S ocial W orkers. Retrieved from www.socialworkers.org/pubs/code/code.Asp
- National Association of Social Workers (NASW). (2017). Poverty. Retrieved from www.socialworkers.org/pressroom/features/issue/poverty.asp
- National Health Care for Homeless Council. (2017). What is the official definition of homelessness? Retrieved from www.nhchc.org/faq/official-definition-homelessness/
- Pierson, J., & Thomas, M. (2010). Dictionary of social work : The definitive A to Z of social work and social care. New York: Open University Press.
- Proctor, B. D., Semega, J. L., & Kollar, M. A. (2016, September). Income and poverty in the United States: 2015. (States Census Bureau, Report #P60-256). Retrieved from https://www.census . gov/library/publications/2016/demo/p60-256.html
- Results: The Power to End Poverty. (2017). Poverty in the United States. Retrieved from http://www.results.org/issues/poverty_in_the_united_states/
- Ritter, J. A. & Vakalahi, H.F.O. (2014). 101 careers in social work [2 nd ed.]. New York, NY: Springer Publishing Company.
- Rodgers, H. R. (2015). American p overty in a n ew e ra of r eform [2 nd ed.]. Armonk, NY: Taylor and Francis.
- Social problems: C ontinuity and change . (2010). Minneapolis: University of Minnesota Libraries. https://doi.org/10.24926/8668.2301
- Stereotype. (2017). Merriam-Webster’s learner’s dictionary. Retrieved from http://www.learnersdictionary.com/definition/stereotype
- Sue, D. W., Rasheed, M. N., & Rasheed, J. M. (2012). Multicultural social work practice : A competency-based approach to diversity and social justice [2 nd ed.]. Hoboken, NJ: Wiley.
- Theory. (2017). Merriam-Webster’s learners dictionary . Retrieved from http://www.learnersdictionary.com/definition/theory
- United Nations Educational, Scientific and Cultural Organization (UNESCO). (2017). Poverty. Retrieved from http://www.unesco.org/new/ e n/social-and-human-sciences/themes/international-migration/glossary/poverty/
- United States Census Bureau. (2016, August). The history of the official poverty measure. Retrieved from https://www . census.gov/topics/income-poverty/poverty/about/history-of-the-poverty-measure.html
- United States Department of Health & Human Services (DHHS). (2017). U.S. federal poverty guidelines used to determine financial eligibility for certain federal programs. Retrieved from https://as p e.hhs.gov/poverty-guidelines
- The World Bank. (2015, September 30). FAQs: Global poverty line update. Retrieved from http://www.worldbank.org/en/topic/poverty/br i ef/global-poverty-line-faq


6.1: Introduction
In the preceding few chapters, we discussed the electrical concepts of voltage, current, and resistance. In this chapter, we use these concepts to begin to learn how to analyze direct-current (DC) circuits. A circuit is a collection of electrical components connected to accomplish a specific task. Figure \(\PageIndex{1}\) shows an amplifier circuit, which takes a small-amplitude signal and amplifies it to power the speakers in earbuds. Although the circuit looks complex, it actually consists of a set of series, parallel, and series-parallel circuits. Direct-current circuits contain current that only flows in one direction in a given section of the circuit.
An early section of this chapter covers the analysis of series and parallel circuits that consist of resistors. Later in this chapter, we introduce the basic equations and techniques to analyze any circuit, including those that are not reducible through simplifying parallel and series elements. But first, we need to understand how to power a circuit.


1.9: Centripetal Acceleration
Learning Objectives
- Explain what centripetal acceleration is.
- Use the formula for centripetal acceleration in simple situations.
We defined acceleration as a change in velocity, either in its magnitude or in its direction, or both. When an object moves along a circular path, the direction of its velocity changes constantly, so there is always an associated acceleration, even if the speed of the object is constant. You experience this acceleration yourself when you turn a corner in your car. What you notice is a sideways acceleration because you and the car are changing direction. The sharper the curve and the greater your speed, the more noticeable this acceleration will become. In this section we briefly examine the direction and magnitude of that acceleration.
Figure \(\PageIndex{1}\) shows an object moving in a circular path at constant speed, called uniform circular motion . The direction of the instantaneous velocity is shown at two points along the path. Acceleration is in the direction of the change in velocity, which points directly toward the center of rotation (the center of the circular path). This pointing is shown with the vector diagram in the figure. We call the acceleration of an object moving in uniform circular motion (resulting from a net external force) the centripetal acceleration (\(a_{\mathrm{c}}\)); centripetal means “toward the center” or “center seeking.”
The direction of centripetal acceleration is toward the center of curvature, but what is its magnitude? If we use the geometry shown in Figure \(\PageIndex{1}\) along with some kinematics equations, we can obtain (detailed derivation skipped)
\[a_{\mathrm{c}}=\frac{v^{2}}{r}, \label{Equation1} \]
which is the acceleration of an object in a circle of radius \(r\) at a speed \(v\). Verify for yourself that \(a_{\mathrm{c}}\) has unit of \(\mathrm{m} / \mathrm{s}^{2}\), as expected for acceleration.
We see in Equation \(\eqref{Equation1}\) that centripetal acceleration is greater at high speeds and in sharp curves (smaller radius), as you have noticed when driving a car. But it is a bit surprising that \(a_{\mathrm{c}}\) is proportional to speed squared, implying, for example, that it is four times as hard to take a curve at 100 km/h than at 50 km/h. A sharp corner has a small radius, so that \(a_{\mathrm{c}}\) is greater for tighter turns, as you have probably noticed.
Section Summary
-
Centripetal acceleration \(a_{\mathrm{c}}\) is the acceleration experienced while in uniform circular motion. It always points toward the center of rotation. It is perpendicular to the linear velocity \(v\) and has the magnitude
\[a_{\mathrm{c}}=\frac{v^{2}}{r}. \nonumber\]
- The unit of centripetal acceleration is \(\mathrm{m} / \mathrm{s}^{2}\).


4.3: Child Growth and Development
As children grow and develop, they go through many physical, cognitive, and emotional changes. These changes are known as human growth and development . All children will go through these stages, but they may not go through them in the same manner or rate as other children. It is important to remember that all children are unique .
Jean Piaget, a famous developmental psychologist developed a theory called the Cognitive Development Theory . It is widely used today to understand the cognitive development of children. He believed that children go through four stages as they construct (make and understand) meaning of the world.
Sensorimotor Stage (birth to 2 years)
Infants construct an understanding of the world as they interact with it using their senses. Infants use the sense of sight, hearing, touch, smell, and even taste to learn about the world around them. Their senses are combined with physical actions and muscle movements such as pushing, pulling, and kicking to make sense of objects around them. For example, a baby kicks a brightly colored ball and learns to understand that they can make the ball move by using their muscles. However, if the ball is out of their sight, they will no longer think about it until they develop object permanence, which occurs at the end of this stage. Object permanence is the understanding that something exists even though it is no longer in sight.
Preoperational Stage (2 to 7 years)
During this stage, children learn about their world beyond just senses and using motor actions. They also learn to understand the meaning of words and images. They learn about the world by looking at pictures, symbols, and books. Piaget believed that children at this stage cannot perform operations or solve problems mentally, but still focus on the physical understanding of the world. For example, a child in this stage could not say if there was the same amount of liquid in two glasses even if they saw you pouring equal amounts of liquid in two cups, with one cup tall and the other short. To a child in this stage, there appears to be more liquid in the short glass because the glass appears to be fuller. Children in this stage also believe that inanimate objects such as toys and trees have human like qualities.
Concrete Operational Stage (7 to 11 years)
In this stage, children learn to perform operations such as math and to reason logically. However, Piaget believed that children at this age can only do this with concrete things (things that are right in front of them). He felt they are unable to reason about abstract things (things we can only think about or imagine). If a child in this stage was shown the same two glasses in the example as discussed above, they would have an understanding that there was an equal amount of liquid, even though one glass is taller than the other.
Formal Operational Stage (11 years to adulthood)
At this stage, Piaget believed that people can move beyond what is concrete (or right in front of them) and think in abstract ways about things that are not right in front of them or which they can only imagine. They are able to reason and perform logical thinking about abstract things. People at this stage begin to think about the possibilities of what could be in the future.
Match the skill with the Cognitive Development Stage it represents.
| Skill | Cognitive Development Stage |
|---|---|
| 1. A baby hits the mobile with her hand and laughs when it starts to spin. | a. Sensorimotor Stage |
| 2. A child says, “The tree is dancing” when he sees the leaves blow. | b. Preoperational Stage |
| 3. A teenager dreams about one day becoming a police officer. | c. Concrete Operational Stage |
| 4. A child is able to understand that liquid poured into two different shaped glasses has the same amount of liquid. | d. Formal Operational Stage |
- Answer
-
1). A
2).B
3).D
4).C
Feedback :
1. In the sensorimotor stage babies learn to explore the world around them by using their sense and physical movements such as pushing and kicking. Exploring the world in these ways helps them to learn about the environment around them and that they can have an impact upon it.
2. Children in the preoperational stage often give inanimate objects such as trees, lifelike qualities. They learn to understand the meaning of words and images. They still have trouble thinking abstractly and are unable to understand that the same amount of liquid poured into two different shaped glasses is still the same amount of liquid.
3. Teenagers are able to think abstractly about things that are in the future. Their thinking is no longer limited to what is concrete and right in front of them. This helps them to imagine what life can be like. This is the Formal Operational Stage.
4. Children who understand that the same amount of liquid poured into two different shaped glasses is still the same amount of liquid are in the Concrete Operational Stage.


2.3: Sociology and Science
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Learning Objectives
- Contrast positivist sociology with “verstehen”-oriented sociological approaches
Early sociological studies considered the field of sociology to be similar to the natural sciences, like physics or biology. As a result, many researchers argued that the methodology used in the natural sciences was perfectly suited for use in the social sciences. The effect of employing the scientific method and stressing empiricism was the distinction of sociology from theology, philosophy, and metaphysics. This also resulted in sociology being recognized as an empirical science.
Positivism and Verstehen
This early sociological approach, supported by August Comte, led to positivism, an idea that data derived from sensory experience and that logical and mathematical treatments of such data are together the exclusive source of all authentic knowledge. The goal of positivism, like the natural sciences, is prediction. But in the case of sociology, positivism’s goal is prediction of human behavior, which is a complicated proposition.
The goal of predicting human behavior was quickly realized to be a bit lofty. Scientists like Wilhelm Dilthey and Heinrich Rickert argued that the natural world differs from the social world; human society has culture, unlike the societies of most other animals. The behavior of ants and wolves, for example, is primarily based on genetic instructions and is not passed from generation to generation through socialization. As a result, an additional goal was proposed for sociology. Max Weber and Wilhelm Dilthey introduced the concept of verstehen . The goal of verstehen is less to predict behavior than it is to understand behavior. Weber said that he was after meaningful social action, not simply statistical or mathematical knowledge about society. Arriving at a verstehen -like understanding of society thus involves not only quantitative approaches, but more interpretive, qualitative approaches.
The inability of sociology and other social sciences to perfectly predict the behavior of humans or to fully comprehend a different culture has led to the social sciences being labeled “soft sciences. ” While some might consider this label derogatory, in a sense it can be seen as an admission of the remarkable complexity of humans as social animals. Any animal as complex as humans is bound to be difficult to fully comprehend. Humans, human society, and human culture are all constantly changing, which means the social sciences will constantly be works in progress.
Quantitative and Qualitative Sociology
The contrast between positivist sociology and the verstehen approach has been reformulated in modern sociology as a distinction between quantitative and qualitative methodological approaches, respectively. Quantitative sociology is generally a numerical approach to understanding human behavior. Surveys with large numbers of participants are aggregated into data sets and analyzed using statistics, allowing researchers to discern patterns in human behavior. Qualitative sociology generally opts for depth over breadth. The qualitative approach uses in-depth interviews, focus groups, or the analysis of content sources (books, magazines, journals, TV shows, etc.) as data sources. These sources are then analyzed systematically to discern patterns and to arrive at a better understanding of human behavior.
Drawing a hard and fast distinction between quantitative and qualitative sociology is a bit misleading, however. Both share a similar approach in that the first step in all sciences is the development of a theory and the generation of testable hypotheses. While there are some individuals who begin analyzing data without a theoretical orientation to guide their analysis, most begin with a theoretical idea or question and gather data to test that theory. The second step is the collection of data, and this is really where the two approaches differ. Quantitative sociology focuses on numerical representations of the research subjects, while qualitative sociology focuses on the ideas found within the discourse and rhetoric of the research subjects.
Key Points
- Early sociological approaches were primarily positivist—they treated sensory data as the sole source of authentic knowledge, and they tried to predict human behavior.
- Max Weber and Wilhelm Dilthey introduced the idea of verstehen , which is an attempt to understand and interpret meanings behind social behavior.
- The difference between positivism and verstehen has often been understood as the difference between quantitative and qualitative sociology.
- Quantitative sociology seeks to answer a question using numerical analysis of patterns, while qualitative sociology seeks to arrive at deeper a understanding based on how people talk about and interpret their actions.
Key Terms
- positivism : A doctrine that states that the only authentic knowledge is scientific knowledge, and that such knowledge can only come from positive affirmation of theories through strict scientific method, refusing every form of metaphysics.
- Verstehen : A systematic interpretive process of understanding the meaning of action from the actor’s point of view; in the context of German philosophy and social sciences in general, the special sense of “interpretive or participatory examination” of social phenomena.
- empirical : Pertaining to, derived from, or testable by observations made using the physical senses or using instruments which extend the senses.


5.7: A Digression into Complexity Theory
We have already introduced in Chapter 4 a few notions about efficient algorithms. We also discussed the difficulty of determining a graph's chromatic number and clique number earlier in this chapter. We conclude with a brief discussion of some issues involving computational complexity for other problems discussed in this chapter.
Let's begin with some problems for which there are polynomial-time algorithms. Suppose you are given a graph on \(n\) vertices and asked whether or not the graph is connected. Here a positive answer can be justified by providing a spanning tree. On the other hand, a negative answer can be justified by providing a partition of the vertex sets \(V=V_1 \cup V_2\) with \(V_1\) and \(V_2\) non-empty subsets and having no edges with one end-point in \(V_1\) and the other in \(V_2\). In Chapter 12 we will discuss two efficient algorithms that find spanning trees in connected graphs. They can easily be modified to produce a partition showing the graph is disconnected.
If you are asked whether a connected graph is eulerian, then a positive answer can be justified by producing the appropriate sequence. We gave an algorithm to do this earlier in the chapter. A negative answer can be justified by producing a vertex of odd degree, and our algorithm will identify such a vertex if it exists. (Depending on the data structures used to represent the graph, it may be most efficient to simply look for vertices of odd degree without using the algorithm to find an eulerian circuit.)
On the surface, the problem of determining if a graph is hamiltonian looks similar to that of determining if the graph is eulerian. Both call for a sequence of vertices in which each pair of consecutive vertices is joined by an edge. Of course, each problem has an additional requirement on yes certificates. However, justifying a negative answer to the question of whether a graph is hamiltonian is not straightforward. Theorem 5.18 only gives a way to confirm that a graph is hamiltonian; there are many nonhamiltonian graphs that do not satisfy its hypothesis. At this time, no one knows how to efficiently justify a negative answer—at least not in the general case.


8.7: Making a Presentation for a Meeting
Learning OUtcomes
- Create a presentation intended for a business meeting
With perspective on the technical tools, communications planning and information design, let’s take this learning for a test drive.
What’s considered an effective (that is, persuasive) presentation structure hasn’t changed fundamentally over the centuries. In his analysis of dramatic structure in the Poetics , Aristotle identified a play as having three parts: a beginning, middle and end. The story begins with a “complication” (problem), ends with an “unraveling” (resolution), and follows a logical sequence of events from beginning to end. Hollywood screenwriters use the same structure and dynamics. Screenwriter, producer and author Syd Field, whom CNN called “the guru of all screen writers,” translated this simple three-step structure into numerous books and workbooks, including the bestsellers Screenplay: The Foundations of Screenwriting and The Screenwriter’s Workbook .
In a business context, a good presentation is an effective presentation. That is, a good presentation achieves its intended outcome. Clearly, in order to achieve a specific outcome or objective, you need to know what it is. So, prior to crafting the drama (in word or slide), you need to hone in on three things:
- The purpose of your presentation
- Your audience
- Your (one) message
For a review of these elements, refer to What’s my Presentation About.
Once you’re clear on those points, let’s proceed.
To build our presentation, we’ll use presentation expert Nancy Duarte’s interpretation of the classic 3-part story structure illustrated in Figure 1. For additional perspective on this structure, watch her TED Talk, “ The Secret Structure of Great Talks, ” or read her Harvard Business Review article, “ Structure Your Presentation Like a Story .”
The Beginning
The story starts with “What is”—the current state. Describe this baseline state in a way that is recognizable to the audience. This allows you and the audience to get in sync. And with this base level of agreement, your audience will be more receptive to your proposed change.
The second step is to introduce “What could be.” The gap between what is and what could be adds tension and drama to your story and largely determines the significance of your presentation. If there’s no conflict, no proposed change, what’s the point of the presentation?
Let’s say you’re an analyst on the new product development team of a retailer known for exclusive, trend-forward “house” branded products. Your company’s reputation and revenue depends on consistent introduction of new consumer-product goods. Marketing and distribution are key strengths, but new-product performance is off, revenue is below expectations and the company’s stock price recently fell 30 percent. Within your company, R&D (research & development) is strictly an insider’s game; any ideas or innovations that weren’t developed in-house are blocked. The problem is, you can’t innovate fast enough—or with enough market demand accuracy—to meet financial and stock market expectations. You and the other analysts on your team have been tracking innovation trends and successes and you think the answer is opening the R&D works to outside ideas and innovations. Here’s how you might lay out your presentation:
- What Is: We missed our quarterly earnings numbers, largely due to a failure to meet our innovation success targets over the last six months.
- What Could Be: Initial data suggests we could get back on track by modifying our R&D model to incorporate external innovations.
The Middle
The bulk of your the presentation is developing the contrast between what is and what could be in order to set up your proposed resolution of the conflict or challenge. The objective is also to establish the validity of your arguments, so your proposed call to action is perceived as a logical, ideally inevitable, conclusion of the conflict.
- What Is: We currently bear the full cost and risk of developing new products and our innovation success rate—the percentage of new products that meet financial objectives—is running 25 percent below target.
- What Could Be: Sourcing promising innovations from outside the company could reduce R&D costs and risk while also increasing our innovation success rate.
- What Is: Our R&D process is taking so long that we’re missing trends and losing our market-leading brand reputation.
- What Could Be: We could license or buy promising innovations for a fraction of the cost it would take to develop them from scratch and leverage our marketing and distribution strengths to claim shelf and market share.
- What Is: Our below-plan performance and new product pipeline is costing us political capital with executive management, and we’re at risk of losing budget and/or layoffs.
- What Could Be: Adopting an open innovation culture would allow us to create partnerships that leverage our strengths and drive revenue, regaining a position of value within the company.
The End
To craft a powerful close, heed Duarte’s advice and avoid a list of bullet point to-dos. Your objective here is to achieve resolution of the conflict introduced at the beginning, to issue a call to action that inspires your audience to support your vision of what could be, a state Duarte refers to as the “new bliss.”
Call to Action
To recover our position of a source of revenue and brand value, we need to start working to build a culture and networks that support open innovation and accelerate the development of new products, regardless of the source of the idea.
New Bliss
Our ability to drive value secures our position and reputations in the company, and in the marketplace, and pays off in employee stock value and profit sharing.
The new bliss articulates the proposed—and a desired future state—incorporating the WIIFM, what’s in it for me, that motivates your audience to buy into and work to support the required change.
Contributors and Attributions
- Making a Presentation for a Meeting. Authored by : Nina Burokas. Provided by : Lumen Learning. License : CC BY: Attribution
- Persuasive storytelling graphic. Provided by : Lumen Learning. License : CC BY: Attribution