College Algebra, Chapter 3, 3.2, Section 3.2, Problem 74

A family of functions is given. In part (a) and (b) graph all the given members of the family in the viewing rectangle indicated. In part (c) state the conclusions that you can make from your graphs.

$\displaystyle f(x) = \frac{1}{x^n}$

a.) $\displaystyle n = 1, 3; [-3, 3]$ by $[-3, 3]$







b.) $\displaystyle n = 2, 4; [-3, 3]$ by $[-3, 3]$







c.) How does the value of $c$ affect the graph?

As the value of $n$ increases, the graph expands. Also when the value of $n$ is odd, the graph is symmetric to the origin. On the other hand, when the value of $n$ is even, the graph is symmetric to $y$-axis.

Why does Eckels travel with Time Safari in "A Sound of Thunder" by Ray Bradbury?

Eckels travels with Time Safari, Inc. because he wants to go back in time to shoot a dinosaur. 
Eckels is an expert hunter looking for a new challenge.  He spends a lot of money to hire the time machine so that he can go back to shoot a dinosaur.  Obviously, it is no longer possible to shoot a dinosaur on Earth since they are extinct.  Therefore this company offers brave hunters the opportunity to shoot an animal far bigger than any alive today. 
Eckels is told that his safety is not guaranteed and that if he does not follow directions he will have to pay an exorbitant fine.  The discussion with his guides is about a recent election, but they tell him not to worry about that.  He is going back in time well before the election ever happened. 

“All you got to worry about is-" 
"Shooting my dinosaur," Eckels finished it for him. 
"A Tyrannosaurus Rex. The Tyrant Lizard, the most incredible monster in history. Sign this release. Anything happens to you, we're not responsible. Those dinosaurs are hungry." 

Eckels is told not to step off a special path, and not to shoot anything else.  It is very important that he not change the future.  Any little thing he does could do it, and that is why the rules are so strict.  When Eckels comes to the point of actually shooting the dinosaur, he panicks. 

It ran with a gliding ballet step, far too poised and balanced for its ten tons. It moved into a sunlit area warily, its beautifully reptilian hands feeling the air.
"Why, why," Eckels twitched his mouth. "It could reach up and grab the moon."

He is so frightened that he is unable to actually shoot.  His guides end up doing it and during the commotion that follows he accidentally steps on and kills a butterfly.  When they return to the present everything has changed, including the outcome of the election.  Travis shoots Eckels.

Intermediate Algebra, Chapter 3, 3.2, Section 3.2, Problem 80

State whether the lines with equation $4x - 3y = 8$ and $4y + 3x = 12$ is parallel, perpendicular, or neither.

We find the slope of each line by solving each equation for $y$

Equation 1


$
\begin{equation}
\begin{aligned}

4x - 3y =& 8
&& \text{Given equation}
\\
\\
-3y =& -4x + 8
&& \text{Subtract each side by $4x$}
\\
\\
y =& \frac{4}{3}x - \frac{8}{3}
&& \text{Divide each side by $-3$}


\end{aligned}
\end{equation}
$


Equation 2


$
\begin{equation}
\begin{aligned}

4y + 3x =& 12
&& \text{Given equation}
\\
\\
4y =& -3x + 12
&& \text{Subtract each side by $3x$}
\\
\\
y =& - \frac{3}{4}x + 3
&& \text{Divide each side by $4$}

\end{aligned}
\end{equation}
$


We know that the slope is given by the coefficient of $x$ and since the product of the slopes is $\displaystyle \frac{4}{3} \left( - \frac{3}{4} \right) = -1$ the two lines are perpendicular.

Link is a student who dared to be Melba’s friend and actually become one her protectors. What event from Link’s background made him more open to African American students being at Central High School? What are his feelings toward his opinion?

Link, like a lot of Southern white children at the time, was raised by a black nanny. In his case, it was Nana Healey. Nana is a kind, caring, considerate lady who takes very good care of Link. He loves her deeply and develops a very close bond with her. In a way, she provides a connection for Link with other African Americans. As a white boy growing up in a segregated community, Link does not have many opportunities to connect with those of a different race. His bond of love with Nana gives him a rare glimpse into another way of life and a different culture.
His subsequent friendship with Melba and his acceptance of African American students at school are rooted in his love for Nana. He has witnessed firsthand that—despite what his father might say or what Southern society thinks—people are really all the same underneath. Yet, there is still more than a hint of ambiguity in Link's attitudes. Nana occupies a lowly position in society, one in keeping with her gender and race. As such, she fits comfortably into Link's world without ever really challenging its underlying preconceptions. Although Link can relate to Nana on a personal level, there will always be an insuperable barrier between them no matter how much he truly cares for her.
This ambiguity spills over into how Link acts toward Melba. He shows her great kindness; in fact, he is the only white student at the High School who does. All the same, he wants to keep his romantic feelings for her a secret and this puts Melba on guard. Link seems more interested in holding on to his privileged position in white society than acting on his true feelings.
Even the death of Nana does not allow Link to break free from his past and reveal his friendship with Melba. Overwhelmed by grief, he wants to run away with Melba to the North, hoping that they can start over in a less hostile climate. However, warriors do not cry or run. Melba knows that running away would allow racism to win. She also senses that Link is running away, not just from the town, but also his fears. In contrast, Melba is showing immense courage in the face of fear by running the gauntlet of a white supremacist mob when she goes to school each day.
Link's attitude towards Melba, though well-meaning, is ultimately somewhat condescending. He sees her in the role of victim, someone needing to be protected, as opposed to a fully-fledged human being endowed with the same rights as him. He shows a degree of bravery in standing up to white supremacist violence, but he lacks the courage to challenge the underlying structures of power and race that give rise to such violence in the first place.
Ironically, it was his loving relationship with Nana which led directly to Link's adoption of such a morally ambiguous and complex position. He loved Nana dearly, but he never really saw her as an equal. His connection to her was a deeply personal one, just like his friendship with Melba. However, Link, unlike Melba, is not prepared to connect the personal to the political, and as a result, he cannot truly begin to confront and overcome the repressive society in which he still faintly hopes to find a place.

Identify the theme of the novel Milkweed.

As with many books that send powerful messages to readers, Milkweed does not have a singular theme. Several themes can be pulled from this story. One main theme is the theme of identity. This is a fairly common theme in books about adolescence, but Milkweed is fairly overt about this theme. Misha is literally searching for identity through much of the book, because he doesn't know where he came from, who he is, or who his family is or was. Uri gives him an identity, and Misha soaks in every detail of the fictitious person. He is once again rebranded an identity in the United States, and seems to find true identity through his granddaughter.
A second major theme is the theme of survival. Again, this is a fairly common theme. What is different about Milkweed is the very real setting. It is taking place during the Holocaust, and people are forced to do anything, no matter how horrible, to stay alive. This is true for Misha, and his talents as a thief pay big dividends for his own survival as well as for the survival of other people.

In the past, why did Harry and his friends visit Mr. Tillian after school?

Since Mr. Tillian owned a candy and nut shop, Harry and his friends visited Mr. Tillian after school to sample the available confections. The boys either bought roasted peanuts or penny candy from the huge bins.
Mr. Tillian enjoyed having Harry and his friends at the store after school hours. As time progressed and the boys reached junior high, however, Mr. Tillian began to see less and less of the boys at his store. Since the boys were now older and had more pocket money, they chose to spend their money on video games, records, and fast food.
Later, Mr. Tillian bought himself a parrot in order to stave off his loneliness. Interestingly, the parrot became the means for Harry to eventually realize how much his father had missed his presence at the store.

In your opinion, which road in Frost's "The Road Not Taken" is better and why?

Neither is better.  They are, essentially, the same.
The speaker says that he comes to a fork in the road, and he examines one road and then the other.  When he looks at the second, he says that it is "just as fair" as the first, and he claims that "the passing there / Had worn them really about the same [...]."  In other words, then, the roads -- although they are not identical and do look somewhat different from one another -- have been traveled approximately the same number of times.  To say that they have been worn about the same amount means that there simply isn't one road that has been more or less traveled than the other.  They have been traveled equally.  In fact, on the morning on which the speaker encounters the fork, he says that the two roads "equally lay" in the leaves, and so they are really not significantly different from one another.  Therefore, when the speaker says that, when he's old, he's going to tell others than he took the road "less traveled by," he basically admits that he's planning to lie.  Everyone wants to believe that their choices are significant and that they are original and unique, but, this poem suggests that there really are no such unique choices.  They have all been made hundreds, thousands, of times before, and these decisions are really not as momentous as they seem at the time.
Thus, one road is no better than the other.

You are being asked to state an opinion based on reading “The Road Not Taken” by Robert Frost. The question asks which road is the better “claim” or choice on that morning.
The traveler comes to the fork in the path, and ponders which is more desirable to take that morning. As the traveler surveys the roads, he finds they are very similar in the morning light.

And both that morning equally lay
In leaves no step had trodden black.
Oh, I kept the first for another day!

After examining the two paths, the traveler decides on the second one. In his perception, the second path calls to him because it is “grassier” and seems to “want wear.” He “claims” the second path and says he will save the other for another day. In the traveler’s opinion, the second path is more to his liking on that particular morning. Later in life, he states his decision “made all the difference” in his life.
When critical analysis is written about this poem, it is often said choosing one path or the other is less about establishing one’s individual path in life, and more about Robert Frost’s indecisive friend. When considering this analysis, the path choice becomes less important to understanding the poem.

In Three Men in a Boat, why did the narrator remember his Uncle Podger and what was the condition when he tried to hang the picture on the wall?

J., the narrator of Three Men in a Boat, tells a lengthy story about his Uncle Podger in Chapter III. Here is a man who thinks he knows how to do something -- maybe he thinks he knows how to do many things -- when in fact, he’s quite helpless and needs the assistance, verification, and admiration of everyone else around him to do the simplest task. The incident J. recalls is when his uncle once decided to hang a picture on the wall. The task only required the framed picture, a nail, a hammer, a step-ladder, and perhaps a pen or pencil to mark the spot where the nail should go. But Podger made a big deal of the challenge. He called on all of his family members to bring him the tools. Then he kept “losing” some of them. He dropped the picture and cut his finger on the glass. He hit his thumb with the hammer. And on and on the ordeal went; until near midnight, when the picture finally hung crookedly on the wall, the room was in a state of shambles, and Uncle Podger commended himself on a job well done. He had sapped the strength of everyone around him.

"There is no king who has not had a slave among his ancestors, and no slave who has not had a king among his." What does this quote refers to?

This quote appears very early in the memoir as part of Keller's reflection on her ancestors. Before writing the sentence quoted, she notes that on her father's side she has a Swiss ancestor who was the first teacher of the deaf in Zurich and wrote a book on the subject. Keller refers to this as a "singular coincidence," then states:

it is true that there is no king who has not had a slave among his ancestors, and no slave who has not had a king among his.

By making this declaration, she dismisses the idea of putting any special weight on her ancestry or bloodlines. What she means is that who your ancestors are is unimportant: it is what you do that counts. She may have had one ancestor who made an important contribution, but she is not going to make too much of that. After all, everyone has had important and unimportant relatives.
This statement, so easy to brush over, is important, given the privileged Southern context in which Keller was born. Southern families such as hers tended to attach outsized importance to their ancestors and their blood lines, asserting that this ancestry made them superior to others. In the broadest terms, blood lines in the form of racial categories determined who did and didn't receives privileges in the South. By dismissing ancestry, Keller was making a statement about equality. She was a socialist and therefore rejected the idea of one social class as inherently superior to others.

Why did explorers still sail west from Europe in the 1500s?

Explorers sailed west from Europe in the 1500s for various reasons. At first, explorers were looking for a shorter water route to Asia. They hoped that they would find this route by sailing west. For example, Christopher Columbus sailed westward in 1492 in search of such a route. Other explorers, such as John Cabot and Jacques Cartier, also sailed west looking for a shorter route to Asia.
As time passed, explorers discovered a new world, the Americas, and they realized that there were benefits to coming to the New World. They discovered minerals such as gold and silver. This encouraged European countries to support additional explorations, as these countries hoped to enrich their treasurers with these minerals. As the European countries claimed land in the New World, this gave people a chance to go there to spread Christianity. These missionaries realized that many people either practiced no religion or practiced a native religion different from Christianity. Thus, the missionaries saw an opportunity to spread Christianity.
Several European countries were in a competition for power, wealth, and land. The desire to be stronger than their rivals also fueled some of the explorations in the 1500s. Great Britain, France, Spain, and Portugal were some of the European countries that sponsored explorers to sail westward.

Calculus: Early Transcendentals, Chapter 4, 4.2, Section 4.2, Problem 13

For the mean value theorem to be valid, the function f(x) = sqrt x must satisfy the following conditions on the interval, such that:
f(x) is continuous over the interval [0,4] and it is because it is an elementary function.
f(x) is differentiable on (0,4).
If both conditions are satisfied, then, it exists a point c in (0,4) , such that:
f(4) - f(0) = f'(c)(4 - 0)
You need to evaluate f(4) and f(0), by replacing 4 and 0 for x in equation of the function:
sqrt 4 - sqrt 0 = (sqrt c)'(4-0)
2 - 0 = 4/(2sqrt c)
Reducing by 2 yields:
2 = 2/sqrt c => 2sqrt c = 2 => sqrt c = 1 => c = 1 in (0,4)
Hence, evaluating the number c that satisfies the mean value theorem yields c = 1.

What are some major events in Black Like Me by John Howard Griffin?

In Black Like Me, major events are things that drive the plot and Griffin's character development.
The most important event is Griffin's decision to change his skin color. It's an exhausting process but it allows him to live as a person of a different race. This is the impetus for everything else that happens in the book; it allows him to see what life is like from another perspective.
Another important event is when Griffin decides that he's ready to be white again. His time living as a black man changed him. He realizes that when he's white, white people respect him and black people seem wary. When he's black, black people respect him and white people are cruel. This makes it difficult for him to come to terms with the way people are treated and treat each other.
Another important event is when Griffin faces a white bully while he appears to be a black man. The boy follows him down the street and says he's going to get him. Only when Griffin fights back does the boy finally go away. People don't seem interested in helping when he appeals to a couple for assistance.
Traveling with Rutledge is also an important event. Because Rutledge is white while Griffin is presenting as black, the differences between the facilities they can use is staggering. It's difficult for Griffin to find bathrooms, water fountains, or businesses that will accept him.

Some major events in Black Like Me include the following:
George Levitan, the publisher of Sepia magazine, gives Griffin money to conduct his research on what it's like to be a black man in the south (page 3).
Griffin, the author, looks in the mirror and does not recognize himself with his dermatologically darkened skin (page 11).
Griffin goes out in New Orleans as a black man (page 12).
Griffin decides to work with the shoeshine man in New Orleans, who knows Griffin is really a white man from the hairs on his hands (page 23).
The author visits his friend, P.D. East (page 73), a white writer and newspaper man who is sympathetic to Griffin.
The author arrives in Biloxi, Mississippi (page 83).
The author goes to Mobile, Alabama (page 96) and then hitchhikes to Montgomery, Alabama (page 102). He stays in a backwoods shack with a black family (page 108). 
The author finds a spirit of hopefulness in Montgomery (page 120), where Martin Luther King had been preaching. 
The author returns to being white (122) and then returns to have dermatologically darkened skin (page 126) and heads to Atlanta (page 132).
The author visits a Trappist monastery (page 135).
The author returns to New Orleans (page 145) and then returns home to his family in Texas (page 147).
The author is interviewed on a TV show that is aired about his work (page 149). He appears on several other TV shows and in several articles, provoking a negative response in his hometown and the environs. He is hanged in effigy (page 159), but he also receives many positive letters, even from the south. 
The author decides to move to Mexico in response to the hatred he has received; his parents have already moved (page 162).

Single Variable Calculus, Chapter 3, Review Exercises, Section Review Exercises, Problem 58

a.) Differentiate the Double-angle Formula $\cos 2x - \cos^2x - \sin^2x$ to obtain the Double-angle Formula for the sine function.


$
\begin{equation}
\begin{aligned}

\frac{d}{dx} (\cos 2x) =& \frac{d}{dx} (\cos ^2 x) - \frac{d}{dx} (\sin^2 x)
\\
\\
- \sin 2 x \frac{d}{dx} (2x) =& \frac{d}{dx} (\cos x)^2 - \frac{d}{dx} (\sin x) ^2
\\
\\
- \sin 2 x =& 2 \cos x \frac{d}{dx} (\cos x) - 2 \sin x \frac{d}{dx} (\sin x)
\\
\\
- 2 \sin 2x =& 2 \cos x \sin x - 2 \sin x \cos x
\\
\\
- 2 \sin 2x =& -4 \sin x \cos x
\\
\\
\frac{-\cancel{2} \sin 2x}{-\cancel{2}} =& \frac{-4 \sin x \cos x}{-2}
\\
\\
\sin 2x =& 2 \sin x \cos x

\end{aligned}
\end{equation}
$



b.) Differentiate the Addition Formula $\sin (x + a) = \sin x \cos a + \cos x \sin a $ to obtain the Addition Formula for the cosine function.


$
\begin{equation}
\begin{aligned}

\frac{d}{dx} [\sin (x + a)] =& \frac{d}{dx} (\sin x \cos a) + \frac{d}{dx} (\cos x \sin a)
\\
\\
\cos (x + a) \frac{d}{dx} (x + a) =& \left[ (\sin x) \frac{d}{dx} (\cos a) + (\cos a) \frac{d}{dx} (\sin x) \right] + \left[ \cos x \frac{d}{dx} (\sin a) + (\sin a) \frac{d}{dx} (\cos x)\right]
\\
\\
\cos (x + a)(1) =& [(\sin x) (0) + (\cos a)(\cos x)] + [(\cos x) (0) + (\sin a)(- \sin x)]
\\
\\
\cos (x + a) =& \cos a \cos x + 0 + 0 - \sin a \sin x
\\
\\
\cos (x + a) =& \cos x \cos a - \sin x \sin a

\end{aligned}
\end{equation}
$

How is "The Kugelmass Episode" an example of the literary genre of magical realism?

Magical realism is a literary movement that blends realistic events with elements of the supernatural. In “The Kugelmass Episode,” Kugelmass is a typical guy who is bored with his life and looking for adventure and affection. The elements of realism in the story include his visit with his therapist, his interactions with his wife and his responses to the various situations in which he finds himself. Although the literary characters discussed in the story are fictional, the books themselves are real. However, the story becomes magical realism when the “magician” enters the storyline with his magical box. The idea of a character traveling into various literary settings to meet fictional characters ensures this story fits into the magical realism genre.

How does the setting of “The Pedestrian” add to the loneliness and isolation felt by Leonard Mead?

Ray Bradbury’s 1951 short story “The Pedestrian” takes place on a November evening in the year 2053. The protagonist, Leonard Mead, is engaging in his favorite pastime—taking a solitary walk around his suburban neighborhood. Bradbury introduces Leonard’s feelings of loneliness and isolation in the first paragraph when he says, “he was alone in this world of A.D. 2053, or as good as alone.” The empty streets Leonard walks down are described as being like a “graveyard,” where “gray phantoms” appear at the windows of “tomb-like” buildings lit up only by the glow of the “viewing screens” everyone but Leonard seems to own and watch nightly.
The autumn setting, with its dead, “skeletal” leaves and misty air, also contributes to the lonely, melancholy mood, and the cold temperature echoes the emotional coldness of this future world. Leonard seems to enjoy the exhilarating feeling of the “good crystal frost,” but it is a lonely enjoyment: he has nowhere in particular to go, so he is wandering aimlessly, alone on his walk and, we gather, in his society. Though he takes these walks all the time, Leonard has never met another pedestrian, and though he is surrounded by houses full of people, he feels as isolated as if he were in the middle of nowhere:

The street was silent and long and empty, with only his shadow moving like the shadow of a hawk in midcountry. If he closed his eyes and stood very still, frozen, he could imagine himself upon the center of a plain, a wintry, windless Arizona desert with no house in a thousand miles, and only dry river beds, the streets, for company.

Bradbury continues this imagery of emptiness, solitude, and desolation when Leonard pauses at a highway intersection, thinking of how busy and chaotic with cars that same intersection is during the day. Now, though, “these highways, too, were like streams in a dry season, all stone and bed and moon radiance.”
Just as he continues to describe the nighttime streets with imagery that evokes a lonely desert, Bradbury continues to compare the “gray and silent” houses in the neighborhood to tombs in a graveyard when Leonard is being interrogated by the patrol car:

Everything went on in the tomblike houses at night now, he thought, continuing his fancy. The tombs, ill-lit by television light, where the people sat like the dead, the gray or multicolored lights touching their faces, but never really touching them.

At the end of the story, Leonard sees his house, where he lives alone, from the window of the driverless patrol car as he is taken to the Psychiatric Center for Research on Regressive Tendencies. It is the only house with all its lights on in “an entire city of houses that were dark.” This image illustrates just how alone Leonard is in this future society. Bradbury then returns to the image of the streets as dry streams one last time, emphasizing the themes of loneliness and isolation through the description of silence and motionlessness, and the repetition of the word “empty”:

The car moved down the empty river-bed streets and off away, leaving the empty streets with the empty side-walks, and no sound and no motion all the rest of the chill November night.

In the Preamble of the Declaration of Independence, what support did Thomas Jefferson say he would provide?

In the Preamble to the U.S. Declaration of Independence, Thomas Jefferson writes about how he will provide the facts to a candid world. He talks about the injustices that the king of Great Britain, King George III, has committed against the colonies. Thomas Jefferson says that since the colonists want independence, they need to show the world the seriousness of these injustices. Governments should not be thrown off and revolted against for "light and transient causes" but for great evils. He states that it is the people's "right, it is their duty to throw off such Government." The colonists have endured this kind of abuse from the British government, and he provides support for this claim by listing these wrongs. In the end, he is hoping that the world will agree with his argument and support the colonists. So, in a broader sense, the support Thomas Jefferson provided was to the colonists; by attempting to convince the rest of the world to agree with him, he helped support the colonists' cause.

Jefferson says that he and the other members of the Continental Congress (the document was of course a joint statement) would, out of a "decent respect to the opinions of mankind," would declare the reasons, or "causes" that the colonists were declaring their independence. The causes were both ideological--Jefferson spends the next paragraph explaining the social contract theory that the revolutionaries cited in support of independence--and pragmatic. While the most famous part of the document is the statement of principles, namely that "all men are created equal," Jefferson devoted far more of the document to a series of accusations against King George. These ranged from his refusal to approve laws that were beneficial to the colonies to his alleged incitement of Native Americans against the revolutionaries after 1775. The idea was that this "long train of abuses" justified separation from the mother country, which was a big step to take.

What were Lafcadio Hearn's first impressions of Japan when he arrived there?

Lafcadio Hearn first visited Japan in 1890 while working as a journalist for Harper's magazine. At that time, Japan was little known in the West; it appeared to all the world as a strange, exotic land full of unusual customs which were poorly understood by outsiders. Hearn did not know it when he first set foot on Japanese soil, but he would, more than any other foreigner in the late nineteenth and early twentieth centuries, come to be responsible for demystifying the Land of the Rising Sun for a Western audience.
Initially, however, Hearn's first impressions of the country were those we would expect from a Westerner totally unfamiliar with Japan. Hearn was deeply enchanted by his encounter with this strange new world in the East, yet, as with virtually all Western visitors, he was unable to initially fathom the sheer richness and depth of Japanese culture:

The country is . . . full of the strangest charm. Artistically it is one vast museum. Socially and naturally it is really a Fairyland. The first impression produced by the Japanese themselves is that of being among the kindest kind of fairies. . . . The religions seized my emotions at once, and absorbed them. I am steeped in Buddhism, a Buddhism totally unlike that of books—something infinitely tender, touching, naïf, beautiful. I mingle with the crowds of pilgrims to the great shrines; I ring the great bells; and burn incense—rods before the great smiling gods.

Hearn's initial impressions of Japan are similar to those of a tourist. He is positively overwhelmed with the exotic profusion of sights, sounds, and smells that assail his senses. However, his evaluation of Japanese culture is, at this early stage, somewhat shallow. Reading his words above, it almost seems as if Japan were some kind of giant theme park populated by charming little sprites. Hearn's description of the Japanese as "among the kindest kind of fairies" comes across as a tad condescending, expressing an attitude that most people today would find unacceptable.
Nevertheless, Hearn's impressions are very much of their time, a common reaction for someone who has just arrived in a strange land for the very first time without knowing much about the indigenous culture. However, the incredible excitement that Hearn must have felt bursts through his excited prose, placing us in his shoes and making us want to want to share in his experiences.
From Hearn's first impressions of Japan, we can understand why he came to develop such an intense fascination with Japanese life and culture. His engagement with Japan transformed over time from a breathless sense of wonderment to a deep, respectful appreciation of an ancient and endlessly engrossing culture.

Why is public opinion in a democracy so important?

Public opinion is important in a democracy because we are the "employers" of those whom we elect. They serve at our behest, so what we think about what they do should matter a great deal to them.  Every few years, we issue a performance review, by way of election or not. However, we seem to be in a period in which our elected representatives are slaves to polling. Whether this is good or bad is a function of one's ideas and expectations about representational governance and decision-making. 
Some people think that when we elect representatives, they should act in accordance with our wishes on all matters. So that if a majority in a congressional district opposes a trade agreement, there is an expectation that the representative will vote against it.  If a majority in a district seek to defund Planned Parenthood, the representative should vote accordingly.
Some people think that we elect representatives to make decisions using their ethics, knowledge, intelligence, and experiences to make the best choices possible for those whom they represent.  Thus, we speak of a senator casting a vote or taking a stance based upon his or her own conscience.  Or a representative will vote for a bill because he or she has investigated it thoroughly and knows far more than the people in the district know about it. 
For both approaches, public opinion matters, of course.  If public opinion turns too greatly on a politician, he or she is voted out of office.  In the first case, public opinion informs the decision to be made, based upon what a majority want the elected representative to do.  In the second case, the representative needs to know how deeply unpopular a decision might be, to weigh the costs of an unpopular decision. 
The problem today is that in the 24/7 world of news that we live in, there should be legitimate concern about what people are basing their polling responses upon.  The latest soundbite, true, false, or as some say, "truthy," can probably sway millions of people to a completely different opinion.  If this continues, polling is likely to become increasingly inaccurate.  No pollster can keep up with so many shifts.  Politicians themselves are responsible for this problem, too, since they frequently change their positions. I personally think that people running for office before the advent of the internet were more likely to state what their positions were consistently, not being able to send up trial balloons so easily and then walk them back after a negative public response.  Technology also gives us all these new means of viewing public opinion, tweets, Facebook posts, and so on, ad nauseum.  Perhaps a Facebook post should be accorded more weight than a tweet, so that five negative tweets equal one Facebook post. How ridiculous can all of this get as politicians seek to take the public's temperature? 
No matter what you believe about how a representative should be representing you, it is clear that what the public thinks matters to our elected representatives.  They need to know how their constituencies want them to vote, and if they vote contrary to their constituency's wishes, they need to be able to calculate the political cost.

Do you think the law of demand accurately reflects most people's behavior?

The law of demand states that as prices changes, the demand for those products will also change. Higher prices tend to lower demand while lower prices tend to increase demand. I would say that this law does reflect the behavior of most people for most products. While there are some products or services that people would buy regardless of the price, such as electricity, medical services, and gasoline, for most products people adjust the amount that they buy based on the price of the product. Even for products with relatively inelastic demand, consumers may use less of those products when prices become too high.
When the price of gasoline reached over $4.00 a gallon, people still bought gasoline, but they also changed some of their driving habits and patterns to allow them to purchase less gasoline. When the price of orange juice increased because the supply of oranges dropped due to extremely cold weather, people began to buy alternative products such as grape juice and apple juice. Some people stopped drinking any kind of juice completely. For the average person who needs to manage his or her finances, the price of a product will impact how much of that product or service they will buy or use.
https://economictimes.indiatimes.com/definition/law-of-demand

https://www.thebalance.com/law-of-demand-definition-explained-examples-3305707

Why didn't president FDR act after the attack on the USS Greer?

The official version of events put out by the Roosevelt Administration was that the USS Greer had been fired upon by a German submarine. The Germans disputed this account and stated instead that it was they who'd been attacked with depth bombs by the Americans. They further accused the government of deliberately trying to provoke the Germans into conflict in order to justify the United States' entry into the war. President Roosevelt responded by authorizing the US Navy to shoot on sight any German submarine, in any waters, deemed a threat to the United States.
Yet FDR didn't use the attack on the Greer as a pretext for going to war. Isolationist sentiment was still pretty high in the United States, and Roosevelt understood that only a major full-scale attack on America would be enough to change the predominant attitude. Just such an attack duly came with the Japanese assault on Pearl Harbor in December, 1941, just over three months after the attack on the Greer.

In "Okay For Now," what does the metaphor "dark woods" represent?

In the book, the Yellow Shank bird is associated with the dark woods. However, the metaphor "dark woods" represents the defining moment of confrontation between Doug and his abusive father. To Doug, the "woods" is a treacherous and frightening place; to confront his abusive father, he must venture into this dark place alone, as no one else in his family dares to accompany him.
In Chapter Five, we learn that Doug's father has appropriated the hundred dollars and signed baseball that Doug won at the Trivia Contest. Later, Doug confronts him, despite knowing that he's putting himself in physical danger by doing so. Mr. Swieteck lies about having received the prizes, but Doug knows what Mr. Ballard told him.
At this time, Doug is ready to call his father a liar (because that's what Mr. Swieteck is), but he's afraid. Doug has never openly challenged his father before. Suddenly, in a moment of inspiration, he remembers the Yellow Shank and how the bird stands facing the dark woods ahead of him. Doug imagines that the Yellow Shank will eventually walk towards the woods, despite the uncertainty that awaits him.

He's staring into this dark place, and he's just about to cross the river that divides him from it...he knows what he's getting into, but he does it anyway, calm and smooth and straight. He's going to step into the middle of the picture, where he should be, with the light in back of him and the dark ahead. His whole world is waiting for him to do that.

He's so inspired by the Yellow Shank that he goes ahead and tells Mr. Swieteck that he's a liar. Mr. Swieteck lunges at Doug, but he misses him three times; he only manages to clip Doug slightly when the boy pushes through Ernie Eco's arms. Apparently, Ernie Eco isn't too successful either in his efforts to help Mr. Swieteck corner Doug. For his part, Doug counts the confrontation a victory. Despite his fears, he has braved the "dark woods," and he's justifiably proud of himself for confronting his abusive father.

Does Greene present Phuong as an object or a character?

The reader learns about Phuong primarily through Fowler, the protagonist of The Quiet American, and Fowler's description of her is limited and superficial, though they are lovers. She appears to have a quiet personality, and she seems to enjoy a passive existence, but Fowler's depiction of Phuong may or may not accurately represent her.
With this observation in mind, a reader of Greene's The Quiet American could argue that Phuong is more object than woman, but that may be Fowler's fault more than Phuong's. Greene's presentation of Phuong through the lens of Fowler means that Phuong's role is ambiguous, so whether Phuong is object or character may depend on how the reader perceives Fowler.
For example, Phuong's need for stability does not receive close examination by Fowler, who even tells Pyle that he has no real investment nor interest in Phuong's experience of their relationship; this lack of engagement allows Pyle to feel justified in his desire to marry Phuong, especially as Fowler is still legally married and cannot marry her himself. Fowler treats Phuong like an object, but Pyle doesn't; Greene offers the reader a similar choice.

http://www.nytimes.com/2001/05/30/sports/golf-disabled-golfer-may-use-a-cart-on-the-pga-tour-justices-affirm.htmlWhat does this case have to do with the concept of “reasonable accommodation?? How do other golfers react to the Casey Martin case? What implications does this case have for other employees with disabilities?

In the case of PGA Tour, Inc. v. Casey Martin (2001), the Supreme Court of the United States ruled that Martin was being denied his rights under the Americans with Disabilities Act of 1990 (ADA) by virtue of the Professional Golfers' Association's insistence that Mr. Martin walk the entirety of the golf courses on which he competed under the association's sponsorship. Martin suffers from a painful, debilitating circulatory condition that makes walking any distance inordinately difficult. Under the ADA, employers and public facilities must make appropriate accommodations for the disabled, a requirement that the PGA argued was not applicable in this case. The association's attorneys argued that the physical challenge of walking the entirety of a golf course was an integral component of the broader athletic competition and that allowing Martin to drive the course in a golf cart provided him an unfair advantage over his competitors. 
Many professional golfers opposed Casey Martin's efforts to be allowed to use a golf cart, arguing that professional athletes are expected to be capable of performing the acts associated with the sport in question without any special accommodations. The PGA, in its opposition to Martin, enlisted the support of two of the game's most venerated personalities, Jack Nicklaus and Arnold Palmer. Some prominent professional golfers, namely Tom Lehman and Greg Norman, supported Martin's cause. 
The implications of Martin's case for others with disabilities was minimal. The ADA had already become law, and its application has been widespread in public and private facilities. A history of case law exists irrespective of Martin's legal efforts. With respect to professional sports, the impact has also been minimal. Either an individual is physically and emotionally capable of performing at the level required or he or she is not, and physically-disabled golfers generally make little effort at competing at the professional level. Most athletes accept that a requirement to make accommodations for their individual physical conditions is irrational considering the multitude of injuries they endure during the course of their careers anyway. Players with torn ligaments or broken bones, for example, do not expect the leagues in which they compete to allow the use of wheelchairs or crutches on fields of play. While the use of a golf cart hardly qualifies as such an example, the underlying rationale remains sound: either an individual can meet the physical standards necessary to compete with his or her colleagues or he or she cannot. Those who cannot compete because they are too small, cannot jump high enough or have a medical condition that precludes competition on a professional level generally move on to other pursuits.
There are other situations that complicate the debate surrounding the case of Casey Martin, and those involve the use of banned medications to address legitimate medical conditions like depression and anxiety and respiratory ailments. Inhalers and anti-depressants may contain controlled substances that are listed under "performance-enhancing" medications, and their presence in urine analyses or blood tests has, in the past, led to problems for athletes. The debate over the long-term implications of PGA Tour, Inc. v. Casey Martin, consequently, continues. 
https://edition.cnn.com/2012/06/14/sport/golf/us-open-martin-woods-golf/index.html

https://www.usatoday.com/story/sports/golf/2013/06/25/casey-martin-golf-cart-oregon-us-golf-association/2458135/

What was George Washington's foreign policy?

George Washington took a foreign policy stance that frequently took a neutral response whenever possible; he held the belief that the United States was far too young a country to get involved in foreign affairs.
This was even the case when France—who had heavily aided the American Revolution by supplying money, weapons, and troops to fight against the British—asked for help in a revolution of their own. Washington, sticking to his neutral foreign policy stances, refused to offer any aid in return.
Washington also aimed to negotiate treaties both domestically and abroad. While Britain was coaxing Creek Native Americans to attack western settlers, Washington avoided significant retaliation, choosing instead to negotiate peace with the Natives and to send Americans overseas to negotiate peace treaties in Europe.
In an exercise of democracy, many members of the newly-formed government (and ordinary citizens, too) disagreed with Washington's policies, frequently challenging them. This included his close friend and fellow politician Thomas Jefferson, with whom Washington had a falling out over the issues of foreign policy. Nevertheless, Washington's resignation speech proudly pushed forward the idea of a neutral, if not uninvolved, foreign policy.
https://millercenter.org/president/washington/foreign-affairs

https://www.thoughtco.com/foreign-policy-under-george-washington-3310346

Why is the theme forgiveness?

Forgiveness can be considered a theme in Langston Hughes's "Thank You, Ma'am" as it is clearly demonstrated in the story. Roger is a boy that makes a mistake in trying to steal the purse of Mrs. Luella Bates Washington Jones. Mrs. Jones holds him in a "half-nelson" and takes him to her home all the while rebuking him for his poor choice.
When they arrive at her home, she lets go of Roger and orders him to wash his face. The door is left open, which gives Roger an opportunity to run. Instead, he does as he is told. Mrs. Jones then asks Roger if he's hungry and tells him he'll eat dinner with her. Roger again observes the open door and again chooses to stay.
Mrs. Jones admits there were times when she wanted things and she shares, "I have done things, too, which I would not tell you, son—neither tell God, if he didn’t already know." Through her comment and her actions, she lets Roger know that while she is holding him accountable, she also forgives him. When Mrs. Jones goes to prepare dinner, and Roger has his second opportunity to run, the author shares that Roger "did not trust the woman not to trust him." It is because she forgives him, and because she allows him the opportunity to be trusted, that he is trustworthy.

Finite Mathematics, Chapter 1, 1.1, Section 1.1, Problem 34

Determine a equation in slope intercept form (where possible) for the line with $y$-intercept of
$\displaystyle -\frac{2}{3}$ and is perpendicular to $2x - y = 4$

If we transform the given line into point slope form, we have

$
\begin{equation}
\begin{aligned}
2x - y &= 4 \\
\\
y &= 2x - 4
\end{aligned}
\end{equation}
$

Now that the line is in the slope intercept form $y = mx + b$. By observation, $m = 2$
Thus, the slope of the perpendicular line is
$\displaystyle m_{\perp} = -\frac{1}{2}$.
Now, if the line has $x$-intercept of $\displaystyle \frac{-2}{3}$, it means that it passes through
the point $\displaystyle \left( -\frac{2}{3}, 0 \right)$. Then,
By using the point slope form,the equation of the line will be $y - y_1 = m(x - x_1)$

$
\begin{equation}
\begin{aligned}
y - 0 &= - \frac{1}{2} \left( x - \left( -\frac{2}{3} \right) \right)\\
\\
y &= - \frac{1}{2} \left( x + \frac{2}{3} \right)\\
\\
y &= -\frac{1}{2} x - \frac{1}{3}
\end{aligned}
\end{equation}
$

What makes Gonzalo feel uncomfortable despite the storm?

In the exciting opening scene of the play, the King of Naples and his group of nobles struggle to survive the violent tempest that threatens to sink their ship. As the Boatswain attempts to rouse the mariners to action by directing them to take in the topsail, Alonso and Antonio begin to give the Boatswain directives. The Boatswain responds by telling the nobles to get below deck because they are in the way. The Boatswain's attitude makes Gonzalo feel uncomfortable. Gonzalo is taken aback and disturbed by the commoner's disrespectful tone towards the King of Naples. The Boatswain continues to disrespect Gonzalo and the nobles by mentioning that he could care less about their titles and is only concerned about his own fate. When the Boatswain briefly exits the scene, Gonzalo reveals his contempt for the commoner by saying,

"I have great comfort from this fellow. Methinks he hath no drowning mark upon him. His complexion is perfect gallows. Stand fast, good Fate, to his hanging" (Shakespeare, 1.1.23-26).

Overall, Gonzalo is uncomfortable with the Boatswain's manner and tone while addressing the nobles on the ship. In the midst of the chaotic storm, the Boatswain completely disregards proper social conventions by rudely addressing the nobles and dismissing their concerns.

Calculus of a Single Variable, Chapter 6, 6.4, Section 6.4, Problem 18

Given,
x^3y' + 2y = e^(1/x^2) and to find the particular solution of differential equation at y(1) = e.
so proceeding further , we get.
x^3 y' + 2y = e^(1/x^2)
=>y' + 2y/(x^3) = e^(1/x^2) /x^3

so , the equation is linear in y
and is of the form
y' +p(x)y=q(x)
so the general solution is given as
y*(I.F)= int q(x) * I.F dx+c
where I.F (integrating factor ) = e^(int p(x) dx)
on comparing we get ,
p(x) = 2/x^3 and q(x) = e^(1/x^2) /x^3
so ,
I.F = e^(int (2/x^3) dx) = e^(2 (x^-3+1 )/ -2) = e^(-(x^-2))
so ,
y (e^(-(x^-2)))= int (e^(1/x^2) /x^3) * (e^(-(x^-2))) dx+c
=>y (e^(-(x^-2)))= int (x^-3) dx+c
=>y (e^(-(x^-2)))= x^((-3+1)/ -2)+c
=> y (e^(-(x^-2)))= x^-2/ -2+c
=> y = (- (x^-2)/2+c)/(e^(-(x^-2)))
= e^((x^-2)) *(c-(x^-2)/2 )
so , now to find the particular soultion at y(1) =e , we have to do as follows
y(x) = e^((x^-2)) *(c-(x^-2)/2 )
=> y(1) = e^((1^-2) ) *(c-(1^-2)/2 )
=> e= (e ) *(c-(1)/2 )
=> 1= c-1/2
=> c= 3/2
so the particular solution is
y= ((e^((x^-2))) ) *(3/2-(x^-2)/2 )
=e^((x^-2)) *((3-(x^-2))/2 )

What is an example of a balanced diagnostic equation, and how does it work?

A diagnostic equation is one in which there is no time derivative. This may mean one of the two: either all the variables used in the equation are independent of time, or all the variables are evaluated at the same point in time (at the same time instant). Some examples of diagnostic equations are ideal gas law, hydrostatic equation, etc.
The hydrostatic equation is given as:
dp/dz = -rhog
where p is the pressure, rho is density, g is acceleration due to gravity and z is the geometric height. In this equation, there is no time variable. And this equation describes the balance between gravitation force (directed downwards) and pressure gradient force (directed upwards). And hence, this is an example of a balanced diagnostic equation.
Similarly, the ideal gas law is given as:
PV = nRT
where P is the pressure, V is the volume, n is the number of moles, R is the universal gas constant and T is the temperature. This equation does not have any time variable or time derivative. It is understood that while all these variables (P, V, n, and T) may have different values at different time points, the equation is applied at a given time instant where the measured values of these parameters are known. In other words, the equation is valid at all time points and that any change in the value of any of these variables will cause a change in the values of one or more variables. Hence this is another balanced diagnostic equation.
Another class of equations is the prognostic equations. These have time derivative of a quantity and hence can be used to determine the value of that quantity at any other time instant (given the values of other parameters at that time). The continuity equation is a good example of a prognostic equation.
Hope this helps.

Single Variable Calculus, Chapter 3, 3.1, Section 3.1, Problem 21

Suppose that $f(x) = 3x^2 - 5x$, find $f'(2)$ and use it to find an equation of the tangent line to the parabola $y = 3x^2 - 5x$ at the point $(2,2)$

Using the definition of the derivative of a function $f$ at a number $a$, denoted by $f'(a)$, is

$\qquad \displaystyle \qquad f'(a) = \lim_{h \to 0} \frac{f(a + h) - f(a)}{h}$

We have,


$
\begin{equation}
\begin{aligned}

\qquad f'(a) =& \lim \limits_{h \to 0} \frac{3(a + h)^2 - 5 (a + h) - (3a^2 - 5a)}{h}
&& \text{Substitute $f(a + h)$ and $f(a)$}\\
\\
\qquad f'(a) =& \lim \limits_{h \to 0} \frac{\cancel{3a^2} + 6ah + 3h^2 - \cancel{5a} - 5h - \cancel{3a^2} + \cancel{5a}}{h}
&& \text{Expand and combine like terms}\\
\\
\qquad f'(a) =& \lim \limits_{h \to 0} \frac{3h^2 + 6ah - 5h}{h}
&& \text{Factor the numerator}\\
\\
\qquad f'(a) =& \lim \limits_{h \to 0} \frac{\cancel{h}(3h + 6a - 5)}{\cancel{h}}
&& \text{Cancel out like terms}\\
\\
\qquad f'(a) =& \lim \limits_{h \to 0} (3h + 6a - 5) = 3(0) + 6 a - 5
&& \text{Evaluate the limit}\\
\\
\qquad f'(2) =& 6a - 5
&& \text{Substitute the value of $(a)$}\\
\\
f'(2) =& 6(2) - 5
&& \text{Simplify}\\
\\


\end{aligned}
\end{equation}
$


$\qquad \fbox{$f'(2) = 7$} \qquad $ Slope of the tangent line at $(2,2)$

Using Point Slope Form where the tangent line $y = f(x)$ at $(a, f(a))$




$
\begin{equation}
\begin{aligned}

\qquad y - f(a) &= f'(a)(x - a)
&& \\
\\
\qquad y - 2 &= 7(x - 2)
&& \text{Substitute value of $a, f(a)$, and $f'(a)$}\\
\\
\qquad y &= 7x - 14 + 2
&& \text{Combine like terms}

\end{aligned}
\end{equation}
$


$\qquad \fbox{$y = 7x - 12$} \qquad$ Equation of the tangent line at $(2, 2)$

(1,40) , (3, 640) Write an exponential function y=ab^x whose graph passes through the given points.

The given two points of the exponential function are (1,40) and (3,640).
To determine the exponential function 
y=ab^x
plug-in the given x and y values.
For the first point (1,40), plug-in x=1 and y=40.
40=ab^1
40=ab        (Let this be EQ1.)
For the second point (3,640), plug-in x=3 and y=640.
640=ab^3      (Let this be EQ2.)
To solve for the values of a and b, apply the substitution method of system of equations. To do so, isolate the a in EQ1.
40=ab
40/b=a
Plug-in this to EQ2.
640=ab^3
640=(40/b)b^3
And, solve for b.
640=40b^2
640/40=b^2
16=b^2
+-sqrt16=b
+-4=b
Take note that in exponential function y=ab^x , the b should be greater than zero (bgt0) . When blt=0 , it is no longer an exponential function.
So, consider on the positive value of b which is 4.
Now that the value of b is known, plug-in it to EQ1.
40=ab
40=a(4)
And, solve for a.
40/4=a
10=a
Then, plug-in the values of a and b to the exponential function
y=ab^x
So this becomes:
y= 10*4^x
Therefore, the exponential function that passes the given two points is y=10*4^x .

What were three reasons the US followed a policy of imperialism at the turn of the century?

I will assume here that you mean the turn of the twentieth century, since that period marked the rise of the US as an imperial power. Their defeat of an old colonial power in the Spanish–American war in 1898 put them in a position to become a major player in the game of empire.
American imperialism was an extension of the idea of "manifest destiny," a particularly American notion that the US was the vanguard of democracy and freedom and it was their duty to expand in territorial terms. This was also an idea of American exceptionalism. As the West had been tamed in the late nineteenth century, America looked beyond its continental borders to larger international interests.
Imperialism was also a logical extension of America's role in the world. Imperial expansion, from the Philippines in the Pacific to Puerto Rico in the Atlantic, marked an important change in American influence, which up to that point had remained focused on the North and South American continents following the Monroe Doctrine. Imperial expansion allowed the US to open up new markets and it was a spur to economic development.
Finally, there was a racial undertone to American imperialism, which might be seen as manifested in the idea of the "White Man's Burden," a concept first embraced by Theodore Roosevelt. There was the idea that American imperialism should be embraced to secure the future of the "European race." Aspects of US imperialism since the early twentieth century have arguably involved the suppression of democracy in non-Western nations.

Why is it effective to have the boy tell his own story in "by the waters of Babylon"

Narrative point of view is always an important choice to authors.  "By the Waters of Babylon" makes use of a first person point of view.  By having a first person narrator, the author is immediately limiting the details that are available to readers.  We only know what John experiences, sees, does, hears, and thinks about.  We have no knowledge of anything else until John either experiences it or tells us about it.  An all-knowing, omniscient narrator could potentially ruin the wonder and mystery that this story contains.  When John experiences the "god roads" for the first time and the Place of the Gods, readers experience John's wonder and fear.  His emotions are basically "our" emotions because we are experiencing the story from his perspective.  It is effective for John to tell readers the story because it allows us to have a deeper connection to John's world.  We get to experience firsthand with John, instead of having an omniscient narrator tell us about John and the world. 

Why were they able to travel out faster on the thirty mile river as opposed to going in?

The difference is the condition of the ice on the river, and Buck’s leadership. On the way in, the river is not completely frozen. The men and dogs are constantly breaking through the ice and getting wet, which meant having to stop and build a fire to dry out. It was exhausting and tedious work. Another factor was the conflict between Buck and Spitz, the lead dog. Buck sought to replace Spitz as lead, and to that end sowed conflict and discord amongst the other dogs. This made the team much less efficient.
On the way out, not only is the river frozen solid, but Buck has defeated Spitz and been installed as the new lead dog. Under these favorable conditions, the team is able to cover “in one day going out what had taken them ten days coming in.” Under Buck’s leadership, the team pulled as a single animal, and discipline was restored. As Francois says, “‘Nevaire such a dog as dat Buck! . . . No, nevaire! Heem worth one t'ousan' dollair, by Gar!’”

What's a holistic theme that can connect "The Great Figure" by William Carlos Williams and its corresponding "The Figure 5 in Gold" painting by Demuth, FDR's First Inaugural Address, The Invisible Man by Ralph Ellison, and The Great Gatsby by F. Scott Fitzgerald? This connection can be historical, thematical, or a culmination of both. However, it has to be deeper than merely the fact that they are all American works created circa the 20s.

These works all comment on the viability of the American Dream--the idea that anyone in America can achieve success through effort alone. "The Great Figure" by William Carlos Williams and the corresponding painting, "The Figure 5 in Gold" by Demuth, paint a bold and exciting view of America as a land of promise and progress, as the figure 5 William Carlos Williams sees painted on the side of the truck is bold and shines out like a beacon of progress in the rain. 
On the other hand, The Great Gatsby, The Invisible Man, and FDR's First Inaugural Address are all commentaries on the inability of people to achieve the American Dream. Gatsby constructs an opulent house and wants to marry Daisy, who is from the upper class; however, he dies friendless and without Daisy. In The Invisible Man, the unnamed narrator faces racism and realizes the futility of the Brotherhood (a socialist or communist group) in helping the African-American community. FDR gave his First Inaugural Address in the midst of the Great Depression, when the American economy seemed on the brink of collapse. These works, literary and historic, comment on the way in which the promise of the American Dream is at times illusory. 

Beginning Algebra With Applications, Chapter 1, 1.2, Section 1.2, Problem 150

On January 22, 1943, the temperature at Spearfish, South Dakota, rose from $-4^{\circ} F$ to $45^{\circ} F$ in two minutes. How many degrees did the temperature rise during those two minutes?

We need to find the temperature rise by adding the temperature at Spearfish. So

$-4+45 = 41^{\circ} F$

The temperature rise is $41^{\circ} F$ in two minutes.

How did movies change in the late 1920s?

Starting in 1927 with the movie The Jazz Singer, movies had sound incorporated into them.  Before this, all movies were silent.  They conveyed stories with facial expressions and cards which aired between scenes.  There was often an organist or a pianist who worked for the theater who supplied the background music.  The "talkies" as they were known, revolutionized film.  Actors were cast based on the quality of their voices—many actors from the silent era lost work because their voices did not translate to the big screen.  Movies incorporated music as well, and soon the musical would become a Hollywood staple.  People would also get their news from the movies, and newsreels soon competed with newspapers for allowing people greater access to events unfolding around the world.  Cartoons before the movies became popular with viewers young and old; Steamboat Willie, starring a whistling Mickey Mouse, was a hit in the late 1920s. Walt Disney soon branched out into longer films with Snow White being the first full-length animated feature.  It is hard to imagine any of this happening without the invention of the "talkie," because audiences needed to hear dialogue in order to maintain their attention for long movies.  

Why is it important for the youth to participate in the lottery?

Via Merriam-Webster:

Indoctrinate: to teach (someone) to fully accept the ideas, opinions, and beliefs of a particular group and to not consider other ideas, opinions, and beliefs

The easiest way to indoctrinate someone is to start with a fresh slate. For humanity, there is no fresher slate than a child who, naturally, has very few preconceived notions of right or wrong, moral or immoral. The village in the story uses this to their advantage, even going so far as to state that "The children assembled first, of course." At the end of the story after Tessie Hutchinson is selected by the lottery, the narrator again points out the participation of the children by saying, "The children had stones already. And someone gave little Davy Hutchinson a few pebbles." The village has so successfully explained away the lottery that even the winner's (or perhaps the loser's from an outside view) children participate without protest.

How is the bond story related to the casket story in The Merchant Of Venice?

The link between the two stories arises as a result of the relationship that Bassanio has with characters in the two plot streams. The association is created when Bassanio, who is out of pocket, approaches his friend and confidante, Antonio, a wealthy Christian merchant, for financial assistance so that he may woo the beautiful Portia, a wealthy heiress from Belmont. Bassanio wishes to stand an equal chance against a number of other suitors, who come from privileged backgrounds and the money will give him such an opportunity.
Antonio does not have the ready cash that Bassanio needs but asks him to seek a loan in Venice by using his name as guarantee. He is a person of good standing and assures Bassanio that he will also seek a loan. Bassanio soon encounters Shylock, the Jewish moneylender, who is prepared to extend him a loan of 3 000 ducats should Antonio sign as surety to the bond.
Antonio agrees to Shylock's harsh terms which state that the loan should be settled in three months without any interest charged. If he should forfeit, Antonio has to allow Shylock to cut out a pound of his flesh. Bassanio asks his friend not to agree to these terms but Antonio, confident that he will be able to settle the debt comfortably, signs the agreement. 
Bassanio takes the money and goes off to try his luck in winning Portia's hand in a lottery, in which a suitor should choose the right casket from three, that her deceased father had concocted. It is through these actions that an association between the two stories is created.
It is important to note that Antonio and Shylock despise each other. Antonio believes that Shylock is committing a grave sin by lending out money and profiting from the interest he charges. Shylock hates Antonio for having severely criticized him openly and humiliating him by spitting on his gaberdine, kicking him and calling him a dog. He seeks revenge against the Christian. 
Bassanio is successful in choosing the right casket and wins Portia's hand. He does, however, receive an unsettling message from Antonio in which he states that he has been imprisoned for forfeiting on the bond. He had suffered a number of mishaps with his ships and could not settle the debt. The vengeful Shylock has been insistent that he should have his pound of flesh.
Bassanio is utterly distraught. Portia notices his distress and after discovering the reason for this, offers to help. She urges Bassanio to rush to his friend's aid immediately after their marriage and offers to repay the debt many times over. She formulates a plan to further assist the traumatized Antonio by going to Venice disguised as a doctor of law with Nerissa as her assistant. It is in this manner that the two plots achieve a confluence.   

The bond plot is related to the casket plot through the characters Bassanio and Antonio. At the beginning of the play, Bassanio asks his friend Antonio for funds to support his efforts to woo the beautiful (and fabulously wealthy) Portia of Belmont. In order to win Portia's love, Bassanio will need to choose the correct casket from a group of three. To secure money for his friend, Antonio obtains a loan and draws up a bond agreement with the moneylender Shylock. In short, Antonio takes out a loan and signs a bond to help his friend Bassanio court Portia by solving the casket riddle, and so the two Venetians act as the bridge between the play's two major plots. Of course, one of the remarkable aspects of the play is the stark difference between these two related storylines: while the Belmont casket narrative is solidly comedic, the bond storyline is decidedly more sinister, as it involves underlying tensions between the Christian and Jewish communities, along with the famous pound of flesh. 

The two events are related because Antonio signs a bond with Shylock in order to secure money for his friend Bassanio, so that Bassanio may have a chance to win's Portia's hand in the casket game. 

What are examples of similes in "Rules of the Game"?

A simile is a figure of speech which uses like or as to compare two things which are basically different. In "Rules of the Game," an excerpt from her novel The Joy Luck Club, Amy Tan recounts the story of a young Chinese girl, daughter of immigrants, who becomes a chess prodigy. Throughout the narration she uses figures of speech such as metaphors, personification and similes. One example of a simile occurs when Waverly is explaining how she learned the strategies of chess after her brothers received a chess set for Christmas: "I learned about the middle game and why tactics between two adversaries are like clashing ideas; the one who plays better has the clearest plans for both attacking and getting out of traps." Here she compares the different ways of thinking which will occur between two opponents in a chess match. Another simile appears after Waverly has become embarrassed by her mother's behavior and has run away. Her anger and shame is at an intense level as she runs into a cold alley: "My breath came out like angry smoke." Often a person's breath can be seen in a cold environment and here the narrator links that smoke with the girl's anger.

Precalculus, Chapter 9, 9.4, Section 9.4, Problem 56

Firstly we need to determine whether the series is linear or quadratic. A linear sequence is a sequence of numbers in which there is a first difference between any consecutive terms is constant. However, a quadratic sequence is a sequence of numbers in which there is a second difference between any consecutive terms is constant.
Now let's determine if the above sequence is linear or quadratic.
Lets begin by finding the first difference:
T_2 - T_1 = 9 - 2 = 7
T_3 - T_2 = 16 - 9 = 7
T_4 - T_3 = 23 - 16 = 7
From above we can see we have a constant number for the first difference, hence our sequence is linear.
Now let's determine the model of this sequence. The equation of a linear sequence is as follows:
T_n = a + d(n-1)
Where
T_n = Value of the term in sequence
a = first number of sequence
d = common difference (first difference)
n = term number
Now let's substitute values into the above equation:
T_n = 2 + 7(n-1)
T_n = 2 + 7n - 7
The model is simplified to:
T_n = 7n -5

Now let's double check our model using terms 1, 3 and 6:
T_1 = 7(1) - 5 =2
T_3 = 7(3) - 5 = 16
T_7 = 7(6) - 5 = 37
Summary:
The sequence is linear.
Model:
T_n = 7n - 5

College Algebra, Chapter 2, 2.2, Section 2.2, Problem 38

Find the $x$ and $y$ intercept of $\displaystyle \frac{x^2}{9} + \frac{y^2}{4} = 1$


$
\begin{equation}
\begin{aligned}

\frac{x^2}{9} + \frac{y^2}{4} =& 1
&& \text{Given}
\\
\\
4x^2 + 9y^2 =& 36
&& \text{Multiply both sides by LCD } 36

\end{aligned}
\end{equation}
$


To solve for $x$ intercept, we set $y = 0$


$
\begin{equation}
\begin{aligned}

4x^2 + 9(0)^2 =& 36
\\
\\
4x^2 =& 36
\\
\\
x^2 =& 9
\\
\\
x =& \pm 3

\end{aligned}
\end{equation}
$


The $x$ intercepts are at $(3, 0)$ and $(-3, 0)$

To solve for $y$ intercept, we set $x =0$


$
\begin{equation}
\begin{aligned}

4(0)^2 + 9(y^2) =& 36
\\
\\
9(y^2) =& 36
\\
\\
y^2 =& 4
\\
\\
y =& \pm 2

\end{aligned}
\end{equation}
$


The $y$ intercepts are at $(0,2)$ and $(0, -2)$

Why does Lonnie betray Clem

“Kneel to the Rising Sun” tells the story of Lonnie Newsome, a white sharecropper who works on the property of Arch Gunnard. Lonnie and his family are underfed and slowly starving, and when the story begins, Lonnie approaches Arch to ask for more rations. Arch, who presumably knows why Lonnie is there, cuts off the tail of Lonnie’s dog before eventually promising to give him some more food in the morning. Lonnie is unable to work up the courage to stop him.
Clem Henry, an African American sharecropper, witnesses the exchange, and Lonnie is aware of Clem’s anger. This opening sequence foreshadows what is to come in the story’s climax. When Lonnie’s father is found dead, Clem confronts Arch, and the two fight. Clem runs off to hide, but Lonnie betrays him by telling Arch where he is.
Lonnie is both envious and afraid of Clem, and these conflicting emotions manifest in his betrayal:

Lonnie looked at Clem fearfully. He knew Clem was right, but he was scared to hear a Negro say anything like that about a white man.

Lonnie is envious of Clem because Clem has the courage to speak up to Arch. Lonnie knows that he is abused by Arch, but he constantly justifies his own behavior. Lonnie knows how much he and his family are struggling, but he lets race dictate his own actions:

He was a white man, and to save his life he could not stand to think of turning against Arch, no matter what happened.

Even though Clem is right, in the final instance Lonnie reduces the situation to a question of race. Clem has more courage than Lonnie, and because Clem is African American, this becomes a source of hatred for Lonnie. Ultimately, this motivates him to betray Clem.

Discuss the external environment of Africa as a setting for doing business.

Most of sub-Saharan Africa falls into the category of emerging or frontier markets. While many external factors make it a promising long-term environment for business, many external environmental factors also limit ways of doing business in the region.
The first external issue is lack of infrastructure. Many areas of Africa lack reliable power, transportation, and communication. This means businesses in Africa either must create their own infrastructure (e.g. by buying generators to supply power) or create workarounds to deal with lack of infrastructure. This means cost reduction procedures such as just-in-time manufacturing are not possible; instead, inventories need to be maintained at high levels due to erratic supply chains. Political instability and corruption are also external factors that affect one's ability to conduct business in the region.
On a more positive note, Africa is richly supplied with natural resources and is reaping a demographic dividend due to a youthful and growing population.

In Topdog/Underdog, what is the central conflict between the characters? How does the writer describe the act of writing this play?

The central conflict between these characters revolves around who ultimately deserves the position of top-dog in the relationship. The writer describes the act of writing the play as an open-ended exploration into the human psyche; she maintains that Topdog/Underdog can be interpreted in a number of ways, and she revels in the beauty of writing such a play. Parks received inspiration for her play from another one of her works: The America Play.
In The America Play, the protagonist is also a Lincoln impersonator. In Topdog/Underdog, Parks uses another Lincoln impersonator to explore the intricacies and dynamics of a dysfunctional sibling relationship. In this, Parks lays bare her naturalist approach to drama. She allows her characters to act and to emote naturally; the expelling of raw emotion is both an authentic and cathartic experience for her characters and for her audience. In Topdog/Underdog, Booth and Lincoln fight to exert control over the other. Each maintains that his masculine virility and intellectual prowess far surpasses that of the other. 
As the play progresses, we learn that Booth wants Lincoln to take up card hustling again. He points to Lincoln's lack of job security as the reason to take up a more lucrative career. For his part, Lincoln is wary of falling back on this unscrupulous way of earning a living. His previous partner, Lonny, had been shot during one of their card hustling ventures, and he remembers vowing that he would never go back to that life again after that tragedy. Booth continues to pressure Lincoln, maintaining that their combined card-hustling skills could be their golden ticket to life-long wealth. He uses sly threats and boastful proclamations about a $500 inheritance to goad Lincoln into action.
Booth reminds Lincoln that it has always been the two of them against the world. Even after their parents abandoned them, the two have always survived by looking out for each other and working together. Booth's demands take on new urgency after Lincoln loses his job. Additionally, he slyly hints that he and Grace will marry soon and that the newlyweds will need the apartment to themselves. Booth's incessant wheedling soon wears Lincoln down, and he decides to practice his game once more.
The play ends on a tragic note, with Booth reprising the role of his historical namesake. As John Wilkes Booth assassinated President Abraham Lincoln, Booth kills his own brother, Lincoln. Booth's last act makes him the top-dog by default, but he derives very little comfort from his Pyrrhic victory. The conflict is resolved but only on a superficial level. Booth will never work with his brother again.
 
https://www.nytimes.com/2001/07/22/theater/theater-this-time-the-shock-is-her-turn-toward-naturalism.html

Calculus: Early Transcendentals, Chapter 7, 7.4, Section 7.4, Problem 16

int_0^1 (x^3 - 4x - 10)/(x^2 - x - 6) dx
First simplify
(x^3 - 4x - 10)/(x^2 - x - 6)
By dividing practically we get the quotient as (x+1) and remainder (3x-4) ,so we can write it as
(x^3 - 4x - 10)/(x^2 - x - 6)
= (x+1)+ ((3x-4)/(x^2 - x - 6))
so now we can write
int_0^1 (x^3 - 4x - 10)/(x^2 - x - 6) dx
=int_0^1 (x+1)+ ((3x-4)/(x^2 - x - 6))dx
Now the simplification is as follows :
First just integrate and then apply the limits
so,
int (x+1)+ ((3x-4)/(x^2 - x - 6))dx
=int (x+1) dx+ int ((3x-4)/(x^2 - x - 6))dx
= ((x^2)/2) +x +int ((3x-4)/(x^2 - x - 6))dx
= ((x^2)/2) +x +int ((3x-4)/((x+2) ( x - 3)))dx
Using partial fractions we get
(3x-4)/((x+2) ( x - 3))= A/(x+2) +b/(x-3)
=> On solving we get A=2 B= 1 so,
(3x-4)/((x+2) ( x - 3))= 2/(x+2) +1/(x-3)
so,
=>((x^2)/2) +x +int ((3x-4)/((x+2) ( x - 3)))dx
=((x^2)/2) +x +int ((2/(x+2)) +(1/(x-3)))dx
= ((x^2)/2) +x +int (2/(x+2)) dx + int (1/(x-3))dx
=((x^2)/2) +x + 2*ln(x+2) + ln(x-3)
Now apply the limits o to 1 we get
=[((x^2)/2) +x + 2*ln(x+2) + ln(x-3)]_0^1
=[((1^2)/2) +1 + 2*ln(1+2) + ln(1-3)] -[((0^2)/2) + 0 + 2*ln(0+2) + ln(0-3)]
= (1/2) + 1 + 2*ln(3) + ln(-2) -[2*ln(2) +ln(-3)]
= 3/2 + 2*[ln(3) - ln(2)] + ln(-2) -ln(-3)
= 3/2 + 2*[ln(3/2)] + ln(-2) -ln(-3)
= 3/2 + 2*[ln(3/2)] + ln(-2/-3)
= 3/2 + 2*[ln(3/2)] + ln(2/3)
= 3/2 + 2*[ln(3/2)] - ln(1/(2/3))
= 3/2 + 2*[ln(3/2)] - ln(3/2)
= 3/2 +ln(3/2)
so ,
int_0^1 (x^3 - 4x - 10)/(x^2 - x - 6) dx =3/2 +ln(3/2)

:)

Who is Cherokee Sal and why is she so unique to the town in "The Luck of Roaring Camp"?

We don't learn much about Cherokee Sal, though she is unique to the Roaring Camp. She is unique because she is the only woman living there among more than a hundred men, and, in addition, she has a baby—something unprecedented in the life of the camp.
Unfortunately, however, given how central she is, she never gets to speak, and we only get the sparsest outline of her physical appearance or interior self. All we learn is that she is "coarse" and "very sinful."
The story is told from the male point of view, and we have to take the male narrator's word about Sal. When she dies after giving birth, the narrator states that the town has been cleansed:

Within an hour she had climbed, as it were, that rugged road that led to the stars, and so passed out of Roaring Camp, its sin and shame, forever.

This is, to put it mildly, a highly misogynist view of Cherokee Sal. She, alone, was the source of sin and shame? Not likely.
However, with Cherokee Sal conveniently out of the way—we are told she is not much mourned—the men decide not to allow another woman into the camp. Stumpy and his ass will raise the boy themselves, and that apparently is fine. Who needs a woman when you have an ass? As Stumpy states:

"Me and that ass," he would say, "has been father and mother to him!"

Cherokee Sal is treated as little more than a plot device that gets the story going so the men can take over. But could it be that without a woman to care for the child their luck runs out?

The famous short story "The Luck of Roaring Camp" by Bret Harte tells of how a town of rough and rugged gold hunters in a remote location is transformed by the birth of a baby. Cherokee Sal is unique to the town for two reasons. First of all, she is the only woman in a town full of 100 rowdy men. Secondly, she is the mother of the baby, Tommy Luck, who becomes known as the Luck of Roaring Camp.

When the story opens, Cherokee Sal has gone into labor, and nobody in the camp really knows what to do. The implication is that Cherokee Sal is a prostitute.


Perhaps the less said of her the better. She was a coarse, and it is to be feared, a very sinful woman. But at that time, she was the only woman in Roaring Camp, and was just then lying in sore extremity, when she most needed the ministration of her own sex.


In the absence of another woman to act as midwife, the men appoint a man named Stumpy to oversee the birth. Cherokee Sal dies shortly after giving birth, but the baby lives and is adopted by the camp.

In the second paragraph of the story, Bret Harte mentions Cherokee Sal: "She was a coarse, and, it is to be feared, a very sinful woman. But at that time she was the only woman in Roaring Camp." The most important statement is the last, that she was the only woman in the camp. This camp was a mining camp, and those tended to be largely male in population. But, Harte also tells the reader that Cherokee Sal was a "sinful woman," which the reader can infer means that she was a prostitute, a lucrative position for a woman in a predominately male town. And Harte does state that hers was "a name familiar enough in the camp."
Cherokee Sal is also important because she gives birth to the character for whom the story is named, the baby "Luck." Some of the coarsest characters in the story become enamored with the baby and see him as a sort of good luck charm for them.

Why does Larraine spend her money the way she does?

It's fair to say that Larraine, a resident of the trailer park, has a bit of a problem when it comes to spending. She thinks nothing of blowing $200 on a jar of beauty cream instead of paying her rent. She's equally improvident when it comes to food stamps, using up her entire month's allocation to buy two lobster tails, shrimp, crab legs, salad, and lemon meringue pie, all of which she consumes at one sitting.
This is very much a "chicken and egg" question we're dealing with here. There's no definitive answer; much depends on one's own political outlook. The author of Evicted, Matthew Desmond, approaches the problem from a liberal perspective. He thinks that Larraine's improvident spending habits are a symptom of her poverty rather than its cause. A chronic lack of money encourages the poor to spend what little they have on things that make them feel good, feel better about themselves. People like Larraine live lives of great hardship and insecurity. Spending money provides a kind of emotional crutch, something to get them through another day without hope or opportunity. That being the case, it's unrealistic to expect responsible behavior from those who've never had the kind of discipline that a regular paycheck would impose.
A more conservative standpoint, however, would of course look at the matter somewhat differently. Conservatives would emphasize the point that it's Larraine's bad choices in life that are the direct cause of her poverty and which prevent her from getting on. If she's trapped in a never-ending cycle of poverty and eviction, then she only has herself to blame. Indeed, those closest to Larraine agree with this assessment, and they certainly have no ax to grind. Some people just lack self-control, irrespective of their income bracket.
Conservatives would further criticize Desmond for what they often refer to as the soft bigotry of low expectations in not holding poor people to the same moral standards as everyone else. Being poor doesn't give you a free pass to shirk your responsibilities. It can be said that Larraine has made a series of bad choices in her life, and she shouldn't expect the government to bail her out. Conservatives would go further and say that the entire system of welfare inadvertently encourages improvident spending habits and lack of responsibility on the part of claimants. In that sense, they would argue that Larraine is indeed a victim of the system, but not in the way that Desmond believes she is.
The debate continues. Again, there's no single answer to this question, but whatever your eventual conclusion it's always important in such cases to examine the issues carefully before making a reasoned judgement.

What character flaws or shortcomings does the main character have?

How you answer this question depends on who you see as the main character of "Everyday Use," so I will explore a couple of possibilities.
We could first think of Mama as the main character. The reason for this is that she is the first-person narrator of the Alice Walker's short story. Mama's major flaw is her limited perspective and favoritism. She obviously favors her daughter Maggie, who lives with her, over Dee, who left the family to attend college. Mama and Maggie spend all their time together and live conservatively. Dee, on the other hand, is more progressive. Mama thinks Dee is snobby and misguided, so she has trouble getting along with her daughter. She takes Maggie's side in the debate over who will inherit the family quilts. When we hear the story from Mama's perspective, we agree with her, because we only get her opinion of Dee.
If we consider Dee the main character, we could identify her main flaw as her insensitivity to her family and her superiority complex. She thinks her education makes her better than her mother and sister. She thinks she knows more about African and African American culture than they do, so she should have the quilts. She comes off as condescending and insults her sister. It is difficult to sympathize with Dee's character, especially since we get the story from Mama's perspective.

Single Variable Calculus, Chapter 3, 3.7, Section 3.7, Problem 25

The equation $\displaystyle \nu = \frac{P}{4\eta \ell}(R^2 - r^2)$ represents the law of Laminar flow.
Where $\eta$ is the viscosity of the blood and $P$ is the pressure difference between the ends of the tube with length $\ell$ and radius $R$. While $r$ is the distance from the axis. Consider a blood vessel with radius 0.01cm, length 3cm, pressure difference $\displaystyle 3000 \frac{\text{dynes}}{\text{cm}^2}$ and viscosity $\eta = 0.027$
a.) Determine the velocity of blood along the centerline $r = 0$, at radius $r = 0.005$cm, and at the wall $r = R = 0.01$cm.
b.) Find the velocity gradient at $r=0$, $r=0.005$, and $r=0.01$
c.) Where is the velocity the greatest? Where is the velocity changing most?


a.) @ $r = 0$


$
\begin{equation}
\begin{aligned}
\nu(r) &= \frac{P}{4\eta \ell} (R^2 - r^2)\\
\\
\nu(0) &= \frac{3000}{4(0.027)(3)}\left( (0.01)^2 - (0)^2\right)\\
\\
\nu(0) &= 0.9259 \frac{cm}{s}
\end{aligned}
\end{equation}
$


@ $r = 0.005$cm


$
\begin{equation}
\begin{aligned}
\nu(0.005) &= \frac{3000}{4(0.027)(3)} \left[ (0.01)^2 - (0.005)^2 \right]\\
\\
\nu(0.005) &= 0.6944 \frac{\text{cm}}{s}
\end{aligned}
\end{equation}
$


@ $r=0.01$cm


$
\begin{equation}
\begin{aligned}
\nu(0.01) &= \frac{3000}{4(0.027)(3)} \left[ (0.01)^2 - (0.01)^2 \right]\\
\\
\nu(0.01) &= 0 \frac{\text{cm}}{s}
\end{aligned}
\end{equation}
$


b.) The velocity gradient $\displaystyle = \frac{d\nu}{dr}$

$
\begin{equation}
\begin{aligned}
\nu &= \frac{P}{4\eta \ell} \left( R^2 - r^2 \right)\\
\\
\nu &= \frac{PR^2}{4 \eta \ell} - \frac{Pr^2}{4 \eta \ell}\\
\\
\frac{d \nu}{dr} &= \frac{d}{dr} \left( \frac{PR^2}{4 \eta \ell}\right) - \frac{P}{4 \eta \ell} \frac{d}{dr} (r^2)\\
\\
\frac{d \nu}{dr} &= 0 - \frac{P}{4\eta \ell} (2r)\\
\\
\frac{d \nu}{dr} &= \frac{-Pr}{ 2 \eta \ell}
\end{aligned}
\end{equation}
$

Velocity gradient at $r=0$

$
\begin{equation}
\begin{aligned}
\frac{d \nu}{dr} &= \frac{-3000 (0)}{2(0.027)(3)}\\
\\
\frac{d \nu}{dr} &= 0 \frac{\frac{\text{cm}}{s}}{\text{cm}}
\end{aligned}
\end{equation}
$

Velocity gradient at $r = 0.005$

$
\begin{equation}
\begin{aligned}
\frac{d \nu}{dr} &= \frac{-3000(0)}{2(0.027)(3)}\\
\\
\frac{d \nu}{dr} &= -92.5926 \frac{\text{cm}/s}{\text{cm}}
\end{aligned}
\end{equation}
$

The velocity gradient at $r = 0.01$

$
\begin{equation}
\begin{aligned}
\frac{d \nu}{dr} &= \frac{-3000(0.01)}{(0.0027)(3)}\\
\\
\frac{d \nu}{dr} &= -185.1852 \frac{\text{cm}/s}{\text{cm}}
\end{aligned}
\end{equation}
$


c.) The velocity is greatest at $r = 0$. While the velocity is changing most (decreasing) at when $r = R = 0.01$cm.

sum_(n=2)^oo lnn/n^p Find the positive values of p for which the series converges.

To find the convergence of the series sum_(n=2)^oo (ln(n))/n^p where pgt0 (positive values of p ), we may apply integral test.
Integral test is applicable if f is positive, continuous, and decreasing function on an interval and let a_n=f(x). Then the infinite series sum_(n=k)^oo a_n converges if and only if the improper integral int_k^oo f(x) dx converges to a real number. If the integral diverges then the series also diverges.
For the infinte series series sum_(n=2)^oo (ln(n))/n^p , we have:
a_n =(ln(n))/n^p
Then, f(x) =(ln(x))/x^p
The f(x) satisfies the conditions for integral test when pgt0 . We set-up the improper integral as:
int_2^oo (ln(x))/x^pdx
Apply integration by parts: int u dv = uv - int v du.
Let: u=ln(x) then du = 1/xdx
       dv = 1/x^p dx
Then , v = int dv
              =int 1/x^p dx
              = int x^(-p) dx
             = x^(-p+1)/(-p+1)
The indefinite integral will be:
int (ln(x))/x^pdx = ln(x)x^(-p+1)/(-p+1)- intx^(-p+1)/(-p+1) *1/x dx
                    = ln(x)x^(-p+1)/(-p+1)-1/(-p+1) int (x^(-p)x)/x dx
                   = ln(x)x^(-p+1)/(-p+1)-1/(-p+1) intx^(-p) dx        
                  = ln(x)x^(-p+1)/(-p+1)-1/(-p+1) *x^(-p+1)/(-p+1)
                   =(ln(x)x^(-p+1))/(-p+1)-x^(-p+1)/(-p+1)^2
                  =(ln(x)x^(-p+1))/(-p+1)*(-p+1)/(-p+1)-x^(-p+1)/(-p+1)^2
                  =(ln(x)x^(-p+1)(-p+1))/(-p+1)^2-x^(-p+1)/(-p+1)^2
                 =(ln(x)x^(-p+1)(-p+1)-x^(-p+1))/(-p+1)^2|_2^oo
The definite integral will only be finite if 1-p<0 or pgt1 .
Thus, the series  sum_(n=2)^oo(ln(n))/n^p converges when pgt1 .

Why does Scout want to stop playing the game?

The "Boo Radley" game begins in chapter 4 of To Kill a Mockingbird. The game involves the children playing various roles, with the part of Boo Radley belonging to Jem. Their drama is "woven from bits and scraps of gossip and neighborhood legend."
Scout wants to quit the game for two reasons. One day, Atticus happens to see the children playing the game. Atticus asks, "Does this have anything to do with the Radleys?" Jem denies that it does. This is the first reason Scout wants to quit the game. She doesn't want to be in trouble with Atticus.
The second reason Scout wants to quit the game involves a previous incident. Earlier, when Scout, Jem, and Dill are playing outside, Jem rolls Scout in a tire. She lands in the Radley's front yard after bumping into the steps of their porch. She doesn't share this information with the others, but when she falls out of the tire, she believes that "Someone was inside the house laughing." This is her second reason she thinks it would be best to stop playing the "Boo Radley" game. She is fairly certain that Boo must have seen them.

Calculus: Early Transcendentals, Chapter 4, Review, Section Review, Problem 33

y=(x-2)e^(-x)
(I) Asymptotes
To determine its horizontal asymptotes, take the limit of this function as x approaches positive and negative infinity.
lim_(x->-oo) (x-2)e^(-x) =-oo
lim_(x->oo)(x-2)e^(-x)=0
So, the function has only one horizontal asymptote. Its horizontal asymptote is y=0 .
Moreover, there are no values of x which make the function undefined. Thus, the function has no vertical asymptotes.
(II) Maximum/Minimum Point
To determine the maximum or minimum point of a function, take its derivative.
y=(x-2)e^(-x)
y'=(x-2)*e^(-x)*(-1) + e^(-x)*(1)
y'= e^(-x) ((-1)(x-2)+1)
y'=e^(-x)(-x + 3)
Set the derivative equal to zero.
0 = e^(-x) (-x+ 3)
To solve for x, we only have to consider the factor (-x + 3). Since the first factor e^(-x) will never be zero for any value of x.
0=-x + 3
x=3
So, there is only one critical number, which is x=3 .
To determine if the function is maximum or minimum at x=3, refer to the change of signs of first derivative before and after the critical number. If the change of signs of y' is from negative to positive, then, the function is minimum at that critical number. If the change of signs of y' is from positive to negative, then, the function is maximum at that point.
At the left of x=3, the interval is (-oo, 3) . And at the right of it, the interval is (3,oo) . Take a test value for each interval and plug-in them to the first derivative.
y' = e^(-x)(-x + 3)
For the interval (-oo,3) , let the test value be x=0.
y'=e^(0)(0+3) = 3
For the interval (3,oo) , let the test value be x=4.
y'=e^(-4)(-4+3)=e^(-4)(-1) = -0.018
Since the change of signs of y' is from positive to negative, then, the function is maximum at x=3. The value of y when x=3 is:
y=(x-2)e^(-x)
y=(3-2)e^(-3)=0.05
Hence, the function has a maximum point (3, 0.05). And it has no minimum point.
(III) Increasing/Decreasing Interval
To determine at which interval is the function increasing and decreasing, refer to the sign of the first derivative. If the sign of the first derivative is positive, the function is increasing at that interval. If the sign is negative, the function is decreasing.
At the left of the critical number, the interval is (-oo,3) . In this interval, the value of y' is positive.
And at the right of the critical number, the interval is (3,oo) . The value of y' here is negative.
Thus, the function is increasing in the interval (-oo,3) and it is decreasing in the interval (3,oo) .
(IV) Inflection point
To determine the inflection point, take the second derivative of the function.
y'=e^(-x)(-x +3)
y'' = e^(-x)*(-1) + (-x+3)*e^(-x)*(-1)
y''=e^(-x)(-1 + (-x+3)(-1))
y''=e^(-x)(x-4)
Set the second derivative equal to zero.
0=e^(-x)(x-4)
To solve for the value of x, consider only the factor (x-4). It is because the factor e^(-x) will never be zero for any value of x.
0=x-4
4=x
So the function changes concavity at x=4 only. The value of y when x=4 is:
y=(x-2)e^(-x)
y=(4-2)e^(-4) = 2e^(-4)=0.04
Thus, the inflection point is (4, 0.04).
(V) Concavity
To determine the concavity of the function, consider the region at the left and right of x=4.
At the left of x=4, the interval (-oo,4) . And at the right of it, the interval is (4,oo) .
Take a test value for each interval and plug-in them to the second derivative.
y''=e^(-x)(x-4)
If the second derivative is negative, the function is concave downward in that interval. If the value of the second derivative is positive, the function is concave upward.
For the first interval (-oo,4) , let the test value be x=0.
y''=e^0(0-4)=-4 (Concave down)
For the second interval (4,oo), let the test value be x=5.
y''=e^(-5)(5-4)=0.007 (Concave up)
Thus, the function is concave down in the interval (-oo,4) and it is concave up in the interval (4,oo) .
(VI) Graph
Therefore, the graph of the function y = (x-2)e^(-x) is:

What are the themes in the story "The Lottery" by Shirley Jackson?

Without question, tradition is a huge theme within "The Lottery," as the very existence of tradition is expressed in such a brutal way. It would be hard to read the story and not wonder about the ridiculous notion of carrying on a tradition where, for no reason, someone has to die, yet there the community is, carrying on the tradition, regardless.
Another theme at work though has to do with selfish interest since the vast majority of the outspoken cries against the lottery are only provided once the family has been chosen. Since the chosen understandably don't want to die, the time for speaking out has arrived, but it's drenched in that selfish interest. Their outcries against the lottery would have felt more solid and unbiased if they would've come before the event happened, which could be a reason why so little happens in consequence to those outcries. From there then, we're stepping into a theme of timing as well. 
Yet another theme would be the prettying up of matters that are unpleasant, perhaps society's tendency to do so. The community holds the lottery in a very organized way, and it has this ironic name that has a connotation of winning and gain. These details are things that make the situation feel less barbaric, though there can be no doubt that the circumstance is, in fact, barbaric.

A couple of major themes of this story have to do with the subject of tradition. First, the story conveys that people do not like to go against tradition, even if they do not particularly care for the tradition itself. The narrator says that when Mr. Summers spoke to the town about making a new black box for use during the lottery, people responded poorly because "no one liked to upset even as much tradition as was represented by the black box." Despite the fact that it's literally just a painted wooden box, and a box that has splintered and cracked and faded over the years, people are resistant to replacing it because it's the only box they really remember ever using. This notion seems pretty ridiculous: they are so stuck in their ways that they cannot see the value in replacing a "shabby" wooden box.
Second, the story conveys the theme that traditions should continually be evaluated for their cultural relevance and humanity. Clearly, this tradition of choosing one person to stone every month is inhumane and does nothing to better the community. There's talk, we learn, of another town over discontinuing their lottery, and so we know that such a reevaluation can take place. We surmise by the cruel way Tessie Hutchinson is stoned to death by her friends and family that such a reevaluation would be positive and right.

How does Grover react when Percy tells him about the yarn-cutting?

Percy witnesses some old ladies at a fruit stand bring out a pair of scissors, large and apparently symbolic, having previously watched them knitting a pair of what seemed to be enormous, electric-blue socks. He then sees them cut the yarn.
Later, Grover asks Percy what he saw at the fruit stand, and Percy, puzzled by Grover's strange behavior, says that he saw the middle of the three old ladies bring out a pair of scissors and cut the yarn. When he hears this, Grover closes his eyes and makes a gesture which Percy interprets as akin to crossing himself, but not quite the same thing. Nervously, Grover begins chewing at his thumb and says he doesn't want things to be "like last time." He mentions that "they never get past sixth" and asks to walk Percy home. He seems very concerned that something terrible is about to happen.
Percy asks whether this is "a superstition thing" or if Grover thinks somebody is going to die. Grover does not respond in words but "looked at me mournfully, like he was already picking the kind of flowers I'd like best on my coffin."
After this, disturbed by Grover's behavior, Percy leaves him at the bus station when Grover goes to the bathroom.

How can behavior be seen as a result of heredity or the environment?

The truth of the matter is that who we are is the result of both heredity and the environment. It is not "nature versus nurture," but a combination of nature and nurture. I also want to point out that "behavior" does not seem to be a very precise term to use in this context, as behavior is simply what we do, which is not necessarily consistent over a lifetime or even over a day. Behavior is situational to a very large degree and seldom consistent enough to try to analyze it in this way. To the degree that this is the exact issue you are expected to address, behavior is environmental because behavior cannot be inherited at all. Our personalities, on the other hand, seem to be fairly consistent over our lives, and it is these that are a combination of nature and nurture.
Some traits, like shyness, are tendencies some people are born with—a genetic predisposition. If that predisposition is reinforced by one's environment, consistently, one is likely to become a shy adult. If that predisposition is not reinforced and a child is provided with opportunities to be more outgoing, he or she may become more outgoing with time. An inhibited child born into a rowdy family may retreat into even greater inhibition. A child who is gently exposed to the opportunity to be gradually more outgoing and uninhibited with very small birthday parties or family get-togethers is unlikely to be an extremely outgoing adult, but is not going to have to hide in the bathroom at a large event.
We are all born with various predispositions that can be enhanced or repressed by our environments. Our behaviors, on the other hand, are situational, as behavior is what we do, and there is nothing hereditary about taking a walk, attending a class, or washing the dishes.
https://www.psychologytoday.com/us/blog/breaking-the-ice/200806/are-we-born-shy

Please explain and analyze the poem "Barbie Doll" by Marge Piercy.

Marge Piercey's poem "Barbie Doll" is an indictment of the socially constructed values of beauty which are forced upon women from the time that they are young.
In the first stanza of the poem, we are introduced to the female character, the "girlchild," who is provided with stereotypically "feminine" toys which imply her inherited responsibilities as a future mother ("dolls that did pee-pee"), homemaker ("miniature GE stoves and irons"), and debutante presented for the visual consumption of others ("wee lipsticks the color of cherry candy").
While the girl is able to survive this childhood and live into puberty, she is soon cut down by the cruelty of a classmate, who comments on her changing body: "You have a great big nose and fat legs."
This is a deeply ironic moment; although the girl has been pushed toward womanhood for the entirety of her life, she is greeted with objectification and disgust the very moment she arrives there. Despite her many wonderful qualities--her health, intelligence, strength, and appetites--all those who are framing her as an object can see are those physical features which they deem unsuitable. 
In the third stanza, the girl is now subjected to the advice of those who wish to shape her into a more easily digested being--a "beautiful" woman. They urge her to "exercise, diet, smile and wheedle," and thereby invert all of her natural qualities. The exhaustion of this playacting wears the girl down until she finally resorts to drastic measures: cutting off her nose and legs to please those around her. 
This, of course, results in the death of the girl. Yet, as she lays in her casket, painted with makeup by the undertaker, she has finally achieved what the rest of the world has desired for her: beauty. It was only in destroying her personhood--her life--that she was able to obtain the approval of others.
This is a disgusting reflection of the kind of subversive thinking that is socialized in young women; girls are brought up to believe that their sole value lies in their appearance and ability to perform as a "feminine" woman. Thus, the last two lines of the poem ("Consummation at last. / To every woman a happy ending.") are sarcastic ones, said with the knowledge that the social systems constructed around women are ones that profit off the death of their dignity.