Graph the polar function and its tangents that are horizontal or vertical for r=sqrt(theta), 0

We are asked to graph the polar function r=sqrt(theta), 0<= theta <= 2pi , along with its vertical and horizontal tangents.
We can graph by plotting points:
theta:          r:0          0pi/6     .7236pi/3    1.0233pi/2    1.2533etc... yielding:

We can find the horizontal and vertical tangents by using:
(dy)/(dx)=((dy)/(d theta))/((dx)/(d theta))=(1/(2sqrt(theta)) sin theta + sqrt(theta) cos theta)/(1/(2sqrt(theta))cos theta-sqrt(theta) sin theta)
The horizontal tangents occur when the numerator ((dy)/(d theta) ) is zero, while the vertical tangents occur when the denominator is zero.
Solving numerically we get the horizontal tangents when x ~~ +- .653
and the vertical tangents when x ~~ -1.83
http://mathworld.wolfram.com/PolarCoordinates.html

Do you agree or disagree with Thoreau's "Civil Disobedience"?

In theory, I agree with Thoreau's ideas. The claim that we ought to always follow our conscience and never do anything that will, in any way, go against our sense of what is just and right seems to make a great deal of sense to me. Further, Thoreau's claim that the majority is not always right seems true as well; rather than follow the majority, or even the law, it seems incumbent on each of us to behave in accordance with our own consciences. For example, Thoreau opted not to pay his poll tax because he did not want to contribute money to a government that might use it to support the unjust institution of slavery or an unjust war with Mexico. He accepted the consequence that he would go to jail, even arguing that jail is the proper place for a just man in an unjust society to be. Likewise, if I choose not to pay my taxes because I disagree with something our government does, I will also go to jail. If I go to jail, though, who will help to support my family and take care of my children? This consequence may not be acceptable to me because I have obligations to people other than myself. So, while I agree with his ideas in theory, I think most people would want to find some other way of registering their dissatisfaction with government policy and practice.

This answer is completely dependent on the individual reader.  Some readers are absolutely going to agree with every word that Thoreau puts forth in "Civil Disobedience," but other readers are going to think that Thoreau is crazy.  
Thoreau's main point in this essay is that a person's first and most important obligation is to do what he/she believes is right.  A person doesn't have to follow the law that is dictated by the majority.  Thoreau also says that people should refuse to follow an unjust government.  Furthermore, Thoreau believes that people should remain distant from government in general.  
I can't say that I agree or disagree with Thoreau 100% either way.  If a government is truly unjust, then I agree that people should refuse to follow it; however, Thoreau introduces a problem to his own argument. If every person is supposed to do what they believe is right, then a society is governed by individual moralism.  Different individuals are going to see different government acts as just or unjust.  With extreme individualism ruling, there is no standard or benchmark that determines what is right or wrong.  Everybody is determining that for himself/herself.  There's no centralized leadership or vision, and I see more potential problems with that than good.  This is where I disagree with Thoreau.  He is absolutely allowed to go live on a pond by himself and do his own thing, but if an entire city does that on a day-to-day basis, then law enforcement serves no purpose and can't administer any kind of realistic judgment.  

What is the theme of "Ripe Figs" by Kate Chopin?

Another theme of this story is that patience can be taught. Young people can struggle with patience, and this is the case with Babette; older folks tend to have a bit more patience because they have the experience to know that time moves more quickly as we age. This is supported by Maman-Nainaine's assertion that the figs have ripened early and Babette's response that it feels as though they have ripened late. For Babette, then, the time has passed slowly, but for Maman-Nainaine, it has gone by quickly.
In addition, the similes used to describe them help us to really see the difference between the goddaughter and godmother in the story's beginning:

Maman-Naiaine was as patient as the statue of la Madone, and Babette as restless as a hummingbird.

We might imagine Maman-Naiaine as very still and contrasting significantly with Babette who is compared to a hummingbird, something that moves so fast that it can appear blurry to our eyes! However, by the story's end, Babette is able to wait through the entire day that she discovers the ripe figs, until the next morning. She patiently waits until Maman-Naiaine is seated and ready to eat, and then she brings "a dainty porcelain platter, which she set down before her godmother. It contained a dozen purple figs, fringed around with their rich, green leaves." It is in this quiet and still way that she lets her godmother know that the figs are ripe. We see that the lesson has worked and Babette has learned some patience: she did not sprint home from the trees the day before and shout her joy. She was able to delay and present proof of the figs, beautifully arrayed, and this helps to demonstrate her growth.

The theme of "Ripe Figs" is that human maturity is related to the seasons of the year, a process that cannot be hastened.
In Kate Chopin's story, the young character Babette wants to go to Bayou LaFourche to visit her cousins, but Maman Nainaine insists that she wait until the figs ripen. Babette, of course, is impatient and watches the green figs each day, hoping that they will soon change their color so that she can depart:

She walked slowly beneath them, carefully peering between gnarled spreading branches.

Each time she comes out, she is dispirited. Finally, Babette comes to Maman Nainaine and shows her a dozen purple figs on a porcelain platter. Maiman Nainaine exclaims that the figs have ripened so early, but Babette insists that they have ripened late. This is the contrast between youth and maturity: the concept of time is different. Hence, the stipulation that Babette wait until the figs mature. For, watching the figs mature may have encouraged patience.
Then, Maman Nainaine takes her knife to the ripened fig, and as she peels it, she tells Babette to give her love to all her cousins. By forcing Babette to pay attention to the maturation of the fig, Maman Nainaine, perhaps, hopes to teach Babette to follow the pattern she has watched and allow time for things to come about.

I'm reading "The House of Asterion" by Jorge Luis Borges and I have a question about the effect and significance of the point of view in the story.

Borges uses point of view to enhance the similarity of his story to the labyrinth it describes. Like the narrator of many Edgar Allan Poe stories (“The Tell-Tale Heart,” for instance), this narrator addresses the reader directly, as if confiding in us; he also seems to be perhaps mentally unbalanced, or, at best, obsessed with his life in the labyrinth. It is the nature of this life that interests Borges. The narrator declares that his house has “fourteen” doors (a “footnote“ suggests paradoxically that “14” might mean infinity), that are open all the time; anyone may come or go as they please, including himself (he calls the idea that he might be a prisoner “a ridiculous falsehood”). He insists that his house is unique in all that world, and that he himself is also unique. For this reason he “is not interested in what one man may transmit to other men“—he is a singular individual, whose only real companion is an imaginary second version of himself. There is a sense in which we understand Asterion’s house to be the world itself; that the maze he lives in and the isolation he feels are not unique, but on the contrary, something he shares with all men.
The idea of the ”redeemer” who will release him from this life gains added irony when the point of view shifts in the last line, and suddenly we hear Theseus express shock that the narrator, the Minotaur, “scarcely defended itself.” Theseus presumably slays the Minotaur to save the youth of Athens from being sacrificed to the beast, but the story suggests that the Minotaur, in fact, is what Theseus “redeems.”

It's safe to say that Borges was obsessed with literal and metaphorical labyrinths. The story begins in the first person point of view. The narrator calls himself Asterion and with the introductory line, it seems to indicate that he is a prince who is not allowed to leave his castle. The narrator goes on to defend himself. He claims that he is not a prisoner even though he never leaves his house. He says that claims about his madness and misanthropy (hating mankind) are just the result of the public's contempt for him.
The footnote adds that fourteen actually means infinite and therefore, there are an infinite number of doors. This is according to Asterion. He, Asterion, also says, "The house is the same size as the world; or rather it is the world." Having never left his house, it would be "the world" to him. We get this unique perspective from the narrator, a being who lives a hermetic life in a seemingly endless labyrinth of a home. Is his perspective based upon psychosis as an effect of being a prisoner or is he actually living in a gigantic labyrinth from which he can not escape? 
This story is reminiscent of Edgar Allan Poe's writing. We don't know if the narrator is misunderstood. It isn't until the final line that we get a clue about who the narrator is or why he lives this way. In the last few lines, the narration shifts from the first person perspective of Asterion to the first person perspective of Theseus. From this line, we learn that Theseus has just destroyed the Minotaur. And from this, we can conclude that the first bulk of the story is narrated by the Minotaur. Theseus is the "redeemer" the Minotaur spoke about. Killing the Minotaur was redeeming him or freeing him from his labyrinthine prison. 
Borges chooses to consider the Minotaur's perspective so the reader can get the sense of his experience. Borges is playing with ideas like the labyrinth, infinity, and perspective. The Minotaur says his house is the world because that is all he's ever known. This is, perhaps, an allusion to Plato's Allegory of the Cave. In this allegory, people are in a cave and they are chained in such a way that they have no knowledge of the outside world. Borges was always interested in how people see the world differently. He was also interested in how perspective is limited or filtered. He uses the Minotaur's perspective to explore these ideas. 

What is the tone or mood of this short story?

Fitzgerald's story in many ways prefigures The Great Gatsby because Dexter possesses many of the same yearnings that Jay Gatsby does. Both men are outsiders who find a way into the worlds they aspire to, only to become disillusioned by what they find.
The mood of the story is not fixed; it could be said that the story begins with yearning and optimism as readers witness Dexter's drive to surpass the successes of the people he serves at the country club. His ambition will not allow him to simply join them; he must best them. However, as the story unfolds and Dexter becomes more financially successful and gains access to the upper reaches of society, including the milieu of Judy Jones, his restlessness does not resolve. Dexter is unable to achieve self-actualization in any enduring sense. Dexter's last words are a haunting expression that suggest the meaning of life is found in the journey of becoming, not in the acquisition of what one thinks he wants:

"Long ago," he said, "long ago, there was something in me, but now that thing is gone. Now that thing is gone, that thing is gone. I cannot cry. I cannot care. That thing will come back no more."

The tone of the story as it concludes is despairing and melancholic.

Why did Alexander Pope write about criticism in verse?

Your question, I think, is really two questions in one. First, why was Pope interested in writing about criticism? And second, why did he choose a poetic format, rather than prose, to deal with this topic?
Pope, like most creative artists, was extremely sensitive about what people thought of his work. At the same time, he himself was critical of other writers. The Essay on Criticism was written in 1709, when Pope was only 21. Much later in his career he produced the mock-heroic satire The Dunciad, an attack on other writers, in particular the playwright Colley Cibber, whom Pope considered incompetent. But throughout his life both Pope and his close friend and fellow satirist Jonathan Swift self-consciously believed in, and expressed, their sense of being above the rest of the English literary world. This fact was noted by Samuel Johnson in his Lives of the English Poets, where he observed that in the correspondence between Pope and Swift the two expressed such a sense of superiority to other writers, and to others in the intellectual world generally, that a credulous person, reading their letters would think that the other writers of the early eighteenth century produced virtually nothing of value. In his Essay on Criticism, when his career was just getting started, Pope felt the need to express, in a didactic fashion, the principles of criticism that were generally accepted in his time. In some sense the young genius was establishing himself as the arbiter of taste in the literary world and also making the statement that critics themselves, to put it colloquially, often did not know what they were talking about.
The second part of your question involves the format in which Pope chose to make this statement: the standard poetic form of the age, rhymed iambic pentameter couplets, as Pope's idol Dryden had used earlier, and as Samuel Johnson and many others were to use later in the eighteenth century. Pope and others held the view that ideas are impressed more forcefully on the reader and become more memorable when they are expressed in meter and rhyme. Just as with his later Essay on Man, the ideas in the Essay on Criticism were not ones Pope himself originated. His intention in both cases was not to put forward new ideas, but to express, in as beautiful and memorable a way possible, ideas that were the standard beliefs of his time, as kind of celebration of neo-classical aesthetics and, in the Essay on Man, the philosophical beliefs of his time.

College Algebra, Chapter 2, 2.2, Section 2.2, Problem 62

Find an equation of the circle lies in the first quadrant, tangent to both $x$ and $y$ axis and with radius 5.

If the circle lies in the first quadrant, then its center is positive. And if the circle is tangent to both axes and with radius 5, then it pass through the intercepts of $x (5, 0)$ and $y (0,5)$. Thus, its center is 5 units from $x$ and $y$ axes which is $(5,5)$. Recall that the general equation for the circle with circle $(h,k)$ and radius $r$ is..


$
\begin{equation}
\begin{aligned}

(x - h)^2 + (y - k)^2 =& r^2
&& \text{Model}
\\
\\
(x - 5)^2 + (y - 5)^2 =& 5^2
&& \text{Substitute the given}
\\
\\
(x - 5)^2 + (y - 5)^2 =& 25
&&


\end{aligned}
\end{equation}
$

In Romeo and Juliet, Mercutio says, ''If love be rough with you, be rough with love. Prick love for pricking, and you beat love down.'' How does the language in this quote develop Mercutio's character?

In Act I Scene 4, Benvolio has convinced Romeo to go to the Capulets and partake briefly in the dancing and feasting. Mercutio accompanies them and he begins to mock Romeo's lugubrious comments about love, changing them into licentious metaphors. Romeo, however, will not engage in this banter because he claims to have had a dream in which he learned that attending the feast was a bad idea. At this point Romeo demonstrates the characteristics of the Petrarchan lover; that is, he moans about the loss of his lover and speaks of her in mournful and passionate tones. Hearing Romeo, Mercutio tries to convince Romeo otherwise by telling him to cast aside his melancholy and stop deprecating love:

If love be rough with you, be rough with love. Prick love for pricking, and you beat love down. (1.4.27-28)

Benvolio, too, encourages Romeo. He suggests that they go in and dance. Still Romeo declines and says that he will not participate. Instead, he will hold the light for them as he believes the evening presages something bad.
In this passage Mercutio's character is developed as one believing in action rather than dwelling in melancholy as Romeo does. As his name suggests, however, Mercutio is mercurial and he can quickly react.

Mercutio makes this remark when he is trying to convince Romeo to give up Rosaline, who does not return Romeo's love. Romeo has complained that love is painful and pricks like a thorn. In response, Mercutio says in the quote in the question that if love treats you badly, treat it badly. If love pricks you, prick it back, and then you'll defeat it. 
The language in this quote is an insight into Mercutio's character because he uses violent words to describe love, showing that he is quickly moved to anger and violence. Later, Mercutio wants Romeo to have a duel with Tybalt, Juliet's cousin, who has challenged Romeo to a duel. Mercutio rushes into fighting with Tybalt first and dies as a result, and Romeo kills Tybalt in revenge. Mercutio is quick to anger, as this quote shows, and his anger results in worsening the feud between the Capulets and Montagues.

What is the theme in When I Was Puerto Rican?

The main theme of the story is identity. Throughout the book, Negi struggles to find a stable cultural identity which will allow her to live in the United States while still retaining her Puerto Rican heritage. This struggle is so intense that Negi's complex, ever-shifting identity manifests itself in a number of out-of-body experiences, which illustrates just how deeply conflicted she is with herself.
Whenever Negi looks inside herself, she finds deep rifts in her cultural and ethnic identity. In turn, those rifts are reflected in the social world outside. As well as the obvious conflict between American and Puerto Rican identity, there's also an even deeper conflict within Puerto Rican society itself. In pursuit of an identity of her own, Negi adopts that of the jíbaros. The jíbaros are simple country folk renowned throughout Puerto Rico for their art and music, yet they're also looked down on by Puerto Rican city-dwellers for their relative lack of sophistication. Negi's mother tells her in no uncertain terms that adopting the identity of a jíbaro is completely inappropriate for someone of her background. In due course, Negi comes to learn from this episode and realizes that identity is not something you can simply choose; it's a good deal more complicated than that.

Describe politics in Fahrenheit 451. What’s happened to them?

In an authoritarian society like the one depicted in Fahrenheit 451, politics are pretty much irrelevant. As politics are largely concerned with managing the choices and preferences of different groups and individuals, it's no wonder that there's no political life to speak of in this society. The government doesn't recognize difference, whether in politics or anything else. It wants everyone to be the same, talk the same, and act the same.
Thus, the political process is nothing more than a charade, a form of entertainment in which people opt for the candidate with the nicest smile. No one's really voting for change; they're just voting for the appearance of change. If the government seriously thought that voting would change anything, they wouldn't allow it in the first place.
Deprived of books and encouraged to rot their brains by zonking out in front of the TV, voters in this society lack the discernment and critical thinking skills necessary to make informed choices. So they stick with the inappropriately named President Noble, for the sole reason that he comes across well on TV.

In part 2, Montag returns home after visiting Faber to find Mildred and her superficial friends watching the parlour wall televisions as usual. Montag immediately unplugs the wall televisions, and the nervous women begin discussing the "quick war" that their nation is fighting. After Mrs. Phelps and Mrs. Bowles reveal their lack of concern and compassion for their husbands and children, Mildred suggests they talk about politics.
Mrs. Bowles begins by mentioning that last election she voted for President Noble because he was "one of the nicest-looking men who ever became president." The women then comment on President Noble's political opponent, Hubert Hoag, who was a candidate from the political party known as the "Outs." Instead of discussing their different policies, the women are appalled that a short, unattractive man with an ugly name would even think about running against a taller, attractive politician. When Montag intervenes and asks what they even know about the two politicians, the women can only recall that one of the candidates was always picking his nose on the screen.
In this brief conversation regarding politics, Bradbury satirizes America's political climate by commenting on how political campaigns are predominately focused on image, appearance, and invoking an emotional connection with the citizens—instead of emphasizing the politicians' actual policies. The fact that Hubert Hoag is representing a party known as the "Outs" suggests that there is a sharp divide between the rich and poor, the privileged and oppressed, in Bradbury's dystopian society. Also, the commentary provided by Mildred and her friends illustrates how ignorant and uninformed the citizens are regarding their country's politics. President Noble also seems more like a male model with a trustworthy name than a capable politician.

A comparison and contrast of myths around the world After reading a variety of myths from three different places around the world, take a closer look at two myths, each from a different place, and compare and/or contrast what these myths reveal about their unique culture. I need some ideal or topic to write about. How do I write it? Links for the story. Persian: Rustam part 1 or part 2 Egyptian: Isis and the Seven Scorpions The Story of Isis and Osiris. The Greek Princess The Book of Thoth The Land of the Dead Norse: The Treasure of the Gods The Mead of Poetry Thor's Journey to Utgard Loki’s Children The Theft of Idun’s Apples The Lay of Thrym The Death of Balder The Binding of Loki Ragnarok

The reason we study myths is that they can reveal much about the culture that generated them. More specifically, myths help explain how people viewed the world. This includes the things they feared, their values, and their general outlook on life. Myths are stories that people told each other in order to explain things that were otherwise beyond their comprehension. A good topic for an essay might be to choose a single topic that you find in a few of the myths. If we look at the myths of the ancient Egyptians, for example, we see that there are several—the Osiris and Isis story, in particular—that focus on death and rebirth. As a result, you can look at this myth, which tells the story of a great king who was murdered and mutilated by his evil brother and then reanimated by his wife, as evidence for the ways ancient Egyptians tried to deal with the very difficult topic of death. How did the Norse understand death? You could look at the stories of Ragnarok and the death of Balder, the latter a story in which his brother tried to have him released from Hel, to get some idea of the ways they understood death as a transition into a new world. Another point of comparison might be found between the malevolent deities Seth and Loki, both of whom sow evil and discord in the world. They play crucial roles in almost all of the myths listed in the question, suggesting that people in both societies grappled for an understanding of why people do evil things. The point is that most of these myths deal with fundamental human concerns. A good essay would pick one or two of these issues to see how they addressed them. 
http://www.egyptianmyths.net/mythisis.htm

https://thenorsegods.com/the-death-of-balder/

Create a Venn diagram with the title The American Dream and two circles, one for each work. Each circle must contain at least four characteristics that make it unique from the contrasting work, and the middle section where the circles intersect must contain at least three points of how the works are similar in their treatment of the American Dream. Points of comparison may include: The definition of the American Dream according to the author/creator Affirmation or repudiation that the American Dream is achievable Obstacles to the achieving the American Dream I need this compared to Of Mice and Men. The American Dream - Poem by Doug Gunderson You can find the poem on the following link to http://www.poemhunter.com/poem/the-american-dream-4/

SIMILARITIES:1) Both Of Mice and Men and "The American Dream" describe financial independence as a key component of achieving the American dream. While in the poem this is not the most important thing to the narrator, he does note that "My house and car are paid for / I have money in the banks." His children are also "on their own" and "doing well." Conversely, none of the workers in Of Mice and Men have any kind of financial stability or independence. Their greatest dream is to not have to work for anyone else; to be their own bosses.
2) Similarly, both works express the idea that the idea of 'belonging' is important. In the poem, the narrator talks about his children, his family, and the fact that they still are a part of his life. In Steinbeck's novel, when discussing his dream, George outright says: "[w]e’d jus’ live there. We’d belong there. There wouldn’t be no more runnin’ round the country..."
3) Despite the above, both works indicate that the American dream is ultimately subjective. While there are certain key components (see above), Gunderson tells the reader, "Each of us has a benchmark / To make us proud of who we are." In Of Mice and Men, each character has their own dream, and while there are many similarities, there are also differences. For example, Curley's wife also wishes she could have "made somethin' of [herself]," but her dream for doing so is totally distinct from George and Lennie's.
DIFFERENCES:
1a) "The American Dream" indicates that the American dream is achievable. For the narrator, his dream has come true because his children have grown into happy, stable adults and are still a joyful part of his life.
1b) Of Mice and Men indicates that the American dream is not achievable to most people. No character in the novel achieves their dream or even comes close to it. Crooks warns them of just this when he says that he has seen hundreds of men with similar dreams, but none of them ever achieve it. Curley's wife remains trapped in her marriage. George and Lennie's dream of the farm dies with Lennie.
2a) "The American Dream" seems to indicate that the chief obstacle to achieving the dream is giving oneself a realistic benchmark. While the narrator has achieved his dream of having a stable and happy family, he also notes that if his aims were higher, he might not feel that he had achieved the dream. He thinks of himself as successful because he has achieved what he wanted, but he expresses some relief that his dream does not hinge on wanting more.
2b) Of Mice and Men indicates that the barriers to achieving the American dream are systemic and ubiquitous; that institutional poverty and social inequity make it impossible for most people to achieve it, no matter how passionate they are nor how hard they work.
3a) To the narrator of "The American Dream," family is a key component to the dream. He is happy because his children are happy and want to be with him. This is related to but not quite the same as the idea of "belonging." For Gunderson's narrator, it is specifically about the children he raised.
3b) Belonging is important in Of Mice and Men, but family is not a necessary component of the dream. Curley's wife actually wishes that she did not have her family so that she could have achieved her dream. George and Lennie have a "found family" in each other, and George's dream dies with Lennie, but the main idea is them being self-sufficient.
4a) "The American Dream" discusses the fact that achieving one's dream does not necessarily mean that life is perfect. The narrator is still missing things in his life: his "poems have not won awards / And [his] novel’s still not done ... [his] weight’s a problem / And his career may be a mess." He is happy, but he knows there is still more out there.
4b) Because none of the characters in Of Mice and Men have achieved the American dream, they do not quite seem to understand that doing so will not solve all of their problems. In fact, Crooks refers to the dream as "heaven." For the men he's talked to, the dream is an ideal, a vision of a perfect life. There is no such thing as unhappiness or burden once the dream has been realized. 

College Algebra, Chapter 1, 1.5, Section 1.5, Problem 76

Suppose that a group of friends decide to buy a vacation home for $\$ 120,000$, sharing the cost equally. If they can find one more person to join them, each person's contribution will drop by $\$ 6000$. How many people are in the group?

If we let $n$ be the number of the people, then the cost per head is $\displaystyle \frac{120,000}{n}$. If the number is increased by 1 then the cost per head will be $\displaystyle \frac{120,000}{n + 1}$. So,



$
\begin{equation}
\begin{aligned}

\frac{120,000}{n + 1} =& \frac{120,000}{n} - 6000
&& \text{Model}
\\
\\
\frac{120,000}{n} - \frac{120,000}{n + 1} =& 6000
&& \text{Add } 6000 \text{ and subtract } \frac{120,000}{n + 1}
\\
\\
\frac{20}{n} - \frac{20}{n + 1} =& 1
&& \text{Divide both sides by } 6000
\\
\\
20(n + 1) - 20n =& n(n + 1)
&& \text{Multiply the LCD } n(n + 1)
\\
\\
20n + 20 - 20n =& n^2 + n
&& \text{Simplify}
\\
\\
n^2 + n - 20 =& 0
&& \text{Cancel out like terms and subtract } 20
\\
\\
(n + 5)(n - 4) =& 0
&& \text{Factor out}
\\
\\
n + 5 =& 0 \text{ and } n - 4 = 0
&& \text{Zero Product Property}
\\
\\
n =& -5 \text{ and } n = 4
&& \text{Solve for } n
\\
\\
n =& 4
&& \text{Choose } n > 0, \text{ the group consists of 4 members}

\end{aligned}
\end{equation}
$

What's an example of external conflict in "A Sound of Thunder"?

Internal conflicts occur within the character's own mind. For example, wrestling with a moral decision or facing fear are kinds of internal dilemmas a character might experience. External conflicts are often categorized as man vs. man, man vs. nature, man vs. supernatural, man vs. technology, and man vs. society. 
Ray Bradbury wrote "A Sound of Thunder" in 1952. The setting is 2055, and the premise of the story is that a man named Eckels is going back in time to hunt a Tyrannosaurus Rex. One of the external conflicts is man vs. nature, which specifically is the hunting of the dinosaur. 

"Some dinosaurs have two brains, one in the head, another far down the spinal column. We stay away from those. That's stretching luck. Put your first two shots into the eyes, if you can, blind them, and go back into the brain." 

Another external conflict occurs as a man vs. man conflict between Eckels, the protagonist, and Travis, the safari guide. Eckels is shocked at the sight of the dinosaur and doesn't have the courage to take a shot. In his fear, he compromises the entire mission. He is told to return to the time machine, and in doing so, he steps off the path. Travis wants to leave him in the past for this egregious error. 

"'Get up!' cried Travis. Eckels got up. 'Go out on that path alone,' said Travis. 'You're not coming back in the Machine. We're leaving you here!'"

A third external conflict is man vs. society. Travis explains that the government doesn't want them conducting time travel expeditions because the consequences are too grave. If anything is disturbed in the past, it can create ripples that change history in inconceivable ways. In order to operate, the company has to pay the government "big graft" (bribes). Travis tells Lesperance the consequences of Eckels's carelessness: 

"This fool nearly killed us! But it isn't that so much, no. It's his shoes. Look at them! He ran off the Path. That ruins us! We'll forfeit! Thousands of dollars of insurance! We guarantee no one leaves the path. He left it. Oh the fool! I'll have to report it to the government! They might revoke our license. Who knows what he's done to time, to history!" 

After Eckels begs them not to leave him and the group returns to the present day, they find that society has indeed suffered as a result of Eckels's actions. Instead of Keith being president, a tyrant holds the office. All of society has been affected negatively by Eckels's failure to follow the rules and the warnings. 

The most obvious external conflict is man v. nature, illustrated by the killing of the dinosaur by going back to prehistoric time. The two Time Safari staff members use their time machine to take three hunters to the exact spot where a Tyrannosaurus rex will be their target. And when it arrives on the scene, it bursts into view with “a sound of thunder,” because it of its size and power. It creates an immense external conflict, which is successfully resolved, though with much blood spilled.
Another external conflict occurs between the hunter Eckels and the group leader Travis. Travis insists on all rules being followed, and Eckels questions the reasons why. Then Eckels is so traumatized by the dinosaur’s appearance that he stumbles back to the time machine and steps off the path. Travis is furious, and with good reason, as it turns out. The outcome of this particular conflict changes all of their lives.

Analyze one poem from The Sun and Her Flowers.

In "Accent," Rupi Kaur addresses the struggle of being from two different worlds. She uses her voice and accent to explain to a reader how something that should not have shame attached to it still can.
Kaur writes that "my voice is the offspring of two countries colliding" in reference to her heritage and living situation. As a child, she moved from India to Canada. According to The Globe and Mail, her father moved shortly after she was born and she and her mother followed 3.5 years later. So she grew up in Canada but was strongly influenced by India and the culture her parents grew up in. This is why she says that her voice comes from two different countries.
She goes on to ask what there is to be ashamed of. She grew up speaking English but speaks it with an accent like her mother. The people she grew up around—people she loved—influenced the sound of her words and the way she speaks. It's clear that in the past, someone shamed her for her accent. If they hadn't, she wouldn't say there was nothing to be ashamed of.
At the end of the poem, she says that her mouth carries two worlds and asks why it matters. Ultimately, it doesn't—unless it matters to Kaur. Her perception of herself and how she's influenced by the people around her are what count. Of course, it's possible that her self-image was influenced negatively by the opinion of people who didn't like the sound of her voice.
https://www.thecut.com/2017/10/profile-rupi-kaur-author-of-milk-and-honey.html

https://www.theglobeandmail.com/arts/books-and-media/rupi-kaur-the-superpoet-of-instagram/article36516870/

What is the rising action of Crispin: The Cross of Lead?

The rising action of Avi's young adult fiction novel, Crispin: The Cross of Lead, is somewhat unusual because the story follows a series of tense events with long, perhaps boring breaks in between. I would say that the rising action begins when Crispin awakes in the forest after the funeral to find Steward Aycliffe and a mysterious partner having a conversation by torchlight. From this moment, we get the sense there is something else going on in the story which Crispin isn't quite aware of. Over the next two days, he hides in the forest to keep away from the Steward's eye. The tension of the story surges again when Crispin intends to meet Father Quinel to prepare for his journey and is chased off by Aycliffe's men. Next, the story lulls again as Crispin journeys to some undetermined village, trying to survive on wild foods. So the pattern of excitement and calm continue with Crispin meeting Bear, performing in Lodgecot, learning to juggle on their journey, and finally arriving in Great Wexley. 
During the portion of the story which occurs in Great Wexley, I feel that the tension of the rising action increases exponentially until the climax of Crispin confronting Steward Aycliffe occurs. 

What story did the man standing near the hardware store tell the passing cop?

The man standing outside "a darkened shop" explains to the cop why he is there. He says that he is waiting for a friend—the two of them agreed twenty years earlier that they would meet here on this particular night. He explains that there was once a restaurant here, where he had dinner with his best friend, Jimmy Wells. The two of them grew up together in New York "like two brothers," and Jimmy loved the city so much that he would never have left. The waiting man, however, moved out to the West. The two agreed that they would meet in this place in twenty years to see what had become of each other. The man has come a thousand miles to meet his friend tonight. He says he was successful in the West and is intrigued to see what has become of his friend.
Ultimately, the twist in the tale is that the cop is Jimmy Wells—he recognizes his old friend as a man wanted by Chicago police. Instead of giving himself away, or arresting the man himself, he "went and got another cop and sent him to do the job."

How does Mary Shelley present a warning to readers of Frankenstein?

Shelley shows how unchecked ambition and a desire for personal glory leads to Victor's unethical actions and ultimate ruin. He tells Captain Walton,

Learn from me, if not by my precepts, at least by my example, how dangerous is the acquirement of knowledge and how much happier that man is who believes his native town to be the world, than he who aspires to become greater than his nature will allow.

Victor describes knowledge as something that can be dangerous, even comparing it in one moment to a "serpent to sting [him]," because he feels that his education and knowledge is what eventually led to his downfall. He'd hoped to create a "new species" that would "bless [him] as its creator and source." He dreams that

No father could claim the gratitude of his child so completely as [he] should deserve theirs.

He becomes too proud, and his pride runs away with him—he thinks that he can play God and create a person who is, essentially, superhuman: taller, faster, stronger, and more beautiful than regular people. Therefore, he actually believes that he can create human beings even better than God does. Such pride contributes to his ultimate ruin and the deaths of almost all his family and friends.

Mary Shelley presents a warning to readers about the pitfalls of pride and overreach by presenting us with the tortured figure of Victor Frankenstein. Frankenstein, his soul tormented when we first meet him, is involved in an epic chase after a monster who has killed his friends, family members, and fiancee.
As the story unfolds, we learn of Frankenstein's quest to create human life out of dead body parts. The story shows Frankenstein to have had an obsessive desire to make new life. This quest isolates him and threatens to ruin his health, as he works night and day. He wants to impress the world by achieving a new and astonishing scientific feat. Yet when he does so, he is appalled at the ugliness of what he has created and rejects his creature, who responds in pain by killing those Frankenstein most loves.
The story was written during a period of rapid scientific and technological advancement in Europe and warns of the consequences when humans become too proud of their own powers and try to play God.

Why do you think the flower girl was worried when she saw the man with the notebook?

The flower girl is worried because she believes that the man with the notebook is a police informer. 
In the play, the gentleman cannot buy a flower from the flower girl because he does not have enough change. Instead, he gives her what he has, which is three halfpence. Meanwhile, a bystander warns the flower girl that a police informer may be nearby taking notes about her behavior and actions. The bystander tells the flower girl to give the gentleman a flower in exchange for the three halfpence; he implies that she could go to prison for appearing to solicit money from respectable men.
The flower girl becomes hysterical upon hearing the bystander's warning. She demands to know what the man with the notebook has written about her. Meanwhile, the gentleman proclaims that the flower girl has done no harm and that she has certainly not accosted him in any way. He tells the notetaker to mind his own business. For his part, the notetaker denies that he is a police informer. During the exchange, he periodically tells the flower girl to cease her hysterics.
The flower girl becomes worried when she sees the man with the notebook because she fears that he is a police informer. There is also the implication (from the bystander's words) that the flower girl could be seen as soliciting money for sexual favors if she failed to hand over a flower to the gentleman who gave her the three halfpence.

How would I analyze the meaning of John Lennon's song "Borrowed Time" as a music critic? Any suggestion would be very helpful and appreciative. I need to stay focused on the argument by asking how is the music organized, what unifies the music, what style is the music, and from what period. What is the larger historical context in which the song was created?

You should analyze song lyrics in the same way that you would analyze a poem. As for the music itself, you need to identify the genre, which is pop. The period is simply when it was created. This comes from Lennon's later career, when he worked solo and with his wife, Yoko Ono. He recorded it in 1980, shortly before he was assassinated, but it was released posthumously in 1984. So the period of the song is the early 1980s, and like many songs of its time, it has a synthesized pop, new-wave sound, with a little bit of psychedelic funk thrown in. 
The lyrics themselves are pretty straightforward, so you should first identify the main theme, which is about growing older, and how aging has brought clarity and greater happiness to the writer. Lennon equates being younger with psychological pain, confusion and delusion.
The reason that the writer is happier now that he is older is that he has come to realize something very basic but important. This realization comprises his chorus, which goes like this:

Living on borrowed timeWithout a thought for tomorrowLiving on borrowed timeWithout a thought for tomorrow

This is just a simple "seize the day"-themed poem put to music, and while it is perhaps overly simplistic, it gained a great deal of poignancy when Lennon was shot and killed a few months later just outside of his apartment building by a deranged fan, Mark David Chapman. It is interesting to see how the circumstances of Lennon's life and tragic, violent death at such a young age imbued what is essentially an upbeat, fluffy, "living for the moment" song into a sadly prophetic exhortation about a man who is happy to be alive and is embracing each moment, when as we the listeners now know, he had so little time left on earth.
This song is a good case study for how circumstances surrounding a piece of art can transform that art into something far more powerful and meaningful than the artist intended or would have achieved otherwise.

Assess the Cold War. How did it affect American diplomacy and what were the results for Europe and Asia? What were the final results of the Cold War on the United Staes ?

The Cold War loomed large over America foreign policy, and virtually every situation was analyzed through the lens of the bilateral conflict between the U.S. and the U.S.S.R. In Europe, this was played out most dramatically in the virtual bifurcation of Europe between democratic Western Europe, allied with the United States, and communist Eastern Europe, dominated by the U.S.S.R. in nearly every way. In Germany, in particular, the construction of the Berlin Wall was the physical manifestation of the Soviet attempt to cut off its citizens from what it deemed to be threatening Western ideology. The Cold War also led directly to the rise of the NATO and Warsaw Pact military alliances which demanded that member nations defend each other in case of war. The Cold War caused a massive increase in defense spending and the stockpiling of conventional and nuclear weapons, an attempt to make true the theory that MAD or mutually assured destruction was the only way to avoid war. In Asia, the Domino Theory—the Cold War-driven notion that the "falling" of one nation to communism would inevitably lead to more nations becoming communist, like dominoes falling in a row—led to American involvement in both the Korean War and the Vietnam War in an attempt to prevent those nations from embracing communism and allying with the Soviet Union.

Beginning Algebra With Applications, Chapter 5, 5.4, Section 5.4, Problem 8

Using the slope intercept form, determine the equation of the line that contains the point whose coordinates are $(-2,3)$ and has slope of $\displaystyle \frac{1}{2}$.


$
\begin{equation}
\begin{aligned}

y =& mx+b
&&
\\
y =& \frac{1}{2}x + b
&& \text{Replace $m$ with } \frac{1}{2}
\\
3 =& \frac{1}{2} (-2) + b
&& \text{Substitute $x = -2$ and $y = 3$}
\\
3 =& -1 + b
&& \text{Solve for } b
\\
\\
4 =& b
&& \text{Add } 1
\\
\\
y =& \frac{1}{2}x + 4
&& \text{Write the equation of the line by replacing $m$ and $b$ in $y = mx+ b$ by their values}

\end{aligned}
\end{equation}
$

How do Squeaky's characteristics create conflict in "Raymond's Run"? What are some of the conflicts in the story?

In Toni Cade Bambara's short story, "Raymond's Run," Hazel Elizabeth Deborah Parker, also known as Squeaky, is the narrator. She has many strong characteristics that cause conflicts in this story.
Squeaky is intensely focused. Her main goal is to be the fastest runner, and she wins every race she can take part in. She practices running everywhere she goes, saying, "I never walk when I can trot." She also practices breathing exercises and high-stepping, which strengthens her knees. This creates conflict with her mother when she goes shopping with her. Her mother is embarrassed about her odd behavior and acts like she doesn't know her.

I’ll high-prance down 34th Street like a rodeo pony to keep my knees strong even if it does get my mother uptight so that she walks ahead like she’s not with me, don’t know me, is all by herself on a shopping trip, and I am somebody else’s crazy child.

Squeaky is also bold and sassy. This creates conflicts because she is poised for a fight in nearly every interaction she has with people. This creates conflict when she encounters Gretchen and her sidekicks. 

I’m ready to fight, cause like I said I don’t feature a whole lot of chit-chat, I much prefer to just knock you down right from the jump and save everybody a lotta precious time."

Squeaky also has a big ego, and this creates conflict in the story. She doesn't like idle chit-chat, and she can't bear with girls who act with false modesty. She knows she is the fastest runner in her neighborhood, and she flaunts that. 

"I always win cause I’m the best," I say straight at Gretchen who is, as far as I’m concerned, the only one talking in this ventrilo-quist-dummy routine. Gretchen smiles, but it’s not a smile, and I’m thinking that girls never really smile at each other because they don’t know how and don’t want to know how and there’s probably no one to teach us how, cause grown-up girls don’t know either. Then they all look at Raymond who has just brought his mule team to a standstill. And they’re about to see what trouble they can get into through him.
"What grade you in now, Raymond?"
"You got anything to say to my brother, you say it to me, Mary Louise Williams of Raggedy Town, Baltimore."
"What are you, his mother?" sasses Rosie.
"That’s right, Fatso. And the next word out of anybody and I’ll be their mother too.”

Squeaky is also fiercely protective of her brother Raymond, who has an extra large head and is mentally challenged. She refuses to allow anyone to talk down to—or about—him. She stands ready to fight for him against anyone, and doesn't let Gretchen and her friends address him directly.

Did Europe's and Europeans' constant need to assert dominance demonstrate weakness or strength? Consider different ways that dominance was asserted

The answer to this question is a matter of debate for historians, and really would depend on the time period. The ability of Europeans to expand and conquer peoples around the world was unquestionably related to their relative strength, particularly in terms of technology. But their desire to do so was largely related (at least at first) to their perceived economic weakness compared to the Muslim world. European merchants and monarchs wanted to force their way into the lucrative gold (Africa) and spice (Asia) trades that were controlled, at least in the Western world, by Asia. So it could be argued that Europeans were driven by their own sense of weakness. In the nineteenth century, many argued that taking colonies around the world was a means of securing captive markets, which were seen as essential to continuing economic growth. So this also could be seen as a motive related to Europeans' belief in the tenuousness of capitalist expansion.
https://www.history.com/topics/exploration/exploration-of-north-america

Without a single shot fired or a drop of blood spilled in the story, Hemingway portrays where the true destruction of war lies in "Old Man at the Bridge". How does the story highlight the destruction?

The story conveys the ravages of war in a variety of ways. Often, the old man is frequently discussed regarding this type of question. He most certainly seems to be in a mental state of complete loss. He can't mentally move past the fact that he has been displaced by the war. Specifically, he mentions artillery strikes, and he is worried about what will happen to the animals. The soldier does convince the old man to get up and try to move, but his age and frailty prevent him from going anywhere. The man conveys a general sense of loss and hopelessness.
Beyond the old man, the story does a nice job of conveying the dismal effects of war through the use of color. Readers are told about the grays and blacks that are present in the faces of people and the surrounding area. Everything is covered in dust too. These are specific choices by the author. Whether there is a war or not doesn't effect the weather, yet the author tells readers that the overcast skies were so thick with gray that the planes couldn't even fly. The sky could have been blue with white clouds, but that weather and color palette would not help to convey the ominous overtones that go with war and coming battle.

The story is set during the Spanish Civil War, a particularly brutal and bitter conflict that dragged on for three years. And as the story opens, a huge convoy is making its way across a bridge in anticipation of the imminent arrival of enemy forces. Men, women, and children are desperately scrambling across to the other side of the bridge, their lives severely disrupted by this seemingly interminable conflict.
The old man's life has also been disrupted. He was forced to leave his hometown at short notice after it was evacuated by government troops. But war doesn't only have a negative impact on humans. The old man is worried about the fate of the animals he used to care for but which he was forced to abandon when he was ordered to leave San Carlos. He keeps telling himself that the animals will be alright, but that simply shows just how worried he is.
Aside from the destruction of life and human property, war can also destroy the human soul. That's what has happened to the old man; and that's why he sits down by the side of the road, unwilling to join the heaving mass of humanity hastily making its way across the bridge. His animals were his whole life; now that they've gone, he has nothing left. And so he awaits his fate. The destruction of his soul is a prelude to his physical destruction.

What are some metaphors in the first twenty pages of Silent Spring?

At the end of chapter one, Carson uses the metaphor of a "grim specter" that has "crept upon us" with a blight that is poisoning the environment and killing plant and animal life.
In chapter two, Carson quotes Albert Schweitzer's metaphor; he said "man can hardly even recognize the devils of his own creation" in reference to nuclear weaponry. Schweitzer and Carson express the idea metaphorically that this technology is evil.
At the end of chapter two, Carson characterizes the responses to public protests against chemical companies as "little tranquilizing pills of half truths" and "the sugar coating of unpalatable facts." She asserts that it is humanity's right to know the full truth about the use of pesticides because it is humanity's "obligation to endure" as a species.
At the beginning of chapter three, Carson metaphorically describes the chemical industry as "a child of the Second World War," as she points out that chemicals designed to kill people were first tested on insects.

In Chapter 1, "A Fable for Tomorrow," Rachel Carson uses an extended metaphor to describe a town in America that lives "in harmony with its surroundings." This idyllic town stands for the state of the environment before the widespread use of chemicals in America. Then, using another metaphor, she describes a "blight" that creeps over the land and changes it, sickening livestock and people. In a later metaphor, Carson describes a "stillness" that develops in which no birds are heard chirping and those that still live are unable to fly. The roadsides, once beautiful, are covered with desiccated vegetation "as though swept with fire" (this is an example of a simile, a comparison that uses "like" or "as" and is a kind of metaphorical language). The blight and stillness that Carson writes about are metaphors for the damage that pesticides and other toxins are causing in the environment. 

Elaborate virtues of houyhonms

In Jonathan Swift's satirical travel novel Gulliver's Travels, his title character travels last to the land of the Houyhnhnms. In his previous travels, Gulliver has come across Lilliput, a land where everyone is tiny compared to himself; Brobdignag, a place where everyone is gigantic compared to himself; and Laputa, a strange world of clouds, philosophers, and misguided experiments. All of the characters in these lands have been human, though different from Gulliver in some fundamental way. When he travels to the land of the Houyhnhnms, however, Gulliver is met with a race of horses who rule over a savage race of yahoos (the humans in this scenario).
Foremost among the traits that Gulliver observes and admires in the Houyhnhnms are their rationality and their love of peace. Gulliver describes these horses as "orderly and rational." They can speak, they can explain themselves, and they choose to live simply and without conflict. The main source of trouble in this land is the yahoo population. The yahoos are described as dirty and barbaric. The Houyhnhnms look down on them and treat them like the animals they seem to be. Gulliver finds himself seeing humans in the same way the horses see them; he does not want to be associated with yahoos, and he even has a hard time returning to life in England because he is so disgusted by humankind. He does hope, however, that readers can learn some of the virtues of the Houyhnhnms, who serve as Gulliver's ideal.

What are the obstacles or hurdles in Holden's way?

Holden presents his story to the reader in a conversational and almost naive manner, revealing elements of his personality and personal details of his life without a fully developed sense of self-consciousness. In this way, he tells the reader about all of the challenges in his life. Here are a few examples of these hurdles.
First of all, Holden has a hard time with his family life. Both of his parents as well as his brother D.B. and his sister, Phoebe, are all grieving the death of Allie, Holden's brother. This tragedy, plus the fact that Holden doesn't feel he knows or understands his parents well, have led Holden to feel a bit stuck and directionless, and so he looks for answers from other people who seem to disappoint him.
Another obstacle Holden experiences is his own way of holding other people to a high expectation and then feeling disappointed when they let him down. For example, while in New York, he has an exchange with a taxi driver he has only just met, and this driver gets impatient with Holden's questions. Holden seems annoyed by this situation, but if he hadn't been so persistent in his line of questioning and so sure of a helpful response, he may not have invested such emotional energy into the conversation.
Also, Holden may have experienced abuse at the hands of Mr. Antolini. This episode of molestation is debated amongst Salinger scholars, but if it is true that Holden was a victim of sexual abuse, it may explain some of Holden's difficulties in life. Without the right care and psychological and emotional treatment, Holden may never be able to move past this obstacle.

Single Variable Calculus, Chapter 5, 5.2, Section 5.2, Problem 2

Suppose that $f(x) = x^2 - 2x, 0 \leq x \leq 3$, find the Riemann sum with $n = 6$, taking the sample points to be right end points. What does Riemann sum represent?

With $n = 6$, we divide the interval $(0,3)$ into 6 rectangles with widths

$\displaystyle \Delta x = \frac{3-0}{6} = 0.5$ at $x = 0, 0.5, 1, 1.5, 2, 2.5$ and $3$.

Evaluating $f(x)$ on the right end points (starting from $x = 0.5$)


$
\begin{array}{|c|c|}
\hline\\
x & f(x) = x^2 - 2x \\
0.5 & -0.75 \\
1 & -1 \\
1.5 & -0.75 \\
2 & 0 \\
2.5 & 1.25 \\
3 & 3\\
\hline
\end{array}
$


Now, the total area of the rectangle is..

$0.5(-0.75 - 1 - 0.75 + 0 + 1.25 + 3) = 0.875$

The Riemann sum represents an estimate of the area between the curve and the $x$-axis. Although in some cases, some areas result to a negative value because some rectangles are located below the $x$-axis. With this, you have to take the absolute values of such areas to get the actual area.

Explain the use of repetition in the poem "Mooses" by Ted Hughes.

The repetition in this poem is subtle. Rather than repeating whole phrases or lines, the poem features frequent alliteration (the repetition of a word's first letter or sound across adjacent words) and anaphoras (the repetition of the first word or phrase at the beginning of successive clauses). 
The poem's final line, "Two dopes of the deep woods," is one great example of alliteration. Notice the "d" sound at the beginning of "dopes" and "deep." Another example of alliteration in this poem is the line "Hopeless drops drip from his droopy lips." Again, the "d" is repeated here. The alliteration in both of these lines, especially in the poem's final line, creates a kind of sonic punch for the reader that helps to make each line stand out. The alliteration also creates a rhythm and a sing-song effect, almost like a child's nursery rhyme, which emphasizes the silliness, helplessness, and "dopiness" of the moose.
The line "He bumps, he blunders, he stands" is one example of anaphora in the poem. Notice the repetition of "he" across the three clauses. Again, this anaphora creates a sing-song rhythm, emphasizing the ridiculousness of the moose and his frantic actions.
Hughes also uses this repetition to create a subtle tone that is both mocking and sad. Using the poem's alliteration and anaphoras, which create a childlike, almost ridiculous sing-song rhythm, Hughes underscores how silly and sad the moose is in his feelings of despair and lostness. The repetition thus helps drive the point home that the moose's blundering in the poem mirrors the ways in which humans blunder around trying to find their identities and meaning in their lives.

Calculus of a Single Variable, Chapter 2, Review, Section Review, Problem 29

You need to evaluate the derivative of the given function and since the function is a product of two polynomials, then you must use the product rule, such that:
f'(x) = (5x^2 + 8)'(x^2 - 4x - 6) + (5x^2 + 8)(x^2 - 4x - 6)'
f'(x) = (10x + 0)(x^2 - 4x - 6) + (5x^2 + 8)(2x - 4 - 0)
f'(x) = 10x(x^2 - 4x - 6) + (2x - 4)(5x^2 + 8)
f'(x) = 10x^3 - 40x^2 - 60x + 10x^3 + 16x - 20x^2 - 32
Combining like terms yields:
f'(x) = 20x^3 - 60x^2 - 44x - 32
Hence, evaluating the derivative of the function, using the product rule, yields f'(x) = 20x^3 - 60x^2 - 44x - 32.

Name 3 reasons why the USA got involved in the Vietnam war and give a detailed explanation for each.

Here are three reasons the U.S. got involved in Vietnam:
1.  The domino theory--this theory refers to how if one nation is taken over by Communists, then the others around it will also.  Kennedy's defense strategy referred to containment of Communism--not to let the Communists take over any more countries.  This meant fighting what America thought was Communist aggression anytime, anywhere.  
2. America needed to look strong in front of its allies.  Western European leaders constantly worried about Soviet aggression.  If America let South Vietnam fall to the North, then Western Europe may feel as though America could not protect them either.  South Vietnam soon became a symbol of America's ability to fight communism, and the U.S. needed to prove to Europe that it was the dominant superpower.  At the time many in American government thought that Communism was controlled by the Kremlin directly--later evidence has proven that this was not the case, even though North Vietnam received weapons and money from the Soviet Union.  
3. The Gulf of Tonkin Resolution--This one is probably the greatest of them all, because after 1965, America sent more than advisers and monetary aid to South Vietnam--it sent ground troops and air support.  The U.S.S. Maddox was carrying out a simulated radar attack on Hanoi in order to test the city's defenses.  Hanoi, understandably, sent a submarine to attack the Maddox.  While the simulated attack was not published in American news, the North Vietnamese attack was publicized, and many in America thought that a war against North Vietnam was the appropriate response.  

What is Shakespeare’s ultimate message in Othello?

One possible interpretation of this play is that it seems to endorse the racist stereotype that all black men are primitive, animalistic, and unintelligent. This was a stereotype prevalent during the early seventeenth century in England, and which, unfortunately, still persists to some degree in some parts of the world today. At the beginning of the play, Iago talks about Othello as "the Moor" and a "Barbary horse." He tells Desdemona's father, Brabantio, that Othello has been "making the beast with two backs" with his daughter, meaning that Othello and Desdemona have been having sex. Brabantio suspects that Othello must have wooed his daughter with "foul charms" or "drugs or minerals." He cannot conceive that a white woman would otherwise find love in, as he puts it, "the sooty bosom / Of such a thing as [Othello]."
When Othello first appears in the play, he seems to speak and behave in such as way as to expose the aforementioned stereotype as nothing more than ignorant and racist. He speaks eloquently and poetically. In fact, the critic G. Wilson Knight coined the term, "The Othello Music," to describe Othello's speech. Othello also seems to be calm, composed, and rational in the face of Brabantio's threats and accusations. He tells Brabantio's men to "Keep up their bright swords," and he advises Brabantio that he "shall more command with years / Than with . . . weapons."
However, by the end of the play, thanks in large part to Iago's machiavellian scheming, Othello is reduced to the racist stereotype he seemed for a time to defy. He becomes animalistic, aggressive, and irrational. He "foams at mouth and by and by / Breaks out to savage madness." He kills Desdemona for a crime she did not commit and for no better proof than a missing handkerchief. As the writer Fintan O'Toole says in his book Shakespeare is Hard, But so is Life, Othello "is driven demented by a handkerchief. He is not tragic, merely pathetic."
Therefore, the demise of Othello and the tragic death of the innocent Desdemona seems to confirm the racist stereotype that we began with. The message that a contemporary audience might have taken from this play—and that perhaps Shakespeare intended—is that black men are essentially and inescapably animalistic, aggressive, and irrational. They may at times seem otherwise, but ultimately, so the play suggests, they can not escape their true nature. This message would have been met with approval from many in Shakespeare's time, which further lends credence to the idea that Shakespeare did indeed intend this to be the central message of the play.

An important moral of the story is the enormously destructive power of jealousy—the green eyed monster itself. Thanks to Iago's cunning insinuations, Othello gets it into his head that Desdemona has been cheating on him with Cassio. She hasn't, of course, but Iago is such a skilled manipulator that he's effortlessly able to play on the Moor's myriad insecurities to convince him of his wife's alleged infidelity.
Yet Iago himself is a victim of the green-eyed monster. He's insanely jealous of Othello for having achieved the kind of social prominence in Venice to which he believes himself entitled by his long-standing military service. By the same token, he cordially loathes Cassio for being promoted ahead of him despite Cassio's lack of experience as a soldier. There's more than a touch of class envy about Iago; he resents his lowly status in life, and in his vile machinations he is attempting to get back at aristocratic society for not giving him his due. Iago is so jealous of the Venetian elite that he's prepared to turn the natural order of society upside down in order to gain revenge. Jealousy doesn't just destroy individuals; it can destroy the very foundations of society too.

I'm a bit unsure as to exactly what "ultimate message" means.  I think it is asking the standard "what is the moral of the story" question, so that is how I'll answer.  Different readers might take slightly different lessons from this particular Shakespeare play, but I think one major message is the importance of not believing in and acting upon unconfirmed rumors.  This entire play is propelled forward by the rumors and lies that Iago spreads around to various people about marital infidelities.  Amazingly, many of the characters take Iago at his word and don't confront the person that supposedly wronged them.  Sure, Othello does confront Desdemona about her infidelity, but it's fairly clear to readers that he's not really willing to hear her side of the story.  He fully believes the rumors that he has been told.  

I cry you mercy, then,
I took you for that cunning whore of Venice
That married with Othello.—You, mistress,
That have the office opposite to Saint Peter
And keep the gate of hell!

Because of his belief in these unsubstantiated rumors, Othello makes a snap judgment about his wife.  He quickly decides to kill her, and she is dead before he learns the truth.  He kills himself out of guilt and grief.  

int (x^2+12x+12)/(x^3-4x) dx Use partial fractions to find the indefinite integral

 
int (x^2+12x+12)/(x^3-4x)dx
To solve using partial fraction method, the denominator of the integrand should be factored.
(x^2+12x+12)/(x^3-4x) =(x^2+12x+12)/(x(x-2)(x+2))
Then, express it as sum of fractions.
(x^2+12x+12)/(x(x-2)(x+2)) = A/x + B/(x-2) + C/(x+2)
To determine the values of A, B and C, multiply both sides by the LCD of the fractions present.
x(x-2)(x+2)*(x^2+12x+12)/(x(x-2)(x+2)) = (A/x + B/(x-2) + C/(x+2))*x(x-2)(x+2)
x^2+12x+12=A(x-2)(x+2) +Bx(x+2)+Cx(x-2)
Then, assign values to x in which either x, x-2 or x+2 will become zero.
So, plug-in x=0 to get the value of A.
0^2+12(0)+12=A(0-2)(0+2)+B(0)(0+2)+C(0)(0-2)
0+0+12=A(-4)+B(0)+C(0)
12=-4A
-3=A
Also, plug-in x=2 to get the value of B.
2^2+12(2)+12=A(2-2)(2+2)+B(2)(2+2)+C(2)(2-2)
4+24+12=A(0)+B(8)+C(0)
40=8B
5=B
And subsitute x=-2 to get the value of C.
(-2)^2 + 12(-2)+12=A(-2-2)(-2+2)+B(-2)(-2+2)+C(-2)(-2-2)
4-24+12=A(0)+B(0)+C(8)
-8=8C
-1=C
So the partial fraction decomposition of the integral is
int (x^2+12x+12)/(x^3-4x)dx
= int (x^2+12x+12)/(x(x-2)(x+2))dx
= int(-3/x +5/(x-2)-1/(x+2))dx
Then, express it as three integrals.
= int-3/xdx + int 5/(x-2)dx - int 1/(x+2)dx
= -3int 1/xdx + 5int 1/(x-2)dx - int 1/(x+2)dx
To take the integral, apply the formula int 1/u du =ln|u|+C .
=-3ln|x| + 5ln|x-2|-ln|x+2|+C
 
Therefore,int (x^2+12x+12)/(x^3-4x)dx=-3ln|x| + 5ln|x-2|-ln|x+2|+C.

Relate the Romantic traits to the continued development of American identity and point to any traits that may still exist in 21st century America.

Many of the traits which originally characterized the British Romantic movement, and which came to be echoed and amplified by American Romanticists, are also traits which are inextricably connected to the idea of American identity as it was first developed. It is not surprising that, in adapting the Romanticism of writers and poets in the United Kingdom, American writers chose to focus upon, and then proliferate, the particular ideas which appealed to them as pioneers in a young and expanding nation. British Romanticism became American Romanticism, and American Romanticism helped shape the American identity.
There are strong connections between the early proponents of the American Revolution, such as Thomas Paine, and the progenitors of Romanticism. Mary Wollstonecraft and her husband William Godwin, the parents of Mary Shelley, were supporters of the American Revolution and ideas of democratic freedom and rebellion against governments they saw to be unjust. William Godwin passed down these beliefs to his daughter, and she moved with a crowd of Romantic writers—including Byron, Keats, and her later husband, Percy Bysshe Shelley—who also promoted revolutionary values in their work. Indeed, all the key English Romantic poets (Mary and Percy Shelley, Byron, Keats, Coleridge and Wordsworth) supported the French Revolution and promoted values of freedom and fraternity in their works. The connection between this trait of Romanticism and the developing American identity is clear: Romanticism had a long tradition of championing the oppressed (see also William Blake) and railing against governments it saw to be unfit to govern. The early, and indeed the current, American identity placed great store by these ideas of brotherhood and liberty and of government by the people and for the people.
Connected to the idea of revolution and liberty in Romanticism is the emphasis upon individualism we also find espoused by the Romantic poets. Coleridge's "Frost at Midnight," in which he celebrates the "babe" who contains "all things in himself," is an excellent example of this, but the idea of the individual's significance in determining his own path can be found in much English Romantic poetry. Likewise, it is a key tenet of the work of American poet Emerson (see his essay "Self Reliance") and a significant part of the American identity. Individualism, or the belief that each person makes of himself what he chooses, is a key principle of what it means to be American. It is the foundation of capitalism, a rejection of state control or collective thought or action, and has contributed to the idea of American exceptionalism. While individualism espouses that self-reliance and originality are what help us succeed, in the USA, this concept has become inextricably connected to the idea that, because America is such a unique nation, it is entirely unlike other countries and can do things others cannot.
There are other, less politicized, traits of Romantic poetry which can also be said to have helped shape the American identity. Perhaps the overriding feature of Romantic poetry is that it celebrates the sublime as it is found in nature, particularly in dramatic landscapes which evoke strong emotion. The celebration of nature is inherent in much American literature and, indeed, in the American character itself. Americans have always wanted to possess land, and there is a strong theme of being "part of" the land in many American writings. As the country expanded westwards, we can also see the Romantic theme of the hinterland—exploring the borders between the known and the unknown—become transmuted into the American Romantic fascination with frontiers. While British Romanticism (and, later, Gothic literature) explores the meaning of borders and hinterlands as places where ideas intersect and dreams can be born, American Romanticism takes this idea a step further, privileging the idea that beyond the known borders of the USA was a new world, or new dream. During the Gold Rush, as Americans expanded westwards and many made a fortune overnight from the natural wealth of California, this idea became solidified in American culture, and the American Dream was born. The love of nature and the belief in individualism combined to create the idea that a fortune can be gained from the land, if only a man is willing to work hard enough. While it is no longer true that a fortune can easily be found in the physical landscape of America, the American Dream is certainly still alive today and concerns with self-reliance and individualism are the bedrock of American capitalism.

“Political and social protest writing focuses on the impact of the clash of cultures.” Explore the significance of cultural difference in the Kite Runner.

Hosseini explores cultural differences by portraying the relationship between Pashtuns and Hazaras in Afghanistan, as well as the reactions of Afghan citizens living under the oppressive rule of the Taliban. Hosseini depicts how Hazaras are discriminated against and marginalized by the Pashtun majority by illustrating how Hassan and Ali are treated throughout their society. Hazaras are an ethnic group of Shiite Muslims, who have Asian features and are a discriminated minority in Afghanistan. The majority of citizens in Afghanistan are ethnic Pashtuns, who are Sunni Muslims that occupy positions of power throughout the nation. Ali and Hassan are both openly ridiculed by Pashtun citizens and live as poor servants in Baba's household. Both Ali and Hassan are uneducated and do not have access to many opportunities throughout Kabul because of their ethnicity. Baba and Amir are essentially Ali and Hassan's masters, who are forced to suppress their true feelings of affection towards them because it is considered socially unacceptable. Baba even hides the fact that he is Hassan's biological father because of the ethnic prejudice surrounding Hazaras. In addition to Hosseini's portrayal of the relationship between the Pashtuns and Hazaras, he also illustrates how the Afghan citizens react to the Taliban regime. When Amir returns to Afghanistan as an adult, he discovers that his home country is destroyed and the citizens live in constant fear. The Taliban is a Sunni Islamic fundamentalist political group that abides by Sharia law, which is a strict interpretation of the Quran. Afghanistan is transformed into an austere nation, where male citizens are forced to wear long beards and follow the religious teachings of the Quran or suffer severe consequences. Amir learns that secular and liberal citizens live as prisoners in a conservative, violent nation.

What does Jem misunderstand about the length of the jury's deliberations? What is the significance of the jury's deliberations, and what effect do they have on Jem?

In Chapter 23, Atticus is discussing aspects of the trial and justice system with his children. After Atticus tells Jem that serving on a jury forces a man to make a declaration about something, Jem says, "Tom's jury sho' made up its mind in a hurry" (Lee 136). Atticus immediately corrects Jem by commenting that Tom's jury took a few hours. Atticus felt that Tom had a slight chance of winning simply because the jury was deliberating for such a long time. Atticus tells his son that in an inevitable verdict, it usually takes the jury several minutes to deliberate. Atticus then explains to Jem that one of the Cunninghams was actually arguing for an outright acquittal. Jem is both shocked and perplexed to learn that one of the Cunninghams argued for Tom's innocence. 
During the trial, Jem did not understand that the jury was inevitably going to convict Tom Robinson because he was black. Jem naively believed that Tom would be given a fair trial. However, Atticus understood that typically a trial involving a black man's word against a white person's word takes a few minutes. The fact that the jury deliberated for a few hours is significant because at least one white juror supported Tom's testimony. Having a white juror argue a black man's innocence in 1930s Alabama was unheard of, which is why Atticus felt somewhat optimistic. Upon hearing Atticus' explanation, Jem mentions that he'll never understand the community members of Maycomb. 

Does Amir have internal scars?

Amir has significant internal scars that haunt him as an adult. They stem from his traumatic childhood experiences and damaged relationships. As a child, Amir longs to have a loving relationship with his father, Baba. Amir wishes more than anything to gain his father's respect and earn his attention as a young boy. Tragically, Amir is not the masculine, athletic child his father always wanted, and Baba continually ignores Amir as a child. Baba constantly overlooks his son and seems to always favor Hassan over Amir, which negatively affects Amir's self-esteem and confidence. As a result of his father's callous nature and lack of admiration, Amir begins developing feelings of jealousy and envy toward his close friend, Hassan. Amir even begins teasing and tricking Hassan as a way to boost his self-esteem but always feels guilty afterward.
On the day of the kite-fighting tournament, Amir and Hassan take first place, and Hassan races to retrieve the enemy's blue kite. After a while, Amir searches for Hassan and sees him surrounded by Assef and his friends in a dead-end alley. Instead of intervening and defending Hassan, Amir watches at a distance as Assef rapes his friend. Following Hassan's rape, Amir cannot live with the guilt, and he even attempts to get Baba to kick Hassan out of the home by planting his toys in Hassan's bed. Unfortunately, Ali and Hassan decide to leave Baba's estate, and Amir eventually travels to America.
As an adult with a successful career, Amir begins losing sleep and is still haunted by his overwhelming guilt. Amir is interally scarred from passively watching Hassan get raped by Assef and then making Hassan leave his home under false pretenses. Fortunately, Amir gets a chance at redemption after receiving a call from Rahim Khan. Amir ends up traveling to Pakistan where he discovers that Hassan was his half-brother, which is astonishing news. Amir then agrees to travel to Kabul to rescue Hassan's son, Sohrab, in order to redeem himself for his past transgressions as a child. Amir ends up finding Sohrab, nearly loses his life in a brutal fight with Assef, and struggles to keep Sohrab alive in order to take him to America. By the end of the novel, Amir ends up healing his internal scars and atoning for his sins by sacrificing his life to save Sohrab.

The amount a taxi driver charges a customer is given by the equation A=1.25+5.25, where A is the total amount charged and k is the kilometers driven. a) What do the numbers in the equation represent? b) Make a table of values for distances 0-10 km. c) Graph this relation. Liner or non-linear? d) Using your graphed relation, how much is charged if a person goes 7.5 km? e) Using your graphed relation, how far can a person go in a taxi for $15?

Hello! I suppose the equation is 1.25+5.25*k . It may also be 1.25*k+5.25.
a. Then we see that the number 1.25 (the free term) is in dollars (or other currency) and it represents the fixed cost. The number 5.25 is in dollars by kilometer and it represents the cost per each kilometer driven.
b. It is not difficult to make the table of values, just substitute different values of k to the formula.
k |    0   |    1   |    2    |    3     |    4    |    5    |    6     |    7    |    8     |    9    |    10     |A | 1.25 | 6.50 | 11.75 | 17.00 | 22.25 | 27.50 | 32.75 | 38.00 | 43.25 | 48.50 | 53.75 |
Of course each next value is 5.25 greater than the previous.
c. The graph is attached. Of course this relation is linear (the formula is in the slope-intercept form).
d. The graph shows that for 7.5 km one will be charged $40.625 (probably $40.63 ).
e. The graph shows that for $15 a person can go as far as about 2.6 km.
Of course the results d and e may be found analytically, too. [Tell me if you need this or if the formula is actually 1.25*k+5.25.]
 

What is the setting of the story?

The novel was written "to induce kindness, sympathy, and an understanding treatment of horses" and focuses on the adventures of the horse Black Beauty and the theme of the mistreatment of horses. The novel is told in first person from Black Beauty's point of view and follows his journey and hardships that arise along the way.
The story is initially set in an English farm, where Black Beauty is living life as a colt with his mother. He is happy and carefree at the beginning, but soon he starts to experience traumatizing events, such as a brutal hare hunt and the pain of having to wear a saddle and bridle.
Black Beauty is then sold to Squire Gordon who owns an estate named Birtwick Hall. There Black Beauty is quite happy for three years, and, although not as carefree as before, he enjoys the company of the other horses.
After that, we follow Black Beauty to London, where he eventually becomes a cab puller. It is hard work but his owner, Jerry, is kind and considerate. The same, unfortunately, cannot be said for other horses Black Beauty encounters.
At the end, Black Beauty is finally allowed to enjoy retirement in the Blomefield's family country meadow.

f(x) = x^3 , (1,1) Set up and evaluate the definite integral that gives the area of the region bounded by the graph of the function and the tangent line to the graph at the given point.

First, determine the slope of the tangent line. Take note that the slope of a line tangent to the curve is equal to the derivative of the function at the point of tangency. So taking the derivative of the function, f'(x) will be:
f'(x) = d/dx (x^3)
f'(x) = 3x^2
The given point of tangency is (1,1). Plugging in x=1 to the derivative yields:
f'(1) = 3(1)^2
f'(1) = 3
Hence, the slope of the line tangent to the function at (1,1) is m = 3.
Then, apply the point slope-form to get the equation of the tangent line.
y - y_1 =m(x - x_1)
y - 1 = 3(x - 1)
Isolating the y, it becomes: 
y - 1 =3x - 3
y = 3x - 2
Thus, the equation of the tangent line is y = 3x - 2 .
Then, determine the intersection points of  y = x^3 and  y = 3x - 2. To do so, set the two y's equal to each other.
y = y
x^3 = 3x - 2
Take note that to solve polynomial equation, one side should be zero.
x^3 - 3x + 2 = 0
Then factor the left side using grouping method.
x^3 - x - 2x + 2=0
(x^3 - x) + (-2x + 2) = 0
x(x^2 - 1) - 2(x - 1) = 0
x(x-1)(x+1) - 2(x - 1) = 0
(x - 1)[x(x + 1) - 2] = 0
(x - 1)(x^2+x-2)=0
(x - 1)(x-1)(x + 2)=0
(x-1)^2(x + 2) = 0
Set each factor equal to zero.
(x-1)^2 = 0

x - 1=0
x=1

x + 2=0

x=-2

Then, plug-in the x values to either y=x^3 or y = 3x - 2, to get the y coordinates of the intersection.
x=1
y = 1^3=1
x=-2
y=(-2)^3 = -8
So, the two equations intersect at (1,1) and (-2,-8). Hence, bounded region of y = x^3 and y = 3x - 2 is:

To determine the area of the bounded region, draw a vertical strip. (See attached image.)
In the figure, the top of the vertical strip touches the graph of y=x^3. And its lower end touches the graph of y = 3x-2. Also, the bounded region starts at x=-2 and ends at x=1.
Applying the formula
A = int_a^b (y_(_(upper)) - y_(_(lower)))dx
the integral needed to compute the area of the bounded region is:
A = int_(-2)^1 (x^3-(3x-2))dx
Evaluating the integral, it results to:
A = int_(-2)^1 (x^3 -3x + 2)dx
A = (x^4/4 - (3x^2)/2+2x) |_(-2)^1
A = (1^4/4 - (3*1^2)/2+2*1) - ((-2)^4/4- (3*(-2)^2)/2+2*(-2))
A =3/4-(-6)
A=27/4
Therefore, the area of the bounded region is 27/4 square units.

Who starts the signal fire by rubbing two sticks together?

In William Golding's The Lord of the Flies, nobody starts a signal fire by rubbing two sticks together. After the boys amass a pile of wood, Ralph and Jack realize they don't actually know how to start the fire. Ralph asks Jack to light it, at which time Jack says "you rub two sticks together." Ralph then foolishly asks for matches, and the boys slowly begin to realize that they have no hope of lighting the fire. However, when Piggy approaches, Jack points suddenly and says "His specs—use them as burning glasses!" Piggy is reluctant to give up his glasses, but the boys take them and

Ralph moved the lenses back and forth, this way and that, till a glossy white image of the declining sun lay on a piece of rotten wood. Almost at once a thin trickle of smoke rose up and made him cough. Jack knelt too and blew gently, so that the smoke drifted away, thickening, and a tiny flame appeared. The flame, nearly invisible at first in that bright sunlight, enveloped a small twig, grew, was enriched with color and reached up to a branch which exploded with a sharp crack. The flame flapped higher and the boys broke into a cheer.

The lighting of the fire essentially comes down to the three principle characters of the text. It is Ralph's initial idea, it is Jack's suggestion of how to make it happen, Piggy provides the means, and Ralph and Jack execute.

Explain how mutations can become established in a gene pool? Why does the frequency of some mutated alleles increase while others decrease in frequency over time in a gene pool of a species?

A mutation can arise from a change in the DNA sequence. If a mutation occurs in a germ cell, the mutation can be passed along to the next generation.
Some mutations are harmful, some have no effect while a small percentage may actually prove beneficial.
In the Theory of Natural Selection put forth by Charles Darwin, it is mentioned that organisms possess variations. These are due to gene mutations. If an organism has a variation that makes it better suited to the environment in which it lives, it may win the struggle for existence, survive and reproduce. Possibly, its variation which is an adaptation to the environment may be passed down to its offspring. In this way, the frequency of the gene that produces this variation may increase over time. However, if a gene mutation is not beneficial, it may become less common in the gene pool because it doesn't benefit the organism or improve its chances of survival.
An example demonstrating how gene frequencies can shift can be seen in the Peppered Moths in England. Before the Industrial Revolution, most moths in the area where the study occurred were of the light-colored variety. However, a few dark-colored moths existed due to a gene variation. Light ones blended into the light- colored background of the trees upon which they rested, while dark ones stood out and were eaten by predatory birds. In this way, natural selection caused the gene that produced the light-colored moths to increase in frequency, while the gene producing the darker-colored moths decreased.
During the time of the Industrial Revolution, the trees in the forest became covered in soot. Dark-colored moths now had an advantage because they blended into the background and escaped predatory birds. These moths lived and reproduced and the gene frequency increased for the dark variety. However, the lighter moths no longer had an advantage and were consumed more frequently. Their numbers due to the selective pressure of predators were drastically reduced.
Life doesn't operate in a vacuum. Because the environment changes, gene frequencies can change over time due to natural selection. I have included a link which elaborates the story of the peppered moths. I have included a second link summarizing Darwin's Theory of Evolution.
 
http://www.millerandlevine.com/km/evol/Moths/moths.html

http://www.pbs.org/wgbh/evolution/educators/course/session2/explain_c_pop2.html

Beginning Algebra With Applications, Chapter 5, 5.4, Section 5.4, Problem 26

Using the point slope formula, find the equation of the line that passes through the point whose coordinates are $(3,-1)$ and has slope of $\displaystyle \frac{2}{3}$


$
\begin{equation}
\begin{aligned}

(x_1, y_1) =& (3,-1)
&& \text{Let $(x_1, y_1)$ be the given point}
\\
m =& \frac{2}{3}
&& \text{$m$ is the given slope}
\\
y - y_1 =& m(x- x_1)
&& \text{Point slope formula}
\\
y - (-1) =& \frac{2}{3} (x-3)
&& \text{Substitute $3$ for $x$, $-1$ for $y$ and } \frac{2}{3} \text{ for $m$}
\\
y + 1 =& \frac{2}{3} x - 2
&& \text{Rewrite the equation in the form } y = mx+b
\\
y =& \frac{2}{3}x - 3
&& \text{Add $-1$}

\end{aligned}
\end{equation}
$

What message do Rosencrantz and Guildenstern have for Hamlet? What lesson does Hamlet teach them with the recorder?

In the scene this question seems to be referring to (late in Act 3, Scene 2), Rosencrantz and Guildenstern bring Hamlet a message from Gertrude and Claudius, Hamlet's mother and stepfather. Claudius, they say, is "in his retirement marvellous distempered," which is to say that the play he's just seen, in which a king is murdered by a close relative who then marries his wife, has struck a little too close to home. This, of course, was Hamlet's intention in selecting the play: he expected Claudius to show his guilt if he saw his own crimes reflected. As a result, Hamlet simply toys with the two men, already knowing exactly why the king is so upset.
Rosencrantz and Guildenstern then tell him that his mother has asked to speak with him in her own private chamber; she hasn't failed to notice Hamlet's (fake) insanity, and she's hoping that she can talk some sense into him. Hamlet responds formally, using the royal "we" and the formal "you," indicating to Rosencrantz and Guildenstern that he doesn't value them as highly as he once did. The men respond by telling him in a few different ways that they still care about him and asking him to tell them what's wrong.
Grabbing a recorder (the "pipe" referenced in the text), Hamlet asks Guildenstern to play it for him, since he claims to be such a loyal and obliging friend. The conversation goes something like this: "Will you play this recorder for me?" "I can't." "Please?" "Believe me, I can't." "I'm begging you." "I don't know how." Hamlet then responds that it's "as easy as lying," implying that Rosencrantz and Guildenstern, who have been lying to him (or at least hiding the truth) since they arrived, should have no trouble doing something just as simple. He points out the stops (the frets or holes in the recorder that you press to play the notes), but Guildenstern protests that he doesn't have the skill to make the instrument play actual music. This is where Hamlet gets to the point of all of this: Rosencrantz and Guildenstern are trying to "play" him (play him for a fool, if you prefer), but it won't work. They've been trying to find his weaknesses ("stops"), sound him out so that they can tell Claudius everything about him, and otherwise get him to do what Claudius wants, but he knows what they're doing and he won't give in. They may think he's like the recorder they hold, easy enough to play, but he warns them that he won't be so easily taken in. Although they can fret him ("fret" meaning both "to annoy" or "to move one's fingers along the frets of an instrument"), they can't play him.

Hamlet's old school chums, Rosencrantz and Guildenstern, have been summoned by Claudius to the Danish court to spy on their friend. They've been instructed to find out what's bugging Hamlet. However, Hamlet's no fool; he's on to Rosencrantz and Guildenstern; he knows what they're up to, so he doesn't let on why he's been acting so strangely lately. Rosencrantz starts getting frustrated and tells Hamlet that he's not doing himself any favors if he doesn't tell his friends what's wrong with him.
Hamlet then resolves to teach his former friends a lesson. He takes a recorder and asks Guildenstern to play it. Guildenstern protests, saying that he doesn't know how. But it's easy, says Hamlet, you simply play the instrument like you've been playing me. Just as Rosencrantz and Guildenstern tried to play Hamlet for a fool by pretending they'd come to Denmark to see him, so all Guildenstern has to do to play the recorder is put his fingers over the instrument's holes and blow into it. It doesn't matter if he can't make a melody; after all, "playing" Hamlet didn't get him to say what Rosencrantz and Guildenstern wanted him to say. Playing a recorder is a cinch; it's as easy as lying, and you don't even have to produce a melody from it.

What does Maniac mean when he says to Mars Bar, "Yeah you're more than bad all right, Mars Bar. You're more than bad. You're good"?

Mars Bar is extremely annoyed, not just for being humiliated at Piper McNab's birthday party, but also at Maniac for taking him there in the first place. When Maniac is originally invited to the party, he agrees to go on one condition: that he can take someone with him. The someone that Maniac has in mind is Mars Bar. He figures that the idea of taking a black kid to a party in the whites-only West Side is so crazy that no one would ever expect him to try it.
But try it he does. Unfortunately, things don't work out all that well. During an impromptu game of "Rebel," a member of the Cobra gang jumps into the air screaming and lands just behind Mars Bar, making him jump. Mars Bar is absolutely furious, and the atmosphere soon becomes tense. Thankfully, Maniac manages to get his party guest away before things turn nasty.
Once safely back on home turf, and finally free from Maniac's protective grasp, Mars Bar lets rip with his anger, hurt, and frustration:

You suckered me. You soften me up with them Pick-peoples, then bring me here. Wha'd you think! I was gonna cry Okay, I come over. I did it. It's done. And don't YOU be comin' 'round no more, ya hear me, fish! 'Cause you ain't only seen me half bad yet.

That's when Maniac says to himself

Yeah, you're bad alright, Mars Bar. You're more than bad. You're good.

Maniac is acknowledging that Mars Bar is a tough kid, and he admires him for it. But even more than that, he's immensely proud of Mars Bar for doing the right thing, the courageous thing, by accompanying Maniac to the party.

I am looking for a Summary of "The day the Universe changed"

“The Day the Universe Changed” is a book based on a British documentary series of the same name that initially aired in 1985. Both the series and book were created by science historian James Burke. The book/series investigates key moments in history and how the world was altered through philosophical, economic, and scientific discoveries. Key moments in Western history are covered including the ancient Greeks; faith and reason; science in the Renaissance; the printing press; mathematics and astronomy; the impact of the marketplace; medical science; evolutionary theory; Newtonian physics; and changing realities.
Burke’s thesis is that the universe was altered through the above events. By "altered," I am referring to the way in which people’s perceptions of themselves and their perspective toward everything around them changed. Changes in mathematics and astronomy or the introduction of Darwinian evolutionary theory altered how people viewed themselves in relation to the universe. People no longer saw themselves as the center of everything but as a species inhabiting a planet that was in motion around a star. This revolution in perception/perspective opened new ways of understanding the universe and forever changed the way Western civilizations functioned.
History is not a hodgepodge of events and unrelated happenings but a series of patterns that can be analyzed and defined. Burke focused on the above events to demonstrate that at certain points in time, people in the West transformed the way they understood the universe. Once these changes in perception/perspective occurred, the universe essentially changed as humans’ view of reality—why they are here, what is the nature of life—moved from a subjective to objective point of view.
http://siouxfallsscientists.com/the-day-the-universe-changed.html

https://www.mkltesthead.com/2010/06/wednesday-book-review-day-universe.html

http://scholarship.law.stjohns.edu/cgi/viewcontent.cgi?article=1550&context=lawreview Please write a summary of the article

This article argues that the Supreme Court case Terry v. Ohio (1968) was not necessary (in New York state) in order to allow police officers to search or frisk someone abut whom they had a "reasonable suspicion." The law was unnecessary because these types of frisk procedures were already largely allowed in the state. Instead, the law allowed the police to submit what they had seized during stop and frisk activities in a court of law as admissible evidence. The author of this article, Raymond, argues against an article by Professor Fyfe, who states that the best way to stop the abuses inherent in stop and frisk activities by the police is supervision by the police department. Instead, Raymond believes that the best way to prevent abuses is to use the courts to "police the police," as she calls it. She believes that police officers often lie and that the police are not capable of developing a sound system of internal review. Instead, the court system, she believes, must play a role in limiting the discretion that the police have in conducting stop and frisk procedures. 

How does Abigail Williams in The Crucible show that she values power over justice?

Abigail Williams is portrayed as an unscrupulous, malevolent young woman who propagates the witchcraft hysteria throughout Salem's community in order to avoid being punished for dancing in the woods. After Abigail initially uses Tituba as a scapegoat, she proceeds to name other citizens of colluding with the devil and notices how Salem's authority figures begin to revere her. As a young woman who is marginalized by Salem's austere community, Abigail Williams is often overlooked and dismissed by the male population. Once Abigail begins making accusations, she earns an elevated status among her neighbors and enjoys her newly gained authority. Abigail manipulates the community members by falsely accusing innocent citizens of witchcraft and enjoys being the center of attention in Salem's court.
She has absolutely no concept of justice and callously imprisons numerous innocent citizens. In order to maintain her elevated status and authority, Abigail continues accusing citizens of witchcraft until John Proctor and Mary Warren challenge her authority. Before John Proctor and Rebecca Nurse are publicly executed, Abigail flees Salem to avoid the impending pushback from the citizens. Overall, Abigail completely rejects the idea of justice and falsely accuses innocent citizens in order to maintain her newly acquired elevated status in the community.

Why does Ponyboy hope that Bob's parents hate him?

When Ponyboy states his preference for Bob's parents' hatred rather than their pity, he is stating his preference for equality and dignity over condescending sympathy. If someone feels pity for someone else, he or she is acknowledging that the other person is lacking something or suffering from a misfortune of some kind, often in a patronizing way. Ponyboy feels resentment toward anyone who feels pity for him and for the other greasers because he is a proud person who believes that he and his fellow greasers are coping just fine with what they have and with what they try to provide one another.
If someone feels hatred, that means that both parties are on equal footing; if someone feels pity, that means that one party is positioned higher than the other. No matter the reason, Ponyboy has the strength of spirit and the pride in himself as a human being to resent the suggestion that the greasers are deserving of a lower status of any kind.

Ponyboy doesn't necessarily want Bob's parents to hate him. What Ponyboy says in chapter 11 is that he would rather have their hate than their pity.

I hoped they hated us, that they weren't full of that pity-the-victims-of-environment junk the social workers kept handing Curly Shepard every time he got sent off to reform school. I'd rather have anybody's hate than their pity.

The reason that Ponyboy would rather have their hate than pity is that he believes pity will cause people to look down on him and his fellow Greasers. Pony is okay with being poor and coming from the rougher side of town. He accepts this, and he never once lets those things make him feel like a less worthy person. Pity makes him feel this way. If Bob's parents pity him, they are essentially looking down on him. Ponyboy is not okay with that. If Bob's parents (or other Socs) hate him, that means they consider him a worthy rival and opponent. They would not look down on him. They might even fear him. That makes Ponyboy an equal to them in a lot of ways. Pity implies that there is something wrong with Ponyboy and his Greaser friends, and Ponyboy doesn't see anything wrong with the way that he lives.

College Algebra, Chapter 8, Review Exercises, Section Review Exercises, Problem 34

Identify the type of curve which is represented by the equation$\displaystyle 32 x^2 + 6 x = 9y^2$
Find the foci and vertices(if any), and sketch the graph

$
\begin{equation}
\begin{aligned}
x^2 + 6x - 9y^2 &= 0 && \text{Subtract } 9y^2\\
\\
x^2 + 6x + 9 - 9y^2 &= 9 && \text{Complete the square: Add } \left( \frac{6}{2} \right)^2 = 9\\
\\
(x + 3)^2 - 9y^2 &= 9 && \text{Perfect Square}\\
\\
\frac{(x+3)^2}{9} - y^2 &= 1 && \text{Divide by 9}
\end{aligned}
\end{equation}
$

The equation is hyperbola that has the form $\displaystyle \frac{(x-h)^2}{a^2} - \frac{(y - k)^2}{b^2} = 1$ with center at $(h,k)$ and horizontal transverse axis
because the denominator of the $x^2$ is positive. Thus gives $a^2 = 9$ and $b^2 = 1$, so $a = 3, b =1 $ and $c = \sqrt{a^2 + b^2} = \sqrt{9+1} = \sqrt{10}$. The
graph of the shifted ellipse is obtained by shifting the graph of $\displaystyle \frac{x^2}{9} - y^2 = 1$ three units to the left. Thus by applying transformation

$
\begin{equation}
\begin{aligned}
\text{center } & (h,k) && \rightarrow && (-3,0)\\
\\
\text{vertices} & (a,0)&& \rightarrow && (3,0) && \rightarrow && (3-3,0) && = && (0,0)\\
\\
& (-a,0)&& \rightarrow && (-3,0) && \rightarrow && (-3-3,0) && = && (-6,0)\\
\\
\text{foci } & (c,0)&& \rightarrow && (\sqrt{10},0) && \rightarrow && (\sqrt{10}-3,0) && = && (-3+\sqrt{10},6)\\
\\
& (-c,0)&& \rightarrow && (-\sqrt{10},0) && \rightarrow && (-\sqrt{10}-3,0) && = && (-3-\sqrt{10},0)
\end{aligned}
\end{equation}
$

Therefore, the graph is