Who said "I really like that thing you do, Funny Guy, when you pretended to kick a football and then you go flyin' up in the air..." in the book Tangerine?

In Edward Bloor's novel Tangerine, it is the character Tino who says "I really like that thing you do, Funny Guy, when you pretend to kick a football and then you go flyin' up in the air and then you land right on your ass." 
This quote is found on page 205 of the novel, in part three. Tino, Theresa and Henry D. have come over to complete a group science project with Paul, who is attending Tangerine Middle School after a sinkhole swallowed up much of his former school. Erik, Paul's older brother, and his friend Arthur, come home while the group is working. Paul braces for the worst, because Paul seems to be the only one in the novel who sees Erik's true colors. 
Erik and Arthur begin to taunt Paul's friends. He says: "Look at this. I think it's great that these farm-labor kids get to spend a day away from the fields." 
This is insulting to Tino, and Paul tries to tell him to ignore it. Tino is not about to ignore it, however, and makes the reply referred to in your question. Following Tino's words, Erik lashes out and punches Tino hard enough to knock him down. He lay on the grass for several minutes. Paul says about Erik's blinding rage: "Then, like a genie sucking back into a bottle, he regained control."
 

Does religion teach fear?

There are many hundreds or even thousands of religions in the world. Within each of those religions, there is tremendous variation not only in doctrine but in how people interpret and react to various doctrines. Therefore, it is not possible to generalize about "religion" in some overarching and uniform way. One can only talk about the teachings of specific religions.
Lucretius in De Rerum Natura argued that traditional Greek religion taught fear of the gods, and that Epicurus, a purely secular philosopher, drove out fear from people's minds in a way that was even more impressive than the deeds of Hercules in driving out fearful monsters from the land. 
Some forms of evangelical Christianity emphasize the importance of the "fear of God." On the other hand, many other religious traditions, including Buddhism and Bahá'í, would emphasize that their proponents strive towards a spiritual peace that cannot be found in purely secular belief systems. Some psychologists argue that religious and spiritual beliefs function as coping mechanisms, helping people through difficult situations such as illness, and thus may reduce fear in so far as people can put their trust in some form of divinity.

Calculus of a Single Variable, Chapter 7, 7.1, Section 7.1, Problem 71

y=x
y=4
x=0
The region bounded by the three equations 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=4. And its lower end touches the graph of y=x. Also, the bounded region starts from x=0 and ends at x = 4.
So, 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_0^4 (4 - x)dx
Evaluating it results to:
A = (4x - x^2/2) |_0^4
A = (4*4 - 4^2/2) - (4*0 - 0^2/2)
A = 8
Hence, the area of the region bounded by the three equations is 8 square units.
Then, draw a vertical line that divides the area of the enclosed region equally. Let the equation of this line be x=a. (See attached image.)
Since it divides the area equally, the area of the region at the left of the vertical line is equal to the area of the region at the right. And the area of each is 4 square units.
A_(_(l eft))= A_(_(r ight)) = A/2 = 8/2=4
Considering the region at the left of x=a, the integral needed to compute its area is:
A_(_(l eft)) = int _0^a (4-x)dx
Evaluating the integral, it results to:
A_(_(l eft)) = (4x - x^2/2) |_0^a
A_(_(l eft)) = (4*a - a^2/2) - (4*0 - 0^2/2)
A_(_(l eft)) = 4a-a^2/2
To determine the value of a, plug-in the area of the region at the left of the vertical line.
4=4a - a^2/2
Take note that to solve quadratic equation, one side should be zero.
a^2/2 - 4a + 4 = 0
To eliminate the fraction in the equation, multiply both sides by 2.
2*(a^2/2 - 4a + 4) = 0*2
a^2-8a+ 8a = 0
Applying quadratic formula, the values of a are:
a = (-(-8)+-sqrt((-8)^2-4*1*8))/(2*1)
a=(8+-sqrt32)/2
a=(8+-4sqrt2)/2
a=4+-2sqrt2
a_1=4-2sqrt2=1.1716
a_2=4+2sqrt2 = 6.8284
Between them, it is only a1=1.1716 that is within the interval of the bounded region.
Therefore, the equation of the vertical line that divides the area of the bounded region equally is x = 1.1716 .

What would be 3 or 4 good quotes that I could include in a paper on the topic of grace (last chapter) in the book "The Road Less Traveled" by Scott Peck? Can you also please explain the quotes?

In his introduction to this final section of the book, Peck sets out his key theses on the topic of grace: it is something which amazes us, and it is actually a "common phenomenon"—just one to which we pay little attention. Peck explains:

Something amazes us when it is not in the ordinary course of things, when it is not predictable by what we know of "natural law." What follows will demonstrate grace to be a common phenomenon and, to a certain extent, a predictable one. But the reality of grace will remain unexplainable within the conceptual framework of conventional science and "natural law" as we understand it.

This quotation summarizes how Peck approaches the idea of grace. He believes grace to be readily found among us but that this does not diminish its miraculous nature. He also identifies "conventional science" as being unable either to recognize or to admit the existence of grace, something which actually leads us to question the stability of those who are actually "amazingly healthy mentally." Peck goes on to point out that psychiatry, too, is an inexact science, yet those who expect psychiatry to explain everything still do not admit the existence of grace. Grace is, according to Peck, "a force, the mechanics of which we do not fully understand, that seems to operate routinely in most people to protect and to foster their mental health even under the most adverse conditions." When psychiatry and conventional science cannot assist or explain, grace intervenes.
Later, Peck questions the idea of humans being "accident resistant" and whether this too is evidence of grace. He asks,

Could it really be that the line in the song is true: "Tis grace hath brought me safe thus far"?

This is an important quotation because it forces the reader to confront his or her own prejudices about the balance of the universe and what maintains that balance. Peck allows that many mainstream scientists will describe this as a "manifestation of the survival instinct," but, Peck says this is not an explanation of the phenomenon. Naming this tendency in humans does not explicate why the instinct exists. Instincts of this kind, Peck emphasizes, are actually manifestations of this force we do not understand: grace.
Peck explains how the "scientific" person still chooses to interpret the machinations of grace in unscientific ways:

The reader may choose to assign the mystery of such incidents to "pure chance," an unexplainable "quirk" or a "twist of fate" and be satisfied thus to close the door on further exploration. If we are to examine such incidents further, however, our concept of an instinct to explain them is not terribly satisfactory. Does the inanimate machinery of a motor vehicle possess an instinct to collapse itself in just such a manner as to preserve the contours of the human body within? Or does the human being possess an instinct at the moment of impact to conform his contours to the pattern of the collapsing machinery? Such questions seem inherently absurd.

The "rational" explanation for whatever it is that protects us from harm, Peck says here, is actually no more rational than the idea that a miraculous force, "grace," is at work.
Drawing upon his psychiatric experience, Peck focuses in this chapter upon the truth of the unconscious, that unexplained part of ourselves that can be said to constitute our true self. Peck says:

We are always either less or more competent than we believe ourselves to be. The unconscious, however, knows who we really are. A major and essential task in the process of one's spiritual development is the continuous work of bringing one's conscious self-concept into progressively greater congruence with reality.

According to Peck, when a person actually achieves this synchronicity between their belief of themselves and the truth of themselves, they experience a sense of having been, as in the song "Amazing Grace," blind while now finally being able to see. This feels like a miracle. But, in fact, it is simply that most of us go through life with a discord between the truth of ourselves and the way we perceive ourselves to be. According to Peck's philosophy, the "grace" achieved through bringing these two selves together is both miraculous and also completely ordinary. Peck believes that we are all capable of achieving this miracle and that science is capable of, to an extent, understanding it. However, this does not diminish the impact it has on our lives or the extent to which it feels like something divine and incredible.

Why do Camera and Smilin call Granny "aunty"?

In "Blues Ain't No Mockin Bird," two men are on Granny's property "makin movie pictures." They are referred to by the narrator as Smilin and Camera based on what they are doing. When Granny comes out to the porch, one of the men approaches her and begins to tell her what they are doing. However, Granny interrupts the man by saying, "Good morning." The man seems to realize he is being rebuked by Granny for his lack of manners because he hangs his head before responding to her. He then says, "Nice place you got here, aunty." He refers to her as "aunty" again when she makes it clear that she does not want him on her property taking pictures. The man calls her "aunty" in an attempt to be familiar and easygoing. However, he shows his ignorance and lack of respect when he thinks that by calling her "aunty" she will allow him to continue. Granny lets him know that she is not related to his mother. "Aunty" is often a derogatory and disrespectful term used to refer to black females.

When did the English settlers arrive in Jamestown?

The English settlers arrived on the west bank of the James River in Virginia on May 14th, 1607. The approximately 100 settlers were members of a joint venture called The Virginia Company and named their new settlement "Jamestown" after King James I. Although the Spanish already had colonies in North and South America, Jamestown was the first permanent English settlement and marked the beginning of England’s expansion throughout North America. The colonists arrived in three ships: the Susan Constant, Godspeed, and Discovery. A council was set up after the colony's founding and included Captain John Smith and Edward Wingfield, who was chosen by the council to be its first president.
Shortly after the settlers’ arrival, the colony was attacked by the Powhatan Indians (also known as Virginia Algonquians). However, the colonists were well armed and were able to repel the raiders. This event, happening so soon after the colony’s founding, has led some historians to conclude that this may have set the tone for the lasting distrust between Europeans and Indians in North America.
Over the next two years the colony’s population was depleted through illness, starvation, and continued strife with the Powhatans. However, The Virginia Company was determined to make the colony succeed and regularly sent out new colonists and provisions to keep it running. The colony was nearly wiped out several times due to starvation and warfare but finally managed to maintain a firm footing after several military campaigns against the Powhatans. By 1646, the expanding colony had pacified local tribes and became the stepping stone for the eventual colonization of eastern North America.

Who holds Prufrock's coat and snickers?

T. S. Eliot’s famous dramatic monologue, The Lovesong of J. Alfred Prufrock, utilizes a number of central images, allusions and metaphors to develop the idea that modern life is riddled with anxieties, and that sometimes, these anxieties result in isolation and paralysis.
After taking the reader on an intimate journey where he shares his insecurities, the speaker, Prufrock, has accepted his passivity at last and has stopped worrying about when and how to take action. Earlier in the poem, he asked, “Do I dare disturb the universe?” (45-46). Towards the end of the monologue, the speaker has, in effect, decided that he does not dare. He says quite emphatically that he has “seen the moment of [his] greatness flicker” (84). Here it becomes clear that the time to act has passed, and that it is too late to do anything about it. After looking back at the passage of time, he looks forward and says, “And I have seen the eternal Footman hold my coat, and snicker,/And in short, I was afraid” (85-86). The eternal Footman who holds his coat seems to be death itself, almost taunting him with a “snicker.” This personification of death suggests that it has been his companion throughout life, holding his coat as if to serve him, when in reality it mocks him. Prufrock had spent the majority of the poem convincing himself that there would be time to act, and that it was not a problem that he hadn’t done so already. He comes to understand that the moment to act has passed, and that in reality death had been his companion all along. This realization makes the already vulnerable Prufrock much more so, as he admits, “I was afraid” (86).

The specific heat of ice is 0.492 cal/(g × °C). How many calories of heat are required to raise 100.0 g of ice from -20.0 °C to -0.5 °C?

Hello!
The specific heat is, by the definition, the quantity of heat that is required to raise the temperature of a mass unit of a substance by one degree. One may use any units of heat (energy), mass and temperature, but the numerical value of the specific heat will depend on this choice.
The specific heat is a characteristics of a substance itself, it does not depend on the mass of a body and the change of the temperature. But it is important that the state of aggregation remains the same.
In our case, the given temperatures are inside the interval where ice remains solid. Therefore the amount of heat is  C*m*Delta t = 0.492*100*(-0.5-(-20)) approx 959.4 (calories). This is the answer. Note that the all data are given in the suitable units (degrees, grams, calories).
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/spht.html

Is the multi-party system a threat to democracy?

On the contrary, multi-party systems are if anything more democratic. Given the large number of people in a nation-state and the wide array of political issues people care about, from tax rates to women's rights to declarations of war, it would be wildly improbable for everyone's political views to be consistently aligned with one of only two parties. By having many parties, a democratic state can more accurately reflect the will of its diverse population.For example, suppose there are three types of voters, A, B, and C, each comprising a third of the population, and they care about two issues: What flavor of ice cream to buy, and how wide the roads should be. (I'm choosing silly issues intentionally to avoid any preconceptions.)A voters want chocolate ice cream and wide roads.B voters want vanilla ice cream and wide roads.C voters want vanilla ice cream and narrow roads.Suppose everyone's preference for ice cream flavor is stronger than their preference for road width. Notice that most people want wide roads, and most people want vanilla ice cream.Now suppose there are only two parties: Chocolatists support chocolate ice cream and wide roads, while Vanillists support vanilla ice cream and narrow roads.Because everyone prioritizes ice cream flavor, A voters vote Chocolatist. B voters vote Vanillist. C voters will also vote Vanillist. Vanillists will win and we'll have vanilla ice cream and narrow roads, even though most people wanted wide roads.But now if a third party came into play, the Wideroadists who support wide roads and vanilla ice cream, now A voters would still vote Chocolatist, but B voters would vote Wideroadist, and C voters would still vote Vanillist. If this is a legislature with voting coalitions, then we'd have wide roads (a Wideroadist-Chocolatist coalition) and vanilla ice cream (a Vanillist-Wideroadist coalition); this would best reflect popular will.There are a few advantages to two-party systems: they are simple for voters to understand, and if public opinion is largely polarized they can protect the majority against the minority in certain cases. It's rare for extreme views to become represented in two-party states, but it's about as rare for extreme views to actually result in legislation in multi-party states. In general these are outweighed by the advantages of multi-party states: Better expression of the public will, more opportunities for compromise, fewer opportunities to game the system with strategic voting or campaigning, and typically greater engagement and turnout among voters, who feel their opinions are really being represented. As a result, a two-party system is really not so much a desirable system to try to achieve, as it is the all-but-inevitable outcome of a winner-takes-all plurality vote. There's also not much incentive for politicians who win in a two-party system to try to change to a multi-party system, whereas there can be incentives for politicians who win some seats in a multi-party system to try to make a two-party system to win even more seats.
https://study.com/academy/lesson/two-party-multi-party-systems-similarities-differences.html

https://testfunda.com/Error.aspx

Single Variable Calculus, Chapter 7, 7.1, Section 7.1, Problem 2

a.) How is the inverse function $f^{-1}$ defined if $f$ is a one-to-one function with domain $A$ and range $B$? What is the domain of $f^{-1}$? What is the range of $f^{-1}$?
b.) If you are given a formula for $f$, how do you find a formula for $f^{-1}$?
c.) If you are given the graph of $f$, how do you find the graph of $f^{-1}$?

a.) If $f$ is a function with domain $A$ and range $B$, then $f^{-1}$ has domain $B$ and range $A$. Thus, $f^{-1}$ is defined as $f^{-1} (y) = x$ or $f(x) = y$
b.) If we have an equation $y = f(x)$, we solve the equation for $x$ in terms of $y$ first, then replace $x$ and $y$. Thus we get the inverse function $f^{-1}(x)$.
c.) Suppose that the graph of $f$ is given, the graph of $f^{-1}$ can be obtained by reflecting the graph of $f$ about the line $y = x$

What are some places important to the story in The Absolutely True Diary of a Part-Time Indian by Sherman Alexie?

There are three major places of importance in the novel The Absolutely True Diary of a Part-Time Indian by Sherman Alexie. The first place that is important to understanding the story is the Rez, or the Indian reservation where the protagonist Junior and many of the main characters live. This is a place which is essential to the story, because it symbolizes the struggle of Junior's tribe but also of Native Americans in general, as they work to find a place to fit in in a country which has attempted to cast them aside to make it easier to ignore them. Junior, the main character, is very aware of this fact, and thus views the Rez as both a blessing and a curse. He sees it as a place which prevents him from finding a better life and a better opportunity for happiness. In Chapter 2, on page 13, Arnold says, "But we reservation Indians don't get to realize our dreams. We don't get those chances. Or choices. We're just poor. That's all we are."
However, he also sees the Rez as a place where he finds a lot of support and unconditional love, which are necessary ingredients for living a full life and growing into a well-rounded person capable of dealing with adversity. There, he sees a lot of bad things; he witnesses racism, violence, death, self-destruction, and the consequences of living in extreme poverty. He also sees people come together in beautiful and moving ways as a community, and this is something that Alexie wants us as the readers to take into account. To see both sides of the Rez is to understand the duality of the experience of being Native American in a country which can be cruel and unforgiving. 
The second important place is Junior's school on the Spokane Indian Reservation. This school is important because it is where Junior has two of the most profound experiences of his young life. The first is when he attempts to be positive about his studies and open his extremely old textbook, only to discover that it was the same textbook that his mother used when she was his age. Rather than be happy about this, Junior realizes the implications of being forced to use such an outdated textbook. He realizes that he is not getting the best education possible on the reservation and he feels very bitter about that. In Chapter 4, he says "My school and my tribe are so poor and sad that we have to study from the same dang books our parents studied from. That is absolutely the saddest thing in the world."
In a fit of anger, he chucks the book at his teacher, Mr. P, and breaks his nose. This is the second important thing which happens to him and influences his actions for the rest of the book. Because of the talk which occurs between himself and Mr. P about leaving the reservation and the opportunities that would be available to him if he did, he decides to attend Reardan High School, a white school which is located outside of the reservation: "Son," Mr. P said. "You're going to find more and more hope the farther and farther you walk away from this sad, sad, sad reservation" (43). 
Reardan is the third important place that Junior visits. This place is important to our understanding of the story because it is a place in which Junior learns to both appreciate the Rez and to realize how his own assumptions about the world were serving to hold him back more than just the assumptions of others about him. It is also a place where he feels "too Indian," just as the Rez is now a place where he feels too "white": "Traveling between Reardan and Wellpinit, between the little white town and the reservation, I always felt like a stranger. I was half Indian in one place and half white in the other" (143). 

How did Washington get the judicial branch in order?

George Washington signed into law the Judiciary Act of 1789, a landmark piece of legislation in American history that established the federal judiciary, most notably the Supreme Court, and the position of Attorney General. The Act was an expression of the Federalist desire to have a strong, centralized system of government, capable of meeting the challenges faced by the new nation. Opponents of Washington's judicial reforms believed that ultimate sovereignty should reside with the states and their legislatures and courts. A system of federal courts was something which they regarded as a possible instrument of tyranny.
The Act certainly gave Washington a great deal of power that could potentially have been dangerous in the wrong hands. But Washington took his duty as President seriously and his overriding concern was with making the law work more effectively rather than undermining it. In any case, as the federal judicial system was being created from scratch, there was no alternative but for Washington to be the one to make the requisite nominations as to who should sit on the Federal bench. But, although Washington could nominate his own candidates, they still needed to be approved by Congress, and this provision remains in place today.

How is Fanny presented as unlikeable in Mansfield Park?

Unlike many of Jane Austen's heroines, Fanny Price isn't feisty, assertive, or especially striking in her personality. She's one of life's outsiders, hanging around the periphery of Mansfield Park and its world, both literally and metaphorically. Fanny has no time whatsoever for the tedious conventions of the Regency marriage market and the arch displays of coquettish flirtatiousness it encourages in young women. This is one game she simply refuses to play.
Whether any of this makes her an unlikable character is entirely a matter of opinion. Certainly, one could well imagine ladies of her milieu being against Fanny on account of her ever so superior airs and ostentatious displays of virtue. Successive generations of literary critics have been even more scathing, railing against what they perceive to be Fanny's insufferable self-righteousness.
But the class-obsessed Jane Austen is at pains to suggest that Fanny's personality is very much a product of her social class. Let's not forget that Fanny is the poor relation to her wealthier, more socially prominent cousins. Fanny herself certainly isn't allowed to forget this, reminded by her rich aunt right from the outset that she is socially inferior:

I should wish to see them very good friends, and would, on no account, authorise in my girls the smallest degree of arrogance towards their relation; but still they cannot be equals. Their rank, fortune, rights, and expectations will always be different. It is a point of great delicacy, and you must assist us in our endeavours to choose exactly the right line of conduct.

Jane Austen's overriding message appears to be this—if Fanny really is unlikable, then it's because her social class is unlikable. Her faults are the faults of her class, in much the same way as her taste for virtue is also a product of her background. Whether we find Fanny likable or not, there's no doubt that her outsider status, with its associated value system, allows her to cast a mordant eye on the often ludicrous conventions and manifest hypocrisies of upper-class life in Regency England.

Who is T.J.’s houseguest?

T.J.'s houseguest is five-year-old Heidi Marshall.
In chapter 9, Georgia (T.J.'s therapist) tells T.J. that he is going to have a houseguest. 
Georgia mentions that Heidi will be staying with T.J.'s family because Heidi's mother, Alicia, made a mistake. Alicia left Heidi and her brothers with Alicia's abusive boyfriend, Rich Marshall, for an entire afternoon. Because of Alicia's actions, the Child Protective Services agency had to put a plan into motion to protect the children. Since the family taking in Heidi's brothers cannot take Heidi in as well, Heidi will be placed with T.J.'s family.
Georgia tells T.J. that she thinks he will be a good influence on Heidi. For his part, T.J. promises to look out for Heidi. Later in the chapter, Rich knocks on the door of T.J.'s home, asking for Alicia. Rich is drunk, and he begins to accuse T.J. of sleeping with Alicia.
During the conversation Rich reaches for his gun, but T.J. manages to wrest the gun out of Rich's possession. A little later, T.J.'s father comes charging out with a baseball bat, prompting Rich to leave. 
So, T.J.'s houseguest, Heidi Marshall, is staying with T.J.'s family for her own protection.

What are the literary techniques found in "The New Colossus"?

"The New Colossus" is what's called a Petrarchan sonnet consisting of fourteen lines with a rhyme scheme of abbaabba in the octet, and cdcdcd in the sestet. In keeping with sonnets of this type, there is a volta, or turn, between octet and sestet. This represents the moment at which there is a slight change in the prevailing thought or argument, leading ultimately to a resolution of the poem's "problem." In the sestet Lazarus contrasts the statue and the hopeful message it proclaims with the monstrous expression of power represented by the Colossus of Rhodes in the first two lines. This new colossus is not like the colossus of old, just as the New World is far removed from the ancient.
Lazarus uses alliteration and assonance to emphasize important lines in the poem. They're particularly useful techniques because they draw attention to themselves, causing us to focus on what's being said. For example:

"sea-washed, sunset gates shall stand . . ." 

Here, the 's' sounds show alliteration; the 'a' sounds assonance.
We are left in no doubt as to the idealized portrayal of the Statue of Liberty being given here. Here are some more examples:

"Glows world-wide welcome;"

Alliteration is used here to draw our attention to the bright shining image of Liberty and the welcome it represents to new immigrants.
The poem is written in iambic pentameter, which gives it a slow, stately rhythm, in keeping with its high moral tone. The combination of this poetic meter with a profusion of vowel sounds in lines 11 and 12 conveys a wave-like motion, like the waves that will bring immigrants to America's shores:

"Your huddled masses yearning to breathe free,The wretched refuse of your teeming shore."

 
 
 
https://interestingliterature.com/2016/08/a-short-analysis-of-emma-lazarus-the-new-colossus/

Why and how does cultural relativism mitigate ethnocentrism? Is cultural relativism desirable?

"Cultural relativism" can mean several different things, and much of the debate over its desirability can be traced to this ambiguity. Descriptive cultural relativism is basically undeniable: Cultures do, in fact, differ in their social and moral norms. But normative culture relativism is not as obviously true: It isn't clear how, if at all, our treatment of people in different cultures should vary based on their culture's norms. So the normative sense of cultural relativism that says we ought to judge other people by the standards of their own culture could be right, but isn't necessarily. There is also methodological cultural relativism, which is a method that many sociologists and anthropologists use to sort of temporarily suspend judgment about other cultures until they get all the facts in. This is probably a good thing, but it's a very weak sense of relativism; in the end they still go home and publish in Western academic journals according to Western cultural norms. It doesn't even require any particular relativism: You can just have the norm in your own culture that you don't judge other cultures until all the facts are in. "Ethnocentrism" can also be an ambiguous word. It normally means something quite negative---the tendency to view people of your own culture as inherently superior and people of other cultures as inherently inferior. It frequently results in hatred and even violence. But sociologists also use "ethnocentrism" in a sort of technical sense, to mean simply that we judge people of other cultures by the standards of our own culture. This latter is not obviously wrong---one culture's ideas can in fact be more correct than another's, and it may turn out that we happen to live in the culture that has the best ideas.I think a key point to keep in mind here is that it matters why you are using the moral standards you are. Is it simply because you grew up with them, and never questioned them? That is probably ethnocentrism. But have you actually analyzed those norms, challenged them, confronted them with evidence, and yet they still held up? Then what you are doing is definitely not the negative kind of ethnocentrism, though it may be "ethnocentrism" in this broader more technical sense.Indeed, it's not clear that the strongest form of normative cultural relativism is even coherent. Most cultures are not cultural relativists; that is, most people in most cultures do not think that one should judge others only by the standards of the others' own culture. They think that their standards are the objectively correct ones that everyone should use. So in order to be a cultural relativist, you need to judge people only by their own culture, but the only culture that actually tells you to do that is your own culture, namely the subculture of Western academic sociologists. So you are in the end still judging based on your own culture, and you are still faced with the question of why your culture's norms are better than anyone else's. Or in fact you could justify being an imperialist, because Western culture has a historical tradition of imperialism and you could simply be acting according to the norms of your own culture---so how can anyone judge you as wrong?Yet I understand where normative cultural relativism comes from; it is an attempt to respond to, and in some sense atone for, the extreme violence and destruction created by colonialism and imperialism. One of the things that our imperialist forebears did was judge other people based on their own culture, so if we don't do that, maybe we won't be imperialists! But that doesn't actually follow. That wasn't what made them imperialists, and indeed getting rid of it doesn't necessarily stop us from being imperialists.A much better approach in my opinion is the concept of universal human rights. By a gathering of global consensus (or something close to consensus), we have established global human rights principles such as those set down in the UN Charter. These are rights that everyone agrees everyone should have. Furthermore, these rights are precisely the sort of rights that explain what is wrong with colonialism and imperialism. What made our forebears imperialists was not that they judged according to their own culture, but that they violated (what we now recognize as) universal human rights. Yet ironically many cultural relativists actually oppose universal human rights, arguing that they are somehow imposing Western values on everyone else---something that I think many of the people from non-Western cultures who helped design and ratify the UN Charter may find baffling.
https://courses.lumenlearning.com/boundless-sociology/chapter/culture-and-society/

https://www.anthropology.udel.edu/

What is an example of Uniform Commercial Code (UCC) Section 2-207? What does it mean and how could it help merchants in their business dealings with other merchants?

Contract Law is a notoriously complicated field of study involving more imponderables than one can imagine. Having drafted legislation that eventually became law, and having interpreted numerous statutes and seen those same statues interpreted differently by others, I can categorically state that contracts are a hopelessly murky subject. The Uniform Commercial Code was established precisely because contracts and contract law is so complicated. The fact that it differs from state to state despite being a part of federal law lends the topic even greater fluidity. 
Section 2-207 of the Uniform Commercial Code, titled "Additional Terms in Acceptance or Confirmation," is an attempt at reconciling the unreconcilable: when is a contract not a contract, or, conversely, when do competing offers and counter-offers constitute a contract? Below is the full text of Section 2-207:

(1) A definite and seasonable expression of acceptance or a written confirmation which is sent within a reasonable time operates as an acceptance even though it states terms additional to or different from those offered or agreed upon, unless acceptance is expressly made conditional on assent to the additional or different terms.
(2) The additional terms are to be construed as proposals for addition to the contract. Between merchantssuch terms become part of the contract unless:

(a) the offer expressly limits acceptance to the terms of the offer;
(b) they materially alter it; or
(c) notification of objection to them has already been given or is given within a reasonable time after notice of them is received.

(3) Conduct by both parties which recognizes the existence of a contract is sufficient to establish a contract for sale although the writings of the parties do not otherwise establish a contract. In such case the terms of the particular contract consist of those terms on which the writings of the parties agree, together with any supplementary terms incorporated under any other provisions of this Act.

Reading this text, one can easily discern the problem, and the reason the Marx Brothers were so successful at satirizing the process of negotiating contracts in their film A Night at the Opera. The process of issuing offers and counter-offers and counter-counter-offers and so on invariably leads to disputes between the parties regarding what precisely the parties agreed to. Suffice it to say the so-called "last shot" rule, in which the final offer immediately preceding the shipment of the goods in question or the issuance of payment for those goods, was supposed to be supplanted by Section 2-207. 
Despite all of the above, for academic or illustrative purposes, conceptualization of a scenario to which Section 2-207 can be applied is not all that difficult. Simply come up with a product for sale by one party and an agreement by another party to purchase that product. The product or good can be anything: a car, furniture, food, or any other item. The transfer from one party to another will occur upon receipt of payment or agreement to pay. The application of Section 2-207 would come into play as soon as one party approaches the other with an offer and the other party responds with additions or variations of language not included in the original offer. Cars make the easiest example because there are so many variations of the same model of car, for example, color, engine size, type of transmission, type and quality of sound system, safety features not standard per government regulations, and so on. It is precisely because of the vast range of options for one model of vehicle that the car business is so daunting for so many people. The Toyota Highlander comes in 4- and 6-cylinder models, with or without a sunroof and with or without running boards, etc. The buyer needs to know precisely what the exact model being negotiated involves, and the precise terms being offered by the seller. And, of particular significance, both parties need to understand and agree to the specifics of the financial transaction. Because businesses purchase automobiles for commercial use, this example qualifies under the merchant-to-merchant parameters of the question.
Staying with the car example, suppose the seller forwards a written proposal with specific terms and conditions. Then, suppose the buyer reviews that proposal, makes deletions and/or additions as he or she deems fit, and sends that counter-offer back to the seller. Right off the bat, we've entered the murky world of contracts. The Uniform Commercial Code exists to ensure that both parties are on the same page, to employ an apt metaphor. The parties in our example, however, are not on the same page. There is a marked difference in their respective proposals to each other. Section 2-207 is intended to address the buyer's counter-offer: Hence, the term "additional terms in acceptance or confirmation." The point of Section 2-207, however, is that it nullifies the concept of a "counter-offer," replacing it with the formalization of an agreement between the two parties that states that the buyer has, in fact, agreed to purchase the vehicle in question, new language added by the buyer notwithstanding. It is important to note the use of the phrase "additional terms." The buyer's "counter-offer," which isn't, under the UCC, a "counter-offer," includes new language that does not necessarily negate or contradict the preexisting language; it simply adds to it. 
The mere existence of an agreement to transfer money or goods in exchange for goods from a seller constitutes a contract. The devil, as always, is in the details, and the UCC does less to clarify or rectify weaknesses in contract law than was intended. There remain definitional issues and the underlying problem is not solved. And that is why lawyers can charge hundreds of dollars per hour to work on contracts.

How environmental factors affect gene expression

Environmental factors can cause changes in the frequency of a particular gene expression within a population or species of organism. For example, if a habitat is fairly light in color, then organisms that are light in color tend to blend in better. This allows them to hide from predators and/or be better camouflaged predators themselves.
If that environment were to drastically change, that species might struggle to survive. For example, if a fire blackened all of the trees in an area, a lightly colored organism would no longer blend well with the environment. Any random genetic changes that occurred that allowed for a darker coloring would likely make that darker individual more fit for that environment. That organism would likely live to pass on its unique adaptation, and after a while, the entire species would be darker than it was before. The gene expression that wasn't advantageous before would now be commonly displayed as a result of an environmental change. This is exactly what happened with the Peppered Moth in the latter half of the 19th century.
http://www.mothscount.org/text/63/peppered_moth_and_natural_selection.html

A solid is generated by revolving the region bounded by y = x^2/2 and y = 2 about the y-axis. A hole, centered along the axis of revolution, is drilled through this solid so that one fourth of the volume is removed. Find the diameter of the hole.

Given ,
y=(x^2)/2 and y=2
A solid is generated by revolving the region bounded by these curves about y-axis.
So ,let us find the volume of the solid generated. It is as follows:
Using the shell method we can find the volume of the solid
V= 2*pi int_a^b p(x)h(x)dx
but we have to find the range of x
so ,
let us find the intersection points
=>
2= x^2/2
=> x^2=4
=>x^2-4=0
so,x=+-2 ,
as only the ranges is between 0 to a positive number,
So, 0<=x<=2
So, volume
= 2*pi int_0^2 (x)(2-(x^2/2))dx
=2*pi int_0^2(2x-(x^3)/2)dx
=2*pi [2x^2/2 -x^4/8]_0^2
=2*pi[[4-2]-[0]]
=4pi
Now given that a hole, centered along the axis of revolution, is drilled through this solid so that one fourth of the volume
so the volume of the hole = 1/4* 4pi = pi
now we have to find the diameter .
as we know that the radius of the hole can be calculated by getting the range of the x with respect to the hole .
now we can find the volume of the hole
it is given as
V= 2*pi int_a^b p(x)h(x) dx
but V_hole = pi
 
=> pi = 2*pi int_a^b p(x)h(x) dx
let a =0 and b = x_0  so we have to find the radiusx_0  and then the diameter.
=>pi = 2*pi int_0^(x_0) (x)(2-x^2/2) dx
=>pi= 2*pi int_0^(x_0) (2x-x^3/2) dx
=>pi = 2*pi [2x^2/2 - x^4/8]_0^(x_0)
=> 1=2[(x_0)^2 - (x_0)^4/8]
=> 1 = 2(x_0)^2 -(x_0)^4/4
let u= (x_0)^2
=>1=2u - u^2/4
=>4= 8u - u^2
=> u^2-8u +4=0
so u = (-(-8)+-sqrt(64-16))/2
       =(8+-sqrt(48))/2
      = (8+-4sqrt(3))/2
      = 2(2+-sqrt(3))
      = 4+-2sqrt(3)
so, u= (x_0)^2
x_0=sqrt(4+-2sqrt(3) )
as x_0<2 if it is beyond the hole is not possibe in the solid
so ,
x_0=sqrt(4-2sqrt(3) ) =0.7320 is the radius of the hole
now the diameter of the hole is 2*(x_0) = 2*(sqrt(4-2sqrt(3) ))=1.464

How does the telling of traumatic experiences through stories act as a method of healing and redemption for individuals who struggle to cope with the past in The Things They Carried?

Tim O'Brien's The Things They Carried is a fictionalized account of the experiences of a group of soldiers during the Vietnam War. The collection of stories bluntly depicts the brutality of war and the struggle soldiers face while serving and after returning from battle.
One story that deals explicitly with storytelling and trauma is "Speaking of Courage." In this story, Norman Bowker has survived Vietnam and returned home, but he feels he is responsible for the death of his friend Kiowa. Bowker spends his days driving around a circular body of water in his hometown. While driving, he imagines himself having conversations with people he feels he cannot yet talk to about his experiences. For example, he wants to tell his father about what happened to Kiowa. However, Bowker struggles to talk to anyone. The story's narrator tells us what Bowker is thinking, but he is never able to share it with other characters. This story suggests how difficult it is for soldiers to make sense of and work through their traumatic war experiences.
"How to Tell a True War Story" is another tale in the collection that deals explicitly with storytelling. In this story, the narrator claims it is impossible to tell a "true" tale of war, because its horrors and nuances cannot be conveyed to someone who has not experienced it directly. Ironically, the story could be interpreted to stand as evidence to the contrary.
According to theories about traumatic experience, survivors need to express their stories to a supportive listener; the telling also allows them to organize and understand their own experiences. O'Brien's The Things They Carried illustrates how difficult that task can be.

The Things They Carried is an account of the character Tim O'Brien's experiences as a solider during the Vietnam War. The account blurs fact and fiction as the author (a veteran) attempts to recall and honor the experience of war through a series of stories. The answer to this question lies in the title of the book: The Things They Carried, indicating that the items the men chose to take on their journey as well as those munitions and gear carried by all soldiers were ways for them to buffer, and even emotionally escape, the trauma they were enduring. The men carried sentimental mementos that one might expect men to carry on a life-threatening venture into a war zone (photos, notes from a girlfriend, pantyhose). But there were other things they carried that were more practical ...insect repellent, cigarettes, chewing gum, pocket knives and extra rations. In addition to the physical items, each man also carries his own emotional baggage throughout his journey. The things they carried are things that provide a framework of meaning and logic to the most chaotic and unpredictable of experiences during war. The human ability to ascribe meaning is what separates us from animals, it is how we interpret life (and death). Meaning is created in story and story becomes a mechanism for painful experiences to be given an arms length objectivity. In reframing these experience into stories to be shared collectively, they thereby help to understand, to forgive, and ultimately, to heal.

To what extent is the Treaty of Versailles fair?

The Versailles Treaty actually was not fair on any level.  Even though an armistice ending the war, Britain still maintained a naval blockade of Germany, thus starving the country.  Germany was faced with two options--sign the treaty and suffer for decades paying off reparations, or hold out for better terms, and risk further ruin to the nation.  Germany was forced to accept all of the blame for the war, even though German leaders initially encouraged Austria-Hungary to act with caution and only fully mobilized when Russia mobilized their troops.  Many of the atrocities that were attributed to German soldiers on the Western front later turned out to be part of an Allied propaganda ploy meant to get America into the war sooner.  While the U-boat was initially considered a war crime, Britain also flouted maritime law by flying the flags of neutral vessels and shipping weapons of war aboard passenger ships.  Not only was Germany forced to accept the blame for this war and to pay reparations, but the nation had to do it while weakened due to manpower and industrial shortages, thus making the expectations more unrealistic.  

In Hamlet, why is the ghost dressed in armor?

In the media studies class that I teach, I teach students that almost nothing in television and movies happens by accident. Viewers are seeing and hearing things exactly the way that the writer and director intend. What is said, how it is said, where an actor is and moves to, and what that actor wears is all carefully crafted to send viewers a specific message. Shakespeare plays are no different. He crafted lines of dialogue intentionally, and stage actions are intentional on his part as well. What each actor wears was also something that Shakespeare would have thought about. Public speaking classes always stress that audiences always remember far more than what was said. They remember how things were said and other non-verbal communication items. Shakespeare wants the ghost in armor because it sends audiences specific messages. Having the ghost in armor sends audiences the message that the ghost is ready for a fight of some kind. Dickens did the same thing with Jacob Marley. He's in chains to show audiences that his living actions wear heavily on him in the afterlife. The second reason that Shakespeare puts the ghost in armor is for quick identification purposes. I'm sure that you know people that always wear something specific, and you can identify them a long way off because of that article of clothing. Shakespeare is doing the same thing. The King's armor is going to be very identifiable because he's the king. He needs to be immediately recognizable so that his orders are never questioned. In Act 1, the armor's uniqueness is even commented on.

MARCELLUS: Is it not like the King?
ORATIO: As thou art to thyself.Such was the very armour he had onWhen he the ambitious Norway combated.

By putting the ghost in that armor, Shakespeare has left no room for doubt about who the ghost is.

The true reason for the ghost of Hamlet's dead father being dressed in armor is not entirely clear.
On the one hand, the armor does serve as an indicator that ghost is, without a doubt, the dead King Hamlet. As Horatio says, "Such was the very armor he had on / When he the ambitious Norway combated" (1.1.73-74).
This little detail, that the armor was what the King wore when he fought Norway, could have foreshadowing implications: At the end of Hamlet, it is Fortinbras, the bold Prince of Norway, who conquers Denmark. The detail of King Hamlet's armor, therefore, might be an indication that King Claudius has been working for Norway throughout the play. It would explain why Denmark was so ill-prepared for Fortinbras's incursion and give new political motivation for King Claudius's usurpation of the throne.

Though the armor worn by King Hamlet's ghost is a small detail, it actually serves an important role in the play. First of all, the armor worn by King Hamlet's ghost signifies that the ghost is on a mission dealing with martial conflict and war; since the ghost essentially wants Hamlet to combat injustice and wrestle the kingdom of Denmark out of Claudius' clutches, this martial theme makes sense. Secondly, the armor is actually important for the practical purpose of identifying the ghost as King Hamlet. For instance, take a look at this exchange between Marcellus and Horatio after they see the ghost in Act 1, Scene 1:

MARCELLUS: Is it not like the King?
ORATIO: As thou art to thyself.Such was the very armour he had onWhen he the ambitious Norway combated. (71-4)

From this exchange, we learn that the ghost is indeed the ghost of King Hamlet, as the apparition is wearing the former king's armor. By dressing his specter in armor, Shakespeare immediately tells the audience that King Hamlet has died and is haunting Elsinore. As such, the ghost in Hamlet wears armor not only to signify his warlike mission, but also to signify that he is the ghost of the former king. 

Single Variable Calculus, Chapter 3, 3.6, Section 3.6, Problem 45

Show that the family curve $x^2 + y^2 = r^2, ax + by = 0$ are orthogonal trajectories of each other, that is, every curve in one family is orthogonal to every curve in the other family. Sketch both families of curves on the same axes.

Taking the derivative of the function $x^2 + y^2 = r^2$ implicitly we have

$\displaystyle 2x + 2y \frac{dy}{dx} = 0$

$\displaystyle \frac{dy}{dx} = \frac{-x}{y}$

So the slope of the tangent line to this curve at point $x_1, y_1$ is

$\displaystyle \frac{dy}{dx} = \frac{-x_1}{y_1}$

Similarly, on the other curve $ax + by = 0$


$
\begin{equation}
\begin{aligned}

a + b \frac{dy}{dx} =& 0
\\
\\
\frac{dy}{dx} =& \frac{-a}{b}


\end{aligned}
\end{equation}
$



But we know from the given equation $ax_1 + by_1 = 0$;

which is the slope of the second curve.. so

$\displaystyle \frac{dy}{dx} = \frac{-a}{b} = \frac{x_1}{y_1}$


We know that if the two curves are orthogonal to each other, their tangent lines are perpendicular at each point of intersection, that is, the product of their slopes is equal to $-1$. Multiplying the slopes we get..

$\displaystyle -\left( \frac{\cancel{x_1}}{\cancel{y_1}} \right) \left( \frac{\cancel{y_1}}{\cancel{x_1}} \right) = -1$


Therefore, the curve must be orthagonal.

int (x+2)/(x^2+5x) dx Use partial fractions to find the indefinite integral

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

Can you explain the phrase "American National Narrative"? Provide some examples based on American culture and ideology.

A national narrative as a concept constitutes a statement of how a nation-state collectively understands or idealizes all or part of its history. National narratives unite the people of a nation-state across space and time, giving an overarching sense of meaning and purpose to that nation's history. Most national narratives begin with an uncontested founding story.
While some scholars have questioned the existence of an American national narrative (see Peter Novick, "The American National Narrative of the Holocaust: There Isn't Any" New German Critique No. 90, Taboo, Trauma, Holocaust [Autumn, 2003], pp. 27-35), most work on the American national narrative begins with the arrival of the Puritans to the Massachusetts Bay, a starting point that is an "explicitly Judeo-Christian story, built on a certain view of God’s providential plan." As David Brooks, Senior Fellow at Yale University's Jackson Institute for Global Affairs and political and cultural commentator, explains, "For most of the past 400 years" America's national narrative "was the Exodus story," beginning with "the Puritans [who] came to this continent and felt they were escaping the bondage of their Egypt and building a new Jerusalem."
America, however, does not have only one national narrative. As America has diversified, America's Puritan founding as a "City upon a Hill," ordained by Providence, has become increasingly contested. America's Manifest Destiny is a common alternative narrative that has helped explain American expansion and diversity. However, scholarship that has increasingly revealed the coercive nature of western expansion has also called this national narrative into question. Cultural and political commentators today bemoan the loss of an agreed-upon American national narrative and see its contested existence today as evidence of an increasingly heterogeneous and polarized American society.
https://www.nytimes.com/2017/05/26/opinion/the-four-american-narratives.html

Does an absolute monarchy have a big or small government?

To answer this question, it is useful to start with a definition. An absolute monarchy is a type of government in which all power lies with the monarch. The monarch might be a king or queen, but, whatever the case, there are no limits on his or her power.
Because the monarch has absolute power, he or she has no need for a large government. Remember that some of the primary functions of a government include making laws and creating policy. However, in an absolute monarchy, these functions are carried out by the monarch and only the monarch, meaning that a big government is not needed.
An absolute monarchy, therefore, functions as a one person show. He or she creates the laws, dictates the policy, and polices the state. It is for this reason that an absolute monarchy would only require the smallest of governments.

Which texts qualify as a "literary tragedy"?

A list of all tragedies in literature is a huge list. I will go ahead and list some of the more famous tragedies in order to keep the list more manageable.  
Shakespeare is a good place to start: 
Antony and Cleopatra
Coriolanus
Hamlet 
Julius Caesar
King Lear
Macbeth
Othello
Romeo and Juliet
Timon of Athens
Titus Andronicus 
Christopher Marlowe is a contemporary of Shakespeare and has a couple of famous tragedies to his name, including:  
The Tragical History of Doctor Faustus
Tamburlaine the Great
John Webster is another good choice for an author of tragedies. He wrote
The Duchess of Malfi
The White Devil
More modern literature has plenty of titles available as well:

The Boy in the Striped Pajamas by John Boyne

The Crucible by Arthur Miller

Death of a Salesman by Arthur Miller
https://www.goodreads.com/shelf/show/tragedy

What are the poet's first thoughts when he sees the solitary reaper in William Wordsworth's "The Solitary Reaper"?

The speaker's first thought, when he observes the solitary reaper—a young maiden who is cutting and binding the grain in the field while she sings a song to herself—is that her song is a "melancholy strain" (line 6). Though he cannot understand the language in which she sings, he identifies the sadness of the tune. He goes on to claim that no song sung by nightingales has ever felt so welcome to weary travelers, who only wish to stop for the night, as this young woman's song was to him; moreover, no notes from a cuckoo have ever been so welcome to sailors on the lookout for land as this woman's song was to him. Her song and voice, then, must be quite beautiful.

Wordsworth's thought process has two main phases in his poem "The Solitary Reaper." His first thoughts tend to be upbeat, as he initially imagines the song "Among Arabian sands" (12) and "Breaking the silence of the seas / Among the farthest Hebrides" (15-16). In short, Wordsworth's first thoughts are that the reaper's song has a freeing power, as the musicality of the young woman's singing initially inspires his imagination to explore distant and exciting locations. This first exciting thought is then tempered by one that is more wary, as Wordsworth imagines the song refers to "unhappy, far-off things" (19), and the poet appears to at least partially take back his initial assessment. With this difference between Wordsworth's first and second thoughts in mind, an interesting duality emerges in the solitary reaper's song, as it appears to be simultaneously exciting, awe-inspiring, and melancholy. That said, the lively imagination that was inspired in Wordsworth's first thoughts runs throughout the poem, effectively fusing the two disparate modes of thought represented in the piece. 
https://www.poetryfoundation.org/poems/45554/the-solitary-reaper

I need a Claim, Evidence, Reasoning paragraph, using images of fossils from the Permian period, that answers the question: "What did prehistoric Oklahoma look like?"

Prehistoric Oklahoma is a term covering several billion years, from the origin of our planet through the sixteenth century. The oldest remaining geological layers are igneous and metamorphic rocks from the Precambrian and Cambrian period. The layers on top of these are the result of Oklahoma being alternately covered and uncovered by shallow seas. According to the Geologic History of Oklahoma, "Following Pennsylvanian mountain building, an Early Permian (Wolfcampian) shallow inland sea covered most of western Oklahoma and the Panhandle."
The Permian period extended from approximately 298.9 million to 252.2 million years ago. The Witchita and Ozark mountains would have been prominent features in the landscape, gradually eroding over the duration of the period. The areas bordering the seas would have included limestones, gray and red shales, and sandstones.
The "Red Beds" of Oklahoma have been a particularly fertile area for paleontologists, revealing samples of several tetrapods (vertebrates with four limbs) including the Dimetrodon, Edaphosaurus, Platyhystrix and Seymouria. Dimetrodons were particularly distinctive features of the landscape, having long tails and dramatic sails on their backs.
As the climate became drier over the course of the Permian period, the lush growth of ferns and horsetails was gradually replaced by seed plants. A display in the Sam Noble Museum includes an artist's reconstruction of a Permian landscape:
http://samnoblemuseum.ou.edu/common-fossils-of-oklahoma/paleocommunities/terrestrial-communities/permian/
http://www.ogs.ou.edu/pubsscanned/EP9_2-8geol.pdf

https://samnoblemuseum.ou.edu/common-fossils-of-oklahoma/gallery/permian-fossil-gallery/

Where in the Great Gatsby does it say, "rich girls don't marry poor boys"?

This quote does not appear in the novel, but it is said by Daisy in the 1974 film adaptation of the story. In the film, Daisy visits Jay Gatsby's home for the first time and has a conversation with Jay about why she decided to marry Tom Buchanan. When Jay asks Daisy why she did not wait until he returned from the war to marry him, she responds by saying, "Because rich girls don't marry poor boys Jay Gatsby." While this quote does not appear in the novel, it emphasizes why Jay Gatsby entered the bootlegging business to attain immense wealth. Gatsby is well aware of the fact that Daisy comes from money, and he has no chance of marrying her because of his lower social status. In order to win Daisy's heart, Gatsby hopes to achieve the American Dream in the hopes that his financial prosperity will be enough to persuade Daisy to leave Tom. Unfortunately, Tom exposes Gatsby as a bootlegger, which ruins Jay's chances of being with Daisy.

The quote “rich girls don’t marry poor boys” does not appear in the novel version of The Great Gatsby. This quote appears in at least one of the film versions and comes from a real-life event in F. Scott Fitzgerald’s life.
While this quote doesn’t appear in the novel, it highlights one of the major themes in the story: the carelessness of the rich. This theme is evident in the ending of the novel through the deaths of Jay, Myrtle, and George, which come at the hands of Daisy and Tom (albeit indirectly). It's also evident in how the younger Daisy allowed the poor Jay Gatsby to court her—Daisy’s decision to agree to marry Jay, but to only break his heart for a more suitable husband in Tom Buchanan. 
The line “rich girls don’t marry poor boys,” if uttered in the novel, would take some of the blame away from Daisy and serve as a warning to Gatsby. But she never mentions this, and, up to the day he dies, Gatsby fully believes that he would have Daisy all to himself one day.

Based on this video on Travelocity, think about what consumers want from online travel services providers. What are five criteria that you think are key to satisfying customers?

Travelocity's focus group information architecture usability analysis showed that what its customers want is an uncomplicated, unconfusing, simplified experience shopping for and purchasing travel packages. As a result, Travelocity modified their online purchasing program to be password-free for those who forget their passwords.
Travelocity's partnership with AARP opened a door for offline direct mail, a marketing avenue Travelocity wouldn't have engaged otherwise because their customers want online experiences, while AARP's want offline experiences. 
Travelocity developed a control group of customers that received no emails so other groups could be tested with variable kinds of emails. They found, because of the effectiveness of having a control group, that the email marketing campaigns producing the most incremental lift were the special-interest, targeted emails. Customers responded when emails were targeted to their reported areas of interest.
Travelocity found success combining marketing approaches with the customer's entertainment media mix. The Travelocity Gnome is a representation of this concept. The Gnome, like the Geico Gecko, personalizes Travelocity while combining a mood of entertainment with marketing exposure.
Travelocity's extremely successful innovation of a publicized Customer Bill of Rights promises that Travelocity stands behind every customer and guarantees every purchase down to the last detail. The Gnome heralds the Bill of Rights and makes it familiar to customers. 
The experiences of Travelocity suggest five criteria that are key to satisfying customers:
1. Remove barriers to success by providing streamlined alternative means of action.
2. Find the avenue of approach that is most functional for the customer segment.
3. Use research and self-reporting surveys to identify true areas of interest so as to bypass a carpeting approach in marketing.
4. Gear marketing to how the customer actually experiences exposure, such as through their media mix.
5. Make the brand personal and approachable, supported by an unflinching promise of excellence and an unwavering guarantee that their experience will be correct in every detail.
http://www.cengage.com/resource_uploads/downloads/0538745401_222757.html

"Getting guns off the streets" was an important part of the New York City Police Department's strategy for reducing violent crime. Why is it important today and why is it chosen?

New York City for many years was among the most violent cities in the country. The most populous city in the United States, it would not be surprising that it had a crime rate commensurate with the size of its population. Even beyond problems traditionally associated with large urban environments, especially those with economically and ethnically diverse demographics, New York was plagued by violent crime involving firearms. In the early 1990s, city officials decided to address the problem of gun proliferation through a multi pronged strategy. The rallying cry of "get the guns off our streets" sent a message to the city's vast population that the police would be empowered to go after illegal firearms while providing incentives to draw out even legally-owned firearms. 
One of the main components of the New York Police Department's strategy for reducing the number of guns on the city's streets was a buy-back program. Under this program, anybody could turn in a gun or guns, no questions asked, and be paid cash in exchange. This strategy successfully removed a large number of guns from the streets. It was not sufficient, however, to fully address the challenge. Mayors and Police Commissioner Bill Bratton also put into place a policy of targeting guns in the hands of gang members, the main category of criminal in New York responsible for a preponderance of gun violence. A special 200-member police unit was established with the mission of focusing on removing guns from the streets. Special courts were also established to adjudicate the cases of those arrested on gun-related charges. These courts had a mandate to hand-out particularly severe sentences in the cases that came before them.
The net result of the NYPD's strategy has been a marked decrease in gun-related violence across the city. The department has been aided in its mission by its use of the CompStat information technology system, which enables analysts within the department to focus on neighborhoods and communities where violent crime is most prevalent.
The NYPD's policy of removing guns from the streets was a vital element in the city's strategy for reducing violent crime. And, it has been successful. To the extent weaknesses remain, however, they originate in the gaps in the city and the state's ability to control the flow of guns across its borders from other states. It is difficult to get guns off the streets when they are as accessible as they are in other states. 
https://www.nydailynews.com/new-york/bronx/nypd-buys-back-165-guns-bronx-gun-violence-article-1.2741355

https://www1.nyc.gov/site/nypd/index.page

Calculus of a Single Variable, Chapter 7, 7.1, Section 7.1, Problem 62

First we need to calculate equation of the tangent line for which we use the following formula
y=y_1+f'(x_1)(x-x_1)
where y=f(x) is the curve and (x_1,y_1) is the point where the tangent touches the curve.
We will first calculate the derivative f'(x).
f'(x)=3x^2-2
f'(-1)=3-2=1
Now we calculate the equation of the tangent line.
y=1+x-(-1)
y=x+2
In order to determine the upper bound of integration we need to calculate the the point of intersection of the tangent line and the graph of the given function. Hence, we need to solve the following system of equations.
y=x+2
y=x^3-2x
x^3-2x=x+2
x^3-3x-2=0
Factor the equation.
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
From this we see that the points of intersection are x=-1 (which we already knew) and x=2. Those are also the bounds of integration.
To calculate the area between two curves we simply subtract area under the lower curve from the area under the upper curve. Looking at the image below, we see that the upper curve is the tangent line. Therefore, we get
A=int_-1^2(x+2-(x^3-2x))dx=
int_-1^2(-x^3+3x+2)dx=(-x^4/4+(3x^2)/2+2x)|_-1^2=
-4+6+4-(-1/4+3/2-2)=6+3/4=27/4
The area of the region bounded by the graph of the given function and tangent to the graph at point (-1,1) is equal to 27/4.

What did Gatsby say he tried to do in the war? What inference could we make about Gatsby from this statement?

In chapter four, Gatsby tells Nick about his past as the two of them are driving from West Egg into Manhattan for lunch. Gatsby's narrative contains some truths and some deceptions as he works to create a persona that Nick will admire; Nick is Daisy's cousin, after all.
Gatsby tells Nick that when the war came along he "tried very hard to die." Just before he said that to Nick, he said that he had been travelling around Europe before the war "trying to forget something very sad" that had been troubling him.
Plausible inferences that readers could take away from Gatsby's story include the possibility that he is a bit melodramatic and prone to exaggeration. He may be trying to elicit sympathy from Nick. It could also mean that Gatsby is somewhat depressive and does not rebound easily from difficulties and disappointments.

In Chapter 4 of the novel, Gatsby reveals that in the war he "tried very hard to die, but [he] seemed to bear an enchanted life," and then recounts his actions leading a dangerous but successful mission in France, resulting in a promotion to major and decorations from multiple governments. Based on this flippant comment about death, as well as his lifestyle and actions throughout the book, we can infer that Gatsby possesses a boldly confident attitude toward life and winning, as well as an internalized belief in his own immunity to death. Gatsby exerts great effort in erasing and fleeing from his roots, vigorously chases and accumulates wealth by any methods necessary, and pursues Daisy relentlessly, despite the fact that she is married to another man. This reckless approach to life ultimately results in an untimely, violent death as Gatsby's enchanted life proves to be a mere illusion.

Why did Holden's parents want to have him psychoanalyzed?

Holden's parents wanted to have Holden psychoanalyzed because he broke all of the windows in the garage with his fist.
Holden even tried to break the windows on the car with his fists that summer as well. At that point, though, his hand was so broken and messed up that he couldn't do it. Holden tells readers that he broke all of those windows "just for the hell of it." That may be what Holden tells readers, but that is not the reason that he broke all of those windows.
Holden broke all of those windows because he was angry and sad at the fact that his younger brother, Allie, had died. Holden idealizes Allie. Allie was basically the perfect child according to Holden. Everybody liked Allie. He was friendly, intelligent, and kind to people.

You'd have liked him. He was two years younger than I was, but he was about fifty times as intelligent. He was terrifically intelligent. His teachers were always writing letters to my mother, telling her what a pleasure it was having a boy like Allie in their class. And they weren't just shooting the crap. They really meant it. But it wasn't just that he was the most intelligent member in the family. He was also the nicest, in lots of ways.

Unfortunately, leukemia killed Allie at the age of eleven. Holden broke all of those windows because he was angry at the injustice of Allie having to die. Holden's parents just didn't understand that for some reason, so they wanted to have him psychoanalyzed by a professional.

Explain how corn is found in a variety of food in the supermarket?

According to the book, corn can be found in a variety of foods in the supermarket. It usually turns up as a processed ingredient.
The author gives the example of chicken nuggets: the corn is present in the "modified corn starch" that is used to keep the nugget's constituent ingredients together. There may also be corn flour in the batter, and the nuggets may have been fried in corn oil.
Many customers also drink soda. The most popular sweetener used in a wide variety of sodas is high-fructose corn syrup. High-fructose corn syrup is also found in many types of fruit beverages. Additionally, if customers purchase beer, the beverage may have been made from fermented corn. Traditionally, beer manufacturers use barley as the main ingredient; however, many also use corn, a cheaper alternative to barley.
The author says that corn can be found in a variety of foods in the form of modified corn starch, crystalline fructose, high-fructose corn syrup, caramel coloring, and dextrose. In total, the author asserts that there are now forty-five thousand food items in American supermarkets that contain corn.

What are the differences between Odysseus and the Devil?

This question seems a bit like asking what the difference is between a banana and an airplane, as Odysseus and the Devil seem to have relatively little in common.  Odysseus is an ancient Greek hero, the man who conceived of the Trojan Horse, the great deception that ended the Trojan War.  He offended the god of the seas, Poseidon, by blinding his son, Polyphemus, a cyclops, and was therefore forced to endure a prolonged and tragic journey to reach his home in Ithaca, some ten years after the war ended.  
The Devil is the great villain of Christianity: he is a fallen angel named Lucifer, who took issue with God's love of humankind and then fell from grace by waging war against God.  He is the ruler of Hell and the tempter of men and women.  He came to Eve in the Garden of Eden, tempting her to eat an apple from the tree of the knowledge of good and evil, causing the destruction of paradise and humanity's loss of innocence.  
Both are cunning, certainly.  Both are intelligent and can be charming when they choose.

What is the main theme of Wordsworth's poem "The World is too Much with Us"?

In Wordsworth's sonnet "The World is Too Much With Us," the narrator contrasts a way of living that is close to nature with a way of living that centers on materialism. He calls the materialist way of the world "getting and spending." In that worldly mode, we focus on earning money and buying things. In doing so, the narrator argues, we waste our power, by which he means we waste our most valuable potential as human beings.
The narrator calls the "boon," or wealth-focused working all the time, "sordid."
His point or theme is that we would become better humans if we lived closer to nature, closer to the sea and moon and wind. He mourns the passing of the Greek myths, which represented a time when people had a greater appreciation of the natural world and the divine spark that exists in it.

The blades of a helicopter exert an upward force of 25,000 Newtons. The mass of the helicopter is 2,000 kg. What is the acceleration of the helicopter?

Use newtons second law where a force downward is negative and upward is positive.
Newtons second law is:
F_(n e t)=sum_i F_i=m a
Which just says the sum of the net force is equal to the sum of the individual forces thats equal to the mass times the acceleration.
Now let F_h be the upward for due to the helicopter and F_g be due to gravity. Then we know:
F_(n e t) =F_h-F_g=F_h-mg=ma
Solve for a.
(F_h-mg)/m=a
Plug in the values and let the acceration for gravity g be 10 m/s/s.
(25,000 N-2,000 kg *10 m/s^2)/(2,000 kg)=a
(25,000 N-2,000 kg *10 m/s^2)/(2,000 kg)=a
(25,000 N-20,000 N)/(2000 kg)=a
(5,000 N)/(2,000 kg)=a
5/3 (m/s^2) =a
Therefore the acceleration of the helicopter is 5/3 meters per second per second upwards.
https://www.physicsclassroom.com/class/newtlaws/Lesson-2/Drawing-Free-Body-Diagrams

How did the Student Nonviolent Coordinating Committee change the emphasis of the Civil Rights Movement?

The Student Non-Violent Coordinating Committee (SNCC) went through two phases. The first was its direction under the leadership of Robert "Bob" Moses who, as field secretary, led efforts to enfranchise black people in Mississippi. In this phase, from 1960-1964, the emphasis was on resisting state efforts to deprive black people of their right to vote, to help increase literacy in the state, and to ensure that black people in the state understood their rights. Moses was also instrumental in organizing the Mississippi Democratic Freedom Party which, with the participation of Fannie Lou Hamer, took the floor at the Democratic National Convention in 1964 to demand representation.
By 1966, when Stokely Carmichael assumed leadership and delivered his "Black power" message, which is the first time that expression was heard publicly, the organization took on a more radical, black nationalist position.
Prior to this SNCC was in league with organizations, such as the NAACP and CORE, which emphasized voting rights and equal access to accommodations. However, after the death of Malcolm X, the 1965 Watts riots, and the murders of civil rights workers in the South, some black civil rights workers grew tired of non-violent resistance, as well as the focus on integration. More began to embrace the late Malcolm X's view that violence was necessary in self-defense, particularly Carmichael.
Out of this, black nationalist ideas developed. These focused on the uplift of black people and their communities and encouraged separatism. The development of the Black Panthers is indirectly linked to the radical shift in the Student Non-Violent Coordinating Committee.
 
 

What are some examples of the attitude that the men have towards the women in the play "Trifles"?

The men in Susan Glaspell's Trifles believe that the issues they care about are more important than the issues that women care about. The men arrive at the Wright farm in order to investigate a murder. The women come to care for their friend in prison. Because of this unwillingness to consider the women's emotions and concerns, the men miss out on vital clues that reveal the means and motives of the murder.
These attitudes are evident within the first few pages of the play as Mrs. Peters notices that Minnie's fruit preserves froze and the jars broke. The Sherrif laughs at this observation, saying,

SHERRIFF: Well, can you beat the women! Held for murder and worryin' about her preserves.

The truth of the matter is that Mrs. Peters and Mrs. Hale are not so much concerned about the preserves as they are about Mrs. Wright's wellbeing. They know that the preserves were something that Mrs. Wright was concerned about, and her concern was well grounded.
The men also mock the women for admiring the quilt Minnie Wright was making and wondering whether or not she was going to quilt it or knot it. At the end of the play, the men's investigation has revealed no new information. The County Attorney makes this last jab at the women:

COUNTY ATTORNEY: (facetiously) Well, Henry, at least we found out that she was not going to quilt it. She was going to - what is it you call it, ladies?
MRS. HALE: (her hand against her pocket) We call it - knot it, Mr. Henderson.

In this moment, Mrs. Hale is using the phrase "knot it" as a double entendre. Mrs. Wright was knotting her blanket in the same way that she knotted the rope around her husband's neck. If the men had paid attention to Minnie's work, they may have understood Minnie's mental and emotional distress. Instead, they continued to be ignorant of what took place at the Wright farm.

What does segregation say about community values?

While the United States is more diverse than ever, many communities and schools remain segregated. Unlike the 1950s and 1960s, when segregation in many southern communities was the law (referred to as "de jure segregation"), today's segregation is de facto, meaning it occurs by fact. According to a study conducted by the Civil Rights Project in 2012 (see the link below), 43% of Latinos and 38% of African-Americans attend schools in which less than 10% of the students are white.
This type of de facto segregation suggests that many communities are not invested in appreciating and encouraging diversity, but it is also a reflection of the values of our educational system. Many people, for example, choose schools that are reportedly performing better on standardized tests rather than choosing schools that have diverse populations. As poorer schools often have a hard time raising their scores on standardized tests, these choices have a cyclical effect--poorer schools tend to attract poorer, more diverse students, while higher-performing schools tend to attract wealthier, less diverse students. Educational policies tend to reinforce segregation. Therefore, segregation in communities can reflect deeply entrenched beliefs about encouraging sameness and avoiding diversity, and it can also be a reflection of the ways in which educational policies reinforce these ideas. 

How had the experience of fighting in World War II changed the mindset and determination of many African American soldiers once they returned home?

African Americans served valuable combat roles in WWII. The Tuskegee Airmen flew many dangerous missions over Europe protecting bomber crews and thousands of African Americans served in infantry roles. WWII had many racial elements to it. The Japanese viewed themselves as the master race of Asia and Hitler promoted Aryans above all in Europe. Many African Americans were marginalized when they came home. They were passed over in terms of receiving the GI Bill and many were barred from living in the suburbs which sprang up all over America during the postwar era. African Americans who worked in defense industries during the war lost their jobs to white soldiers coming home from the war. Black soldiers were sometimes attacked when returning home and forced to ride on segregated buses. African Americans served their country in various capacities in a war in which the United States fought against racist regimes. African Americans wanted the United States to uphold the ideals for which it supposedly fought. One of the first postwar attempts at integration happened within the US armed forces when they desegregated in 1948.

Fighting in World War II convinced many African American soldiers that there was a discrepancy between the way they were treated at home and the service that they gave their country. In other words, they felt that since they had risked their lives for their country fighting in the war (as many African American soldiers served in combat roles), they should not be treated like second-class citizens at home. Many African Americans were denied the right to vote in the South, and they were subjected to segregation and discrimination in employment, housing, education, and other areas.
After returning home, many African American veterans (joined by others at home) launched the "Double Victory" or "Double V" campaign to win civil rights at home and to foster democracy both at home and abroad. However, many African American veterans were met with violence, even on the way home from the war via bus or train, as they encountered people who opposed the idea that African Americans could fight in the war and win honors from their country. Nonetheless, the experience of having fought for their country gave African Americans a sense of pride and the determination to fight for civil rights at home.

What were some of the many warning signs that Andy was extremely depressed?

Andy clearly exhibited symptoms of major depression in the novel. 
For example, Andy was constantly plagued by feelings of guilt and hopelessness. He told his coach after a winning game that he should have been the one who died. Later, he admitted to feeling guilty for taking over Robbie's position on the team.
He told his psychologist that he would never have won the position of center had Robbie been alive. Andy thought that Robbie was the best center Hazelwood ever had, and he thought that he could never match his friend's prowess on the court.
Andy was also easily irritated and exhibited extreme mood swings. For example, he could be cheerful one moment and belligerently angry the next. During an interaction with Keisha, Andy complimented Keisha on her looks, which prompted Keisha to comment on his apparently good mood. Yet, a few minutes later, Andy became extremely angry when Keisha mentioned that she had to study for her chemistry test and could not go to the movies with him. 
Andy also experienced frequent bouts of sadness, which left him feeling deflated and apathetic. For example, Andy became melancholy after seeing a Santa Claus display. He told Keisha that Santa Claus reminded him of Robbie. Keisha admitted that she did not see the connection, as Robbie was African American and six-foot-five when he was alive.
However, Robbie immediately shut down, refused to talk, and ignored her. Keisha related that she had to call her mother to take them both home, especially since Andy no longer drove. Later, Andy told Keisha that he never turned in one of his school assignments. He admitted that he did not care if his grades suffered.
There were many warning signs that Andy was extremely depressed. He exhibited apathy, experienced frequent bouts of sadness, struggled with feelings of guilt and hopelessness, and displayed extreme mood swings.

y' - y = y^3 Solve the Bernoulli differential equation.

Given equation is y' -y =y^3
An equation of the form y'+Py=Qy^n
is called as the Bernoullis equation .
so, to proceed to solve this equation we have to transform the equation into a linear equation form of first order as follows
=> y' (y^-n) +P y^(1-n)=Q
let u= y^(1-n)
=> (1-n)y^(-n)y'=u'
=> y^(-n)y' = (u')/(1-n)
so ,
y' (y^-n) +P y^(1-n)=Q
=> (u')/(1-n) +P u =Q
so this equation is now of the linear form of first order
Now,
From this equation ,
y' -y =y^3
and
y'+Py=Qy^n
on comparing we get
P=-1 , Q=1 , n=3
so the linear form of first order of the equation y' -y =y^3 is given as
 
=> (u')/(1-n) +P u =Q where u= y^(1-n) =y^-2
=> (u')/(1-3) +(-1) u =1
=> (-u')/2 -u=1
=> u'+2u = -2
 
so this linear equation is of the form
y' + py=q
p=2 , q=-2
so I.F (integrating factor ) = e^(int p dx) = e^(int 2dx) = e^(2x)
 
and the general solution is given as
u (I.F)=int q * (I.F) dx +c
=> u(e^(2x))= int (-2) *(e^(2x)) dx+c
=> u (e^(2x))= (-2) int (e^(2x)) dx+c
let us solve int (e^(2x)) dx
=>let t= 2x
dt = 2dx
=> int (e^(t)) dt/2
=>1/2 (int (e^(t)) dt) = 1/2 e^t = (e^(2x))/2
so, int (e^(2x)) dx =(e^(2x))/2
so  ,now
u (e^(2x))= (-2) ((e^(2x))/2)+c
=>u (e^(2x))= -(e^(2x))+c
=> u = ((-(e^(2x)))+c)/(e^(2x))
but u=y^-2
so,
y^-2=((-(e^(2x)))+c)/(e^(2x))
=> y^2 = (e^(2x))/((-(e^(2x)))+c)
=> y = sqrt((e^(2x))/((-(e^(2x)))+c))
 
=> y = e^x/(sqrt(c-e^(2x)))
the general solution. 

1. Pride and Prejudice begins with one of the most famous first lines in English literature: “It is a truth universally acknowledged that a single man in possession of a good fortune must be in want of a wife” (p.3). This sentence tells us much about the author’s purpose and attitude. It states one of the novel’s main themes: the relationship between money and marriage. It also sets an ironic tone. Based on your knowledge of Regency England and the “marriage market” of the time, explain how this opening sentence is ironic.

As the reader comes to understand the characters in this novel, it becomes clear that the character most likely to utter such a line is Mrs. Bennet. It is also clear that we are supposed to find Mrs. Bennet to be a ridiculous character with few redemptive qualities and no sense. She is a neglectful parent, failing to properly educate her daughters to secure the kind of husbands she insists they have; she is indulgent and at least partially responsible for Lydia's horrible temperament; she is witless and dull, taking more interest in balls and gossip than she does in practically anything else. Further, the fact that Elizabeth Bennet, a young woman who is kind and loving as well as witty and intelligent, is Mrs. Bennet's least favorite child tells us a great deal about her lack of judgment. Mrs. Bennet is loud when she should be discreet, rude when she should be polite, and entitled when she ought to be grateful. Throughout the narrator's descriptions of her, we come to understand that we are not to respect her character or agree with her opinions, and because we can most easily imagine her character taking the position stated in the first line, it is a good clue that we are not supposed to agree with it either.
In fact, Mrs. Bennet often says things that others think and feel but are too tactful to actually say aloud. For example, at the Netherfield ball, she speaks loudly of her expectation that Jane and Bingley will soon marry—a not unreasonable supposition, but one not to be spoken of since he has not yet proposed—and her happiness that it will "throw the other girls into the path of other rich men." Now, most mothers in her position would also rejoice at her daughter's good fortune in having caught the eye and heart of a man who is rich as well as handsome and kind. However, most mothers would know better than to shout it from the rooftops before the pair are even engaged. Further, most mothers in her position would equally rejoice at the advantages which one daughter's marriage will confer upon her other daughters, but these mothers would also know better than to crow—publicly—about their daughters' new proximity to wealthy bachelors. Mrs. Bennet, like most mothers at this time, wants the best for her daughters, and what is considered "the best"—what makes a match a good and advantageous one—is wealth. She is far from being alone in her belief that this is so; what sets her apart from her peers is that she is too tactless to keep quiet about it.
The narrator speaks this line, however, and not Mrs. Bennet, but given the characterization of Mrs. Bennet, and the marriage traditions of the era, we can understand this line to be an example of verbal irony on the part of the narrator. She, who is so apt to point out Mrs. Bennet's flaws (and, through her, society's flaws), does not believe that "It is a truth universally acknowledged that a single man in possession of a good fortune must be in want of a wife." The narrator, based on the love matches made between Elizabeth and Darcy, and Jane and Bingley, as well as the loving relationship of the most idealized couple in the book—the Gardiners—seems to believe that love should come first and foremost. Financial security will not necessarily make one happy: consider the Collinses and the Bennets. Thus, the narrator says the opposite of what she means in this first line; instead, the line gives voice to the idea that society would most support (though might not say aloud).

f(x)=sqrt(x) ,n=3,c=4 Find the n'th Taylor Polynomial centered at c

Taylor series is an example of infinite series derived from the expansion of f(x) about a single point. It is represented by infinite sum of f^n(x)  centered at x=c.  The general formula for Taylor series is:
f(x) = sum_(n=0)^oo (f^n(c))/(n!) (x-c)^n
or
f(x) = f(c) + f'(c) (x-c)+ (f'(c))/(2!) (x-c)^2+ (f'(c))/(3!) (x-c)^3+ (f'(c))/(4!) (x-c)^4+...
 To evaluate the given function f(x) =sqrt(x) , we may express it in terms of fractional exponent. The function becomes:
f(x) = (x)^(1/2) .
Apply the definition of the Taylor series by listing the f^n(x) up to n=3.
 We determine each derivative using Power Rule for differentiation: d/(dx) x^n = n*x^(n-1) .
f(x) = (x)^(1/2)
f'(x) = 1/2 * x^(1/2-1)
          = 1/2x^(-1/2) or1/(2x^(1/2) )
f^2(x) = d/(dx) (1/2x^(-1/2))
         = 1/2 * d/(dx) (x^(-1/2))
         = 1/2*(-1/2x^(-1/2-1))
         = -1/4 x^(-3/2) or -1/(4x^(3/2))
f^3(x) = d/(dx) (-1/4x^(-3/2))
          = -1/4 *d/(dx) (x^(-3/2))
          = -1/4*(-3/2x^(-3/2-1))
          = 3/8 x^(-5/2) or 3/(8x^(5/2))
Plug-in x=4 , we get:
f(x) = (4)^(1/2)
         = 2
f'(4)=1/(2*4^(1/2))
         =1/(2*2)
         =1/4
f^2(4)=-1/(4*2^(3/2))
          = -1/(4*8)
          = -1/32
f^3(4)=3/(8*4^(5/2))
          = 3/(8*32)
          = 3/256
Applying the formula for Taylor series centered at c=4 , we get:
sum_(n=0)^3 (f^n(4))/(n!)(x-4)^n
    =f(4) + f'(4) (x-4)+ (f'(4))/(2!) (x-4)^2+ (f'(4))/(3!) (x-4)^3
    =2+ (1/4) (x-4)+ (-1/32)/(2!) (x-4)^2+ (3/256)/(3!) (x-4)^3
    =2+ (1/4) (x-4)+ (-1/32)/(2!) (x-4)^2+ (3/256)/(3!) (x-4)^3
    =2+ 1/4 (x-4)-1/(32*2) (x-4)^2+ 3/(256*6) (x-4)^3
   =2+ 1/4 (x-4)-1/64 (x-4)^2+ 3/1536 (x-4)^3
   =2+ 1/4 (x-4)-1/64 (x-4)^2+ 1/512 (x-4)^3
The Taylor polynomial of degree n=3  for the given function f(x)=sqrt(x)  centered at  c=4  will be:
P(x) =2+ 1/4 (x-4)-1/64 (x-4)^2+ 1/512 (x-4)^3

Calculus: Early Transcendentals, Chapter 7, 7.1, Section 7.1, Problem 10

intsin^-1xdx
If f(x) and g(x) are differentiable functions, then
intf(x)g'(x)dx=f(x)g(x)-intf'(x)g(x)dx
If we write f(x)=u and g'(x)=v, then
intuvdx=uintvdx-int(u'intvdx)dx
Using the above method of integration by parts,
intsin^-1xdx=sin^-1x*int1dx-int(d/dx(sin^-1x)int1dx)dx
=sin^-1x*x-int(1/sqrt(1-x^2)*x)dx
=xsin^-1x-intx/sqrt(1-x^2)dx
Now evaluate using the method of substitution,
Substitute t=1-x^2,=> dt=-2xdx
intx/sqrt(1-x^2)dx=intdt/(-2sqrt(t))
=-1/2intdt/sqrt(t)
=-1/2(t^(-1/2+1)/(-1/2+1))
=-1/2(t^(1/2)/(1/2))
=-t^(1/2)
substitute back t=1-x^2
=-(1-x^2)^(1/2)
intsin^-1xdx=xsin^-1x-(-(1-x^2)^(1/2))
adding constant C to the solution,
=xsin^-1x+sqrt(1-x^2)+C

What beliefs and character traits that typified the Pilgrims enabled them to survive in the hostile environment that greeted them in the New World? Did some of the same traits that helped them survive limit them in other ways? How so?

The Pilgrims were originally known as Separatists because they wanted to separate from the Church of England, select their own leaders, and establish their own practices. The persecution they endured as a result of their beliefs caused them to flee to Holland. However, this was unsatisfactory, because they wanted to retain their English language and way of life. The leaders eventually decided to relocate to America. They obtained two ships to transport the colonists to the New World, the Speedwell and the Mayflower. Because the Speedwell quickly developed leaks and had to return to England, the Mayflower carried on the voyage alone.
The Pilgrims, who called themselves Saints, were joined by numerous other colonists, whom they referred to as Strangers. The voyage was rough, and many passengers became sick on the way. They were originally supposed to settle near the Virginia Colony, but bad weather caused them to change their plans and settle on the shore of Cape Cod in Massachusetts. Because they were no longer in the Virginia Colony's territory, the men signed a document known as the Mayflower Compact that became the foundation of government for the fledgling colony.
During the first winter, over half the colonists died due to severe weather conditions, poor shelter, and lack of adequate nutrition. The Native Americans in the area assisted the Pilgrims in learning how to fish, hunt game, and plant crops.
The beliefs and character traits that enabled the Pilgrims to survive the persecution, difficult voyage, and hostile environment of the New World included their solidarity and respect for their leaders. These traits enabled them to remain united in the face of adversity and agree on basic governing principles such as those found in the Mayflower Compact.
The text of this compact expresses their commitment to remain united and obey laws established for the good of the colony "for the glory of God." Their belief that God was with them in their search for a place where they could freely practice their religious beliefs was a strong factor in their survival.
The same religious zeal that caused the Pilgrims to remain steadfast in establishing their colony in the New World eventually caused a negative and limiting effect on Native American relations.
As in the rest of New England, the Pilgrims were intent on expanding their colony, which involved the acquisition of more and more land. This eventually resulted in the Native American uprising known as King Philip's War. While there were quite a few casualties among the colonists, the vast majority of those killed were Native Americans.
https://www.history.com/topics/colonial-america/pilgrims

https://www.nps.gov/caco/learn/historyculture/pilgrims.htm

https://www.plimoth.org/learn/just-kids/homework-help/who-were-pilgrims

In Philbrick's book Mayflower, he examines the very human aspects of the Pilgrims, even the parts that don't coincide with the tolerance they themselves sought. This group of 102 English passengers hoped to find religious tolerance in a new setting, so tradition leads all of us (centuries later) to put a positive spin on the Thanksgiving story. We all sort of envision this brief struggle between the Pilgrims and Native Americans which fast forwards quickly to a happy scene of Thanksgiving and tolerance for everyone. But Phibrick asserts that this leaves out much of the truth.
When the Pilgrims arrived in this area, they didn't know that disease had greatly lessened the Native American population over the previous two years there; this contributed to the sparse populations they believed inhabited this area. It was a tough climate at a tough time of the year, and they surely had to cling to their religious faith to give them hope of survival. However, they also had very human instincts to survive (at all costs, perhaps), and when they found a stash of native corn buried and hidden, they took it for themselves. This directly contradicted their Puritan views, but it shows that the Puritans were as complex as any other group of people and clung to any means of possible survival, even if it put them in conflict with their new neighbors.
The Pilgrims did believe in loving their neighbors, as commanded by the Bible, and this surely had some foundation in forming an alliance with the Pokanoket sachem, Massasoit. Both Massasoit and the Pilgrims realized that together they could offer and receive more protection than they could hope to accomplish alone, so this made strategic sense. Again, this shows the complexities of the Pilgrim culture in the New World. While they continued to worship and study the Bible, they also faced situations they had no experience in working through, and they ultimately needed to survive these unknown conditions. Their new alliances showed that they were people of faith but also practical human beings.
The behavior of the Pilgrims is also not what one would expect from a group who initially sought religious tolerance and who is often characterized as a solely peace-seeking group. Miles Standish once placed the head of a Native soldier atop a Plymouth fort, which is not the characteristic, typical Pilgrim image. He was a calculating and cruel soldier, and his behavior was denounced by Reverend John Robinson: "It is . . . a thing more glorious, in men’s eyes, than pleasing in God’s or convenient for Christians, to be a terror to poor barbarous people. And indeed I am afraid lest, by these occasions, others should be drawn to affect a kind of ruffling course in the world."
All of this goes to show that the Pilgrims were as diverse a group of people as any other, and though they sought religious freedom in the New World, they were also human and desperately clung to hope of survival. Their actions did not always reflect the God they served, and their relationships with the Native Americans was complex and constantly changing, depending on shifting needs of both groups.

The Pilgrims were Puritans, and they were given their name because they wanted to purify the Anglican Church. Unlike most of the later Puritans who colonized Massachusetts Bay Colony, the Pilgrims were Separatists, in that they wanted to separate themselves entirely from the Anglican Church rather than purifying it from within. The Pilgrims were persecuted in England, and so they were motivated to immigrate to the New World and to establish a settlement. Their ability to survive the rigors of the New World came in part from their knowledge that England was a hostile environment to them--one they could not easily return to. In addition, the Pilgrims, like other Puritans, believed in predestination--the idea that one's status as saved or not saved was determined before birth. Being successful on earth was a sign that one had received God's favor and was among the elect, or saved, so the Puritans practiced the Protestant work ethic. They were determined to prove their elect status so they worked diligently, surviving in the New World.
Their beliefs also limited them in that they were not open to new cultures, such as the Native Americans, and so they treated them with hostility. They believed the Native Americans were not among the elect, so the Pilgrims were not tolerant of them. The Pilgrims and other Puritans could not tolerate any dissent.