Intermediate Algebra, Chapter 2, Cumulative Exercises, Section Cumulative Exercises, Problem 32

Shamil Mamedov invested some money at $5\%$ simple interest and $\$2,000$ more than that amount at $6\%$. The interest for the year totaled $\$670$. How much was invested at each rate?

Step 1: Read the problem, we are asked to find the amount invested on each rate.
Step 2 : Assign the variable. Then organize the information in the table.
Let $x = $ amount invested at $5\%$ interest rate.
Then, $x + 2000 = $ amount invested at $6\%$ interest rate

$
\begin{array}{|c|c|c|c|c|c|}
\hline
& \rm{Principal} & \cdot & \text{Interest Rate} & = & \rm{Interest} \\
\hline
5 \% & x & \cdot & 0.05 & = & 0.05x \\
\hline
6 \% & x + 2000 & \cdot & 0.06 & = & 0.06(x + 2000) \\
\hline
\end{array}
$


The total interest earned is equal to the sum of the interests at each rate.

Step 3: Write an equation from the last column of the table
$0.05x + 0.06(x + 2,000) = 670$

Step 4: Solve

$
\begin{equation}
\begin{aligned}
0.05x + 0.06x + 120 &+ 670\\
\\
0.11x &= 670 - 120\\
\\
0.11x &= 550\\
\\
x &= 5000
\end{aligned}
\end{equation}
$

Then by substitution,
$x + 2,000 = 5,000 + 2,000 = 7,000$

Step 5: State the answer
In other words, Shamil invested $5,000$ and $7,000$ at $5\%$ and $6\%$ interest rates respectively.

Compare Lincoln's Gettysburg Address to letters by Lincoln.

Lincoln's Gettysburg Address is a masterpiece of hope, graceful writing, and brevity. His letters at times show the same mastery of style. For example, in 1846, Lincoln wrote to Allen N. Ford, the editor of the Illinois Gazette, refuting charges Lincoln's opponent a congressional campaign that Lincoln scoffed at religion. Lincoln wrote of his opponent, "I have little doubt now, that to make the same charge -- to slyly sow the seed in select spots -- was the chief object of his mission." This excerpt shows his ability, also expressed in the Gettysburg Address, to make a strong claim and to support it with language that is both concise and beautiful. Lincoln's use of alliteration ("slyly sow the seed in select spots") in this letter mirrors the alliteration he used at the beginning of the Gettysburg Address: "Four score and seven years ago our fathers brought forth on this continent, a new nation" ("score" and "seven" and "new" and "nation" are alliterative).
Lincoln's letters show a sense of humor that he did not display in formal speeches such as the Gettysburg Address. For example, in his 1860 letter to 11-year-old Grace Bedell, who suggested that Lincoln grow a beard to improve his chances of being elected president, Lincoln wrote, "As to the whiskers, having never worn any, do you not think people would call it a piece of silly affection if I were to begin it now?" This letter shows a wry and personal tone that Lincoln did not use in his speeches. Later, as president, he visited Grace Bedell while sporting a beard.
Lincoln also showed more emotionality in his letters than in his speeches. For example, he wrote to the Ellsworths in 1861 upon the death of their son, who was a colonel in the Union Army. Lincoln not only expressed his condolences to the family but also showed his own sense of connection with the younger man when he wrote, "My acquaintance with him began less than two years ago; yet through the latter half of the intervening period, it was as intimate as the disparity of our ages, and my engrossing engagements, would permit." Lincoln displayed a sense of emotion that he did not show in his speeches. In both his private letters and his speeches, Lincoln was a graceful writer who managed to express deep sentiments and hopes for the future with a rare sense of concision. In this, he is rare among presidents. 
http://www.abrahamlincolnonline.org/lincoln/speeches/letters.htm

What is the role of non renewable resource in nations development?

The most important thing about non renewable resources for developing countries is ease of use and cheap availability.
To use the energy in a fossil fuel, often times all that is required is fire. Coal, gas, and oil all produce high amounts of energy when burned. Developing countries often lack the infrastructure and technology to adequately use or develop advanced technologies like solar cells and hydro-power, but setting up a coal engine is relatively easy.
To access coal and oil, all you need to know is where the field is and how deep you need to go to reach it. Strip mining and oil drilling easily accessed fields is an easy way to harvest massive amounts of energy.
In addition, fossil fuels can be transported and sold much easier than nearly any other form of energy. As such, they often make up a significant portion in the developing country's GDP.
Eventually, developing countries will reach a point where technology allows them to utilize advanced energy sources in addition to non renewable energy, as happened in the US and Europe.

Calculus of a Single Variable, Chapter 8, 8.1, Section 8.1, Problem 20

int (4x - 2/(2x+3)^2)dx
To solve, express it as difference of two integrals.
= int 4x dx - int 2/(2x+3)^2dx
Then, apply negative exponent rule a^(-m)=1/a^m .
= int 4xdx - int 2(2x+3)^(-2)dx
For the second integral, apply the u-substitution method.

u = 2x + 3
du = 2dx

Expressing the second integral in terms of u variable, it becomes:
=int 4xdx - int (2x+3)^(-2) * 2dx
=int 4xdx - int u^(-2) du
For both integrals, apply the formula int x^ndx= x^(n+1)/(n+1)+C .
= (4x^2)/2 - u^(-1)/(-1) + C
=2x^2 + u^(-1) + C
= 2x^2 + 1/u + C
And, substitute back u = 2x + 3
=2x^2+1/(2x+3)+C

Therefore, int (4x - 2/(2x+3)^2)dx=2x^2+1/(2x+3)+C .

Calculus of a Single Variable, Chapter 8, 8.3, Section 8.3, Problem 42

Indefinite integrals are written in the form of int f(x) dx = F(x) +C
where: f(x) as the integrand
F(x) as the anti-derivative function
C as the arbitrary constant known as constant of integration
For the given problem int cos(5theta)cos(3theta) d theta has an integrand in a form of a trigonometric function. To evaluate this, we apply the identity:
cos(X)cos(Y) =[cos(X+Y) +cos(X-Y)]/2
The integral becomes:
int cos(5theta)cos(3theta) d theta = int[cos(5theta+3theta) + cos(5theta -3theta)]/2 d theta
Apply the basic properties of integration: int c*f(x) dx= c int f(x) dx .
int[cos(5theta+3theta) + cos(5theta -3theta)]/2d theta = 1/2int[cos(5theta+3theta) + cos(5theta -3theta)] d theta
Apply the basic integration property: int (u+v) dx = int (u) dx + int (v) dx .
1/2 *[int cos(5theta +3theta)d theta+cos(5theta -3theta)d theta]
Then apply u-substitution to be able to apply integration formula for cosine function: int cos(u) du= sin(u) +C .
For the integral: int cos(5theta +3theta)d theta , we let u =5theta +3theta =8theta then du= 8 d theta or (du)/8 =d theta .
int cos(5theta +3theta)d theta=int cos(8theta)d theta
=intcos(u) *(du)/8
= 1/8 int cos(u)du
= 1/8 sin(u) +C
Plug-in u =8theta on 1/8 sin(u) +C , we get:
int cos(5theta +3theta)d theta=1/8 sin(8theta) +C
For the integral: intcos(5theta -3theta)d theta , we let u =5theta -3theta =2theta then du= 2 d theta or (du)/2 =d theta .
int cos(5theta -3theta)d theta = intcos(2theta) d theta
=intcos(u) *(du)/2
= 1/2 int cos(u)du
= 1/2 sin(u) +C
Plug-in u =2 theta on 1/2 sin(u) +C , we get:
intcos(5theta -3theta)d theta =1/2 sin(2theta) +C
Combing the results, we get the indefinite integral as:
int cos(5theta)cos(3theta)d theta = 1/2*[1/8 sin(8theta) +1/2 sin(2theta)] +C
or 1/16 sin(8theta) +1/4 sin(2theta) +C

How can you tell from the story that the policeman is Jimmy in "After Twenty Years"?

O. Henry must have understood the way he told his story could cause some confusion. We do not know the names of either the beat cop or Bob during the time they are talking. One thing O. Henry uses to identify the cop as Bob's old friend is the cigar. In the note handed to Bob by the arresting plainclothes officer at the end of the story, one sentence reads

When you struck the match to light your cigar I saw it was the face of the man wanted in Chicago.

When the unidentified policeman is talking to Bob in the doorway of the hardware store, we read the following:

The man in the doorway struck a match and lit his cigar. The light showed a pale, square-jawed face with keen eyes, and a little white scar near his right eyebrow. His scarf pin was a large diamond, oddly set.

This places Jimmy at the hardware store. He not only recognizes his old friend Bob, but also sees Bob has the face of the man wanted in Chicago. Bob would not have recognized Jimmy because he could not have seen beyond the light of the match he was holding. Jimmy would be just as unrecognizable with the matchlight as he was in the darkness.

Jimmy's letter shows he was the policeman who conversed with Bob in the beginning of the story.
In the letter, Jimmy mentions he was on time to meet Bob. While speaking with him, however, he recognized Bob as a criminal wanted by Chicago cops. Jimmy asks a plainclothes officer to impersonate him because he can't bring himself to arrest a man he used to call a friend.

I didn’t want to arrest you myself. So I went and got another cop and sent him to do the job.

The contents of the letter make it clear Jimmy was the police officer. As we look back at the story, the letter explains why Jimmy asked how long Bob was willing to wait:

“I’ll go on my way,” he said. “I hope your friend comes all right. If he isn’t here at ten, are you going to leave?” “I am not!” said the other. “I’ll wait half an hour, at least. If Jimmy is alive on earth, he’ll be here by that time. Good night, officer.”

Based on Bob's answer, Jimmy may have concluded half an hour was plenty of time for another officer to impersonate him and meet with Bob.
Bob's answer also shows he still has some affection for his old friend, Jimmy. The men may not be close now, but past memories and shared experiences are often difficult to forget. This is perhaps the reason Jimmy sends another officer to do his job.

What were the economic, administrative, and legislative weaknesses of the government under the Articles of Confederation? How were these weaknesses different?

The Articles of Confederation created economic, administrative, and legislative weaknesses in the US government. These issues, while each distinct, were also interrelated, as they created a situation of political confusion and instability.
The economic weaknesses were that the government could not tax people directly and relied on the states for money. As the states did not give the government the funds it needed, the federal government was strapped for funds and could not often pay soldiers or bondholders. In addition, the central government and states could both issue currency, resulting in too much currency in circulation and rampant inflation. The legislative problems related to the government under the Articles of Confederation were that it could not regulate any inter-state issues, including commerce, and there were no standard tariffs (which are taxes on imports). With regard to administration, the Articles of Confederation made it very difficult to conduct relations with foreign countries (in part because there were no standard tariffs and in part because there was no President), and administer to the new lands that were admitted to the country after the Revolutionary War. These weaknesses resulted in the call for a new government and the creation of the Constitution in 1787. 

Single Variable Calculus, Chapter 2, 2.3, Section 2.3, Problem 26

Determine the $\displaystyle \lim \limits_{t \to 0} \left( \frac{1}{t} - \frac{1}{t^2 + t} \right)$, if it exists.


$
\begin{equation}
\begin{aligned}
\lim \limits_{t \to 0} \left( \frac{1}{t} - \frac{1}{t^2 + t} \right)
& = \lim \limits_{t \to 0} \frac{t^2 + \cancel{t} - \cancel{t}}{t(t^2 + t)} = \lim \limits_{t \to 0} \frac{t^2 }{t(t^2 + t)}
&& \text{ Get the LCD and combine like terms}\\
\\
& = \lim \limits_{t \to 0} \frac{\cancel{t^2}}{\cancel{t^2} (t + 1) } = \lim \limits_{t \to 0} \frac{1}{t + 1}
&& \text{ Factor the denominator and cancel out like terms}\\
\\
& = \frac{1}{0 + 1} = \frac{1}{1}
&& \text{ Substitute value of $t$ and simplify}\\
\\
& = 1


\end{aligned}
\end{equation}
$

What could IR feminist theory add to the understanding of war? Think, for example, about the ongoing US war in Afghanistan, from the point of view of IR feminism – does this war look any different? Does it change assessment/goals/constituents? (You can use any other war in this thought experiment)

One way of thinking about what IR feminist theory is would be to look at the field of International Relations through the lens of feminist theory. This means that feminist commitments to asking questions about gender and sexuality in particular—but of course always race, class, citizenship, ability, and many other identities—reshape the questions we ask in International Relations.
Here, we are talking about an IR perspective on war, which means we are interested in the ways in which states (i.e., nations) interact with one another in times of war. Feminist theory asks us to think about how these international relationships are informed by power, and how, in turn, that power is shaped by our perceptions and constructions of difference (e.g., categorizing people by gender, race, class, and nation).
For example, one justification given by the Bush administration for the US invasion of Afghanistan was that it was America's responsibility to save Afghani women from Afghani men. The thought behind this was that Afghani women, many of who wear the burqa (a form of Muslim veiling), were oppressed by an overt and violent patriarchal society (Jabbra). Indeed, it is often the case that pictures of suffering women and children are what circulate in the media in times of war, evoking feelings of compassion and humanitarianism within the public. One recent example of this can be seen in the way that pictures of women and children affected by chemical attacks in Syria have made their way to the tops of our news feeds. Another example is that during the 2015 European refugee "crisis," it was a picture of a little Syrian boy's body washed up on a Turkish shore that sparked outrage in the international community. (See, for example, the NPR report called "That little Syrian boy.")
A feminist reading of this particular justification would require asking one or more of the following questions:
Do Afghani women really need saving? Who is saying they need saving, and why?
What do Afghani women themselves actually think about "being saved"? Do they want to or need to be saved?
While the US government justifies their actions in Afghanistan by saying that a major reason for this war is to save Afghani women, what is happening that may contradict and/or challenge this so-called "justification"?
What binaries are being set up that might be based on false claims? For example, is the idea that all Afghani women are victims and all Afghani men are perpetrators warrant further thinking? What about the idea that the US is "more civilized" in that it is "more egalitarian" than Afghanistan? On what sort of preconceived notions about the relationship between Afghanistan and the US does this idea rely?
For further reading, I definitely recommend Cynthia Enloe's book Nimo's War, Emma's War: Making Feminist Sense of the Iraqi War. Enloe was one of the first feminist international relations scholars, and this particular book is all about women's perspectives and experiences of the Iraqi War.

How is Metamorphosis by Franz Kafka a coming of age story?

Like with most of the work of Franz Kafka, "The Metamorphosis" can be interpreted in innumerable ways. Among other things, it can quite justifiably be read as a coming-of-age tale. In the novella, Gregor Samsa still inhabits a room in his parents' home when he is suddenly (and inexplicably) transformed into a giant insect. As his family recoils in horror at Gregor's new form, he is ultimately outcasted from his own home, and, once he dies, he is completely forgotten about.
In a sense, one can read this tale as a metaphor for the transition into adulthood. At a certain point, children become adults and are forced to leave the homes they grew up in. While not entirely forgotten, they are soon removed from the daily routines that occur in the house; Gregor is literally treated as a sort of grotesque inconvenience by his family. They hope for him to leave because he is no longer wanted.
Meanwhile, Grete, Gregor's sister, becomes increasingly dissatisfied with taking care of him. She, too, begins to grow older as she acquires her own responsibilities and duties. Gregor becomes an increasing burden on her and the rest of the family. While Gregor initially rejects this transformation and the stresses it puts upon him and his family, he soon dies; his family is relieved. Gregor's transition into an independent adulthood is ultimately a failure. He is a burden and is unable to live alone.

Using examples, explain feminist standpoint theory.

The feminist standpoint theory has roots in Marxism and critiques patriarchal societies. The idea is that a woman's role in society, often an oppressed one, gives her a unique perspective, especially in relation to a man's. Women should use their unique experiences to educate society in order to benefit future generations and hopefully create social change. A standpoint is any political achievements made by people from a marginalized group (Feminist Standpoint Theory Explained).
One striking example of a standpoint that reflects the feminist standpoint theory is women's suffrage, specifically the right for women to vote. Susan B. Anthony, Elizabeth Cady Stanton, and Lucy Stone are a few key women credited with leading this movement by joining the forces of their individual women's rights movements. This fight to win the right to vote for women lasted decades, but the continual exposure to women's experiences eventually changed laws surrounding voting rights for women in 1920.
The Women's Rights Movement gave rise to many other feminist standpoints and is still active today. This movement is typically described as having appeared in two waves, the first in the nineteenth century stemming from the abolitionist movement, and the second in the 1960s and 1970s. Some would say we are currently in a third wave of a push for women's rights, particularly women's reproductive rights. This detailed timeline contains more specific examples of these standpoints.
https://nationalwomenshistoryalliance.org/resources/womens-rights-movement/detailed-timeline/

https://healthresearchfunding.org/the-feminist-standpoint-theory-explained/

What does darkness suggest in the poem "Stopping by Woods on a Snowy Evening" by Robert Frost?

Before answering this question, it helps to check out the final stanza in Robert Frost's "Stopping by Woods on a Snowy Evening":

The woods are lovely, dark and deep,But I have promises to keep,And miles to go before I sleep,And miles to go before I sleep. (13-16)

Many scholars, critics, and readers have proposed that this seemingly simple poem is actually a depiction of an individual contemplating death and/or suicide. One of the factors that points to such an interpretation is this final stanza, especially the first line: "The woods are lovely, dark and deep." The darkness Frost references, especially when combined with the reference to sleep, seems to symbolize a kind of death. Moreover, the idea that the speaker of the poem eschews such darkness based on the fact he has "promises to keep" suggests that he has some control in choosing whether or not to give into the referenced darkness. This fact could be seen as a suggestion of suicide and, once that idea comes into one's head, it becomes difficult to read the poem and its suggestion of darkness as anything else but a contemplation of death.
That's not to say that this is the only way to read the poem. The meaning of darkness remains fairly ambiguous and, while it certainly could refer to death, it could just as easily refer to something else entirely. Some readers, for instance, point out that the speaker could be talking about rest in general, and so one might not need to wrestle with death at all. In short, there are many readings of this poem, and many interpretations of its "darkness." That said, the idea that darkness suggests death or suicide has proven to be one of the poem's most long-lasting interpretations. 

What does Polonius believe is the cause of Hamlet's grief?

In act 2, scene 2, Polonius tells the king and queen, Hamlet's uncle—now his stepfather—and mother that the cause of Hamlet's madness is his love for Ophelia, a love that Polonius would not let her return. Polonius says that he told Ophelia, his daughter, "'Lord Hamlet is a prince, out of thy star: / This must not be'" (2.2.150-151).  In other words, Hamlet is out of her league because he is royalty; therefore, you cannot be with him. Then he instructed her to withhold her presence from Hamlet, to return any love letters he sent her, and to, essentially, completely break off the relationship between them (even though she loves him, and Hamlet, Polonius now admits, seemed to truly love her too). Polonius conjectures that Hamlet, once

repelled . . .  Fell into a sadness, then into a fast, Thence to a watch, thence into a weakness, Thence to a lightness, and, by this declension, Into the madness wherein now he ravesAnd all we mourn for (2.2.155-160).

Therefore, Polonius believes that when Ophelia began to refuse Hamlet's advances, rejecting his once-welcome overtures of love, he grew sad, then stopped eating, then stopped sleeping, became weakened, became light-headed, and, ultimately, went totally insane. Thus, Hamlet is now crazy, Polonius says.

Single Variable Calculus, Chapter 4, 4.1, Section 4.1, Problem 72

The equation $f(x) = ax^3 + bx^2 + cx + d$, where $a \neq 0$ represents a cubic function (Polynomial of degree 3).

a.) Prove that a cubic function can have one, two or more critical number(s). Give examples and sketches to illustrate the three possibilities.

$f(x) = ax^3 + bx^2 + cx + d$

Taking the derivative,

$f'(x) = 3ax^2 + 2bx + c$

We know that $f'(x)$ is a quadratic function that might have either $0, 1$ or $2$ real roots. This means that $f(x)$ has either $0, 1$ or $2$ critical numbers.

For 1 critical number:

Let $f(x) = x^3$, then $f'(x) = 3x^2$, thus $x = 0$ is the only critical number.







For 2 critical numbers:

Let $f(x) = 4x^3 - 12x$, then $f'(x) = 12x^2 - 12$, thus $x = \pm 1$ are the two critical numbers.







For 0 critical number:

Let $f(x) = 4x^3 + 12x$, then $f'(x) = 12x^2 + 12$, there are no real roots, thus, no critical numbers.







b.) How many local extreme values can a cubic function have?

If the function has one or no critical values, it has no extremum.

But if the function has 2 critical values, it can have at most 2 extrema.

Therefore, a cubic function can have either 2 extrema or none.

When do plants take in oxygen?

Plants take in oxygen constantly during a process called respiration; they take in oxygen to derive energy from their food and produce carbon dioxide as a waste product. All living things use this process for energy. A major difference between plants and other living things, however, is the process of photosynthesis. Photosynthesis is the process of a plant taking in sunlight as an energy source (e.g., food source). During photosynthesis, a plant takes in carbon dioxide and releases oxygen as a waste product. Photosynthesis only happens in sunlight, or during the day. Plants give out significantly more oxygen in sunlight, or during the day, than they take in. At night, however, they don't photosynthesize; they only respire. This means that at night, plants take in oxygen but don't produce any.
https://indianapublicmedia.org/amomentofscience/sleeping-with-plants.php

https://www.bbc.co.uk/bitesize/guides/zpwmxnb/revision/3

What does the beach symbolize in the story "Through the Tunnel"?

Doris Lessing's story "Through the Tunnel" can be understood as a coming-of-age story.  Jerry and his mother are on vacation together, and Jerry is a typical, young boy.  He loves his mother, but he also wants to gain some independence from her.  He wants to test himself and see what he is capable of doing without a parent hovering right over him.  Readers realize much of this about Jerry from the first paragraph.  Jerry sees a rugged looking beach off in the distance.  It has some some rocks and is free from the crowd of vacationers, and Jerry wants to go explore it. However, he also feels badly about leaving his mother.  

Contrition sent him running after her. And yet, as he ran, he looked back over his shoulder at the wild bay; and all morning, as he played on the safe beach, he was thinking of it.

The next day, Jerry gathers up the courage to go to the other beach.  He is proud of himself, yet he does feel a bit lonely and maybe even a bit guilty at leaving his mother alone. 

There she was, a speck of yellow under an umbrella that looked like a slice of orange peel. He swam back to the shore, relieved at being sure she was there, but all at once lonely.

Jerry puts his mother out of his mind when he sees some native boys swimming in the water and diving through a long underwater tunnel.  Being able to make that swim through the tunnel becomes Jerry's sole focus for almost the rest of the story, but in order to do it, he must practice.  He cannot do that with his mother.  This is where the symbolism of the beach begins to come into play.  The tourist beach, where his mother stays, is the safe beach.  It is the beach for kids.  It is not the beach for brave teenagers and young men.  Jerry fully embraces this concept, and he even begins thinking of the tourist beach as "her beach."  His beach is the wild and rugged beach where he goes to train for his underwater swim to adulthood.  

It was a torment to him to waste a day of his careful training, but he stayed with her on that other beach, which now seemed a place for small children, a place where his mother might lie safe in the sun. It was not his beach.
He did not ask for permission, on the following day, to go to his beach.

The one beach is symbolic of childhood, safety, comfort, and security, but the wild beach is symbolic of danger, growth, adventure, uncertainty, and manhood. 

College Algebra, Chapter 3, 3.6, Section 3.6, Problem 24

Evaluate the expression (a) $(f \circ f) (-1)$ and (b) $(g \circ g)(2)$ using $f(x) = 3x -5$ and $g(x) = 2 - x^2$
a.) $(f \circ f) (-1)$
Solving for $f \circ f$,

$
\begin{equation}
\begin{aligned}
f \circ f &= f(f(x)) \\
\\
f \circ f &= 3(3x-5)-5 && \text{Substitute } f(x) = 3x - 5\\
\\
f \circ f &= 9x - 15 - 5 && \text{Simplify}\\
\\
f \circ f &= 9x - 20 && \text{Model}
\end{aligned}
\end{equation}
$

For $(f \circ f )(-1)$,

$
\begin{equation}
\begin{aligned}
(f \circ f )(-1) &= 9(-1) - 20 && \text{Substitute } x = -1\\
\\
(f \circ f )(-1) &= -9 -20 && \text{Simplify} \\
\\
(f \circ f )(-1) &= - 29
\end{aligned}
\end{equation}
$


b.) $(g \circ g)(2)$
Solving for $g \circ g$,

$
\begin{equation}
\begin{aligned}
g \circ g &= g(g(x))\\
\\
g \circ g &= 2-(2-x^2)^2 && \text{Substitute } g(x) = 2- x^2\\
\\
g \circ g &= 2-\left( 4 - 4x^2 + x^4 \right) && \text{Apply Distributive Property}\\
\\
g \circ g &= 2- 4 + 4x^2 - x^4 && \text{Simplify}\\
\\
g \circ g &= -2 + 4x^2 - x^4 && \text{Model}
\end{aligned}
\end{equation}
$


For $(g \circ g)(2)$,

$
\begin{equation}
\begin{aligned}
(g \circ g)(2) &= -2 + 4(2)^2 - (2)^4 && \text{Substitute } x = 2\\
\\
(g \circ g)(2) &= - 2 + 16 -16 && \text{Simplify}\\
\\
(g \circ g)(2) &= -2
\end{aligned}
\end{equation}
$

Why does Paul laugh uncontrollably over Billy Boy dying in "Where Have You Gone, Charming Billy?"

Tim O'Brien's short story "Where Have You Gone, Charming Billy?" is the tale of Private First Class Paul Berlin's first night of the Vietnam War as he and his platoon march through the countryside toward the coast. The two recurring themes in the story are Paul's fear and the death of fellow soldier, Billy Boy Watkins, who died of a heart attack that afternoon.
The platoon marches silently, trying to avoid the notice of enemy forces. Paul is therefore left alone with his thoughts in the dark, humid night—thoughts he is strenuously trying to avoid:

He was pretending he was not in the war, pretending he had not watched Billy Boy Watkins die of a heart attack that afternoon. . . . In the dark, with his eyes pinched shut, he pretended.

The men move single-file through the night without speaking, passing rice paddies, villages, and a graveyard. Paul follows obediently, though feelings of isolation persist.

The soldiers were quiet and hidden and faraway-seeming in a peaceful night, strangers on a long street, and he felt quite separate from them.

The silence, the darkness, and the foreign nature of Paul's surroundings, coupled with his sense of isolation, give the story a dreamlike feel, and the language is dense with references to sleep, dreams, and nightmares. The soldiers move "like sheep in a dream," and when roused from his thoughts, Paul shivers "as if emerging from a deep nightmare." It is only while "sleeping in his walking" that Paul's fear subsides, because his daydreams allow him to escape back to his family home or to a temporary oblivion. When he tries to engage with his surroundings, he cannot get any purchase on them: the stars overhead are strange and nameless, like the men in his platoon,

The string of shadow soldiers whose names he did not yet know moved with the silence and slow grace of smoke.

Everything is unreal to Paul, so it is natural to disengage and let his mind wander. His fellow soldier, however, emphasizes that Paul needs to stay alert despite the hypnotic nature of their milieu by saying,

You got a lot to learn, buddy. I’d shoot you if I thought you was sleepin’.

But Paul continues to drift into reveries as they march, even as he actively tries not to think. He counts his steps, he sings songs in his head, he imagines describing this place to his mother, and he imagines describing his actions to his father. He is attempting to distance himself from the reality he is moving through—to think of it in the past tense or not at all. He imagines things from a future perspective: "when he reached the sea," "after the war," "he would forget."
What Paul is trying to forget and distract himself from is the spectacle of Billy Boy Watkins's death. It intrudes on his thoughts throughout the story, although for most of it, the reader only knows that Billy Boy died of a heart attack—Paul's thoughts will not go further than that. It is when Paul is forced to engage with reality, in talking to Buffalo, that the memory of Billy Boy's death breaks through.
Billy Boy stepped on a land mine and blew off his foot. The pain and the fear he suffered caused his heart to fail. His body bag then fell out of the Medevac chopper into a rice paddy, and the soldiers had to spend the afternoon retrieving Billy Boy's corpse.
The scenario, from start to finish, is absurd, foolish, and sadly ugly. There is no dignity in Billy Boy Watkins's death, which should not have happened, anymore than his body should have fallen from a great height into a muddy, leech-infested paddy like a bundle of garbage. Death is sudden, unexpected, and weird. It is crude and stupid. No amount of retelling or distance will make the story of Billy Boy's death any less ridiculous, and it is the sheer absurdity of the situation which seems to terrify Paul the most. He has spent the entire day gripped by fear. At first, he felt completely paralyzed by it, but now he feels it to be "diffuse and unformed"—like mist. It surrounds him but does not prevent forward movement. His fear has become just another surreal element of the landscape to accept and ignore.
When Paul talks to Buffalo, a more experienced soldier, Buffalo wryly acknowledges the bizarre nature of Billy Boy's death:

Can’t get over it—old Billy Boy croaking from a lousy heart attack. . . . A heart attack—can you believe it?

He says Billy Boy was "tough as nails" and shakes his head at the thought of such a man succumbing to a heart attack—a heart attack which Doc Peret said was caused by fear:

He was scared he was gonna die—so scared he had himself a heart attack—and that’s what really killed him. I seen it before.

Confronted with the memory he has been trying to repress all day, Paul's fear ceases to be diffuse and takes on a distinct form: hysteria. Billy Boy was, like Buffalo, an experienced soldier, yet he "scared [himself] to death." No amount of experience could save him from his own terror, and nothing can make death more dignified. To really hammer the lesson home, Billy Boy's body "executed a long and dangerous dive [from the Medevac chopper], as if trying to escape Graves Registration," showing that the formal symbols of death (the registration, the flag-covered coffin, the telegram to family members) are nothing compared to the farcical reality of it. Paul's fear transforms into a kind of appalled hilarity, and he bursts out laughing thinking about it.

Giggling and remembering, he covered his mouth. His eyes stung, remembering how it was when Billy Boy died of fright.

His laughter now is compared to Billy Boy's crying that afternoon, showing that both are just symptoms of profound, unshakeable fear. No amount of reassurance or even sedation from Doc Peret could calm Billy Boy, and no amount of frantic warnings and shaking from Buffalo can stop Paul's hysterical giggling:

“Shut up!” the soldier hissed, but Paul Berlin could not stop giggling, remembering: scared to death.

It is only when Buffalo smothers him—literally deprives Paul of air—that Paul finally regains control of himself, distracted from his fear by the need to breathe. As the platoon marches on, Paul takes his temporary hysteria and uses it to distance himself from Billy Boy's death through humor, imagining it now as a "funny war story that he would tell to his father, how Billy Boy Watkins was scared to death. A good joke." As Buffalo tells him,

You got to stay calm, buddy. Half the battle, just staying calm.

Although Paul has discovered a coping mechanism, his fear does not go away and possibly never will.

Why might people have identified Richard Cory as the embodiment of success?

The townspeople in Robinson's "Richard Cory" look at Richard Cory as an example of success based on his appearance and mood while walking around the town. This is why the ending of the poem—when Cory commits suicide—is such an ironic and surprising twist.
The first stanza reads:

Whenever Richard Cory went down town,
We people on the pavement looked at him:
He was a gentleman from sole to crown,
Clean favored, and imperially slim. (1-4)
 

Cory is described as a "gentleman," which could indicate both good manners and high social class. The word "imperially" links to the latter meaning, as it is related to emperors. He seems powerful and attractive. 
The next stanza continues:

And he was always quietly arrayed,
And he was always human when he talked;
But still he fluttered pulses when he said,
"Good-morning," and he glittered when he walked. (5-8)

Even though Cory is described here as "always human," so not that different from the townsfolk, "he fluttered pulses" and "glittered." He is placed on a pedestal by the town, and every action is considered special.
 
The third stanza makes Cory's wealth obvious:


And he was rich—yes, richer than a king—
And admirably schooled in every grace:
In fine, we thought that he was everything
To make us wish that we were in his place. (9-12)



Here, he is said to be "richer than a king," and due to his wealth and "grace," the townspeople want to be "in his place." This becomes ironic in the final stanza because, as they struggle, he "Went home and put a bullet through his head" (16). This is surprising because the townsfolk think his wealth, manners, and gentlemanly nature make his life perfect. They envy him and wish to trade places with him. Obviously, there was something about his life, though, that was not perfect. His own perception of himself does not match the perception of the town.

What type of poetry did Edgar Allan Poe write (haikus, free verses, limericks)?

Edgar Allan Poe primarily wrote narrative poems, poems which tell stories in metered verse. While Poe's work wasn't explicitly meant to be recited or sung, he referred to many of his narrative poems as "ballads" for their highly lyrical and dramatic quality.
"Annabel Lee," one of Poe's most famous works (of poetry or otherwise), demonstrates his general style and approach to poetry. The common characteristics of this and many of his other poems are: alternating yet imperfect rhyme schemes, traditional stanza structure, and considerable length. (These are certainly no haikus!)
Consider the opening lines of "Annabel Lee:"
It was many and many a year ago,
In a kingdom by the sea,
That a maiden there lived whom you may know
By the name of Annabel Lee;
And this maiden she lived with no other thought
Than to love and be loved by me.

The stanza structure is traditional, and governed by an alternating rhyme scheme. Generally, the scheme is "ABAB," but Poe does not abide by this scheme rigidly. The poem tells a story about the death of a beautiful girl in a tone of rapture and despair. Poe's emotionally charged subject matter suits the narrative form. The poems harken to love songs or elegies with their rhyme schemes, and are long enough to create compelling narrative arcs with fully developed subjects.

What are some Restoration period features, important writers and their works?

The Restoration period in English literature is a short one, lasting from 1660–1688 and corresponding with the restoration of the Stuart monarchy to the English throne. A prominent feature of Restoration literature was the burst of theatre activity and the writing of new plays. The theater had been banned as immoral under the Puritan rule of Oliver Cromwell, so it came back with renewed vigor. Plays were often bawdy, comic, and risqué, a reaction to the soberness of the preceding period. Playwrights associated with the period include William Wycherley, most famous for the risqué drama, The Country Wife.
Puritanism, however, did not disappear with the end of Cromwell's reign. In this period, Bunyan published Pilgrim's Progress, while Milton published Paradise Lost. As dissenting religious groups faced increasing persecution after the Restoration, there was a growth of spiritual memoir. Newspapers began to become popular too, leading to the rise of the essay. John Dryden, a playwright, poet, and essayist, rose to prominence in this era. Aphra Behn, a woman playwright and writer, published Love Letters Between a Nobleman and his Sister.
All in all, this was a fertile and vibrant artistic era that set the stage for both the eighteenth century's comic literature and literature of sentiment.

The term “Restoration” refers to the return from France of Charles II in 1660.  The major literary changes took place in Drama/Theatre, because that is the genre that reflected the social changes that accompanied Charles' return. Some of the drama’s changes (and drama is the most public and visible literary form to reflect the changes) are actresses, comedies of wit, indoor theatre, wing-and-drop sets, the actor/manager configuration, and short runs, compared to Elizabethan, Jacobean, and Carolinian plays.    The French influences on Charles II are reflected in the risqué sexual references in the scripts, and the “party” atmosphere of theatre attendance.
 Some notable writers for Restoration theatre are William Congreve (Love for Love, The Way of the World), John Dryden (Aureng-Zebe, All for Love), George Etheridge (The Man of Mode), and George Farquhar (The Beaux' Stratagem, The Twin Rivals).   Aphra Behn (City Heiress), the first female playwright, should also be mentioned.
 

Just because a government has a constitution, does that mean that the constitution has to be followed?

The answer to this is “absolutely not.”  A constitution is just a piece of paper.  It can only be enforced on the government if the people are willing to do so.  This means the government does not have to obey the constitution unless the people force it to do so.
A constitution sets the rules that a government is supposed to follow.  However, a government cannot be coerced by outside forces.  Only the government has the legitimate right to engage in violence in a given society.  There is no force higher than the government that can physically compel it to act in a certain way.  This means that there is no entity that can force the government to obey its constitution. 
As an example of this, we can say that there was a long time when the US government did not obey some parts of its constitution.  The Constitution of the US (specifically, the 14th Amendment) says that all Americans have to enjoy the equal protection of the law.  However, African Americans and other people of color were not treated equally by the government for decades after the 14th Amendment was ratified.  There was no entity that could force the US government to obey the 14th Amendment.
Constitutions are only relevant if the people force the government to obey them.  In the 1950s and 1960s, public protests showed the American government that the people wanted it to honor the 14th Amendment.  At that point, it started to do so.  It was only pressure from the public that could force the government to obey. 
Constitutions are not strong walls against government misbehavior.  The government can violate the constitution if the people allow it to.  Governments only have to obey their constitutions if their people force them to do so.
 

Explain the process of animals genetically modified using DNA microinjection?

DNA microinjection is a process that is used, and has been used since 1980, to produce genetically modified organisms. It is most commonly used with mammalian DNA. Specifically, the technology is more often than not tested on and used with mice. Furthermore, DNA microinjection typically introduces DNA sequences that are not present in that particular species. This means that DNA microinjection technology is used to create transgenic organisms. Finally, the success rate of the process is incredibly low. It is reported as being successful only 10 percent to 20 percent of the time. This is because the DNA incorporation is random and might not happen, or it might interfere with critical DNA sequences that the organism needs to live in the first place.
The process of DNA microinjection is fairly straightforward and relatively low tech. A very fine pipette is used to "manually inject" DNA from one organism into the fertilized egg of another organism. The hoped for result is that the injected DNA will be incorporated/integrated into one of the chromosomes of the fertilized egg. Mitotic divisions will occur, and the new DNA sequences within that chromosome will be replicated. The fertilized egg is then transferred into the oviduct of a female. The organism is now pregnant and will hopefully give a normal birth to an organism that hopefully displays the transgene trait.
https://research.uci.edu/facilities-services/tmf/services/dna-micro.html

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3459342/

https://www.thebalance.com/microinjection-375568

What is the lesson in Jane's rebellion and attempt at freedom? Is there a better way she could have handled her oppression? Do we see this in the world today?

Jane's rebellion takes place within the context of the patriarchal society that oppresses her. The room with the yellow wallpaper is symbolic of her imprisonment within the system set up by her husband, a doctor, and her brother, who is also a doctor. Trapped by the system they have set up for her, which is intended to be coddling but is also infantilizing, she sinks deeper and deeper into depression. Her husband's treatment of her is representative of the male medical establishment of the time, in which women's complaints, which often arose out of boredom (for wealthy women, who also had servants), were treated with a debilitating "rest cure." 
Jane's rebellion consists only of peeling the wallpaper off her walls, which is, of course, not a rebellion at all. To fully resist the patriarchy of the time would have required her to leave the room with the yellow wallpaper. She would have had to escape from the infantilizing care of the men around her and to enter the world, in which she could do what she enjoyed, including writing. 
Many people today would agree that the patriarchy controls women. While women are becoming more outspoken about their oppression, the systems of medicine, politics, business, and other realms are still controlled largely by men. In other words, these systems still ensnare women in a system that many people deem oppressive and unfair. It is only by enabling women to construct their own systems or change these systems that they can escape from the oppression of sexism.

Why do you need history to be a lawyer?

History is important for the study of law because studying history teaches one to look for cause and effect relationships.  In order to fully appreciate an action, one must look at the reasons why the action took place.  This ability to analyze is important for both historians and lawyers.  Historians are also excellent writers who carefully check facts and are comfortable citing outside sources.  Lawyers have to write well in order to have influence and they cite precedents to make their arguments even stronger.  
 
Also, much of history, especially political and legal history is the study of laws.  The Constitution is the supreme law of the United States.  Lawyers base their defenses and prosecutions on whether or not someone's constitutional rights were violated.  The more one can study the Constitution, the more likely one is to know his/her rights and can better exercise them.  

Calculus of a Single Variable, Chapter 5, 5.6, Section 5.6, Problem 49

y = 2arccos(x) - 2sqrt(1-x^2)
First, express the radical in exponent form.
y = 2arccos(x)-2(1-x^2)^(1/2)
To take the derivative of this, use the following formulas:
d/dx(arccos(u)) = -1/sqrt(1- u^2) (du)/dx
d/dx(u^n)= n*u^(n-1) *(du)/dx
Applying these formulas, the derivative of the function will be:
(dy)/dx = d/dx[2arccos(x) - 2(1-x^2)^(1/2)]
(dy)/dx = d/dx[2arccos(x)] - d/dx[2(1-x^2)^(1/2)]
(dy)/dx = 2d/dx[arccos(x)] - 2d/dx[(1-x^2)^(1/2)]
(dy)/dx = 2 * (-1/sqrt(1-x^2))*d/dx(x) - 2 * 1/2(1-x^2)^(-1/2) * d/dx(1-x^2)
(dy)/dx =2 * (-1/sqrt(1-x^2))*1-2*1/2(1-x^2)^(-1/2)* (-2x)
(dy)/dx =2 * (-1/sqrt(1-x^2))*1-2*1/2*1/((1-x^2)^(1/2))* (-2x)
(dy)/dx =2 * (-1/sqrt(1-x^2))*1-2*1/2*1/sqrt(1-x^2)* (-2x)
(dy)/dx = -2/sqrt(1-x^2) +(2x)/sqrt(1 -x^2)
(dy)/dx = (2x-2)/sqrt(1-x^2)

Therefore, the derivative of the function is (dy)/dx = (2x-2)/sqrt(1-x^2) .

Explain why acid rain is unevenly distributed across the world.

Acid rain is rain that has a slightly more acidic pH level than normal.  Pure water has a pH level of 7.  Rain is generally slightly acidic to begin with, so "acid rain" is rain that tends to have a pH of 5.0 - 5.5.  The acid rain itself can be created through a combination of natural and man-made sources.  For example, volcanic eruptions give off elements that help to produce acid rain.  Human sources come from car exhausts and various fossil fuel burning activities.  
Both of the above natural and man-made sources of acid rain are not evenly distributed across the globe.  Population densities vary across continent to continent.  Additionally, natural soil compositions differ as well.  Lastly, prevailing winds can carry acid rain and its components far away from their source regions.  All of those reasons combined explain why acid rain is not evenly distributed across the globe.  In the United States for example, acid rain tends to occur most in the Northeastern United States.  This is because of the high population density, the number of large cities (with their power plants), and the winds tend to carry Midwest pollution to the Northeastern United States.  
 

What is the difference between a natural disaster and a natural hazard?

To understand this, we must first provide definitions for "disaster" and "hazard" in order to differentiate between the two. According to Merriam-Webster, there are a few definitions each for disaster and hazard; however, we will use the definitions that relate to our discussion. Disaster is “a sudden calamitous event bringing great damage, loss, or destruction,” whereas hazard is “a source of danger.” 
A natural hazard would be a theoretical natural source of danger—something that has the potential to cause harm. A natural disaster, by contrast, would be the result of a natural hazard, should that hazard wreak havoc and destruction on land, communities, resources, etc. For example, Hurricane Harvey was a natural hazard that became a natural disaster once it made landfall and wreaked destruction. 
https://cnx.org/contents/ZFLM8Ssk@1/The-difference-between-natural

What was the New Deal?

The New Deal was the name given to President Franklin D. Roosevelt’s programs to try to help deal with the effects of the Great Depression. When President Roosevelt got elected, the American people were suffering tremendously. Many people were unemployed, and many had lost their savings when the stock market crashed and banks failed. The New Deal programs tried to help the American people deal with the devastating effects of the Great Depression.
There were several kinds of programs. There were reform programs to try to ensure the Great Depression wouldn’t happen again. The Securities Act and the Glass-Steagall Act placed regulations on banks and on the investment industry. There were relief and recovery programs also. Several programs were established to create jobs. The Civilian Conservation Corps and the Civil Works Administration are two examples of programs designed to get people back to work. The Agricultural Adjustment Act paid farmers to not grow crops. The National Industrial Recovery Act had businesses, workers, and the government working together to set prices and establish wages. The Social Security Act provided a pension to people who retired at age 65 or later.
These New Deal programs were designed to deal with the effects people experienced as a result of the Great Depression.
https://www.history.com/topics/great-depression/new-deal

What are the kennings used during Beowulf's battle with Grendel?

A kenning is basically a two-word description in place of a more common one-word noun or name. Kennings are often seen in Anglo Saxon poetry, which was originally transmitted orally. In Beowulf, as in other poems of the time, the poet uses kennings to add variety to the wording and to more vividly paint a picture of the action for the reader.
In the section of the poem where Beowulf fights Grendel, we see a couple of kennings to describe Grendel. The poet calls Grendel a "terror-monger," which is a kenning that conveys the fear evoked by Grendel. Grendel is also referred to as a "hell-serf," which shows that he is a servant and devotee of Satan. Both of these kennings enhance the description of Grendel as evil.
A couple of other kennings are used throughout the battle to describe places or things. Grendel's presence in the mead hall is referred to as "a hall-session," which, unlike the kennings applied to Grendel, seems to de-intensify the event. Grendel's sinews, muscles, or tendons are referred to twice as "bone-lappings," a vivid description of Grendel's physique that adds to the gore and violence of the battle scene.
Beowulf is described as "the earl-troop's leader" in a kenning as well. This kenning indicates his position and contrasts with the more loaded descriptions of Grendel discussed above.
These kennings give the poem more stylistic variety than if the poet had used Grendel's name or simple nouns. The poetic descriptions also enhance the imagery and mood of the scene.

Beowulf's battle with Grendel begins on line 750 when Grendel seizes Beowulf's arm, not knowing that it is Beowulf, nor knowing anything of his strength. However, he immediately realizes that Beowulf is not like the other men, nor any man he has ever encountered. The battle ends on line 823, when Grendel flees, and is concluded on line 836 when we are told that Beowulf has fully ripped off Grendel's arm.
Kennings are compound metaphors common in Old Norse and its derivative languages and literary cultures. One of the first encountered in "Beowulf" is "whale-road" in line 10, a metaphor for the ocean. At first glance these might seem frivolous and unnecessary to the casual reader—why not just say "sea"? Part of the answer lies in the fact that "Beowulf" originated as oral poetry, and thus it would serve the poet to have an array of imaginative phrases, with different sounds and length, to drive the telling more in the direction of art than a simple relaying of facts. Some translations attempt to preserve the extensive alliteration present in the original text, some of which is supported by kennings. For example,

syndolh sweotol·      seonowe onsprungon·
burston bánlocan·      Béowulfe wearð
gúðhréð gyfeþe·      scolde Grendel þonan
feorhséoc fléön      under fenhleoðu,

This section from lines 817-819 employs frequent kennings to construct a "s - b - g/th - f" alliterative scheme with one sound dominating each line.
Kennings used in the battle include:
bone-adorned (probably meaning "armored")
life-days and day-count (lifespan)
sin-scather (using an archaic form of "scathe", meaning injury)
bone-locks (muscles)
slaughter-storm (massacre or gory battle)

Kennings are a type of metaphor in which a descriptive phrase is substituted for the word itself.  There are many modern examples of kennings such as "four eyes" for someone who wears glasses.  Kennings are prevalent in Anglo Saxon literature, and in Beowulf's battle with Grendel, there are many examples.  Here are a few:
"gold-shining hall" for Herot
"shepherd of evil" for Grendel
"mighty protector of men" for Beowulf
In the description of the battle, the poet uses many different kennings to describe the major players.  You can find kennings for Hrothgar, Beowulf, Grendel. These serve to emphasize the magnitude of the battle between good and evil.  There is no ambiguity here.  Through the kennings, we see Grendel as unequivocally evil and Beowulf as the ideal Anglo Saxon hero, who is championed by god. 
 

Calculus: Early Transcendentals, Chapter 6, 6.1, Section 6.1, Problem 35

y=3x^2-2x , y=x^3-3x+4
Refer the attached image. Graph of y=3x^2-2x is plotted in red color and graph of y=x^3-3x+4 is plotted in blue color.
From the graph, the x-coordinates of the intersection of curves are x ~~ -1.1 , x ~~ 1.25 , x ~~ 2.875.
Area of the region bounded by the curves A =int_(-1.1)^(1.25)((x^3-3x+4)-(3x^2-2x))dx+int_1.25^2.875((3x^2-2x)-(x^3-3x+4))dx
=int_(-1.1)^1.25(x^3-3x+4-3x^2+2x)dx+int_1.25^2.875(3x^2-2x-x^3+3x-4)dx
=int_(-1.1)^1.25(x^3-3x^2-x+4)dx+int_1.25^2.875(-x^3+3x^2+x-4)dx
=[x^4/4-3x^3/3-x^2/2+4x]_(-1.1)^1.25+[-x^4/4+3x^3/3+x^2/2-4x]_1.25^2.875
=[x^4/4-x^3-x^2/2+4x]_(-1.1)^1.25+[-x^4/4+x^3+x^2/2-4x]_1.25^2.875
=(1.25^4/4-1.25^3-1.25^2/2+4*1.25)-((-1.1)^4/4-(-1.1)^3-(-1.1)^2/2+4(-1.1))+(-(2.875)^4/4+2.875^3+2.875^2/2-4(2.875))-(-(1.25)^4/4+1.25^3+1.25^2/2-4(1.25)) =(2.875976563)-(-3.307975)+(-0.683654785)-(-2.875976563) =8.37627334

How does Gulliver reach Brobdingnag?

Gulliver describes himself as "condemned, by nature and fortune, to active and restless life," and about two months after he returns from Lilliput, he leaves home again to seek new adventures. The ship is blown far off course by numerous storms and strong winds, and though everyone is safe and healthy, the crew finds that they are now experiencing a scary shortage of water. Finally, one day, they spot land, and Gulliver "desire[s] . . . leave to go with them, that [he] might see the country, and make what discoveries [he] c[an]." When the small group arrives on the coast, they see no sources of fresh water and no sign of inhabitants. Gulliver wanders off by himself while the other men go to look for water; he discovers that the land looks totally barren and rocky—unlikely to satisfy their needs—so he heads back toward the others. However, he says, "I saw our men already . . . in the boat, and rowing for life to the ship" with "a huge creature walking after them in the sea as fast as he could." In other words, he is abandoned by the other members of the crew because they have to run for their lives from this huge creature! At this point, Gulliver takes off in the direction from which he came and finds an area that was "fully cultivated." He takes a road through a field and eventually comes to a farm.

The short answer is: by accident. A restless, adventure-starved Gulliver sets sail from Bristol. His destination is India. But a voyage involving Gulliver just wouldn't be the same without some trouble on the high seas; and so it proves once more. One day, a sudden westerly wind whips up and knocks Gulliver's ship, the appropriately named Adventure, off course. The ship is forced to land at the Cape of Good Hope, where the crew spends the winter. Then the Adventure takes to the sea once more, and everything seems plain sailing until it passes along Madagascar. For twenty terrifying days, the ship is battered by a violent, savage storm which drives it off course completely.
Eventually, the ship finds dry land. Gulliver and a party of men step ashore to fetch water. Gulliver becomes separated from the men, and when he returns to the shore, he's shocked to discover the other men rowing furiously away in the distance towards the ship, followed by a giant creature. Gulliver is all alone on Brobdingnag, the land of the giants.

What is the distance between the sun and the moon during a solar eclipse?

During a solar eclipse, the Moon is in between the Earth and the Sun, but much, much closer to the Earth than the Sun.The precise distance would depend upon where the Earth is in its orbit; at perihelion the Earth is about 146 million kilometers from the Sun, while at aphelion the Earth is about 152 million kilometers from the Sun. The average is precisely one AU, or about 149.6 million kilometers.Then, it depends where the Moon is in its orbit around the Earth. At perigee the Moon is about 363,000 kilometers from the Earth; at apogee it is about 407,000 kilometers from the Earth. On average, it is about 384,000 kilometers away.As you can see, the distance from the Moon to the Sun really doesn't depend all that much on where the Moon is relative to the Earth; it depends almost entirely on where the Earth is relative to the Sun. In this sense, the "during a solar eclipse" part is kind of redundant; even during a lunar eclipse the Moon would only be about 800,000 kilometers further away from the Sun, while the Earth's orbit can shift the distance by some 6,000,000 kilometers.The minimum possible distance between the Moon and the Sun during a solar eclipse would be when the Moon is at apogee but the Earth is at perihelion; this would be 146,000,000 - 363,000 = 145.7 million kmThe maximum possible distance would be when the Moon is at perigee but the Earth is at aphelion; this would be 152,000,000 - 407,000 = 151.6 million kmAnd the average distance between the Moon and the Sun would be 149,600,000 - 384,000 = 149.2 million km
https://www.space.com/17081-how-far-is-earth-from-the-sun.html

What time period is The Crucible depicting? Explain why a time period of 1693 was used and why is this relevant today.

This question is asking several questions, but a part of the question states that Arthur Miller set The Crucible in 1693. That time period is the very beginning of the Age of Reason. It's also called the Enlightenment. The Age of Reason emphasized using reason as a way of obtaining truth about the world and reality. As for why Miller chose that particular date, he didn't really have any choice. The play is about the Salem Witch Craft Trials, and 1693 is the actual historical date of that event in American history. Miller's play is a cleverly woven historical fiction. Characters in the play are real people that lived in Salem and were involved. The accused were actually accused, and the judges were actual judges. Miller does take some creative liberties with Abigail and how she lead the girls through fear and was in love with John Proctor; however, there are court sequences in which Miller used portions from the actual trials.
I'm not sure what the final part of the question is asking. It could be asking why the Enlightenment is relevant today or why Miller's choice to write a play about this Salem event is relevant. In either case, it is a "what do you think" type of question, so you can feel free to give your own reason and defend it. Perhaps there is a modern day parallel about people or judicial systems taking a person at their word about a particular kind of accusation. As people believe the accusation, more and more people start accusing other people of the same thing in an attempt to gain power or recognition.

Single Variable Calculus, Chapter 7, 7.4-1, Section 7.4-1, Problem 82

Determine the area of the region bounded by the curve $\displaystyle y = \frac{2}{x-2}$, $x$-axis, $x = -4$ and $x = 1$.

By using vertical strips,

$
\begin{equation}
\begin{aligned}
A &= \int^{-1}_{-4} \left( y_{\text{upper}} - y_{\text{lower}} \right)\\
\\
A &= \int^{-1}_{-4} \left(0 - \left( \frac{2}{x-2} \right) \right) dx\\
\\
A &= \int^{-1}_{-4} \frac{-2}{x-2} dx
\end{aligned}
\end{equation}
$

Let $u = x- 2$
$du = dx$

Make sure that the upper and lower units are in terms of $u$.

$
\begin{equation}
\begin{aligned}
A &= -2 \int^{-1-2}_{-4-2} \left( \frac{1}{u} \right) du\\
\\
A &= - 2 \int^{-3}_{-6} \frac{du}{u}\\
\\
A &= -2 [\ln u]^{-3}_{-6}\\
\\
A &= -2 [\ln(-3)-\ln(-6)]
\end{aligned}
\end{equation}
$

We can't evaluate the area since $\ln$ of negative number doesn't exist. However, since the function is reflected about $x = 2$ its area is equal to the region bounded by the curve, $x$-axis and the lines $x = 5$ and $x = 8$. $A = 1.3863$ square units.

Why did Bambi admire the old stag?

I am unsure about whether or not the question is asking about the Disney film version of this story or the actual text written by Felix Salten. For this particular question, it probably doesn't matter. The film presents the old stag in a way that runs true to the book. Chapter 6 is probably a reader's best place to look for why Bambi admires the old stag. The narrator does a nice job of including a lot of Bambi's thoughts when he first encounters the old stag. We are told that the old stag looked more powerful than the other male deer. The stag also appeared "taller and prouder." Everything about him commands attention from others because of how regal and stately he looks and acts.

His coat shone with a deeper, richer red, but his face silver gray. And tall, black, beaded antlers rose high above his nervous ears.

The old stag's voice even commands obedience. Readers are told that Bambi was "completely dominated by his masterful voice, and at the same time, he admired it." Bambi admires the old stag for the same reasons that the other young deer, other males, and females admire him. He is big, powerful, handsome, and commands attention. He does this as a nobleman would and not how a dictator would, and Bambi admires that.

When Athena departs from Telemachus and Nestor, how does she reveal that she is a goddess?

In book 3 of The Odyssey, Athena shape-shifts from Mentor, a seeming mortal, into an eagle, right in front of Telemachus, the old king Nestor, and the Achaeans. As Athena flies away, the king is astonished, and Telemachus's status is suddenly elevated. The fact that a young person like Telemachus has the personal protection of Athena means he is a truly special prince worthy of particularly special treatment.
Immediately after Athena's exit, King Nestor and the rest of the Achaeans realize that Mentor was actually the goddess in disguise. As Mentor accompanied Telemachus during their arrival to King Nestor's banquet, the king realizes that the goddess had been there all along. The king summons his queen to begin preparations to honor Athena with a ceremony, as he feels honored to have had the presence of the goddess at one of his own feasts.

After Nestor, the King of Pylos, invites Telemachus to stay in his palace in Book Three, Athena, disguised as Mentor, tells Nestor and Telemachus that she will go back to the ship. Then, "With that the bright-eyed goddess winged away/in an eagle's form and flight" (lines 415-416; Fagles translation). In other words, she turns into an eagle and flies away in front of Nestor and Telemachus. Nestor seizes Telemachus's hand and tells him that he, Telemachus, will never be a coward or "defenseless" because he is protected by the gods. Nestor immediately knows that Mentor was really Athena, and he makes a sacrifice to her right away, as mortals are supposed to do. The next day, Nestor orders the slaughter of a heifer, and he summons a goldsmith to coat the heifer's horns in gold. He then makes a sacrifice to Athena, who attends the ritual. 

Give me three reasons why Lyddie should have signed the petition and three reasons why she shouldn't.

Three reasons why Lyddie should sign the petition:
1). It's important for all the workers at the factory to show solidarity, to stick together. If pay and conditions can be improved, then Lyddie will benefit as much as anyone. It's in her own interests to sign.
2). There are no labor unions at the factory. Signing a petition is one of the only ways that the women can campaign for change. If they just hunker down and do nothing, then things will only get worse.
3). It's the right thing to do. Conditions at the factory are so bad that something has to change. The bosses need to know the strength of feeling among the workers, that they're not happy with how things are going. If they're not made aware of any grievances, then they can't do anything to address them.
Three reasons why Lyddie shouldn't sign the petition:
1). Lyddie is one of the most productive, hardworking women at the factory. If wages in general are increased, then hers might be reduced. Then she won't be able to help out her family back home.
2). Signing the petition is pointless. The bosses don't care, and they're not about to listen to the grievances of their workforce, whether it's through a petition or any other means.
3). The bosses effectively have their employees over a barrel. They know that they can always hire new workers relatively quickly and cheaply to replace the old ones. The petition is risky because it might give the bosses an excuse to lay off existing workers and hire new ones. Then where would Lyddie be?

In "Battle Royal," who are the protagonist and the antagonist? Give examples from the story to support your answer.

The protagonist in "Battle Royal" is the narrator. The other nine African-American youth do not "care too much" for him and are, therefore, not pleased that he will be at the fight, so they feel antagonistic toward the narrator. In addition, there are other antagonists: the white men who exploit them during the battle.
Ralph Ellison's narrator is invited to give a graduation speech, and since he is going to be in the hotel for this speech, he is told that he might as well participate in the battle royal with some of his schoolmates. This is a fight among the youths that the town's "big shots" attend in their tuxedos.
The narrator has his doubts about participating in this fight with them: he says, "I felt superior to them in my way, and I didn't like the manner in which we were all crowded together into the servants' elevator. Nor did they like my being there."
When they arrive in the ring, the narrator hears the school superintendent yell, "Bring up the shines, gentlemen! Bring up the little shines!"
The young men find themselves there facing a naked white women. They are embarrassed, worried, aroused, and laughed at during the exhibition. The narrator's teeth chatter in fear. As the woman begins to dance, one boy pleads to go home, embarrassed at his uncontrollable physical reaction.
The older white men become very excited by the young woman and they delight in the discomfort of the young men. After the young woman is removed, the African-American youth are further exploited as they are blindfolded and told to hit each other. As the white men yell for them to kill each other, the narrator recalls that "everyone fought hysterically. It was complete anarchy." After the fight is over, the youths are told that their money for fighting is on the rug. But, when they grab for it, they receive electric shocks. The narrator finds himself knocked around and shocked repeatedly, and he later realizes that the coins are brass advertising tokens.
When he finally is allowed to give his speech, the narrator accidentally says "social equality" when he has meant to say "social responsibility." Quickly, the narrator apologizes. Then, he is given a briefcase that contains inside a scholarship to the state college for Negroes. The narrator is so overjoyed that he does not even mind that the coins given him are merely brass pocket tokens that advertise a certain make of an automobile.

Why did Mr. Lewis stop for Bud?

The answer to this question can be found in chapter 10. Bud has decided that he is going to walk to Grand Rapids, and he's trying really hard to not be noticed. He hides in a bush or off to the side of the road every time a car passes, but he quickly grows tired of this action.

I was getting so tired that I started to forget to duck in the bushes when a car would roar by.

Bud is noticed by a car that stops and reverses back to Bud, and the man in the car gets out and starts whistling loudly and calling out to Bud. Bud is still hiding, but the man knows what he saw. He yells out that being a "brown boy" outside of Owosso is not the place to be.

And I'll tell you, I've seen some things out of place before and a young brown-skinned boy walking along the road just outside of Owosso, Michigan, at two-thirty in the morning is definitely not where he ought to be. In fact, what is definite is that neither one of us should be out here this time of night.

Bud eventually will get into the car with the man, and the man further explains that Owosso is an unsafe place for black people.

Bud-not-Buddy, you don't know how lucky you are I came through here, some of these Owosso folks used to have a sign hanging along here that said, and I'm going to clean up the language for you, it said, "To Our Negro Friends Who Are Passing Through, Kindly Don't Let the Sun Set on Your Rear End in Owosso!"

Mr. Lewis stops for Bud because he is a kind man, and he knows that Bud is young and in a dangerous location. Mr. Lewis wants to help get Bud to safety.

Explain how greed appears in The Death of Ivan Ilyich and Hedda Gabler.

"Greed" is present in these two works not so much in the conventional sense of avarice for money or possessions, as in the valuing of the material life over the spiritual one.
Ivan Ilyich, though a man without glaring faults of any sort, has lived in the normal way people do, for work and for the support of his family and the ordinary things of earthly life. So have his wife and daughter. When he becomes ill, it's as if this is the first time he realizes that he is vulnerable and that earthly life will come to an end. His wife and daughter still don't sense that basic truth, and seem to have little empathy, just wanting to go on, uninterrupted, with their own material concerns. When he comes back from the doctor and tries to tell them what he has learned about his illness, they are unconcerned, more interested in going out shopping than in listening to him. The only person who does have a degree of empathy is Ilyich's footman, Gerasim. We're told that Gerasim is of peasant background, and so, being part of a class that has never had material wealth, he understands Ivan Ilyich's plight in the way middle-class people and the aristocrats cannot.
Hedda Gabler finds her marriage boring and empty because the rarefied, intellectual world of her husband is meaningless to her. One could conclude that Hedda's "greed" is based on a wish for a level of excitement and action (partly requiring money her husband Tesman does not have) that's lacking in her marriage. But it's also a more fundamental emptiness about life in general that she feels. Hedda emerges as a personality always in need of something more than a basic, comfortable life. The way she plays around with a gun is symbolic of this desire, or greed if we will, for thrills, for danger. The attitudes of both Tesman and Thea concerning Ejlert's destroyed manuscript are inappropriate and ridiculous to her. But behind this there is an existential incompleteness in her character, deeper and more radical than the unhappy materialism of the people in Tolstoy's novella. The linking element is the absence of "higher" values, with which both Tolstoy and Ibsen find fault, and this accounts for the characters' materialism and greed.

In Hedda Gabler, there are several different types of greed. George Tesman, Hedda's husband, and Eilert Løvborg are greedy for a certain type of esteem as writers and scholars and for greatness in their fields. Tesman is also greedy for social standing. The central conflict of the play is the men's competition over esteem and prestige. Hedda herself is greedy for several things: the lifestyle she feels is her due because of her birth, the admiration of men, and self-determination. This brings her into conflict with her husband and with Thea Elvsted, who is greedy for her role as a muse and inspiration to Løvborg. Judge Brack's main form of greed is lust.
Ivan Ilyich is a character primarily motivated by greed for material goods and power. His marriage and his career are focused on attaining these, and it is not until he becomes ill that he realizes that his pursuit of material goods has not brought him happiness. Praskovya Fyodorovna, his wife, is also more concerned about her husband's salary and pension than about him as a person—she also illustrates that greedy people live unhappy lives. 

Please explain the metaphor, "we cling to out last pleasures as the tree clings to its last leaves." How does it contribute to the story?

The direct context of the quote is that the retired Woodifield, who has had a stroke, is only allowed out to visit the City--central London--once a week by his wife and daughters. They can't imagine what he does there, but then the narrator explains that "we cling to our last pleasures as the tree clings to its last leaves."
A tree clinging to its last leaves is an image of a tree near to death. This statement implies that Woodifield too is nearing death. He is an older man, and it does give him pleasure to get out and visit an old friend, as well as smoke a cigar.
By more than simply a reference to Woodifield, it sets the tone for a very bleak story which primarily concerns death: the death of Woodifield and the boss's sons in World War I (Woodifield has come to report that his daughters saw both graves). It provides a context and becomes a metaphor for the disturbing high point of the story, in which the boss deals with his grief over his dead son by torturing a fly to death, perhaps enacting how he feels he is slowly being tortured to death, drop by drop, by a malevolent god--or how he feels his son died, tortured on the battlefield, drop by drop. In the end, however, the boss does not derive "pleasure" from playing god, for

such a grinding feeling of wretchedness seized him that he felt positively frightened.

Mansfield shows us in this story a life with few pleasures as the older generation grapples with the destruction World War I has wrought.

Strictly speaking, this is a simile, not a metaphor. (Note the use of the word "as" being used for comparison.) What Mansfield means by this is shown in the line immediately after:

"So there sat old Woodifield, smoking a cigar"

Since his stroke, old Woodifield doesn't get out much. In fact, he's only allowed to venture out once a week (on Tuesdays) by his wife and daughters. And as this is a Tuesday, here he is, sitting in the plush, comfortable office of his old friend, the boss. Woodifield's health problems and his enforced captivity at home appear to suggest that he does not have much to look forward to in life. They also hint that Mr. Woodifield has very much entered into his "autumn" years, so to speak. So, by smoking a cigar, he is clinging onto one of the last pleasures he has left in life. In that sense, he is like a tree approaching autumn whose dying leaves are about to fall.

How did Zero and Stanley go missing in Holes?

In chapter thirty, tensions peak when Zigzag and the other boys begin bullying Stanley for allowing Zero to dig part of his hole. When things turn physical and Zigzag begins to beat Stanley, Zero intervenes and starts choking Zigzag. After the truth about Stanley teaching Zero is revealed, the Warden quizzes Zero, and Mr. Pendanski makes fun of his illiteracy, which prompts Zero to swing his shovel at the counselor and knock him unconscious. Zero immediately leaves the camp and the Warden instructs the counselors to wait for his inevitable return to Camp Green Lake.
Stanley understands that Zero's only chance of survival is to make it to God's Thumb and attempts to steal Mr. Sir's water truck to save him but ends up crashing it into a hole. Stanley then gets out of the vehicle and runs into the desert in search of Zero.
Essentially, the two boys go missing in the desert after fleeing the camp. The two boys reunite in the middle of the desert, survive on sploosh for a short time, and travel to God's Thumb, where Stanley carries Zero to the top of the mountain, and the two boys replenish themselves with onions and fresh water.

Zero first goes missing in chapter 30, after the Warden discovers that Zero is helping to dig Stanley's holes in exchange for reading lessons. The Warden subjects Zero to humiliation in front of all the other boys, and Mr. Pendanski tells Zero "digging is all you'll ever be good for." Zero knocks him out with his shovel and takes off into the desert. Stanley knows that Zero's only chance of surviving out there is to find God's Thumb. Angry and afraid for his friend, Stanley gets inspiration from the new kid Twitch and tries to hijack Mr. Sir's car to drive out and search for Zero, but he ends up crashing the car into a hole. His only choice is to run away with his empty canteen. The Warden, Mr. Pendanski, and Mr. Sir have destroyed Zero's files, so to them, he never existed. In a sense, Stanley sacrifices himself by venturing out into the desert in order to save Zero's life.

Single Variable Calculus, Chapter 3, 3.5, Section 3.5, Problem 47

Find the first and second derivatives of $h(x) = \sqrt{x^2+1}$
Solving for the first derivative of the given function


$
\begin{equation}
\begin{aligned}
h'(x) & = \frac{d}{dx} \left( \sqrt{x^2+1} \right)\\
\\
h'(x) & = \frac{d}{dx} (x^2+1)^{\frac{1}{2}}\\
\\
h'(x) & = \frac{1}{2} (x^2+1)^{\frac{-1}{2}} \frac{d}{dx} ( x^2 +1 )\\
\\
h'(x) & = \frac{1}{2} (x^2+1)^{\frac{-1}{2}} \left[ \frac{d}{dx} (x^2) + \frac{d}{dx} (1) \right]\\
\\
h'(x) & = \frac{1}{2} (x^2+1)^{\frac{-1}{2}} (2x+0)\\
\\
h'(x) &= \frac{\cancel{2}x}{\cancel{2}(x^2+1)^{\frac{1}{2}}}\\
\\
h'(x) &= \frac{x}{\sqrt{x^2}+1}
\end{aligned}
\end{equation}
$


Solving for the second derivative of the given function


$
\begin{equation}
\begin{aligned}
h''(x) &= \frac{d}{dx} \left( \frac{x}{\sqrt{x+1}} \right)\\
\\
h''(x) &= \frac{d}{dx} \left[ \frac{x}{(x^2+1)^{\frac{1}{2}}} \right]\\
\\
h''(x) &= \frac{\left[ (x^2+1)^{\frac{1}{2}} \cdot \frac{d}{dx}(x) \right]- \left[ (x) \cdot \frac{d}{dx} (x^2+1)^{\frac{1}{2}}\right] }{\left[ (x^2+1)^{\frac{1}{2}}\right]^2}\\
\\
h''(x) &= \frac{\left[ (x^2+1)^{\frac{1}{2}} (1)\right] - \left[ (x) \left( \frac{1}{2}\right) (x^2+1)^{\frac{-1}{2}} \cdot \frac{d}{dx} (x^2+1) \right] }{x^2+1}\\
\\
h''(x) &= \frac{(x^2+1)^{\frac{1}{2}} - \left[ \left(\frac{x}{2} \right)(x^2+1)^{\frac{-1}{2}} (2x+0)\right]}{x^2+1}\\
\\
h''(x) &= \frac{(x^2+1)^{\frac{1}{2}} - \left[ \left( \frac{x}{\cancel{2}} \right) (x^2+1)^{\frac{-1}{2}} (\cancel{2}x)\right] }{x^2+1}\\
\\
h''(x) &= \frac{(x^2+1)^{\frac{1}{2}} - (x^2)(x^2+1)^{\frac{-1}{2}}}{x^2+1}\\
\\
h''(x) &= \frac{(x^2+1)^{\frac{1}{2}} - \frac{x^2}{(x^2+1)^{\frac{1}{2}}}}{x^2+1}\\
\\
h''(x) &= \frac{\frac{\cancel{x^2} +1 - \cancel{x^2}}{(x^2+1)^{\frac{1}{2}}}}{x^2+1}\\
\\
h''(x) &= \frac{1}{(x^2+1)(x^2+1)^{\frac{1}{2}}}\\
\\
h''(x) &= \frac{1}{(x^2+1)^{\frac{3}{2}}}
\end{aligned}
\end{equation}
$

Calculus of a Single Variable, Chapter 9, 9.1, Section 9.1, Problem 44

cos(pi n)={(1 if n=2k-1),(-1 if n=2k):}, k in ZZ i.e. it is equal to 1 for odd n and -1 for even n. Therefore, we can break this into two cases.
n=2k-1 (n is odd)
lim_(n to infty)a_n=lim_(n to infty)1/n^2=1/infty^2=1/infty=0
n=2k (n is even)
lim_(n to infty)a_n=lim_(n to infty)-1/n^2=-1/infty^2=-1/infty=0
Since the limit is the same in both cases, the sequence is convergent and its limit is equal to zero.
Image below shows first 15 terms of the sequence. We can see that the odd-numbered terms are negative, while the even-numbered terms are positive, but they are both approaching the x-axis implying convergence to zero.

What works of literature does Paul Kalanithi reference in When Breath Becomes Air?

Paul Kalanithi’s moving memoir When Breath Becomes Air, which Kalanithi wrote while dying of cancer in his thirties, is peppered with references to and quotes from other works of literature. Kalanithi, who was trained as a neurosurgeon, earned degrees in literature and philosophy at Stanford and Cambridge before enrolling in medical school at Yale. His lifelong love of reading was encouraged from an early age by his mother, who gave him books recommended for students planning to take the SATs. Although Kalanithi eventually decided to seek answers to his questions about the meaning of life and death in science and medicine, his memoir shows that his earlier passions remained important touchstones for him. The title itself is a reference to “Caelica 83,” a poem by Elizabethan poet Baron Brooke Fulke Greville. Kalanithi also begins each section of the book with an epigraph, quoting from T. S. Eliot’s poem “Whispers of Immortality,” the King James Bible, and Montaigne’s essay “That to Study Philosophy Is to Learn to Die.” Kalanithi’s favorite book was Sir Thomas Browne’s 1643 spiritual memoir Religio Medici (The Religion of a Doctor), which he describes his teacher Shep Nuland as having quoted on his deathbed. Other classic works Kalanithi references include (but are not limited to) Shakespeare’s Hamlet, Aldous Huxley’s Brave New World, Alexandre Dumas’s The Count of Monte Cristo, Daniel Defoe’s Robinson Crusoe, Walter Scott’s Ivanhoe, Machiavelli’s The Prince, Thomas Malory’s Le Morte d’Arthur, Cervantes’s Don Quixote, and T. S. Eliot’s The Waste Land.

Precalculus, Chapter 7, 7.1, Section 7.1, Problem 55

Since the equations of the system are not transcendental equations, you may solve the system algebraically.
You need to use substitution method, hence, you may use the second equation to express x in terms of y, such that:
2x = 4y - 7 => x = (4y - 7)/2
Replacing (4y - 7)/2 for x in equation xy - 1 = 0 , yields:
((4y - 7)/2)*y - 1 = 0 => 4y^2 - 7y - 2 = 0
You may use quadratic formula, such that:
y_(1,2) = (7+-sqrt(49 + 32))/8
y_(1,2) = (7+-sqrt(81))/8
y_(1,2) = (7+-9)/8
y_1 = (7+9)/8 => y_1 = 2 => x_1 = 1/2
y_1 = (7-9)/8 => y_1 = -1/4 => x_2 = -4
Hence, evaluating the solutions to the given system, yields (1/2,2) and (-4,-1/4).

Calculus of a Single Variable, Chapter 9, 9.7, Section 9.7, Problem 16

Maclaurin series is a special case of Taylor series that is centered at a=0. The expansion of the function about 0 follows the formula:
f(x)=sum_(n=0)^oo (f^n(0))/(n!) x^n
or
f(x)= f(0)+(f'(0)x)/(1!)+(f^2(0))/(2!)x^2+(f^3(0))/(3!)x^3+(f^4(0))/(4!)x^4 +...
We may apply the formula for Maclaurin series to determine the Maclaurin polynomial of degree n=4 for the given function f(x)=e^(x/3) .
Apply derivative formula for exponential function: d/(dx) e^u = e^u * (du)/(dx) to list f^n(x) as:
Let u =x/3 then (du)/(dx)= 1/3
Applying the values on the derivative formula for exponential function, we get:
d/(dx) e^(x/3) = e^(x/3) *(1/3)
= e^(x/3)/3 or 1/3e^(x/3)
Applying d/(dx) e^(x/3)= 1/3e^(x/3) for each f^n(x) , we get:
f'(x) = d/(dx) e^(x/3)
=1/3e^(x/3)
f^2(x) = d/(dx) (1/3e^(x/3))
=1/3 *d/(dx)e^(x/3)
=1/3 *(1/3e^(x/3))
=1/9e^(x/3)
f^3(x) = d/(dx) (1/9e^(x/3))
=1/9 *d/(dx) e^(x/3)
=1/9 *(1/3e^(x/3))
=1/27e^(x/3)
f^4(x) = d/(dx) (1/27e^(x/3))
=1/27 *d/(dx) e^(x/3)
=1/27 *(1/3e^(x/3))
=1/81e^(x/3)
Plug-in x=0 on each f^n(x) , we get:
f(0)=e^(0/3) = 1
f'(0)=1/3e^(0/3) = 1/3
f^2(0)=1/9e^(0/3)=1/9
f^3(0)=1/27e^(0/3)=1/27
f^4(0)=1/81e^(0/3)=1/81
Note: e ^(0/3) = e^0 =1.
Plug-in the values on the formula for Maclaurin series, we get:
f(x)=sum_(n=0)^4 (f^n(0))/(n!) x^n
= 1+(1/3)/(1!)x+(1/9)/(2!)x^2+(1/27)/(3!)x^3+(1/81)/(4!)x^4
=1+1/3x+1/18x^2+1/162x^3+1/1944x^4
The Maclaurin polynomial of degree n=4 for the given function f(x)=e^(x/3) will be:
P_4(x)=1+1/3x+1/18x^2+1/162x^3+1/1944x^4

What concept of fame or glory is presented in "The Seafarer?"

The short answer is that the poem presents two contrasting conceptions of glory or fame. One is connected with the heroic values of pre-Christian, Germanic culture, and concerns one's reputation for having committed brave, daring deeds -- vanquishing demons and other evil forces -- that kings reward and people praise. It's the social and political prestige that bold warriors receive for being perceived as valiant, strong, and physically brave.
The other is the sort of glory that transcends earthly reputation. It's the glory of God, and it is the best and longest-lasting type of glory.
To understand this in more detail, it is helpful to realize that the original Anglo Saxon poem uses at least four different words that modern scholars have translated as "glory." These words didn't all mean exactly the same thing to people living at the time.
For instance, consider lines 72-80, where the narrator speaks of the good actions that heroic men may do -- battling against "malice of fiends" and devils. People praise heroes for these deeds, and this praise leads to what Jonathan Glenn translates as "glory:"

that children of men after may praise him, and his glory hereafter live among angels always for ever, eternal life’s splendor, joy among noble ones.

But the original word used is "lof," which the Bosworth-Toller Anglo Saxon dictionary has defined as "praise, glory, song of praise, hymn." So here the poet is referencing a kind of glory or fame that comes from being made the subject of heroic tales told by others.
But that bit about "eternal life's splendor" (original word: blǽd) has also been translated as "glory," for instance by Gavin Bantock:

Then the children of men will praise him afterwards,
and his glory shall live with the angels,
and he shall abide in glory always,
sharing glory with the host.

The word " blǽd" has defined by the dictionary as "enjoyment, prosperity, abundance, success, blessedness, gift, reward, benefit, glory, honour." This word is used again in line 88, this time in the context of its shortcoming: It doesn't last forever.  As Jonathan Glenn translates it:

Glory is humbled, honor of earth grows old and withers, as does now every man over this Middle-Earth.

So while this sort of glory is good, its benefits are limited. As the narrator explains (lines 81-82, in a translation by Burton Raffel):

"The days are gone
When the kingdoms of earth flourished in glory;"

And here the original word Raffel translates as "glory" is especially telling: It's "onmedlan," which according to the dictionary has connotations of the puffed up sort of glory -- implying undertones of pomp, magnificence, arrogance, and boldness.
Nowadays, says the narrator, pursuing this sort of glory isn't even a realistic goal. In the past, great kings bestowed great prizes on heroes are gone. But society has changed, says the narrator. The age of great kings is over; the opportunities for heroes to aggrandize themselves in this way are past. The fame and prestige has faded. As noted above, the narrator returns to the word, "blǽd," in line 88, concluding that honor/glory/rewards-for-being-a-bold-hero has been humbled, diminished, or subdued.
The narrator goes on to note that you can't take your earthly prizes with you after death, and they won't help you when God judges you for your sins. But by living up to the harsh demands of Christianity, you may enter into a blessed state with "wuldres Ealdor," the father or master of glory (lines 123-124, translated by Jonathan Glenn):

thanks that he honored us, master of Glory, God of Eternity, in all our time. AMEN.

----
References (in addition to the links below):
Marsden R. 2004. The Cambridge Old English Reader. Cambridge University Press. 
Mitchell B and Robbins FC. 1986. A Guide to Old English. Blackwell.
Raffel B. 1964. Poems from the Old English. University of Nebraska Press.
http://bosworth.ff.cuni.cz/

https://lightspill.com/poetry/oe/seafarer.html

Why are some people including John Proctor inclined to stay away from Sabbath meeting?

John Proctor makes it clear that he is not a fan of Reverend Parris and believes that he is a superficial man, who does not possess the light of God. In act 1, John Proctor admits to Thomas Putnam that he does not appreciate the fact that Reverend Parris only preaches on hellfire and damnation. He tells Reverend Parris,

"Take it to heart, Mr. Parris. There are many others who stay away from church these days because you hardly ever mention God anymore" (Miller, 29).

Rebecca Nurse even agrees with John's assessment of Reverend Parris's preaching and says that there are many citizens who refuse to bring their children to church for that reason. In addition to preaching solely on hellfire and God's wrath, Proctor is also tired of Parris's greedy personality. Proctor views Reverend Parris with contempt for demanding a deed to his house and insisting on having golden candlesticks at the altar. Overall, John Proctor and many other citizens are tired of listening to Reverend Parris preach about hellfire and are beginning to take note of his greedy, superficial personality, which is not becoming of a minister. Parris's judgmental, severe preaching style and his selfish personality dissuade the Salem citizens from attending church.

Many people in Salem are inclined to avoid Sunday mornings at the meetinghouse because they dislike the minister, Mr. Parris.  John Proctor tells Mr. Hale that he doesn't see the "light of God" in Parris, and he has even avoided having his youngest son christened by Parris because he doesn't want the man to lay hands on his child.  In addition to these concerns, Proctor says that it "hurt[s] [his] prayer" that Parris insisted on -- and evidently got -- golden candlesticks for the altar when there were already perfectly good pewter candlesticks that were handmade by Francis Nurse, a well-respected member of the Salem community.  When Proctor sees those golden candlesticks gleaming at Parris's elbow when he preaches, it seems to make Proctor feel that Parris's priorities are out of line.

Religious faith is vital to the following: a. Animals b. Human beings c. Heavenly bodies d. Gandharvas

The correct choice is human beings. According to the Hindu religion, religious faith is important to humanity. Religious faith provides information about the universe and all life forms. It also offers guidance and explains the interaction between man and the universe. Religious faith is important because it provides an opportunity for man to connect with divine beings.
Religious faith is viewed as man’s attempt to seek answers to some serious life questions.  Adherents of Hinduism observe diverse beliefs. However, there exist core beliefs that define the Hindu religion. These views form the common bond among followers of the faith. The belief system ascertains the existence of a Supreme Being.  It also explains the sacred nature of life. Hindus believe in Karma and reincarnation. These aspects explain how human beings should live and what to expect after death. Thus, the concepts of religious faith are mostly targeted to human beings.
The answer has been provided based on Hinduism because of choice D. Gandharvas. The option provided some context and direction for the answer.

How would you describe the effect of poverty on children?

While my description and yours may differ, it is hard to deny that Jacob Riis's How the Other Half Lives was one of the more influential books in late nineteenth-century America.  Riis, an immigrant himself, took a detective camera and went to various tenement houses in order to show the squalor in which the immigrants lived.  While conditions were bad for the people who lived in these unregulated deathtraps, they were especially bad for children.  The children who lived in these situations faced extreme poverty.  Their diets lacked some vitamins due to an inability to afford food, and this led to more children getting sick.  Childhood mortality was quite high in the tenements.  The children often did not have access to school because they had to work in the factories.  This meant that they would likely be poor their entire lives.  Children were also vulnerable to criminals who sought to exploit them.  Riis pointed out all of this in a series of lectures with his books over a hundred years ago.  While the tenement is considered a thing of the past, childhood poverty is still relevant today, and it often breeds generational poverty and other social problems.  

Single Variable Calculus, Chapter 2, 2.2, Section 2.2, Problem 30

Find the infinite limit for $\lim\limits_{x \rightarrow \pi^-} \cot x $


$
\begin{array}{|c|c|}
\hline
x & f(x)\\
\hline
\pi - 0.1 & -9.9666\\
\pi - 0.01 & -99.9966\\
\pi - 0.001 & -999.9996\\
\pi - 0.0001 & -9999.9999\\
\hline
\end{array}
$


According to the table, as the values of $x$ approaches $\pi$ from the left side, the values of the limit approaches $-\infty$


$
\begin{equation}
\begin{aligned}
\lim\limits_{x \to \pi^-} \cot x & = \lim\limits_{x \to \pi^-} \displaystyle \frac{1}{\tan x} = \frac{1}{\tan (\pi - 0.0001)}\\
\lim\limits_{x \to \pi^-} \cot x & = -9999.999
\end{aligned}
\end{equation}
$

Was Cleopatra Greek?

Cleopatra was a member of the Ptolemaic Dynasty.  Family members and ancestors in the Ptolemaic Dynasty had come from Macedonia on the Greek Peninsula.  Ancient Macedonians had expanded from today's Greece into other regions.  Alexander the Great had invaded Egypt, and from this the Ptolemaic Dynasty had come into power through his general.  Cleopatra was descended from Alexander the Great.  She was of Greek ancestry through him.  Members of the Ptolemaic Dynasty continued to speak Greek rather than Egyptian.  Cleopatra, by contrast, learned to speak Egyptian.  Her name was of Greek origin.
Upon the death of her father, Cleopatra became a joint monarch with her younger brother.  In the culture of the Ptolemaic Dynasty, female rulers were considered secondary to male rulers in the case of a joint monarchy.  Cleopatra challenged this when she tried to militarily overthrow her brother.
 

In what ways are Isabel and America different?

This is an interesting question. Most of the time, Isabel and America are compared to each other instead of contrasted from each other.
A simple difference is that America is a country and Isabel is a person, but that is an incredibly simple contrast and not likely what your teacher wants to hear.
One difference is that Isabel starts the story as a free slave, but America is not free from British rule. The country hasn't declared independence yet. The story begins in May of 1776. While America might be getting ready to declare independence from Britain, it has not happened yet; however, Isabel begins the story having recently been set free. She is forced back into slavery, and soon after, America becomes its own free country. This is a sort of role reversal that occurs in the story.
I would say that another key difference is that Isabel is willing to work with the British in order to become free again. That is why she tries to escape the Lockton household by going to the British military. Isabel has heard that the British are willing to free slaves that help them. Seeking help from the British is not something that the newly formed American country can do.

Did Anthony and Gloria cheat on each other?

Anthony certainly cheats on Gloria. During the war, when he was stationed in South Carolina, he had an affair with a local girl by the name of Dorothy Raycroft. It's not hard to see why Anthony succumbs to temptation. Dorothy is just so incredibly real, certainly not the kind of woman he's used to meeting in his rarefied social world. And she's absolutely nothing like Gloria, the shallow, superficial, would-be movie star going crazy over the prospect of hitting thirty. Dorothy may not be as beautiful or as sophisticated as Gloria, but she has a wonderfully grounded air about her. In some ways, Anthony envies her. He's spent the whole of his pampered existence trying desperately to find a purpose in life. Yet here is someone with her feet firmly planted on terra firma.
Unlike Anthony, however, Gloria does at least grow as a character throughout the story. And crucially, she has a conscience. She abjures her youthful nihilism to embrace a weird religion called Bilphism. Whether it's due to her new-found spirituality or perhaps because she doesn't want to miss out on a share of Anthony's forthcoming inheritance, Gloria remains faithful to her husband. However ostensibly modern and sophisticated they may seem, Mr and Mrs. Patch are still in thrall to the prevailing double standards pertaining to relations between men and women.

In Macbeth, how does Shakespeare characterize the witches and what is their thematic significance?

Shakespeare characterizes the three Weird Sisters by allowing them to establish the mood of the play in the very first scene. Right away, the dark and ominous mood is set with thunder and lightning and these three creepy women making plans for what they are going to do after the battle's over; these plans sound somewhat nefarious. During their conversation, they also speak to their familiar animal spirits—"Graymalkin" and "Paddock"—a very strange and off-putting behavior.
In addition to interacting with these spirits, the sisters' speech pattern helps to establish their characterization as well. They speak in rhyming couplets, a pattern that sounds hypnotic and spell-like: "witchy" if you will. They also speak in a particular rhythm called trochaic tetrameter. This means that there are four (tetra-) feet per line and each foot is called a trochee (which is two syllables: one stressed syllable followed by one unstressed). Most of the other characters in the play speak in iambic pentameter, a meter made up of five feet per line (penta-) where each foot (called an iamb) has two syllables: one unstressed followed by one stressed‚—the opposite of a trochee. Because the Weird Sisters' speech begins on a stressed (or accented) syllable, unlike the vast majority of other characters, it sounds more menacing and aggressive, an auditory clue to their menacing and aggressive characters.
Finally, in the last couplet of the scene,

Fair is foul, and foul is fair;Hover through the fog and filthy air,

the Witches employ alliteration, the repetition of an initial consonant sound. The wispy, misty, snaky "f" sound begins six words in these two lines alone. This sound is airy rather than vocal, adding to the sisters' mystery. All of these auditory clues—the rhyming, the meter, and the alliteration—seem to point to the fact that these women should not be trusted; even their use of paradox in the first line of the quotation above seems to confirm this. They speak in riddles, they seem to delight in mystery and menace; nonetheless, Macbeth will believe them. We learn from them, and from their paradox, that appearances are often deceiving.

The memorable Three Weird Sisters in Shakespeare's Macbeth perform a significant role throughout the play by manipulating Macbeth to make rash decisions which lead to his tragic downfall. In the opening scene of the play, Shakespeare introduces the audience to the Three Weird Sisters, who discuss meeting Macbeth when the battle is over before delivering their famous line "Fair is foul, and foul is fair" (Act I, Scene 1, line 12).
Thematically, this statement introduces the concept that nothing is what it seems, which is significant to the plot of the play. Continually, Macbeth and other characters will be fooled into believing that things are opposite of their true nature. In Act I, Scene 3, the Three Weird Sisters discuss how they will avenge a woman who refused to share her chestnuts. They mention that they will influence the winds to make her husband's journey across the sea difficult. Throughout this conversation, Shakespeare indirectly characterizes the witches as being petty and vengeful. The fact that they have the power to influence the weather, yet lack the ability to directly harm or kill the woman's husband suggests that their control over people's fates is limited and ambiguous.
Later in the scene, Macbeth and Banquo meet the Weird Sisters and are repulsed by their appearance. Banquo comments,

What are these so withered and so wild in their attire, that look not like th' inhabitants o' th' Earth, and yet are on ’t?—Live you? Or are you aught that man may question? You seem to understand me, by each at once her choppy finger laying upon her skinny lips. You should be women, and yet your beards forbid me to interpret that you are so (Act I, Scene 3, lines 39-48).

The witches proceed to prophesy about Macbeth's eventual kingship and Banquo's descendants before disappearing into thin air. During their encounter, Shakespeare characterizes the Three Weird Sisters as grotesque, evil characters who use their knowledge of the future to ruin Macbeth.
In Act IV, Scene 1, the Three Weird Sisters concoct a charm that will negatively affect Macbeth's ability to interpret their prophecy accurately by using various animal parts and crude ingredients as they chant, "Double, double toil and trouble, Fire burn and cauldron bubble" (Act IV, Scene 1, lines 20-21).
When Macbeth enters the scene and demands to know his future, the witches conjure three apparitions that give Macbeth a false sense of confidence. The nature of the witches is nefarious, and their prophecies are ominous. Their function is to the set the tone of the play and confuse Macbeth into making terrible decisions that will result in his demise. Overall, Shakespeare characterizes the Three Weird Sisters as wicked, vengeful, grotesque witches whose sole purpose is to cause chaos and trouble.