What was Pontiac's Rebellion? How did this rebellion affect the colonies?

Pontiac’s Rebellion began in 1763. Many Native American tribes had been very friendly with the French. The Native Americans were concerned when Great Britain got control over the land that France had previously controlled. When France lost the French and Indian War, they gave this land to Great Britain. Many of the Native Americans didn’t like or trust the British.
Pontiac was a chief of the Ottawa tribe. He led a group of Native American tribes in several attacks against the British. These battles lasted several years until Pontiac signed an agreement with the British.
This rebellion was important for the colonists. The British were concerned that the colonists would be harmed by these attacks. Thus, the British Parliament passed the Proclamation of 1763. This law prevented the colonists from moving into the land that Great Britain had just received from France. The colonists were unhappy because they wanted to go and settle in this area. Some colonists disobeyed the law and went into this area. When the British passed the Quartering Act, which required the colonists to provide housing for the British troops that were enforcing the Proclamation of 1763, the colonists became more upset. These two laws were some of the early actions that eventually led to the start of the Revolutionary War.
https://www.history.com/this-day-in-history/pontiacs-rebellion-begins

https://www.history.com/topics/native-american-history/1763-proclamation-of

https://www.ushistory.org/us/9a.asp

Revise and edit an essay written about Edgar Allan Poe's "The Black Cat." Look for weaknesses in writing and errors in capitalization, spelling, and punctuation.

Based on this prompt, it looks like you have been asked to find "an" essay online which a student has written about Poe's "The Black Cat" and then do some work in editing and revision, thus hopefully improving your knowledge of the story and sharpening your editing and revision skills.
The link I'm providing is an essay which a student wrote and submitted online. The first thing I always tell students to consider is the thesis. If the thesis is awkward or confusing, the entire paper can head off track. Here is the thesis of this paper:

This paper endeavors to show how the writer has used various images and plot development to create a horrifying and dreadful atmosphere that drawing the reader into the narrators demented and haunted mind.

The core idea is there, but the phrasing is long with lots of clauses. There are also some grammatical errors (narrator's should be possessive and drawing is the wrong tense). I also tell students to avoid referring to "the paper" itself and to instead just say what needs to be said. Here's a revision of that thesis:

Poe uses first person point of view, vivid imagery, and unexpected plot developments to create a horrifying mood.

This thesis also more closely aligns to the majority of the content that follows, so I would recommend restructuring the information into paragraphs that follow these three main ideas. Create one paragraph to explain how the point of view increases the horrific mood, another explaining how the imagery is horrifying, and a third that tackles unexpected plot developments.
This revision would certainly make the ideas in the paper more organized and understandable. And then I'd tackle some of the grammatical issues, such as:

Numerous run-on sentences—See the last sentence in paragraph 2 for an example.
Lots of sentences that are far too long and awkwardly constructed—See the sentence that begins with "Later" in the introduction.
Incorrect use of the semicolon, which should be used to combine two complete sentences. This has been incorrectly done in both the introduction and in the second paragraph.

The paper has some good ideas, but a thorough revision that better organized the ideas and eliminated the many run-on sentences could produce a paper that is more academically sound.
https://studentshare.org/english/1490968-the-black-cat-by-edgar-allan-poe

I am not sure if this prompt is asking for you to revise and edit an essay that you wrote or an essay that a classmate wrote. There is also the possibility that the prompt is asking you to find an online essay and revise and edit that essay. I am going to base this response on the last option being correct.
I have provided a link to an online essay about "The Black Cat," presumably written by a student. The essay could definitely benefit from a revision. Structurally, the essay is broken into different sections, and those sections are labelled with headings. This is generally not an acceptable format. The entire essay should be broken into paragraphs that have identifiable content from individual topic sentences. Another problem is the inclusion of the first person. The essay shouldn't contain sentences that say "I think" or similar. Your personal opinion can be stated, but the first person can't be used. Just state something like it is fact. For example, change "I think what Poe was trying to express . . ." to "Poe is trying to express . . . "
The linked essay is full of errors that need to be revised. It has subject and verb agreement issues as well as the incorrect word being used. The following is the first line from paragraph three:

A key aspect in the beginning of the opening with the main character giving inform of their life to date.

The main character is giving "information" not "inform." Additionally, the main character is a single person, so he shouldn't be referred to as "their." The end of the sentence should read " . . . character giving information of his life to date."
My main recommendation when doing this kind of revision work is to read the entire paper aloud to yourself. This will catch quite a few mistakes regarding word choice and/or the accidental omission of words.
https://www.ukessays.com/essays/english-literature/a-look-at-the-black-cat-english-literature-essay.php

The first reference listed below is a link to an English class blog that features a student-composed essay about Edgar Allan Poe's short story "The Black Cat." In the essay, you will immediately notice some errors that need to be corrected.
First, short story titles must have double quotation marks around them. Each of the three words in this story's title must be capitalized. In this essay, the student calls the story a "book," a mistake that weakens the author's credibility from the start. The essay also contains some run-on sentences and sentence fragments. You should revise those. For example, the third sentence is a run-on.
The fragment that begins with "A cat who" has been punctuated as a sentence. You'll need to join that to the previous sentence with a comma. In addition, change the who to which; use who for people and which for things and animals.
You should proceed through the essay, correcting errors in usage and punctuation as you go. Some of the sentences are rather garbled; for example, the third sentence of the second-to-last paragraph (beginning with "It has been established") is rather indecipherable. You'll need to make a guess at what the author means and rewrite the sentence accordingly.
If your assignment requires you to correct problems with the content of the essay and not just grammar and usage, this essay deserves a significant rewrite. The author has made a critical mistake in attributing moral "sins" to Poe because Poe has written a story about violence and murder. Many authors write about such dark subjects because these types of stories interest readers and make money. It doesn't mean the authors themselves are evil.
This student-written essay does not display excellent critical thinking or writing. It will give you plenty of mistakes to correct.

Please analyze line by line the meaning and use of vowel/consonant sounds of the poem "Mushrooms" by Mary Oliver.

"Mushrooms" by Mary Oliver reflects on how mushrooms grow and the different forms they take. 
The first ten lines describe how mushrooms grow. The lines read,

Rain, and thenthe cool pursedlips of the winddraw themout of the ground -red and yellow skullspummeling upwardthrough leaves, through grasses, through sand; (1-10)

The speaker explains how the rain and the wind play their parts in coaxing the mushrooms "out of the ground." The mushrooms are described as "red and yellow skulls," which gives them a humanlike quality. The mushrooms are "pummeling upward," which indicates the speed and force with which they develop. They move up "through leaves / through grasses / through sand" (8-10). The repetition of the word "through" and the repeated consonant ("T") and vowel ("ou") stylistically describes the growth process of the mushrooms.
In the middle of line 10, the next idea continues:

astonishingin their suddenness, their quietude, their wetness, they appearon fall mornings, somebalancing in the earthon one hoofpacked with poison, others billowingchunkily, and delicious - (10-19)

Following the idea of the previous lines, the mushrooms are described as "astonishing / in their suddenness," again emphasizing their force and speed. However, they are also characterized by their "quietude" or stillness, which seems to be the opposite of "their suddenness." Further, a variety of mushrooms is detailed by the speaker: some are "packed with poison," while others are "delicious." The alliteration of "packed with poison" emphasizes the potential force and violence of the mushrooms that are dangerous to eat. The safe mushrooms are described with more appealing words like "billowing" and "chunkily," in addition to the aforementioned "delicious."
Next, the speaker introduces humans to this natural scene:

those who knowwalk out to gather, choosingthe benign from flocksof glitterers, sorcerers, russulas, panther caps, shark-white death angelsin their town veilslooking innocent as sugarbut full of paralysis: (20-29)

The speakers refers to "those who know," presumably meaning people who can tell the difference between poisionous and edible mushrooms. They pick "the benign" mushrooms from amongst the other, more threatening species. The dangerous mushrooms can be "glitterers" or "sorcerers," because they may trick people into eating them. The "russulas" are edible, but other types can serve as "shark-white death angels." This is a very threatening image, and the pairing of "death" and "angels" may be construed as oxymoronic. This metaphor continues through line 29, as the "death angels" appear "innocent" but are actually "full of paralysis." They can entice through their appearance, but they will ultimately kill you.
Finally, the poem ends with these lines:

to eatis to stagger down fast as mushrooms themselveswhen they are done being perfectand overnightslide back under the shiningfields of rain. (30-36)

The person who eats the poisonous mushrooms will "stagger down / fast as mushrooms themselves." The deadly effects of the mushrooms is compared to the quick destruction they can cause. We then return to the natural life cycle of the mushrooms as the speaker reflects on the way the mushrooms die; they "slide back under" the earth from which they arose.

The Federalists were in favor of the Constitution while the Antifederalists were not. How did these two groups agree to the new constitution? (What was the compromise?)

The Federalists were in favor of ratifying the Constitution. They believed a stronger national government was needed because of the issues faced by the government under the Articles of Confederation. The Federalists saw a government that struggled with finances, keeping order, and dealing with other countries. They believed a new plan of government was needed.
The Antifederalists were opposed to the Constitution. They believed the federal government that would be created by the Constitution would have too much power. One of the bigger concerns that the Antifederalists had dealt with the fear that the Constitution didn’t protect individual rights. Many states said they wouldn’t ratify the new Constitution unless something was done to protect the people’s rights. As a result, a promise was made to add a Bill of Rights to the Constitution. The Bill of Rights became the first ten amendments to the Constitution. Once this promise was made, the states that were concerned about the new Constitution voted in favor of ratifying it.
https://www.constitutionfacts.com/us-articles-of-confederation/the-great-debate/

https://www.ushistory.org/us/16b.asp

Calculus: Early Transcendentals, Chapter 4, 4.6, Section 4.6, Problem 34

Although this question looks tough, it is really simple if you break it down into familiar component parts.
f(x) is composed of the component "basis" functions which include x^2 and e^-x. I would first graph these familiar functions and study how they behave over their respective domains. f(x) will have an overall behavior which is determined by the behavior of each of these familiar component functions.
It is important to realize that c is a real constant. Thus, f(x) actually represents a "family of functions" where the MAGNITUDE and SIGN of c will determine which member of the family of functions we are dealing with.
I would recommend that you graph f(x) when c = 0, 1, and -1. These members of the f(x) family will give you a quick sense of how the family of functions will behave for different values of c over the domain of f(x).
Lastly, I would recommend that you look at the "end behavior" of f(x) as x approaches positive infinity as well as negative infinity.
This is the type of logic that must be employed when one attempts to graph functions like f(x). Build upon what you already know to better understand f(x).
If you go to https://mathway.com/graph , you will find a graphing calculator that will allow you to perform the aforementioned explorations.
Michael

How does Shakespeare present Lord Montague and Benvolio as concerned?

Benvolio and Lord Montague are clearly worried about Romeo—and with good reason, too. For one thing, he's regularly taken to wandering round the sycamore grove on the West side of the city first thing in the morning for no apparent reason. When Benvolio approached him one time, he hid in the forest. It's obvious that Romeo wants to be alone, but why? What is the cause of such strange behavior? Benvolio's more than happy to leave Romeo alone if that's what he really wants, but it's obvious that there's something not quite right, all the same.
As for Montague, he observes how Romeo returns home as soon as the sun comes up, hoping to escape the sunlight. By anyone's standards, this is not normal behavior, not even for a lovesick adolescent. Montague doesn't understand why his son locks himself away in his bedroom all day, shutting out the sunlight. Clearly, there's something eating the young man, but neither Montague nor Benvolio know what it is, and that's causing them no little concern.

Benvolio and the Montagues have a conversation about Romeo, each expressing their concern over his recent behavior. Romeo's mother asks Benvolio if he has seen Romeo today, and he tells her that he did see Romeo that morning, walking very early in the sycamore grove. When Benvolio went toward him, however, Romeo "stole into the covert of the wood" (1.1.115). Obviously his cousin didn't want to talk to him, and so Benvolio left him alone.
Lord Montague says that this is typical behavior for Romeo to walk early, crying and sighing, only returning home at sunrise as if to escape the light. Once home, "private in his chamber [he] pens himself, / Shuts up his windows, locks fair daylight out, / And makes himself an artificial night" (1.1.128-130). He just wants to be alone and sit in the dark. Neither Lord Montague nor Benvolio knows the cause of Romeo's despondence; Lord Montague has tried to encourage Romeo's confidence in him, but to no avail. Benvolio finally offers to speak to Romeo and try to find out what's bothering him so much.

In his acceptance speech for the 1964 Nobel Peace Prize, Martin Luther King, Jr. likens his experiences in the civil rights movement to traveling on a road. Explain how using a road as a symbol for his experiences impacts the meaning of the speech. Be sure to use specific details from the speech to support your ideas.

In Oslo, on December 10, 1964, Martin Luther King, Jr. accepted the Nobel Peace Prize and likened his struggle in the civil rights movement to a road he is traveling. In his speech he says,

The tortuous road which has led from Montgomery, Alabama to Oslo bears witness to this truth. This is a road over which millions of Negroes are traveling to find a new sense of dignity.

King likely made this comparison for many reasons. Through his activism, King was literally marching and traveling on many American roads across the country. He is famous for his March on Washington in 1963, in which he advocated for a change in civil rights. He also helped to organize the Selma to Montgomery March in 1965, which aimed to register African-American voters. In this particular march, protesters walked 54 miles.
Notably, roads also represent progress and change. King says,

This same road has opened for all Americans a new era of progress and hope.

King discusses how the violence of the past must end and make way for peace in the future. He sees their marches as a walk towards progress. Furthermore, this was around the time when American highways were being built and expanded upon. Roads represented progress, patriotism and growth for American people. King likely attributed this to the civil rights movement:

It has led to a new Civil Rights Bill, and it will, I am convinced, be widened and lengthened into a super highway of justice as Negro and white men in increasing numbers create alliances to overcome their common problems.

The image of a road that Dr. King uses in his speech is a metaphor for the long fight for freedom that African Americans have waged. He writes:

The tortuous road which has led from Montgomery, Alabama to Oslo bears witness to this truth. This is a road over which millions of Negroes are travelling to find a new sense of dignity.

It is a particularly apt metaphor for King, because he rose to national and international prominence during the Montgomery Bus Boycott of 1955-56, when African Americans in that city chose to walk, rather than ride, on segregated buses. Their roads were literally and figuratively long, as the boycott lasted for over a year before seating on the buses was desegregated.
Using the symbol of a road also implies a long and ongoing journey. African Americans' journey on this road started before Dr. King joined the journey, and Dr. King also suggests that the journey on this road will continue after he is gone. He writes:

This faith can give us courage to face the uncertainties of the future. It will give our tired feet new strength as we continue our forward stride toward the city of freedom.

By using the image of a road, Dr. King suggests that the journey towards freedom and equality will continue in the future, and this image changes the meaning of the speech, because he implies that he is just one figure in the journey along this road.

King uses the road metaphor in the fourth paragraph of his 1964 Nobel Prize acceptance speech.  During his presentation, he cites the brutality against civil rights marchers in Birmingham, Alabama, and Philadelphia, Mississippi.  He wonders why he is even chosen to win the award, given the violence against his movement.  King goes on to state that civil rights is part of mankind's progress and even gives it a holy goal when he states that the races will be considered equally before God.  He even states that the alternative to this journey toward civil rights is a journey to "thermonuclear destruction," which was a very real concern at the height of the Cold War.  King says that the new Civil Rights Bill (which was just signed into law in 1964) will be part of a new civil rights "superhighway" of justice in which people of all races will unite to solve their common problems.  King uses the highway metaphor sparingly, but he uses it to describe humanity's progress.  

Calculus of a Single Variable, Chapter 7, 7.2, Section 7.2, Problem 6

For the region bounded by y=2 and y =4-x^2/4 revolved about the x-axis, we may apply Washer method for the integral application for the volume of a solid.
As shown on the attached image, we are using vertical rectangular strip that is perpendicular to the x-axis (axis of revolution) with a thickness of "dx" . In line with this, we will consider the formula for the Washer Method as:
V = pi int_a^b [(f(x))^2-(g(x))^2]dx
where f(x) as function of the outer radius, R
g(x) as a function of the inner radius, r
For each radius, we follow the y_(above) - y_(below) , we have y_(below)=0 since it a distance between the axis of rotation and each boundary graph.
For the inner radius, we have: g(x) =2-0=2
For the outer radius, we have: f(x) =(4-x^2/4 )-0=4-x^2/4

To determine the boundary values of x, we equate the two values of y's:
4-x^2/4 =2
-x^2/4 =2-4
-x^2/4 =-2
(-4)(-x^2/4 ) =(-4)(-2)
x^2=8 then x= +-sqrt(8) or +2sqrt(2) and -2sqrt(2)
Then, boundary values of x: a=-2sqrt(2) and b=2sqrt(2) .
Plug-in the values in the formula V = pi int_a^b( (f(x))^2 -(g(x))^2) dx , we get:
V =pi int_(-2sqrt(2))^(2sqrt(2)) [(4-x^2/4)^2 -2^2]dx .

Expand using the FOIL method on: (4-x^2/4)^2 = (4-x^2/4)(4-x^2/4)= 16-2x^2+x^4/16 and 2^2=4 .
The integral becomes:
V =pi int_(-2sqrt(2))^(2sqrt(2)) [16-2x^2+x^4/16 -4]dx
V =pi int_(-2sqrt(2))^(2sqrt(2)) [12-2x^2+x^4/16 ]dx
Apply basic integration property: int (u+-v+-w)dx = int (u)dx+-int (v)dx+-int(w)dx to be able to integrate them separately using Power rule for integration: int x^n dx = x^(n+1)/(n+1) .
V =pi *[int_(-2sqrt(2))^(2sqrt(2))(12) dx -int_(-2sqrt(2))^(2sqrt(2)) (2x^2) dx + int_(-2sqrt(2))^(2sqrt(2)) (x^4/16)dx]
V =pi *[12x-2 *x^3/3+1/16*x^5/5 ]|_(-2sqrt(2))^(2sqrt(2))
V =pi *[12x-(2x^3)/3+x^5/80 ]|_(-2sqrt(2))^(2sqrt(2))
Apply the definite integral formula: int _a^b f(x) dx = F(b) - F(a) .
V =pi *[12(2sqrt(2))-(2(2sqrt(2))^3)/3+(2sqrt(2))^5/80 ]-pi *[12(-2sqrt(2))-(2(-2sqrt(2))^3)/3+(-2sqrt(2))^5/80 ]
V =pi *[24sqrt(2)-(32sqrt(2))/3+(8sqrt(2))/5 ] -pi *[-24sqrt(2)+(32sqrt(2))/3-(8sqrt(2))/5 ]
V =(224sqrt(2)pi)/15 -(-224sqrt(2)pi)/15
V =(224sqrt(2)pi)/15 +(224sqrt(2)pi)/15
V =(448sqrt(2)pi)/15 or 132.69 (approximated value)

Calculus of a Single Variable, Chapter 5, 5.8, Section 5.8, Problem 8

coth^2(x) - csc h^2(x) =1
Take note that hyperbolic cotangent and hyperbolic cosecant are defined as
coth (x) = (e^x+e^(-x))/(e^x-e^(-x))
csc h^2(x) =2/(e^x - e^(-x))
Plugging them, the left side of the equation becomes
((e^x+e^(-x))/(e^x-e^(-x)))^2 -(2/(e^x - e^(-x)) )^2=1
(e^x+e^(-x))^2/(e^x-e^(-x))^2 -2^2/(e^x - e^(-x))^2=1
(e^x+e^(-x))^2/(e^x-e^(-x))^2 -4/(e^x - e^(-x))^2=1
((e^x+e^(-x))^2-4)/(e^x - e^(-x))^2=1
Then, simplify the numerator.
((e^x + e^(-x))(e^x + e^(-x)) - 4)/(e^x- e^(-x))^2=1
(e^(2x)+1+1+e^(-2x) - 4)/(e^x- e^(-x))^2=1
(e^(2x)+2+e^(-2x) - 4)/(e^x- e^(-x))^2=1
(e^(2x) - 2 +e^(-2x)) /(e^x- e^(-x))^2=1
Factoring the numerator, it becomes
((e^x - e^(-x))(e^x-e^(-x)))/(e^x- e^(-x))^2=1
(e^x - e^(-x))^2/(e^x- e^(-x))^2=1
Cancelling common factor, the right side simplifies to
1=1
This verifies that the given equation is an identity.

Therefore, coth^2(x) - csc h^2(x)=1 is an identity.

What is a summary of Chapter 15 in No Talking?

Background information--
In the exposition of the novel No Talking, the main character, Dave Packer, has been affected by what he has read about Mahatma Gandhi, who would not speak at all on one day a week, believing that this was a way to bring order to his mind.  Perhaps, Dave considers, if he practices being quiet, he might do better in his studies. So, he decides to practice silence one day at Laketon Elementary School. At lunch in the cafeteria, when Dave hears a classmate named Lynsey loquaciously describing her shopping trip, he becomes annoyed. He shouts at her, claiming her head would explode if she had to be quiet for a few minutes. Lynsey takes this as a challenge and they agree that for two days their entire class will say no more than three words at a time, nor will they talk at home. In a sense, Dave and Lynsey become team captains and keep tallies of anyone who breaks the rules. 
In Chapter 15--
Mrs. Hiatt, the principal, has a meeting with the teachers in which they discuss the uncharacteristic silence of the fifth graders to whom the teachers have given the moniker "The Unshushables." At this meeting Mrs. Hiatt listens to the opinions of the teachers. It is interesting how the teachers respond to the fifth graders' acts of silence as their classes are affected differently depending upon the academic discipline that they teach.
The math teacher, Mrs. Escobar, says that being quiet is a game to the class.
The English teacher, Mr. Burton, feels that being silent in competition is inventive and creative because it allows the students to think and devise alternative ways to express themselves, such as in writing.
The Physical Education teacher, Mrs. Henley, declares that the students' silence is no problem; in fact, this silence eliminates their complaining.
The Music teacher, Mrs. Akers, complains that she cannot teach students songs if students refuse to sing. She adds that the Art teacher, Jim Torrey, concurs with her opinion that the silence is counterproductive.
Mr. Burton interrupts, reminding the teachers that the class they speak of is the same group called the Unshushables. He suggests that they be patient a few days and not "start them back up." Of course, he has a personal interest in the students' behaviors because he is composing a study on the students' alternative communication methods for a Human Development course he is taking.When the teachers display a growing disagreement with each other, the principal intervenes, thanking the teachers for their input. Further, she explains that the situation is not one that calls for a vote; she has made her decision. She explains that while it is tempting to go along with the students' being silent, neither their game of silence nor their usual talkativeness are acceptable behaviors. The students need to learn the appropriate times to be quiet and to speak, not arbitrarily choose their own times. She adds that she thinks that Dave and Lindsey are the ringleaders, but Mrs. Marlow interjects, "I think it's more like Dave and Lindsey are sort of team captains." Mrs. Marlow explains that the boys are against the girls and are keeping score because she has intercepted a note. Mrs. Hiatt is rather displeased that Mrs. Marlow has not told her this information. Then, Mr. Burton asks what action Mrs. Hiatt will take if the students do not respond to her instructions at the assembly. So, Mrs. Hiatt promises that she will do what she can to resolve the situation. Interestingly, the teachers leave the meeting in a silence not unlike that of the fifth grade students. Perhaps, they, too, have discovered a significance to silence.

Where was Grampa buried in The Grapes of Wrath?

Grampa dies as the Joad family travels to California in John Steinbeck's 'The Grapes of Wrath'. On one of the family's stops, they meet the Wilson family. As Grampa exits the truck, Sairy Wilson invites Grampa to rest in the Wilsons' tent because is clear that he is very ill. He does not live long. Casy, the former preacher, and Siary Wilson believe he is having a stroke. When he dies, Casy tells Pa Joad that Grampa has died of "a good quick stroke."
The family has one hundred and fifty dollars, and they know the authorities will charge forty dollars for the undertaker if the death is reported. If they don't pay the fee, the county will bury Grampa as a pauper. "We never did have no paupers," Uncle John says.
After discussion, the family decides to bury Grampa themselves. He is buried at the place where he has died on Route 66, never making it all the way to California with the family. The group buries bottle that contains a note with Grampa's name so that no one will think he has been murdered if the body is eventually discovered.

Grampa has a stroke when the family stops and joins with the Wilsons in Chapter 13. Sairy Wilson helps care for Grampa and Granma while they are suffering, thus the Joads and Wilson become like a family. While the Joads know that they should go into town and have Grampa buried properly, they also know that it will cost $40 just to have him buried, which is a lot of money for them. Instead, they decide to bury Grampa right near where they are camped on the side of the road along Route 66. They decide to leave a note with the body, in case someone happens to dig up his bones and think he may have been murdered. The family asks Preacher Casy to say a few words so the process feels more like a funeral than just a sad end to Grampa's life.

In contrast to Edwards as "the Last Puritan," how does Benjamin Franklin in the dawn of the American Enlightenment represent the new Enlightenment generation that founded the US? What aspects are more or less attractive or admirable?

In order to approach this topic and to properly compare and contrast Jonathan Edwards and Benjamin Franklin, let us first establish some of the main principles of the two camps they represent: Puritanism and the Age of Enlightenment respectively.
Puritanism
This way of thinking is based on the beliefs of English Protestants in the late sixteenth and seventeenth centuries. Puritans believed in plainness and hard work—in the responsibility of the individual—and in the concept of a God who rewards and punishes.
Puritans also believed in literal interpretation of the Bible and in personal conversion.
Jonathan Edwards, an evangelical minister and theologian, embodied this philosophy in some ways, and in other ways, he represents a departure from traditional Puritanism (he called for unity in the church instead of intolerance, for example). He led the first "Great Awakening in America," a period of great revivalism, in the 1730s from his church in Northampton, Massachusetts.
What are Edwards's key messages? One is the importance of the individual. For Edwards and the Puritans, the responsibility for improvement rests on individual conversion and individual spiritual experience, not the building of a community. His best-known sermon is called "Sinners in the Hands of an Angry God." Here is an excerpt:

Thus it is that natural men are held in the hand of God, over the pit of hell; they have deserved the fiery pit, and are already sentenced to it; and God is dreadfully provoked, his anger is as great towards them as to those that are actually suffering the executions of the fierceness of his wrath in hell, and they have done nothing in the least to appease or abate that anger, neither is God in the least bound by any promise to hold them up one moment; the devil is waiting for them, hell is gaping for them, the flames gather and flash about them, and would fain lay hold on them, and swallow them up.

As we'll see below, this emphasis on the individual is a key difference between Puritanism and the Age of Reason.
Age of Enlightenment / Age of Reason
The Age of Reason centers around freedom of speech and individual rights. Proponents of this way of thinking were not interested in the afterlife, like the Puritans were, and they believed in a reasonable God. As opposed to focusing on "sinners" and "an Angry God," these thinkers assumed that people are basically good and decent.
Benjamin Franklin was a key figure in this movement. He pursued knowledge and enlightenment (and contributed major inventions to the fields of science and technology) not for his own personal prestige, but for the betterment of the society he lived in. This is a key point: the Age of Enlightenment was about the community, the free exchange of ideas, and the concept that teamwork could yield more significant results than individual endeavors.
"If a man empties his purse into his head, no one can take it away from him," Franklin once said. "An investment in knowledge always pays the best interest."
So, how did the Age of Enlightenment shape the founding of the United States? Our entire governmental structure is based on it. Consider the following: separation of church and state, a system of checks and balances, a Congress composed of many individuals that make decisions together. All of this is based on ideals that arose out of the Age of Enlightenment and not the Puritan way of thinking.
The question of which aspects of the Enlightenment generation are attractive or admirable is a matter of opinion: it is also something you will have to decide for yourself. However, you might consider the points in the paragraph above, which are reiterated below:
Community is more important than the individual.
Scientific advancements are for the benefit of everyone.
Teamwork is valued and varying opinions are welcome.
No one, not even the President, can make decisions unilaterally.
https://www.sciencefriday.com/articles/benjamin-franklin-americas-first-social-networker/

How did the assassination of Robert F. Kennedy affect society as a whole?

The assassination of Robert F. Kennedy had a tremendous impact on American society. Robert F. Kennedy’s assassination came just a few months after the assassination of Dr. Martin Luther King, Jr. Americans had believed that their country was free from the political assassinations that had plagued other countries. This assumption was shattered by the assassination of John F. Kennedy in 1963 and the assassinations of Dr. Martin Luther King, Jr. and Robert F. Kennedy in 1968.
The assassination of Robert F. Kennedy came at a time of great political upheaval in the United States. Americans were beginning to believe that the country was falling apart. The number of protests held in opposition to the Vietnam War were growing. People were beginning to believe that the government was not being honest with them about how the United States was really doing in the Vietnam War. There had been riots in many American cities dealing with the issues of racism and poverty. This assassination was another blow to the positive self-image many Americans had about their country.

In The Strange Case of Dr. Jekyll and Mr. Hyde, what comments does Stevenson make about the social world of the novel?

Stevenson invites us to consider late Victorian society as ”doubled” in some way. The Jekyl/Hyde dichtomy can be understood in Freudian terms, in the sense that Jekyl, as the moral center of authority, represents the superego, while Hyde, the chaotic character of violence and passion, represents the id. What’s missing, of course, is the consciousness that controls both. I’m not sure that Stevenson felt that humans are basically two beings; I think it is more accurate to say that societal pressures split people into two parts: a moral “mask” they show the world, and a darker, perhaps truer, identity that can exist only in the shadows. The missing “ego” in the book, the synthesis of Jekyl and Hyde, takes the form of the narrative itself. The logic of the mystery/thriller genre provides a way to resolve the Jekyl/Hyde split and understand the story. Like the ego, the “rules” of the genre neutralize the more extreme elements of superego and id, and join them together into a recognizable whole. In this way the narrative itself can be seen as a kind of critique of social expectations and customs.

In The Strange Case of Dr. Jekyll and Mr. Hyde Stevenson is providing us with a critical commentary on Victorian society. Its says a lot about this society, he suggests, with its numerous restrictions on adult behavior, that the only way a man can be free is by turning himself into a monstrous, murdering psychopath. The stifling mores and rigid social standards of Victorian England prevent people from getting in touch with their deepest emotions. Those emotions become repressed, which in turn causes great psychological damage.
Mr. Hyde acts as a salutary warning of what lurks deep within our souls, which we ignore at our peril. Yet Victorian society as presented by Stevenson chooses instead to suppress human emotion beneath a rigid, unyielding moral code. Dr. Jekyll, a respectable upper middle-class gent, outwardly conforms to this code, but at the cost of suppressing his true individuality. It is only by resorting to dangerous, diabolical experiments that he can enjoy the kind of freedom denied him by society.

In creating Dr. Henry Jekyll, a relatively ethical character who feels such intense societal pressure to be perfect, Stevenson seems to comment on, indeed criticize, the society that would drive a man to such lengths in order to rid himself of what seems to be a natural part of human nature.  Jekyll felt the need to "conceal his pleasures," as he writes in his final letter, and he felt a "morbid sense of shame" concerning them.  He "stood already committed to a profound duplicity of life," and the need to hide any moral imperfection (as determined by his society) compelled him to try to eliminate those imperfections altogether. 
However, he reasoned, and it seems that Stevenson would expect us to agree, that "man is not truly one, but truly two," and so Jekyll's attempt to rid himself of his socially unacceptable desires amounts to the attempt to eliminate a fundamental part of himself as a human being.  Further, his inability to control this side of himself, once he has unleashed it, indicates that his experiment should not have been attempted, that, in trying to eliminate his immorality utterly, he actually allowed it to become stronger.  Therefore, society's attempt to regulate morality to such a great degree, such that a well-respected doctor fears for his reputation over a few minor desires, must be considered not only unrealistic but also dangerous.  The more people feel repressed, the more urgent the desire to break through the boundaries imposed.

What would be a character sketch of the Emperor of Lilliput from Gulliver's Travels by Swift?

The Emperor of Lilliput is a little man in every respect. Vain, petty, and susceptible to flattery, he doesn't present a particularly inspiring vision of kingship. To add to his ever-growing list of sins, he's also an inveterate warmonger, obsessed with defeating and enslaving the neighboring Blefuscans. He tries to enlist Gulliver in this diabolical scheme, but the big man's having none of it, which earns him the undying enmity of the Emperor.
Although the Emperor likes to think of himself as being the man in charge, in actual fact he's controlled by his wily ministers Flimnap and Skyresh Bolgolam, who manipulate him into trying to destroy Gulliver, despite all he's done to protect Lilliput from a Blefuscan invasion. This would appear to suggest a certain lack of self-awareness on the Emperor's part. He labors under the impression that he's top dog on Lilliput, when in reality it's more a case of the tail wagging the dog.

The Emperor of Lilliput is described as being a little taller than his subjects and generally handsome. However, he's also proud, petty, swayed by corruption, and preoccupied with meaningless political formalities and traditions. Scholars often say that the Emperor of Lilliput is meant to be a satirical representation of King George I, and while this analogy is true and logical, it's also worth mentioning that the Emperor of Lilliput can be seen as representative of all bad or corrupt politicians. Moreover, he can be seen as a culmination of all the problems in Lilliputian society, which is also wracked by petty, "small-minded" problems and squabbles. All in all, the Emperor of Lilliput is a brilliant satirical attack on the political world, as his petty personality acts as a perfect critique of many politicians, both past and present. 

Calculus of a Single Variable, Chapter 7, 7.6, Section 7.6, Problem 17

For an irregularly shaped planar lamina of uniform density (rho) bounded by graphs y=f(x),y=g(x) and a<=x<=b , the mass (m) of this region is given by,
m=rhoint_a^b[f(x)-g(x)]dx
m=rhoA , where A is the area of the region
The moments about the x- and y-axes are,
M_x=rhoint_a^b 1/2([f(x)]^2-[g(x)]^2)dx
M_y=rhoint_a^bx(f(x)-g(x))dx
The center of mass (barx,bary) is given by,
barx=M_y/m
bary=M_x/m
Now we are given y=x^2,y=x^3
Refer the attached image. Plot in red color is of y=x^2 and blue color is of y=x^3
Curves intersect at (1,1)
Now let's evaluate the area of the region,
A=int_0^1(x^2-x^3)dx
A=[x^3/3-x^4/4]_0^1
A=[1^3/3-1^4/4]
A=(1/3-1/4)=(4-3)/12
A=1/12
Now let's evaluate the moments about the x- and y-axes,
M_x=rhoint_0^1 1/2[(x^2)^2-(x^3)^2]dx
M_x=rho/2int_0^1(x^4-x^6)dx
M_x=rho/2[x^5/5-x^7/7]_0^1
M_x=rho/2[1^5/5-1^7/7]
M_x=rho/2(1/5-1/7)
M_x=rho/2(7-5)/(35)
M_x=rho/35
M_y=rhoint_0^1x(x^2-x^3)dx
M_y=rhoint_0^1(x^3-x^4)dx
M_y=rho[x^4/4-x^5/5]_0^1
M_y=rho[1^4/4-1^5/5]
M_y=rho[5-4)/(20)
M_y=rho/20
barx=M_y/m=M_y/(rhoA)
Plug in the values of M_y and A ,
barx=(rho/20)/(rho1/12)
barx=12/20
barx=3/5
bary=M_x/m=M_x/(rhoA)
bary=(rho/35)/(rho1/12)
bary=12/35
The coordinates of the center of mass are (3/5,12/35)

In The Dispossessed by Le Guin, what can we glean about how economic systems are influenced by human relationships?

The novel essentially addresses two types of collectivist societies: anarchistic and communistic. While a communist society is predicated on a dictatorship of the proletariat (working class), an anarchistic society is predicated on the notion that a central authority is unnecessary. Communism relies on one-party rule; thus relationships within the party are extremely important. Since the controlling authority is based on a hierarchical system, each layer within that hierarchy is subordinate to the one above it. Thus, the integrity of the one-party system largely depends on how well individuals can leverage relationships to their own advantage within that system.
As can be seen in China, the one-party communist rule is rife with power struggles and conflict. In her book, Le Guin proposes a collectivist model that does away with the centralism of the communist model. As an example from the novel, Anarres is predicated on an anarchistic model.

There was to be no controlling center, no capital, no establishment for the self-perpetuating machinery of bureaucracy and the dominance drive of individuals seeking to become captains, bosses, chiefs of state.

On Anarres, the idea is that "no community should be cut off from change and interchange." The free exchange of ideas is central to anarchism; on the other hand, the central authority in a communist society unilaterally sets party policy for all members, regardless of individual input. Dissent and debate are scarcely tolerated as a practice in any communist society that relies on this one-party rule. While individuals within a communist hierarchy must cultivate key relationships to preserve their political interests, anarchists can choose to cultivate fulfilling relationships according to individual preferences and desires.
On Anarres, there is no forced labor; instead, a loosely-bureaucratic computerized system (Divlab) allocates assignments to individuals based on their education and abilities. Everyone shares with another (or at least, is expected to). There is a degree of trust between individuals on Anarres that is not common to either Terra or Urras. In fact, on Anarres, "solitude (is) equated with disgrace." If one is banished to a single room within a domicile, it usually means that one has "egoized" to the detriment of social harmony. Generally, relationships are based on free will. These support an economic system largely predicated on mutual reliance, tolerance, and egalitarianism.

Aside from sexual pairing, there was no reason for not sleeping in a dormitory. You could choose a small one or a large one, and if you didn't like your roommates, you could move to another dormitory. Everybody had the workshop, laboratory, studio, barn or office that he needed for his work; one could be as private or as public as one chose in the baths; sexual privacy was freely available and socially expected; and beyond that, privacy was not functional.

On A-Io in Urras, the producers are totally banished from the face of commerce. The most powerful relationships are those between the buyers and sellers. Shevek asserts that Urras has everything: "enough air, enough rain, grass, oceans, food, music, buildings, factories, machines, books, clothes, history." However, he argues that Urras does not have true human freedom; the masses are slaves to their material wealth. The whole economic system on Urras is sustained by the principle of the survival of the fittest.

On Anarres, nothing is beautiful, nothing but the faces...We have...nothing but each other...our men and women are free--possessing nothing, they are free. And you, the possessors are possessed. You are all in jail. Each alone, solitary, with a heap of what he owns...

On the other hand, the economic system on Anarres is sustained by its emphasis on individual rights and its focus on social harmony. The thesis of the story is that the free exchange of ideas between worlds (human cooperation across political ideologies) can sustain an optimal economic system that simultaneously values egalitarianism, technological progress, mutual reliance, and tolerance.

Calculus of a Single Variable, Chapter 3, 3.4, Section 3.4, Problem 19

f(x) is concave up

First derivative,
f'(x) = 1*(x-4)^3+x*3*1*(x-4)^2
f'(x) = (x-4)^2(x-4+3x)
f'(x) = 4(x-4)^2(x-1)
There are only two critical points, x = 4 and x = 1
Second derivative,
f''(x) = 4(2*1*(x-4)*(x-1)+ (x-4)^2*1)
f''(x) = 4(x-4) (2x-2+x-4)
f''(x) = 4(x-4)(3x-6)
f''(x) = 12(x-4)(x-2)
For inflection points, f''(x) = 0.
Therefore, the inflection point is at x = 4, not at x = 1.
x<2
f"(x) >0, therefore f'(x) is increasing, which means f(x) is concave up at x<2.
2f"(x) < 0, therefore f'(x) is decreasing, which means f(x) is concave down at 2x>4
f"(x) > 0, therefore f'(x) is increasing, which means f(x) is concave up at x>4

What does the pilot want in the Tom Godwin story "The Cold Equations"?

Tom Godwin's story "The Cold Equations" is a science fiction story about a girl who stows away on a supply ship bound for a planet called Woden.
Like any good science fiction, the story derives its drama from a realistic and believable situation that involves science. The story is set in the future when interplanetary travel has become frequent and mankind has begun to colonize other worlds. 
The story takes place inside a space vehicle called an Emergency Dispatch Ship, or EDS. These ships carry a relatively small amount of rocket fuel that is carefully calculated to be just enough to get them to their destination and back. When the girl stows away in hopes of visiting her brother on Woden, she adds extra weight to the ship. This will cause the ship to burn more fuel than expected, which would lead to its destruction.
The ship's pilot, Barton, discovers the stowaway and contacts his superior for instructions. In fact, Barton knows that he is supposed to jettison the girl to save the ship and its supplies, but he is hoping that his commander will give him permission to try to carry out the mission with her on board. Instead, the commander says this:

So you called me in the hope I could do something? I'm sorry--I can do nothing. This cruiser must maintain its schedule; the life of not one person but the lives of many depend on it. 

So what Barton wants is to try to save the girl. What he actually does is follow orders and jettison her to her death in space. You possibly also argue that what he most wants is to survive and stay out of trouble with his superior, since he is unwilling to defy his orders. 

What are Percy Jackson's character traits?

I would like to add that Percy is ambitious and, despite his propensity for getting into trouble, responsible. He feels bad that he has to leave Yancey Academy, because he takes the responsibility for Grover's well-being (before he finds out that, all along, Grover has been responsible for his). He takes the responsibility for Zeus's stolen master bolt and considers himself capable of fixing the situation. In the incident on the Gateway Arch, he takes the responsibility for the welfare of the "mortals," unwilling to leave them alone with the monsters.
Also, despite his learning disability and difficult home life, Percy has a strong sense of self-worth: he refuses to be bullied by some of his classmates, Gabe, and the gods (particularly Ares and Hades). That said, however, he lacks any vanity. When confronted with a difficult choice in the Underworld, he demonstrates a surprising amount of level-headedness for his age (or for any age, really): he does not heroically stay behind to rescue his mother but saves himself and plans to return for her in the future. He thinks about what she would like him to do, not how this would look to others. After coming home at the end of the adventure, he resists the temptation to take revenge on Gabe. Again, he thinks of his mother instead, giving her the space to handle the relationship herself.

Let's start with simple and straightforward character descriptions. First, Percy Jackson is a young male character (he's 12 years old). Being a young white male hero is basically industry standard, so Percy Jackson doesn't exactly stand out there; however, he has a much more developed sense of humor than most hero characters that readers encounter. Some ready evidence for Jackson's sense of humor can be found in the chapter titles. Jackson is the story's narrator, so it makes sense to assume that he is the one naming the chapters. Chapter titles like "A God Buys Us Cheeseburgers" and "We Get Advice from a Poodle" help readers get a solid picture of what kind of boy Percy Jackson is.
His sense of humor is likely a learned defense mechanism against his not-so-easy childhood. Jackson might go to school with kids whose every need is catered to through having wealthy parents, but Jackson's family is not wealthy. 

I couldn't remember the last time I had so much fun. I came from a relatively poor family. Our idea of a splurge was eating out at Burger King and renting a video.

This kind of upbringing has made Jackson well aware of life's simple pleasures, and he has learned to be grateful for what he does have. He's a humble kid from a humble background. Again, that's fairly industry standard when making a hero. Peter Parker, Barry Allen, Luke Skywalker, and Steve Rogers can all claim the same kind of humble upbringing (as well as all being young, white, and male).
While Jackson does have a well-developed sense of humor, that doesn't mean he has a positive outlook on life. In fact, Jackson can be quite negative. 

I could start at any point in my short and miserable life to prove it.

His learning disability doesn't help his situation, either. He works hard at school and his studies, but despite his best efforts, he is not optimistic about his ability to learn and keep facts straight.

Words had started swimming off the page, circling my head, the letters doing one-eighties as if they were riding skateboards. There was no way I was going to remember the difference between Chiron and Charon, or Polydictes and Polydeuces. And conjugating those Latin verbs? Forget it.

He's not proud of his family's financial situation, nor is he glad that he doesn't have a father figure present in his life. Behind his humor is some bitterness and distrust. That's especially true when it comes to adults.

Believe whatever lie your mom or dad told you about your birth, and try to lead a normal life.

As the post below states, Jackson is indeed quite brave and loyal. He has to be in order to be a worthy hero character and stand and fight against the forces of evil. What I like a lot about Jackson is that he is never tempted to reach beyond his powers. He's incredibly powerful, and he isn't tempted by the possibility of gaining more power. It's why he doesn't steal the master bolt.

"I don't care about the master bolt. I agreed to go to the Underworld so that I could bring back my mother."

Jackson might not be the most optimistic character in the world, but he has a good sense of humor and a strong sense of right and wrong.

I think we could certainly describe Percy as loyal and brave.  He is courageous in his willingness to undertake a dangerous quest that includes a cross-country trip (without much money or any adult assistance), encountering numerous deadly monsters and one or two angry gods, and traveling to the underworld to meet with an unpredictable and vengeful god, all to prove his innocence and to right the wrongs committed by others.  He is fiercely loyal to his mother and his friends, willing to risk his own safety for the well-being of others. 
Likewise, Percy has a well-developed sense of justice.  He recognizes the unjust way his mother is treated by Gabe, his step-father, as well as the way his birth and life were handled by his own father.  And yet he is also capable of forgiveness, as he does forgive his own absentee and rule-breaking father, Poseidon. 

What type of salt is formed when a weak acid and a weak base are mixed?

A strong acid and a strong base will ionize completely, therefore when they are mixed, they will react together to form salt and water. However, weak acids and weak bases only ionize partially. Therefore, when they are mixed, it generally results in a reversible reaction with the formation of a conjugate acid and a conjugate base as products instead of salt and water.
When a weak acid reacts with a weak base the weak acid will lose a proton and the species formed is called a conjugate base. The proton lost by the weak acid is accepted by the weak base to form a conjugate acid. So, a conjugate base is what is left after a weak acid has donated a proton in the reaction.
The reaction that occurs can be depicted as follows:          
weak acid + weak base ⇌ conjugate base + conjugate acid. A common example is the reaction between ammonia (weak base) and water (weak acid).

What is the main conflict and resolution in A Single Shard?

A Single Shard is set in a small village in Korea in the 12th century. The story centers around Tree-ear, a young orphan who lives under a bridge with an old man named Crane-man.
There are, in my view, two main conflicts in this story. The first conflict revolves around Tree-ear's desire to learn how to be a potter.
Min is a potter in their area who creates very fine pottery. Often, Tree-ear surreptitiously watches Min at work, and develops a fantasy of learning how to spin clay like Min can. As a homeless orphan, Tree-ear has practically no way to make this dream come true. One day, he enters Min's yard when no one is around to take a surreptitiously take a closer look at the pottery. He accidentally breaks an expensive piece of pottery, and agrees to work for a furious Min to pay off the debt. After he pays off his debt, he begins to work for Min in exchange for food from Min's wife. Tree-ear hopes that Min will teach him how to become a potter, but when he asks him, Min tells him that the craft is only passed down from father to son.
The second conflict occurs when a royal emissary comes to town to find a potter for a royal commission. Min produces good enough work to merit consideration from the emissary over the other potters in town. However, what the emissary really wants to see Min produce is a revolutionary form of inlay that one of the other potters in town had just created (and received a royal commission for). So Min and Tree-ear go to work to produce vases with the new inlay before the emissary leaves the next day. Due to truly bad luck and no one's fault, the vases all misfire in the kiln, ruining the batch. Fortunately, the emissary understands. He tells Min that if he brings a good sample of his work to the capital, he will consider him for a commission. However, Min is too old to go himself. Out of gratitude for the kindness Min and his wife have shown him and Crane-man, Tree-ear offers to go to the capital in his stead with two precious vases.
What occurs on the journey is the second conflict of the book. While traveling, Tree-ear is robbed by two thieves. When they see that he only has two expensive vases that they can't sell without raising suspicion, they are infuriated. In spiteful rage, they break the vases. Can you imagine how crushed Tree-ear felt? After an entire journey, he had nothing left to show for his efforts. With a last shred of hope, he finds a single shard of pottery on the ground that clearly shows the fine inlay. He brings it to to the capital and finds the royal emissary, successfully procuring the commission. The conflict here was partially internal—Tree-ear felt that all hope was lost. What was the point of struggling to reach the capital if his efforts there might not pay off anyway? But he persevered, and achieved what he came to do.
The first conflict I detailed earlier (Tree-ear's desire to learn the pottery trade) is resolved at the end of the book. Tree-ear returns home elated to share the good news with Min. When he finds Min, he is devastated to find out from him that Crane-man died in an accident in Tree-ear's absence. Min offers to adopt him, and teach him how to be a potter. With his feelings a cocktail of loss and hope for the future, Tree-ear joins Min's household as a son.

Precalculus, Chapter 7, 7.4, Section 7.4, Problem 35

(2x^2+x+8)/(x^2+4)^2
Let(2x^2+x+8)/(x^2+4)^2=(Ax+B)/(x^2+4)+(Cx+D)/(x^2+4)^2
(2x^2+x+8)/(x^2+4)^2=((Ax+B)(x^2+4)+Cx+D)/(x^2+4)^2
(2x^2+x+8)/(x^2+4)^2=(Ax^3+4Ax+Bx^2+4B+Cx+D)/(x^2+4)^2
:.(2x^2+x+8)=Ax^3+4Ax+Bx^2+4B+Cx+D
2x^2+x+8=Ax^3+Bx^2+(4A+C)x+4B+D
Equating the coefficients the like terms,
A=0
B=2
4A+C=1
4B+D=8
Plug the value of the A and B in the above equations,
4(0)+C=1
C=1
4(2)+D=8
8+D=8
D=8-8
D=0
:.(2x^2+x+8)/(x^2+4)^2=2/(x^2+4)+x/(x^2+4)^2
Now let's check it algebraically,
RHS=2/(x^2+4)+x/(x^2+4)^2
=(2(x^2+4)+x)/(x^2+4)^2

=(2x^2+8+x)/(x^2+4)^2

=(2x^2+x+8)/(x^2+4)^2
=LHS
Hence it is verified.

Beginning Algebra With Applications, Chapter 4, 4.1, Section 4.1, Problem 52

A cyclist traveling at a constant speed completes $\displaystyle \frac{3}{5}$ of a trip in $\displaystyle 1 \frac{1}{2} h$. In how many additional hours will the cyclist complete the entire trip?

Recall that the formula that relates velocity $(v)$, distance $(d)$ and time $(t)$ is represented by

$\displaystyle v = \frac{d}{t}$

Then, if we let $d_1$ be the distance of the entire trip, we have


$
\begin{equation}
\begin{aligned}

v =& \frac{\displaystyle \frac{3}{5} d_1}{\displaystyle 1 \frac{1}{2}}
\\
\\
v =& \frac{\displaystyle \frac{3}{5} d_1}{\displaystyle \frac{3}{2}}
\\
\\
v =& \left( \frac{\cancel{3}}{5} d_1 \right) \left( \frac{2}{\cancel{3}} \right)
\\
\\
v =& \frac{2}{5} d_1

\end{aligned}
\end{equation}
$


And since the cyclist is traveling at a constant speed, we get


$
\begin{equation}
\begin{aligned}

v =& v
\\
\\
\frac{2}{5} d_1 =& \frac{d_1}{t}
\\
\\
\frac{2}{5} =& \frac{1}{t}
\\
\\
t =& \frac{5}{2} \text{ hours}

\end{aligned}
\end{equation}
$


In other words, in order for the cyclist to complete the trip, the additional hours must be spend is $\displaystyle \frac{5}{2} - 1 \frac{1}{2} = \frac{5}{2} - \frac{3}{2} = \frac{2}{2} = 1 $ hour.

What household chores did young women do in 1910?

In 1910, a women's primary realm was the home.  Most women were housewives in this time and married women rarely worked.  Daughters were taught how to someday care for a home themselves, as that was the expectation.  They assisted their mothers or other female relatives with all chores relating to the home.  Among these chores were cooking, sweeping, mopping, canning, gardening, sewing, dusting, and laundry.
Young women living in rural areas might also weave cloth and care for animals, such as chickens.  Wealthier households usually had a small or large staff of servants to complete household tasks.  Women with servants usually managed household affairs and social engagements.  Their daughters would not do many chores around the house, if any at all.  Instead, they would focus on their educations and learning social graces.

What is The Horse and His Boy about?

The Horse And His Boy is part of the Chronicles of Narnia series of books by C.S. Lewis. It is the fifth book of the series.
This book takes place during a time when the Pevensie children (Lucy, Susan, Peter, and Edmund) are kings and queens of Narnia. By contrast, in the book The Lion, The Witch, and The Wardrobe, the Pevensie children have only just discovered Narnia. 
The protagonist of this book is Shasta. He is a Narnian boy, but he has been raised as the son of a fisherman in Calormen. The man he knows as his father plots to sell him into slavery to a Tarkaan (which is what the noblemen of Calormen are called.) Shasta begins talking to the Tarkaan's horse, who is a Narnian horse. Together, they decide to run away and return to Narnia. 
Shasta and the horse meet Aravis on their journey. She and her horse (Hwin) are running away to avoid the marriage her parents are trying to arrange for her.
On the journey, Shasta discovers he is a doppelganger for the Prince of Archenland, a kingdom that sits between Calormen and Narnia. In Narnia, Shasta meets Queen Susan who is being courted by a prince. Aravis learns that the prince is planning a secret attack on Archenland and Narnia, so Aravis and Shasta team up to try to warn the King of Archenland about the plot. They meet up with Aslan along the way, who has been guiding and protecting them. They join up with the King of Archenland for a battle against the prince and his people. Shasta finds out that he is actually the son of a king who had been lost long ago, and Shasta will now one day rule a kingdom. 

Yeats wrote "The Second Coming" as a response to the atmosphere of the postwar Europe. How are the anxieties expressed in the poem similar to those that might have been felt during and after wartime?

Yeats had a rather strange, esoteric idea of historical change. In very broad terms, he believed that history developed in a specific pattern which he visualized according to gyres or spirals. Each gyre represents a specific historical era, lasting roughly 2,000 years, and has its own unique set of characteristics. One gyre would be characterized by order and stability, only then to give way to another one marked by chaos and upheaval. In its turn, the new gyre would eventually vacate the stage of history, and order would prevail once more. 
Although rather unusual, Yeats's idea is not completely alien to us. When most people think about history, they have a particular shape in mind that they use to represent change, whether it is a straight line or maybe a circle. Yeats is simply using a different shape to help us understand his unique theory of history.
When Yeats wrote "The Second Coming" in 1919, much of Europe was in the throes of economic recession, disorder, and violent revolution. We do not have to look very far in the poem to pick up oblique references to the prevailing situation:

Turning and turning in the widening gyre.

The spiral of the old epoch of history is widening, and, as such, is ready to turn into another one. The existing gyre is associated with the birth, rise, and establishment of Christianity. It has brought some measure of order and stability to the world, but now its course has almost run. The gyre is about to change into the next historical cycle, one of a radically different, and more disturbing, nature:

Things fall apart; the centre cannot hold; 
Mere anarchy is loosed upon the world, 
The blood-dimmed tide is loosed, and everywhere   
The ceremony of innocence is drowned;

In the aftermath of the First World War, many of the old certainties had gone. Several royal houses had fallen; revolutions and armed uprisings were breaking out, and the very foundations of society appeared to be crumbling.


The best lack all conviction, while the worst   
Are full of passionate intensity.



Yeats was an unabashed elitist with a profound distrust for democracy. He tended to idolize (and idealize) the governing classes of Europe, especially the old families of the Protestant ascendancy in Ireland, many of whom he knew personally. In Ireland, as elsewhere in Europe, the postwar period brought about a decline in the political power of the aristocracy. In its place came a variety of mass movements, some of them democratic, while others, like fascism and communism, were considerably less so. In any case, Yeats and those who thought like him were deeply disturbed by what they saw as the rise to prominence of "mob rule," which threatened the aristocratic order they so venerated and cherished.
 
However, there is little that can be done about it. The change from one historical epoch to the next is inevitable. It will be a "Second Coming," alright, but it will be absolutely nothing like the return of Christ:


Somewhere in sands of the desert   
A shape with lion body and the head of a man,   
A gaze blank and pitiless as the sun,   
Is moving its slow thighs"



We do not know exactly what will replace our dying epoch. However, it will not be very pleasant, that much is certain; in the Bible, the desert is traditionally the home of the devil. Any creature emerging from there is likely to bring great evil with it. The bloodshed and chaos tearing large swathes of Europe apart is bad enough as it is, but much worse is to come:




And what rough beast, its hour come round at last,   
Slouches towards Bethlehem to be born?



The outgoing gyre was heralded by the birth of Christ. The one about to descend upon us has an altogether darker provenance. Though not intended as an exact prophecy of the tragic events of the 1930s and beyond, Yeats's apocalyptic vision still resonates due to the terrible fate that ultimately emerged out of the arid desert of postwar life and slouched its way towards Bethlehem.
https://www.poetryfoundation.org/poems/43290/the-second-coming

What are the differences and similarities between the melancholy of Antonio and Portia in Act I of The Merchant of Venice?

It is quite difficult to pinpoint exactly what the similarities between these two characters' melancholy could be. One could suggest that the similarities lie, first, in the fact that they share their sentiments with those close to them. Antonio speaks with Salarino and Salanio, while Portia confides in Nerissa. In both instances, the characters discuss their condition with their friends.
The difference lies in the fact that Antonio does not know why he is sad, while Portia knows precisely what the source of her sadness is, as she tells Nerissa:

O me, the word 'choose!' I mayneither choose whom I would nor refuse whom Idislike; so is the will of a living daughter curbedby the will of a dead father. . .

It also appears as if the depth of each character's misery is somehow similar. Both deem their melancholy as disturbingly unwelcome and unpleasant. The difference lies in the fact that Antonio cannot possibly have a solution for his sadness since he does not know what causes it, while Portia, to a certain extent, has hope for a solution. She dreams of Bassanio choosing the right casket. That would, obviously, bring an end to her despair, while for Antonio there seems to be no resolution, as he tells Gratiano:

I hold the world but as the world, Gratiano;A stage where every man must play a part,And mine a sad one.

In the end, Antonio's despair worsens due to the ensuing events in the play, whilst Portia's issue is resolved since Bassanio chooses the right casket and she marries him. 

How did Coraline's journey redefine her concept of "home"?

Coraline's journey makes her realize the importance of home.
Coraline recognizes that "home" has limitations. Coraline's mother shows love for her, but has no time for her. While her father is good to her, the food he makes is not to her liking. A combination of curiosity and restlessness compels Coraline to unlock the door into the world of Other Mother and Other Father. Coraline finds herself entranced by Other Mother's love for her and Other Father's sense of humor. As the toys come alive, Coraline revels in how this setting contains everything that her real world lacks.
Over time, Coraline realizes the dangers beneath this alluring vision. She understands Other Mother's desire for control. Like so much of this world, she recognizes that Other Father is merely a part of Other Mother's plan. Coraline realizes she will be trapped if she stays. As a result, she recognizes the need to get back home.
Coraline understands that a flawed home is better than the world of Other Mother. Imperfection is better than imprisonment. Having buttons sewn on her eyes and becoming another member of the mournful parade of ghost children is no way to live. Coraline's aching to go back home helps her redefine it. She understands its real value. Ultimately, while it might not be perfect, home is where Coraline can be free.

How many pounds in tons

1 ton is 2000 pounds.

There are multiple types of "tons". If you are referring to the American unit of mass, otherwise known as the "short ton", is equivalent to 2,000 pounds. This "ton" is mainly used by those in the United States, and formerly, Canada. The United Kingdom unit, known as "long ton", is equivalent to 2,240 pounds. This type of "ton" is mainly used in the United Kingdom and nations that formerly or currently use the Imperial system. There is also the "tonne" or "metric ton" which is used worldwide. The "tonne" is equivalent to 1,000 kg, or 2,204.623 pounds. This "tonne" is defined in the International System of Units.

The ton is a unit of measurement for weights. According to the Encyclopedia Britannica the word “ton” originates from the word “tun” which refers to big wine casks. Initially, the word “ton” was used to denote large weights of any form. Later on, it was “standardized at twenty hundredweight”. The hundredweight is also known as quintal or centum weight. It is a unit of weight that takes on various values, depending on whether one uses the American or Imperial systems of measurement—American English refers to the two systems of measurement as the “short” and “long” hundredweight, while British English calls them the “cental” and “imperial” hundredweight respectively. Thus, based on these definitions, we have the following conversions for the ton:
For the short hundredweight, 1 hundredweight = 100 lb (45.3592 Kg). Thus, 1 ton = 20 x 100 lb = 2000 lb (907.184 Kg)
For the long hundredweight, 1 hundredweight = 112 lb (50.8023 Kg). Thus 1 ton = 20 x 112 lb = 2240 lb (1016.046 Kg)
However, the most commonly used form of the ton is what is called the “metric ton” or “tonne”, where 1 metric ton = 1000 Kg = 2204.62 lb. The tonne is defined in the International System of Units.
https://www.britannica.com/science/ton

Calculus of a Single Variable, Chapter 7, 7.2, Section 7.2, Problem 30

The region bounded by y=sqrt(x) , y =-x/2+4 , x=0 ,and x=8 revolved about the x-axis is shown on the attached image. We may apply Disk Method wherein we use a rectangular strip representation such that it is perpendicular to the axis of rotation. In this case, we need to sets of rectangular strip since the upper bound of the rectangular strip before and after x=4 differs.
The vertical orientation of the rectangular strip shows the thickness of strip =dx.
That will be the basis to use the formula of the Disc method in a form of:
V = int_a^b A(x) dx where A(x) = pir^2 and r =y_(above)-y_(below) .
The r is radius of the disc which is the same as the length of the rectangular strip.
As shown on the attached file, the r= sqrt(x)-0 = sqrt(x) from the boundary values of x=0 to x=4 .
For the boundary values from x=4 to x=8 , we have r=-x/2+4-0 =-x/2+4 .
Then the integral set-up will be:
V = int_0^4 pi(sqrt(x)) ^2dx+ int_4^8 pi(-x/2+4)^2dx
V = int_0^4 pixdx+ int_4^8 pi(-x/2+4)^2dx
We may apply the basic integration property: int c f(x) dx - c int f(x) dx
V = pi int_0^4x dx+ pi int_4^8 (-x/2+4)^2dx
For the integration of piint_0^4x dx , we apply the Power rule for integration: int x^n dx = x^(n+1)/(n+1) .
pi int_0^4xdx =pi*x^((1+1))/((1+1)) |_0^4
= pi*x^(2)/(2) |_0^4
or (pix^2)/2|_0^4
Using the definite integral formula: int_a^b f(x) dx = F(b) - F(a) , we get:
(pix^2)/2|_0^4=(pi(4)^2)/2-(pi(0)^2)/2
= 8pi - 0
=8pi

For the integration of piint_4^8 (-x/2+4)^2dx ,we apply FOIL method to expand.
(-x/2+4)^2 = (-x/2+4)(-x/2+4) = x^2/4-4x+16 .
The integral becomes:
piint_4^8 (x^2/4-4x+16)dx
Apply basic integration property: int (u+-v+-w) dx = int (u) dx +- int (v) dx+- int (w) dx.
piint_4^8 (-x/2+4)^2dx=pi [int_4^8 (x^2/4) dx -int_4^8(4x)^2dx+int_4^8 16 dx]
Apply Power rule for integration: int x^n dx = x^(n+1)/(n+1) and basic integration property: int c dx = cx .
int_4^8 (x^2/4) dx=1/4 int_4^8 x^2 dx
=1/4x^((2+1))/((2+1))|_4^8
=1/4*x^3/3|_4^8
=x^3/12|_4^8
int_4^8 (4x) dx=4 int_4^8 x dx
=4x^(1+1)/(1+1)|_4^8
=4*x^2/2|_4^8
=2x^2|_4^8
int_4^8 16 dx = 16x|_4^8
Then,
pi [int_4^8 (x^2/4) dx -int_4^8(4x)^2dx+int_4^8 16 dx]=pi[x^3/12-2x^2+16x]|_4^8

Using the definite integral formula: int_a^b f(x) dx = F(b) - F(a) , we get:
piint_4^8 (-x/2+4)^2dx=pi[(8)^3/12-2(8)^2+16(8)]-pi[(4)^3/12-2(4)^2+16(4)]
= pi[128/3-128+128] -pi[16/3-32+64]
=(128pi)/3-(112pi)/3
= (16pi)/3

or use u-subtitution by letting u =-x/2+4 then du =-1/2dx or -2 du =dx
pi int (-x/2+4)^2dx =pi int(u)^2* -2 du
= -2pi* u^3/3
Plug-in u= -x/2 +4 or u=(-x+8)/2 on -2pi* u^3/3 , we get:
pi int (-x/2+4)^2dx =-2pi((-x+8)/2)^3/3|_4^8
=-2pi((-x+8)^3/8) *1/3|_4^8
= ((x-8)^3pi)/12|_4^8
Using the definite integral formula: int_a^b f(x) dx = F(b) - F(a) , we get:
piint_4^8 (-x/2+4)^2dx = ((8-8)^3pi)/12 -((4-8)^3pi)/12
= 0 - (-16pi)/3
=(16pi)/3

Then combining the result of the integrals, we get:
V = pi int_0^4xdx+ pi int_4^8 (-x/2+4)^2dx
V=8 pi +(16pi)/3
V =(24pi)/3+(16pi)/3
V=(40pi)/3 or 41.89 (approximated value)

How does removing several secondary consumers impact the entire ecosystem?

In an ecosystem, the plants are producers, herbivores are primary consumers (as they feed on the plants), carnivores are the secondary consumers (as they consume primary consumers) and higher carnivores or omnivores are the tertiary consumers. If any single component of the food chain is disturbed the rest are also disturbed.
For example, wolves can be thought of as secondary consumers in a grassland that also contains deer. If wolves are removed, the deer population will increase unchecked since their natural predator has been removed from the ecosystem. This will overburden the grasslands since the primary consumers are increasing in numbers. Over time, the deer population will start reducing due to the lack of food. Similarly, tertiary consumers (such as lions, etc.) may also be experience shortage of food since the secondary consumers are no longer available.
Thus, if we remove several secondary consumers from the ecosystem, the primary consumers, the producers, and the tertiary consumers are all affected.
Hope this helps.

Calculus of a Single Variable, Chapter 3, 3.2, Section 3.2, Problem 6

You need to find the two x intercepts of the function, hence, you need to solve for x the equation f(x) = 0, such that:
f(x) = x^2 + 6x = 0
You need to factor out x, such that:
x(x + 6) = 0 => x = 0
x + 6 = 0 => x = -6
You need to evaluate the derivative of the function:
f'(x) = (x^2 + 6x)' => f'(x) = 2x + 6
You need to solve for x the equation f'(x) = 0:
2x + 6 = 0 => 2x = -6 => x = -3
Notice that -3 is found between x intercepts -6 and 0.
Hence, the derivative of the function cancels at x = -3, which is found between the x intercepts -6 and 0.

College Algebra, Chapter 5, 5.5, Section 5.5, Problem 8

Initially there are 1500 bacteria in a culture and it double every 30
minutes.

a.) Determine a function that will model the number of bacteria n(t) after t minutes.

b.) Determine the number of bacteria after 2 hours

c.) After how many minutes will the culture contain 4000 bacteria?



a.) Recall the formula for growth rate

$n(t) = n_0 e^{rt}$

where

$n(t)$ = population at time $t$

$n_0$ = initial size of the population

$r$ = relative rate of growth

$t$ = time

If the population doubles every 30 min (0.5 hours) then $n = 2n_0$


$
\begin{equation}
\begin{aligned}

2n_0 =& n_0 e^{r(0.5)}
&& \text{Divide both sides by } n_0
\\
\\
2 =& e^{r(0.5)}
&& \text{Take $\ln$ of each side}
\\
\\
\ln 2 =& r(0.5)
&& \text{Recall that } \ln e = 1
\\
\\
r =& \frac{\ln 2}{0.5}
&& \text{Solve for } r
\\
\\
r =& 1.3863
&&
\end{aligned}
\end{equation}
$


Therefore, the model is represented as

$n(t) = 1500 e ^{1.3863 t}$

b.)


$
\begin{equation}
\begin{aligned}

\text{if } t =& 2 \text{ hours, then}
\\
\\
n(2) =& 1500 e^{1.3863(2)}
\\
\\
=& 2400

\end{aligned}
\end{equation}
$


c.)


$
\begin{equation}
\begin{aligned}

\text{if } n(t) =& 4000 \text{ then}
&&
\\
\\
4000 =& 1500 e^{1.3863 (t)}
&& \text{Divide both sides by } 1500
\\
\\
\frac{8}{3} =& e^{1.3863 t}
&& \text{Take $\ln$ of each side}
\\
\\
\ln \left( \frac{8}{3} \right) =& 1.3863 t
&& \text{Recall that } \ln e = 1
\\
\\
t =& \frac{\displaystyle \ln \left( \frac{8}{3} \right) }{1.3863}
&& \text{Solve for } t
\\
\\
t =& 0.7075 \text{ hours } \times \frac{60 \text{ minutes}}{1 \text{ hour}}
&& \text{Convert hours into minutes}
\\
\\
t =& 42.45 \text{ minutes }
&&
\end{aligned}
\end{equation}
$


It shows that the population of bacteria will be 4000 after 43 minutes.

Calculus of a Single Variable, Chapter 2, 2.4, Section 2.4, Problem 64

Given the function y=cos(sqrt(sin(tan(pi x)))) . We have to find the derivative.
Let us begin,
(dy)/(dx)=-sin(sqrt(sin(tan(pi x)))).d/(dx)[sqrt(sin(tan(pi x)))] ------>(1)

Now,
d/(dx)[sqrt(sin(tan(pi x)))]=1/(2sqrt(sin(tan(pi x)))).d/(dx)[sin(tan(pi x))] ----->(2)
Again,
d/(dx)[sin(tan(pi x))]=cos(tan(pi x))d/(dx)[tan(pi x)]-------->(3)
=cos(tan(pi x)). pi sec^2(pi x)
Now substituting this in (2) we get,
d/(dx)[sqrt(sin(tan(pi x)))]=1/(2sqrt(sin(tan(pi x)))).cos(tan(pi x)).pi sec^2(pi x)

Substituting this in (1) we get,
(dy)/(dx)[cos(sqrt(sin(tan(pi x))))]=-sin(sqrt(sin(tan(pi x)))).pi/(2sqrt(sin(tan(pi x)))).cos(tan(pi x))sec^2(pi x)

How does Coriolanus' relationship with his wife compare to his relationship with his mother?

In Shakespeare's play, Caius Martius Coriolanus is a warrior par excellence; in fact, he's very good at being a soldier. The main influence in his chosen lifestyle is his mother, Volumnia, one of Shakespeare's most influential maternal figures.
Volumnia cherishes a warrior spirit to rival that of the most battle-hardened Roman soldier. In fact, Coriolanus is inevitably drawn to Volumnia by virtue of his emotional connection to this dominating matriarch. One can argue that he seeks her acceptance and approval as much as he seeks victory on the battlefield. It is Volumnia who encourages her son to excel in warfare and to pursue a course in politics. Coriolanus thinks her "the most noble mother of the world" (Act 5, Scene 3), while Volumnia assures him: "Thou art my warrior; I holp to frame thee" (Act 5, Scene 3). Indeed, Volumnia proudly asserts that "there's no man in the world more bound to 's mother" (Act 5, Scene 3).
On the other hand, Coriolanus' relationship with Virgilia, his patient and long-suffering wife, is fraught with emotional tension of a different sort. Virgilia, the stereotypical quiet and submissive Roman wife, doesn't think very much of Volumnia's emphasis on war and bloodshed. She finds no joy in her husband's absences. In Act 1 Scene 3, the main point of contention between Volumnia and Virgilia is Coriolanus' preoccupation with warfare.
Volumnia maintains that Virgilia needs to stop moping about her husband going off to war. She simultaneously lectures and patronizes her daughter-in-law; Volumnia basically refuses to sympathize with Virgilia. Here's what she proclaims:

"I pray you, daughter, sing; or express yourself in a more comfortable sort: if my son were my husband, I should freelier rejoice in that absence wherein he won honour than in the embracements of his bed where he would show most love...I tell thee, daughter, I sprang not more in joy at first hearing he was a man-child than now in first seeing he had proved himself a man...I had rather had eleven die nobly for their country than one voluptuously surfeit out of action" (Act 1 Scene 3).

While Virgilia shrinks from the prospect of Coriolanus shedding his blood, Volumnia calls her a "fool" for not appreciating what a warrior has to sacrifice for victory. So, Volumnia essentially overshadows her daughter-in-law; she leaves no room for Virgilia to assert her wifely concerns.
Meanwhile, Coriolanus sees Virgilia as his better self; he does not seek her approval because she approves of him already. Virgilia's respectful address of "My lord and husband" is in turn lavishly rewarded by his adoring "Best of my flesh, Forgive my tyranny." To Coriolanus, a kiss from Virgilia makes up for his long exile away from her; to this battle-hardened warrior, his wife is his "gracious silence."
So, the difference between Coriolanus' relationship with his mother and with his wife lies in his differing approach to both. With Volumnia, Coriolanus must evince consistent evidence of his exploits on the battlefield to satisfy the dictates of her expectations. Yet, in the midst of the biggest decision in his life (to withdraw from attacking Rome), it is Virgilia's kiss which fills his mind and heart:

Now, by the jealous queen of heaven, that kiss I carried from thee, dear, and my true lip Hath virgin'd it e'er since.’

While Coriolanus sees Volumnia as the inspiration behind his warrior ethos, he views Virgilia as the one woman whose gentle love inspires his sexual passion and loyalty.

Why do you think Godwin chose third person?

Tom Godwin's story "The Cold Equations" has very few characters—just Barton the pilot, Marilyn Cross the stowaway, Gerry her brother, Commander Delhart, and an unnamed records officer. These characters are factors within the equation of the plot: Barton, Delhart, and the records officer represent the known quantities, while Marilyn and Gerry are unknowns which the plot must "solve for" to determine how they will influence the result.
Every character is subject to the titular "cold equations" that rule life on the galactic frontier, but perhaps none more so than Barton himself, for he is the one who must choose whether to submit to those equations or try somehow to find a way around them. When Barton finds Marilyn hidden on his supply ship, her presence throws Barton's personal equation out of balance. The appearance of this unknown quantity changes the calculation used to determine how far Barton's ship can safely travel, and logic dictates that Barton must jettison Marilyn, or her weight will cause the ship to run out of fuel before it reaches its destination.
Barton accepts the fact that he must execute the stowaway as an uncomfortable but necessary duty:

"There could be no alternative [...] What he must do would be unpleasant for both of them; the sooner it was over, the better."

He is not prepared for Marilyn's childlike innocence, however, and finds it difficult to justify killing her on the basis of mathematics. Marilyn appeals to Barton's humanity, pleading to be spared and insisting that there must be some way to complete the journey without ending her life. By telling the story from Barton's third-person-limited point of view, Godwin forces the reader to go through all of Barton's calculations as he tries to find an alternative solution to his dilemma. Barton slows the ship down to conserve fuel,and radios Commander Delhart to explain the situation, hoping against hope that the commander will be able to suggest something:

"The call would be futile, but he could not, until he had exhausted that one vain hope, seize her and thrust her into the air lock as he would an animal — or a man."

The commander, however, enforces the rules:

"'I’m sorry — I can do nothing. This cruiser must maintain its schedule; the life of not one person but the lives of many depend on it. I know how you feel but I’m powerless to help you. You’ll have to go through with it.'"

Marilyn is anguished and argues desperately against this sentence. The reader, tied to Barton's third-person viewpoint, must continually reassess Barton's available options, and continually return to the conclusion that Marilyn must be jettisoned—the one sacrificed to save the many who are depending on the ship's supplies. And yet Barton still tries to spare Marilyn her fate for as long as possible:

"She would have to go when deceleration began; it could be no other way. When would that be—how long could he let her stay?"

Because the reader is limited to what Barton knows, feels, and understands, there is still some hope right up to the final paragraphs that Barton will somehow be able to save Marilyn. Likewise, because the reader is limited to what Barton knows, feels, and understands, they are left with Barton's doubts about the rightness of his actions, and haunted by the consequences of his decision.

I would argue Godwin uses third person in his classic science fiction short story to provide emotional distance.
As the title indicates, much of the theme of the story revolves around Barton (the pilot) thinking coldly. He and the stowaway are living in a universe determined by these equations. All actions are determined by mathematical formulae, which are fundamentally third person and objective. There is (ideally) no subjective element to math. In the same sense, a third-person perspective allows Godwin to maintain emotional distance and objectivity. A first-person perspective would permit too much intimacy.
A second, related reason is to maintain tension. Readers must wait for Barton to reach his decision. They have no access to his internal processes. They don't know what he is thinking or feeling, and must wait for the decision to emerge, waiting along with Marilyn (the stowaway) to learn her fate.

Why do managers need to understand the people working in their organization?

Managers need to understand the people in their organizations because they have to be able to understand what their superiors want and get their subordinates to fulfill those desires. Neither is possible without an understanding of the people involved.
Managers, in a sense, serve as intermediaries between the upper echelons of a firm and its workers. They are in charge of getting the workers to perform the tasks the upper levels lay out. To do this well, they have to understand both groups of people in their organization. First, they have to understand the people above them in the hierarchy. They have to understand how those people think and what they expect from the rank-and-file workers. Secondly, managers have to understand those who work for them. They have to understand how to motivate their employees and how to get them to feel happy in their jobs. They have to be able to put their employees in situations that allow them to do their jobs as well as possible, thus pleasing the managers’ own bosses.
Because managers have to take orders from above and transmit them to people below, it is important for them to understand both their superiors and their subordinates.
http://guides.wsj.com/management/developing-a-leadership-style/what-do-managers-do/

Precalculus, Chapter 5, 5.4, Section 5.4, Problem 25

-165^@=-(120^@+45^@)

sin(-165)=-sin(165)
sin(u+v)=sin(u)cos(v)+cos(u)sin(v)
[sin(-(u+v))]=-[sin(u)cos(v)+cos(u)sin(v)]
[sin(-(120+45))]=-[sin(120)cos(45)+cos(120)sin(45)]
[sin(-(120+45))]=-[(sqrt3/2)(sqrt2/2)+(-1/2)(sqrt2/2)]=-sqrt2/4(sqrt3+1)

cos(-165)=cos(165)
cos(u+v)=cos(u)cos(v)-sin(u)sin(v)
cos(-(u+v))=cos(u)cos(v)-sin(u)sin(v)
cos(-(120+45))=cos(120)cos(45)-sin(120)sin(45)
cos(-(120+45))=(-1/2)(sqrt2/2)-(sqrt3/2)(sqrt2/2)=-sqrt2/4(1+sqrt3)

tan(-165)=-tan(165)
tan(u+v)=(tan(u)+tan(v))/(1-tan(u)tan(v))
-tan(u+v)=-[(tan(u)+tan(v))/(1-tan(u)tan(v))]
-tan(120+45)=-[(tan(120)+tan(45))/(1-tan(120)tan(45))]=-[(-sqrt3+1)/(1-(-sqrt3)(1))]=(sqrt3-1)/(1+sqrt3)
After rationalizing the denominator the answer is 2-sqrt3.

What can we infer about the girls based on what they want for Christmas?

Well, all of the girls except Beth grumble about being so poor, and Jo even feels that Christmas won't seem very Christmas-y without gifts to exchange. Apparently, Marmee thinks that presents seem like a trivial concern when there is such a terrible war going on and their father is away, serving the troops and in danger. Meg, Jo, and Amy's responses are, at first, somewhat materialistic, and they seem to indicate a certain lack of maturity. 
The girls, at first, decide to buy themselves gifts: Jo wants to buy a book that she's coveted for a long time, Beth will buy new piano music, Amy wants some drawing pencils, and Meg "[thinks] regretfully about all the pretty things she [wants]." These desires tell us a bit about each girl's personality and tastes: Meg is somewhat vain and cares a great deal about her appearance; Jo doesn't care at all about her appearance, only her mind, and she lives to read and write; Beth is the sweet homebody whose desire for herself is actually something that will brighten the household for everyone in it, music; and Amy is rather self-centered, sort of a stereotypical artistic type. The girls aren't evil or mean or selfish to a fault. Rather, they just seem to lack the perspective granted older folks who've witnessed tragedy and felt pain, but the girls do seem to develop perspective quickly as they turn their attention toward treating Marmee and the Hummels generously.

Explain the phrase, “Boy, was she lousy with rocks.”

Holden is making another of his close observations about other people; how they act, how they behave, how they dress. In this case, he's referring to Mrs. Morrow's penchant for wearing lots of expensive jewelry. In this specific context, "lousy" doesn't mean "very bad" as in "this coffee's lousy" for example. Instead, it suggests an infestation of lice. Only Mrs. Morrow isn't infested with any kind of bugs or critters, but precious gemstones, or "rocks."
Though super-judgmental as always, it seems that Holden kind of likes Mrs. Morrow, which is especially unusual given that her son is someone Holden regards as a "bastard." Indeed, the very thing that seems to have drawn Holden to Mrs. Morrow is his sense that she understands precisely what kind of a "bastard" her son really is. But then Holden immediately reverts to type and distances himself from Mrs. Morrow, insisting that mothers are all slightly insane.

As Holden is leaving Pencey Prep for the last time, he encounters on the train the mother of one of his classmates, Ernest Morrow. She recognizes a Pencey sticker on one of Holden's suitcases and strikes up a conversation with him. It is late in the evening, and Holden notes that Mrs. Morrow is wearing an orchid corsage and assumes that she has been to a party. As they talk, she removes her gloves and Holden observes "boy, was she lousy with rocks." This is a slang expression. To be "lousy" with anything means that there is a large quantity of it. A louse is a singular expression of the more common plural of lice, which are known to proliferate. In this context, "rocks" refer to precious gemstones, likely diamonds. So, what Holden is observing is that Mrs. Morrow is wearing a collection of rings and/or bracelets that look expensive.

What are images that depict Beowulf as an epic hero?

The epic hero is a literary convention that defines a specific type of character. This kind of character typically possesses a number of particular traits, including some sort of extraordinary ability.
Beowulf’s extraordinary ability is his strength--no man alive, and almost no monster alive, can match it. The most famous image demonstrating Beowulf’s strength comes early in the story when he fights the monster Grendel:

He twisted in pain,
And the bleeding sinews deep in his shoulder
Snapped, muscle and bone split
And broke.

This passage shows Beowulf defeating Grendel. But Beowulf doesn't simply win the battle; he does so in grand style (or we might say, in “epic” style) by ripping Grendel's arm from his body. The image of Grendel's arm slung over a rafter in Herot is one of the most famous in all of English literature.
Another key trait of the epic hero is his embodiment of his culture's ideals. Beowulf, as part of the early Middle Ages warrior culture, shows the courage that was so highly prized. We see this most poignantly in the poem's final battle, as Beowulf and his trusted friend Wiglaf battle the dragon. Beowulf is an old king now, no longer the fearsome warrior of his youth. In this passage, he has been mortally wounded by the dragon, but continues to fight on, with Wiglaf's help:

And Beowulf drew
His battle-sharp dagger: the bloodstained old king
Still knew what he was doing. Quickly, he cut the beast in half, slit it apart.
It fell, their courage had killed it.

This is Beowulf's last act on Earth. Moments later he dies from the dragon-inflicted wounds. But, as we can see, his courage holds until the end.

How does Harry feel about Draco Malfoy and why does he feel this way?

Throughout the seven Harry Potter novels, Harry and Malfoy engage in what is one of the most famous rivalries in young adult literature. Early on in Harry Potter and the Sorcerer's Stone, Harry meets Malfoy aboard the Hogwarts Express. Initially impressed by Harry's fame, and seeing that Harry has become friends with Ron Weasley (who comes from a poor family), he offers friendship to Harry. He says,

You’ll soon find out some wizarding families are much better than others, Potter. You don’t want to go making friends with the wrong sort. I can help you there.

Harry rejects this hateful idea that Malfoy presses upon him. Harry has already made close friends with Ron, whom he likes and respects, and is upset at the idea of someone claiming his newly acquired friend is inferior.
Part of the reason for their rivalry is Malfoy's intense arrogance and jealousy of Harry's fame. Malfoy, a self-proclaimed wizard at Quidditch, is revealed to have comparable, but not superior, skills to Harry's.
Ron says of Malfoy's Quidditch skills,

Anyway, I know Malfoy’s always going on about how good he is at Quidditch, but I bet it’s all talk.

Once Gryffindor defeats Slytherin in a Quidditch match, it becomes clear that Harry and Malfoy's rivalry will only continue. Malfoy vows revenge, confident that his skills are still greater than Harry's. Malfoy's arrogance, pretentiousness, classism, and general nastiness repeatedly repulse Harry, who prefers to be in good company.
https://www.hp-lexicon.org/2008/01/25/quotes-draco-malfoy/

https://www.wizardingworld.com/writing-by-jk-rowling/draco-malfoy

In Leskov's "The Sealed Angel," which Old Believers convert to the ruling church and in what order? Who are the two characters most responsible for this?

Luke is converted first to the Orthodox Church, followed by Maroe and the rest of the Old Believers. The responsibility for this conversion is harder to pin down because of the story's ambivalent attitude toward the faith of Luke and the others. The chain of events that leads to the theft of the icon theoretically begins with the double-dealing of Pemen, so, in a sense, he could be held responsible. The Englishman's sympathy for the Old Believers also emboldens Luke and the others to attempt the theft, so he (and his wife) can be thought of as responsible as well. Of course, the priest to whom Luke confesses and who provides absolution is also responsible for their conversion.
True responsibility, however, perhaps lies with the notion of belief itself. The Old Believer's reliance on miracles is behind both their belief in their icons and, ironically, their turning toward Orthodoxy, when Luke is made to believe that the "miracles" that enabled their escape over the river were the work of "the angel of the Orthodox Church."

Luka, sometimes referred to as Luke or Uncle Luke, is the first of the "Old Believers" group to convert to the ruling Orthodox Church. Luka is persuaded when an elaborate scheme to steal a church icon is foiled by his conscience. Threatened by a movement to clean and restore religious texts and icons to remove errors within them, the Old Believers wish to keep their iconography the way it is. To do so, they are willing to go to great lengths and even steal from the ruling church. The group is obsessed with the icon of an angel that is due to be restored by the Orthodox Church, so they hire an icon painter to create a duplicate of it. The original icon has been sealed for safe transport, so the artist removes the wax seal and places it on the copy. The group takes the original angel, but a strange occurrence makes them question their plan. During a church service, the wax seal falls off the fake icon on its own.
Upon witnessing what he perceives to be a miracle, Luka is the first to be filled with regret, and he repents to the bishop. Although he asks to be thrown in jail for his sin, the bishop is understanding and decides that the copy angel is better than the original since the seal fell off on its own. He invites Luka and the other Old Believers to rejoin the Orthodox Church and tells them that the seal falling off the copy angel is proof that the Orthodox Church is in the right. In this sense, both the bishop and Luka are the ones responsible for the group's conversion. Uncle Maroe converted alongside Luke the day after the kindly bishop's pardon. Following their conversions, the narrator also agrees to convert on behalf of the other Old Believers who are present, saying, "We agree with you, Uncle Luke, and so we shall all be gathered under one shepherd like lambs."
https://archive.org/details/russiansketchesc00tolliala

Calculus: Early Transcendentals, Chapter 6, 6.2, Section 6.2, Problem 42

The formula provided represents the volume of the solid obtained by rotating the region enclosed by the curves y = 1 + cosx, y = 1, x = 0, x = pi/2 , about y axis, using washer method:
V = pi*int_a^b (f^2(x) - g^2(x))dx, f(x)>g(x)
You need to find the endpoints by solving the equation:
1 + cosx = 1 => cos x = 0 => x=-pi/2, x = pi/2
V = pi*int_0^(pi/2) (1 + cosx )^2 - 1^2)dx
V = pi*int_0^(pi/2) (1 + 2cos x + cos^2 x - 1)dx
V = pi*int_0^(pi/2) (2cos x + cos^2 x)dx
V = pi*(int_0^(pi/2) (2cos x) dx + int_0^(pi/2) (cos^2 x)dx)
V = pi*(2 sin x + int_0^(pi/2) (1+cos 2x)/2 dx)
V = pi*(2 sin x + x/2 + (sin2x)/4)|_0^(pi/2)
V = pi*(2sin(pi/2) + pi/4 + 0 - 2*0 - 0/2 - 0/4)
V = pi*(2 + pi/4)
V = (pi*(8+pi))/4
Hence, evaluating the volume of the solid obtained by rotating the region enclosed by the curves y = 1 + cosx, y = 1, x = 0, x = pi/2, about y axis, using washer method, yields V = (pi*(8+pi))/4.

When the president makes a nomination, what should be the nature of the Senate's "advice and consent"?

Article II, Section 2, Clause 2 of the Constitution states that the President

"shall nominate, and by and with the advice and consent of the Senate, shall appoint ambassadors, other public ministers and consuls, judges of the Supreme Court, and all other officers of the United States, whose appointments are not herein otherwise provided for, and which shall be established by law.”

In other words, the advice and consent of the Senate is necessary before nominees such as Supreme Court justices take their positions.
The Constitution does not explicitly state what the Senate must do to provide or deny consent for the president's nominees; however, Article I, Section 5 of the Constitution states that “each House may determine the rules of its proceedings." The way in which the Senate generally determines how to vote on nominees is that once the president makes a nomination, the nominee's candidacy is sent to the Senate Judiciary Committee. The committee holds hearings and then decides whether to submit the nomination to a vote; if the vote is held and the nomination passes, the Senate Majority leader can decide whether to submit the nomination to the entire Senate. Then, more hearings might be held, and the Senate can have a cloture vote (that passes with 60 votes) to end discussion and have a general vote. If the Senate cannot reach 60 votes to close the discussion and have a vote, there is what is called a filibuster. The Senate must generally overcome a filibuster with 60 votes. 
People disagree on what the nature of the advice and consent provided by the Senate should be. Many people, particularly conservatives, believe that the Framers of the Constitution did not intend the Senate to explicitly vote on each nominee. However, that has been the practice of the Senate.