In what ways were the lives of African Americans affected by the Second World War?

African Americans were affected in a number of ways by World War Two. More than 2.5 million African American men registered for the draft during the war, and over one million actually served in the armed forces. Many African American women also volunteered for military duty. Many hoped that by patriotically serving the United States during the war, they could improve their station once they returned home.
During the war, many African Americans started calling for a "double-victory campaign." They hoped to help defeat the enemy abroad by serving bravely in the fight against fascism. Additionally, they hoped to achieve a victory at home against racism and discrimination. To help achieve these goals, several new civil rights organizations were formed. The most well known of these was the Congress of Racial Equality (C.O.R.E.). These groups sought to use the African American war effort as a backdrop to address racial equality in the North. They also took on the issue of unequal pay since most African Americans working in factories that provided military materials received less pay than their white counterparts.
On the home front, the ramp-up in industry to support the war effort meant a lot of new jobs became available to African American workers. This resulted in a migration of many from the South to the Mid-West, the Northeast, and to a lesser extent, the West Coast. As such, many African Americans were able to escape the Jim Crow laws of the South.
Once African Americans arrived in new parts of the country, they often encountered new problems. They certainly were not welcomed with open arms. There was often resentment towards African Americans as they moved into previously all white neighborhoods and factories. In fact, in certain cities, such as Detroit, there were race riots in which many African Americans were violently attacked.
The double victory campaign brought attention to the contribution of African Americans in the Allied victory. However, it would be several decades more until its goals of desegregation were achieved.
https://www.smithsonianmag.com/history/why-african-american-soldiers-saw-world-war-ii-two-front-battle-180964616/

https://www.umbc.edu/che/tahlessons/pdf/Continuity_or_Change_African_Americans_in_World_War_II(PrinterFriendly).pdf

Give an account of Harris' visit to the maze at Hampton Court and getting lost there.

This is yet another humorous adventure in a book detailing the comic capers of three men in 1880s Britain who decide to take a two-week long boating vacation on the Thames, traveling from Kingston-on-Thames to Oxford. The three are comically ill-suited to handle their many adventures. The Hampton maze episode illustrates not only Harris's incompetence as a tourist but also the incompetence of tourists in general--and perhaps the way they are deceived by being assured that difficult tasks are easy.
Harris decides he wants to go through the maze at Hampton Court, a royal palace once occupied by Henry VIII. A "country cousin" tells him that the maze is simple to navigate: you keep turning right and you'll be out in ten minutes:

Well just go in here, so that you can say you’ve been, but its very simple. Its absurd to call it a maze. You keep on taking the first turning to the right. Well just walk round for ten minutes, and then go and get some lunch.

Once inside, Harris meets up with tired, lost tourists who want to get out of the maze. In short order, Harris has:

absorbed all the persons in the maze. People who had given up all hopes of ever getting either in or out, or of ever seeing their home and friends again, plucked up courage at the sight of Harris and his party, and joined the procession, blessing him. 

Naturally, Harris has no idea what he is doing, and they all continue to be hopelessly lost. Harris becomes "unpopular." In the end, the crowd of lost souls calls out to the "keeper," who climbs into the maze with a ladder, but he is new and cannot lead them out either. They remain lost until the "old keeper" returns from dinner. With dry humor, Harris decides it is a "very fine maze" and that he will try to get George "into it" on their way back. 
 
 

Harris tells this story in Chapter VI. We’ve already gotten a hint that Harris is the kind of person who thinks he knows everything about a subject, when he really knows very little. This tale supports the assessment.
Harris got a map of the hedge maze, and he thought he knew very well how to navigate it. He took a cousin along and assured him that they would need only 10 minutes to pass through the hedges successfully. Once in the maze, the two men kept meeting people who were lost inside it. Harris invited everyone to follow him, since he knew what he was doing. Well, naturally, the whole group ended up getting lost. They just couldn’t find their way back out, no matter which way they turned. Consulting the map didn’t help at all. Eventually the group yelled for the keeper of the maze for help. The keeper was young and new to the job, though. He brought a ladder and climbed into the maze to help the visitors – and promptly got lost, himself. They all had to wait until an older and more experienced keeper came back from his dinner, before everyone was led successfully out of the maze.
All this being said: both Harris and J. thought they should take George to the maze, on their way back past Hampton Court.
https://www.hrp.org.uk/hampton-court-palace/whats-on/the-maze/

Calculus of a Single Variable, Chapter 5, 5.1, Section 5.1, Problem 79

We are asked to locate the relative extema and any inflection points for the graph of y=x^2/2-lnx :
Extrema can occur only at critical points; i.e. points in the domain where the first derivative is zero or fails to exist. So we find the first derivative:
y'=x-1/x This is a continuous and differentiable function everywhere except x=0, which is not in the domain of the original function. (The domain, assuming real values, is x>0.)
Setting the first derivative equal to zero we get:
x-1/x=0 ==> x=1/x ==> x^2=1 ==> x=1 (x=-1 is not in the domain.)
For 01 it is positive, so there is a minimum at x=1. This is the only minimum or maximum.
Inflection points can only occur when the second derivative is zero:
y''=1+1/x^2 ==> y''>0 forall x so there are no inflection points.
The graph:

Questions about dystopia: Please answer the followings questions about E. M. Forster’s “The Machine Stops”. Each answer should use details in the story. 1. What makes this story dystopian? How is this world different from our own? How is it similar? 2. How are people in the story different from us? How are people in the story similar to us? 3. How do politics shape the lives and personalities of people in the story? 4. How is language shaped or warped by the world in which it is practiced?

In "The Machine Stops," E.M. Forster tells the tale of a mother and son who live in separate compartments across the world from each other. The bulk of the population lives in individual units under the surface of the Earth and is tended to by something called the Machine, which provides sustenance, entertainment, and connection. Kuno and his mother, Vashti, talk about the supposedly uninhabitable surface of the world during one of their rare visits. Later, the Machine breaks down even as people develop a religion that considers it an omnipotent being, and the people in charge fail to fix it. The story ends with much of the population, including Vashti and Kuno, dying as the Machine fails.
1. What makes this story dystopian? How is this world different from our own? How is it similar?A dystopian story is one set in a world where people are oppressed, and things are usually not good. Often the societies are characterized by a small, wealthy upper class that has access to resources and a large lower class living in poverty or illness. While people in "The Machine Stops" still live on the same planet, they live below the ground and receive sustenance and communication via the Machine. They are governed by the committee that works with the machine. People still have friends and family, but they communicate with video messaging and text messaging and rarely meet in person. Scientific and technological advances have allowed people to control the weather and the night and day to some extent. Vashti later thinks that the silence when the machine stops is going to kill her; the narrator says that thousands did die from it because they were surrounded by noise their whole lives.
2. How are people in the story different from us? How are people in the story similar to us?
People still have friends and outside interests, but they only explore them via the Machine and technology. People still flock to religion, but the religion in the story begins to focus on the Machine. Though the Machine was created by people and is slowly breaking down, people come to see it as an omnipotent God. People in the story still give birth naturally as well, but the children are then given to public nurseries where parents can visit them. Once the child is old enough, they are assigned their own room. Kuno's room is on the other side of the world from his mother, Vashti. The book of the Machine says that parental duties stop as soon as the child is born. The committee that governs everyone for the Machine decides whether or not people can become parents as well.
3. How do politics shape the lives and personalities of people in the story?
People are governed by the Machine and the Central Committee. Kuno explains that he tried to go to the surface of the Earth—where he claims people live—but was brought back to his room. Every rule and procedure put in place is designed to keep people isolated and alone with only technology to connect them to the outside world. Vashti even feels like her bed is too big because her entire life has been contained, and the idea of something as large as a bed is not comforting. This is the world created by the Machine and by the people who built the Machine to govern the world. People are scared and isolationist. They are unused to being in the same space as each other or addressing each other directly. They believe that exposure to the air kills them, which is why disobedience is punished with Homelessness—which entails being expelled from the living areas.
4. How is language shaped or warped by the world in which it is practiced?
When Vashti is traveling to meet with Kuno, the stewardess calls the land below them Asia. This surprises and confuses Vashti, who is used to different mechanical names. The stewardess says, "I have got into the habit of calling places over which I pass by their unmechanical names." She tells Vashti to remember that ancient names were dictated by the people who lived in those times. She says that they are more advanced now and thankful for it; she says old civilizations called the Himalayas the roof of the world because they did not have the same understanding of science and space that they do in modern times. People also do not understand the concept of the Machine stopping. A friend of Vashti says that "the phrase conveys nothing to me."

How does word choice affect the emotional impact of “She Walks in Beauty”? Pay special attention to connotation rather than denotation. Use evidence from the text to support your response.

This small masterpiece by Byron could be considered a textbook guide to writing poetically as well as, as is usual in Byron, naturally and almost conversationally.
The first line, stating that "She walks in beauty" (italics added) instead of simply stating that "she is beautiful" or "she possesses beauty," suggests a kind of higher dimension into which the poet's love has entered, above the cold earthly world. Similarly, the comparison of her to "night" rather than "day" implies some degree of mystery about her. It's too ordinary, Byron seems to be saying, to employ the usual means of describing a beautiful woman as being "bright as day" or with a similar phrase. The "night" connotes something more interesting and possessing a deeper attraction.
In the second stanza, the characterization of her "nameless grace" implies something exceeding one's ability to describe it—a descriptive adjective is beyond the poet's ability. Also, in saying "one shade the more, one ray the less," the poet is suggesting that both shade and light are generated from within his love, not granted to her externally—since we have already pictured her walking "in the night." "Raven tress," though perhaps sounding somewhat conventionally poetic, also contributes to the connotation of that which is above the ordinary, above earth-bound human nature.
The last stanza, of course, is a kind of summation, and it seems the least striking poetically of the three. "The tints that glow," however, because this is simply an unusual way of getting across the idea of the radiance of his beloved's face, again impresses the reader with a suggestion of a magical quality, leading up to the beloved's "mind at peace with all below / A heart whose love is innocent!" The central point about his beloved's character comes at the very close and seems to tie the entire poem together into a single thought.
"She Walks in Beauty" demonstrates a recurring feature of Byron's verse: his ability to establish an almost conversational tone and simultaneously—through suggestion and the appropriate use of specialized, poetic language—to give an impression of transcendent beauty and divinity in women and in human beings overall.

g(t) = log_2(t^2+7)^3 Find the derivative of the function

g(t) = log_2 (t^2+7)^3
Before taking the derivative of the function, apply the logarithm rule log_b (a^m)= m*log_b(a) . So the function becomes:
g(t) = 3log_2(t^2+7)
Take note that the derivative formula of logarithm is d/dx[log_b (u)] = 1/(ln(b)*u)*(du)/dx .
So g'(t) will be:
g'(t) = d/dt [3log_2 (t^2+7)]
g'(t) = 3d/dt [log_2 (t^2+7)]
g'(t) =3 * 1/(ln(2) * (t^2+7)) * d/dt(t^2+7)
g'(t) = 3 * 1/(ln(2) * (t^2+7)) * 2t
g'(t) = (3*2t)/(ln(2) * (t^2+7))
g'(t) = (6t)/((t^2+7)ln(2))
 
Therefore, the derivative of the function is g'(t) = (6t)/((t^2+7)ln(2)) .

Who in modern politics or leadership can you compare to Julius Caesar?

The answer to this question depends, of course, on how recent a period of time we would restrict ourselves to in looking for a Caesar-like leader. If by "modern times" we mean our immediate, present-day political world of the early twenty-first century, then we're extremely limited in the candidates available to fulfill this comparison. Caesar was a man who presided over a transition from the Roman Republic to the beginnings of an imperial state at a time of crisis, all with the purported rationale of preventing Rome from descending into chaos. He was then assassinated because others believed he had gone too far and that the changes he had made would result in the very outcome Caesar supposedly wanted to prevent: the destruction of the Roman state. No leader today is genuinely like Caesar with regard to the actions he carried out or the circumstances surrounding them.
Nevertheless, if forced to pick someone from the late twentieth- and early twenty-first century, I would say the only political leader who might resemble Caesar in some sense is Vladimir Putin, though the comparison is unfair to Caesar. Putin rose to power at a time when post-Soviet Russia was going through a severe economic crisis. Russia had never been a democracy or a democratic republic, but in the first few years after the Communists were expelled in 1991, there was at least a degree of freedom in Russia—imperfect but genuine—that had not existed during the Soviet period. After his appointment by Boris Yeltsin as his successor, Putin consolidated power for himself, moved against the so-called "oligarchs" and confiscated their wealth, and clamped down on freedom of speech and the political opposition, such as it was. He also prosecuted a brutal war in Chechnya and now has the obvious intention of regaining territories previously part of the Russian and Soviet empires.
Putin's aggrandizement of personal power and his military exploits and intentions are somewhat analogous to Caesar's actions, but the other details of Putin's rise to power and the history of the Soviet Union and post-Soviet Russia do not correspond to Caesar and the last period of the Roman Republic. For all his faults, Caesar was nonetheless a brilliant statesman and military strategist, a charismatic leader, and a gifted writer. His actions (and those of his grand-nephew and successor Octavian/Augustus), dictatorial as they were, can be said to have laid the foundations of modern Europe and the entire Western world. It's extremely unlikely that Putin, an ex-KGB officer and would-be totalitarian leader, will ever have the achievements of Julius Caesar.

I do not think that you can compare Julius Caesar to anyone in modern politics.  He was a successful general who managed to invade Britain and Gaul.  This involved a great deal of strategic thinking and the ability to manage logistics in order to keep his troops fed and equipped.  Caesar also wrote a history of the conquest of Gaul, which was still being used by academics centuries later.  Caesar survived a severe civil war which placed him at the head of the government.  He was known for his oratorical skill at a time when one could not rely on cameras to make oneself look presentable.  He provided housing for his soldiers and relief for the poor.  When he assumed total power over the Roman government, he became the most powerful man in the West's only superpower.  There is no one that can be easily compared to Julius Caesar because he combined military, scholastic, and political achievement in one person.  I do not see anyone who could potentially measure up to that standard today.