In the months after the destruction of Hiroshima and Nagasaki, President Harry Truman spoke of his ambition to make the atomic bomb “an overwhelming influence toward world peace.” Meanwhile, the Bulletin of the Atomic Scientists warned that “all we can gain in wealth, economic security, or improved health will be useless if our nation is to live in continuous dread of sudden annihilation.” Using specific events, people, and policies, analyze the impact of nuclear weapons on US foreign policy and the lives of Americans from the Manhattan Project through the Cuban Missile Crisis. How did different Americans perceive and make use of the bomb in debates about freedom and national security?

In the years that followed Hiroshima and Nagasaki, and certainly after the Soviets successfully tested the atomic bomb in 1948, annihilation by nuclear weapons was a constant fear for many Americans.
Atomic and nuclear weapons played a major role in foreign policy. Generally speaking, the United States spent billions expanding and testing its arsenal. The National Security Council memo NSC-68 advocated massive buildup of nuclear weapons in response to what it saw as the global threat posed by communism. This was seen as the only way to avoid war with the Soviets, a policy stance that would persist until the 1970s. The United States rapidly built up its capability, developing far more powerful weapons than the Hiroshima and Nagasaki bombs. On the other hand, no American leader was eager to use these weapons, and the fact that the Soviets also had nuclear capability was a major factor in promoting restraint in the escalating Cold War. In the Korean War, for example, President Harry Truman declined to use atomic bombs against Chinese troops and cities because he feared it would escalate a regional conflict into a global one. President Kennedy decided not to attack Soviet missile silos in Cuba (or to order a direct assault of the island) for similar reasons. Overall, the United States was committed to developing a massive nuclear arsenal even beyond the Cuban Missile Crisis.
Nuclear weapons also affected the everyday lives of ordinary Americans. The threat, imagined or otherwise, of nuclear destruction led to a sense of anxiety in the United States. Children regularly took part in air raid drills in public schools. Americans dug fallout shelters in their backyards, often at great expense. Many Americans, sensing that the stakes were raised, supported repressive measures against suspected communists: the HUAC proceedings and the McCarthy hearings were the most egregious examples of this phenomenon. On the other hand, the fear of nuclear attack fostered a renewed focus on education, especially in science and mathematics. The Soviet launch of Sputnik in 1957 caused many Americans—including policy makers—to conclude that the Americans had fallen behind the Soviets in terms of technology. Educating young scientists became a patriotic mission, one which led to the passage of legislation in the form of the National Defense Education Act that equated science education with national security.
All in all, "the bomb" was at the center of American foreign policy and the American consciousness for much of the Cold War era.
https://history.state.gov/milestones/1945-1952/NSC68

https://news.harvard.edu/gazette/story/2007/10/how-sputnik-changed-u-s-education/

How did Mr. Fix feel when he saw Mr. Fogg in Egypt?

The tireless Inspector Fix of Scotland Yard is hot on the heels of Phileas Fogg, wrongly believing him to be a thief who's robbed the Bank of England. Fix is motivated to catch Fogg, not just by professional pride, but by the substantial reward on offer for apprehending this most dangerous of criminals. Fix is absolutely certain that he's got the right man. Years of experience as a detective have told him that all the biggest criminals look like respectable gentlemen.
When Fogg and Passepartout arrive in Egypt on the next leg of their epic journey, Fix is waiting for them. As soon as he sets eyes on the intrepid duo, Fix is elated. Now all he has to do is inform Scotland Yard of the supposed thief's arrival in Egypt, wait for the arrest warrant, and then the reward will be his.

What are three symbols in "Rappaccini's Daughter"?

Giovanni sees "the ruin of a marble fountain in the centre [of the garden], sculptured with rare art, but so wofully shattered that it was impossible to trace the original design from the chaos of remaining fragments.  The water, however, continued to gush and sparkle in to the sunbeams as cheerfully as ever."  It inspires Giovanni with a sense that it is an "immortal spirit," which sings its song without ceasing or taking any notice of the comings and goings of life around it.  We might interpret this fountain and its "immortal spirit" as symbolic of God, a God who watches the world become more and more corrupt around him and yet does nothing to stop it.  God continues to exist and watch, but he does not stifle or prevent the danger and corruption bred around him.
Further, we find symbolism in the shrub with gigantic "purple blossoms, each of which had the lustre and richness of a gem"; this plant seems to be symbolic of Beatrice herself.  She, too, is gorgeous, but—like the beautiful purple flowers—she, too, is deadly.  Also, like the flowering plant, she is not purposefully deadly; she bears no ill will toward anyone or anything she might hurt.  It is just a part of her nature, a nature that has been corrupted, as the plants have, by her father.
Likewise, the narrator says, "Every portion of the soil was peopled with plants and herbs."  Some are in rich urns and others in simple pots, some creep low like snakes and others climb high.  Giovanni then wonders if this garden is "the Eden of the present world."  The garden seems to be symbolic of the world in general; some plants are fancy and rich-looking, others not.  Some plants are high and some are low.  The garden's variety seems to echo the world's variety.  For Giovanni to wonder if this garden is the new Eden makes it seem as though, in the world of the story, corruption pervades paradise.  Real paradise is gone and what exists now is only that which perverts it.

What do you think is real about realism? Please also give me some specific reasons why Jewett's "A White Heron" is an example of local color realism. In your response, please be as specific as possible.

Realism is a movement in literature in which authors attempt to depict life realistically. This means that authors tend to describe the minutiae of daily life in detail and tend to feature characters who are average and ordinary. Unlike works of romanticism, realist works are not very dramatic and do not center around crisis moments as plot points. Regionalism (also called local color fiction) is a more specific subgenre of realism in which authors capture a realistic vision of life in a particular area of the country.
In Sarah Orne Jewett's "A White Heron," the landscape and culture of the rural northeastern United States is portrayed. As in most regional works, Jewett's narrator begins with a detailed physical description of the setting. The main character, Sylvia, is also introduced, and she is immediately connected with the natural setting that surrounds her. As the narrator explains, "it was her greatest pleasure to hide herself away among the huckleberry bushes" (paragraph 2) and to go out and find the cow that had wandered into the pasture. Local color is also introduced into the story through dialogue, and when Mrs. Tilley and the sportsman speak in the story, we can understand speech patterns and concerns of people in the region. Later in the story, Sylvia must resolve a conflict in which she can either tell the hunter where to find the white heron or keep the information to herself. Sylvia decides to do the latter, aligning herself with her natural environment. The story is an example of regionalism because it showcases the landscape and the people of the setting, but Jewett takes this a step further in actually connecting the protagonist to the region on a deeper level due to her emotional bond with the heron.

What would be a good outline of The Glass Menagerie by Tennessee Williams that focuses on the psychology of Laura?

Laura suffers from what we would today call social anxiety, but in Tennessee Williams' time might be referred to as being "painfully shy." Her ability to function in the everyday world of work and social interaction is severely limited by this psychological issue. We can certainly take a guess at what may have made this condition develop in Laura. Her self-consciousness over her disability has contributed to it; the leg brace she is forced to wear is very noticeable.
Laura's mother is also partly responsible. Amanda is very outgoing, aggressive and flirtatious, and it is very difficult for Laura to assume any form of social dominance because she is not capable of matching her mother's extroverted qualities. Amanda tried to get Laura to fit in by sending her to business school, but Laura's shyness and awkwardness prevented her from being able to participate.
It also seems that Amanda's own somewhat delusional personality (she has a tendency to live in the past) interferes with Laura's ability to become more socially outgoing. Amanda insists Laura remain "fresh and pretty" for any young men who might come to visit. But in the scene where Tom brings a friend home for dinner (the "Gentleman Caller," who is also a former schoolmate of Laura), Amanda dresses in an inappropriate youthful outfit and flirts with the young man herself. This causes Laura some embarrassment, party because she is incapable of behaving in this way. Laura is so sheltered by her home life and what she finds "normal" that she misconstrues the Gentleman Caller's intentions when he tries to break her out of her shell by dancing with her and kissing her. 
At the beginning of this scene, the description of Laura's appearance compares her to the glass animals in her collection, a hint that she is destined to be looked at and admired, but unsuitable for physical intimacy: 




The arrangement of Laura’s hair is changed; it is softer and more becoming. A fragile unearthly prettiness has come out in Laura: she is like a piece of translucent glass touched by light, given a momentary radiance, not actual, not lasting. 

Calculus of a Single Variable, Chapter 5, 5.5, Section 5.5, Problem 61

y=log_3(x)
The line is tangent to the graph of the function at (27,3). The equation of the tangent line is _____.
To solve, the slope of the tangent line should be determined. Take note that the slope of a tangent line is equal to the value of the derivative at the point of tangency.
To determine the derivative of the function, apply the formula d/dx[log_a(u)]=1/(ln(a)*u)*(du)/dx.
(dy)/dx = d/dx[log_3 (x)]
(dy)/dx =1/(ln(3)*x) * d/(dx)(x)
(dy)/dx =1/(ln(3)*x)*1
(dy)/dx = 1/(xln(3))
The point of tangency is (27,3). So plug-in x = 27 to the derivative to get the slope of the tangent.
m=(dy)/dx = 1/(27ln(3))
Hence, the line that is tangent to the graph of the function at point (27,3) has a slope of m = 1/(27ln(3)) .
To get the equation of the line, apply the point-slope form.
y-y_1=m(x - x_1)
Plugging in the values of m, x1 and y1, it becomes:
y - 3= 1/(27ln(3))(x - 27)
y-3=1/(27ln(3))*x - 27 * 1/(27ln(3))
y - 3 =x/(27ln(3)) - 1/ln(3)
y =x/(27ln(3)) - 1/ln(3)+3

Therefore, the equation of the tangent line is y =x/(27ln(3)) - 1/ln(3)+3 .

What problems do David and Rosalind face?

The world that David and Rosalind inhabit is a post-apocalyptic one, where the vast majority of the relatively civilized population known as the Waknuk believe that an apocalyptic event occurred due to God sending a "tribulation" as punishment for mankind's sins. Out of fear of a second tribulation, the government of this new world practices a strict form of fundamentalist Christianity and follows a school of eugenics so strict that a hot religious debate occurs over a tailless dog. People with mutations are killed or banished to the dangerous fringes. David and Rosalind are two members of the Waknuk society who have a mutation that manifests itself as telepathy. They eventually are forced to leave their home for the fringes and have to spend their lives being hunted because of their abnormalities.

David and Rosalind are both "Deviants." They have a genetic mutation that gives them telepathic abilities. The entire Waknuk society is scared of any kind of change to the gene pool that falls outside of what they consider normal. Consequently, the entire society is watchful for any kind of genetic mutation, and the society deals quick and brutal punishments to anybody displaying genetic abnormalities.  David and Rosalind face this problem. If they are discovered, they risk being banished to the Fringes, being sterilized, or even being killed.

If the worst comes to the worst, and you can't save Petra, it would be kinder to kill her than let her go to sterilization and banishment to the Fringes—a lot more merciful for a child. You understand? Do the rest of you agree?

Many of the problems that David and Rosalind face are a result of having the telepathic gene mutation. They are forced to keep their secret, and they must behave in such a way as to not make people suspicious of their gift. They are eventually discovered, and they are forced to run away to the Fringes. The Waknuk people then try to hunt them down, and the people in the Fringes are not welcoming either. Throughout the novel, David and Rosalind are either in hiding or on the run to protect their lives.