What is the climax of the story ''Raymond's Run'' by Toni Cade Bambara?

The climax of Toni Bambara's "Raymond's Run" occurs with the action described in the title. As Hazel Elizabeth Deborah Parker races during the May Day race, she glances to the other side of the fence and sees her brother Raymond speeding along with his arms at his side and the palms of his hands tucked up behind him, and she is stunned.

[i]t’s the first time I ever saw that and I almost stop to watch my brother Raymond on his first run.

Squeaky's remark on Raymond's running indicates how thrilled she is with her brother's ability. His style is unique, and his speed incredible. Fortunately, Squeaky catches herself in time and rushes past the white ribbon to win first place. Although she jumps up and down, Squeaky is more excited about Raymond's run. She notes that the crowd must think that she is thrilled about her win rather than about her brother's amazing accomplishment. As Raymond climbs over the fence, Squeaky grows even more excited,

By the time he comes over I’m jumping up and down so glad to see him—my brother Raymond, a great runner in the family tradition.

After realizing Raymond can also run swiftly, Squeaky considers the idea of being his coach. No longer focused on her own running, Squeaky looks at Gretchen, who smiles and recognizes Squeaky as the winner. Squeaky returns the respect, realizing Gretchen can help her coach Raymond.

We stand there with this big smile of respect between us. It’s about as real a smile as girls can do for each other.

Squeaky's consideration for her brother Raymond's talent at the climax of the story leads to her resolution to ask Gretchen to help her train Raymond. Truly, Hazel Elizabeth Deborah Parker matures from her experiences on May Day.

Glencoe Algebra 2, Chapter 2, 2.6, Section 2.6, Problem 30

f(x) = |2x| , the the domain and range is given as follows
(i)Domain definition:
The domain of a function is the set of the input or argument values for which the function is real and defined.
In this function, the function has no undefined points, so the domain is
-oo (ii)Range definition
It is the set of values of the dependent variable for which a function is defined.
For this function the interval has a minimum point at x = 0 with value f(x) = 0
so the range of |2x| is f(x) >= 0
It can also be observed from the graph below:

Single Variable Calculus, Chapter 3, 3.5, Section 3.5, Problem 87

Show that $\displaystyle \frac{d}{d \theta} (\sin \theta) = \frac{\pi}{180} \cos \theta$ by using Chain Rule such that $\theta$ is measured in degrees.


$
\begin{equation}
\begin{aligned}

\frac{d}{d \theta} =& \frac{d}{d \theta} \left( \sin \frac{\pi}{180} \theta \right) \text{ with $\theta$ in radians. So,}
\\
\\
\frac{d}{d \theta} \left( \sin \frac{\pi}{180} \theta \right) =& \frac{d}{d\left( \frac{\pi \theta}{180} \right) } \left( \sin \frac{\pi}{180} \theta \right)
\\
\\
\frac{d}{d \theta} \left( \sin \frac{\pi}{180} \theta \right) =& \cos \frac{\pi \theta}{180} \cdot \frac{d}{d \theta} \left( \frac{\pi \theta}{180} \right)
\\
\\
\frac{d}{d \theta} \left( \sin \frac{\pi}{180} \theta \right) =& \cos \frac{\pi \theta}{180} \cdot \frac{\pi}{180} = \frac{\pi}{180} \cdot \cos \left( \frac{\pi \theta}{180} \right)
\\
\\

\end{aligned}
\end{equation}
$




But we have in degrees,

$\displaystyle \frac{d}{d \theta} \left( \sin \frac{\pi}{180} \theta \right) = \frac{\pi}{180} \cdot \cos \theta$

The Lifeboat: You are the captain, and your ship struck an iceberg and sank. There are thirty survivors, but they are crowded into a lifeboat designed to hold just seven. With the weather stormy and getting worse, it is obvious that many of the passengers will have to be thrown out of the lifeboat, or it will sink and everyone will drown. Will you have people thrown over the side? If so, on what basis will you decide who will go? Age? Health? Strength? Gender? Size? After thinking carefully about the situation, describe the decision that you would make in this situation and explain why. Identify the moral value(s) or principle(s) on which you based your decision. Based on this analysis, describe your general conclusions about your own moral compass.

This is, in some ways, a variant on the "trolley problem" in philosophy. One of the main issues here is that it forces a choice in a way that may not be entirely realistic. Thus my response would be to return to the flaw in the premise of the argument and use it to suggest how I would approach the problem.
A key part of the premise is that the lifeboat is an absolute dictatorship in which all authority is ceded to one person. I think that in this sort of situation that authoritarianism is a morally problematic approach to the issue. I do not support dictatorship. In a situation in which everyone is affected by a decision, everyone needs to have a voice in the decision.
The first step would be to ask for volunteers. In the crisis in the aftermath of the Fukushima nuclear power station disasters, many elderly people volunteered to expose themselves to radiation to help save others. As many people are willing to sacrifice themselves for the common good, this would be the ideal solution.
If volunteers were not sufficient, one good way to choose would be by lot. Because this is random, it would be ultimately fair. I would still want to vote on whether people accepted this method, though. Even if I thought it fair, I would not consider that I had a right to impose my will on all the other people in the lifeboat.
https://www.bbc.com/news/world-asia-pacific-13598607

Calculus: Early Transcendentals, Chapter 4, 4.6, Section 4.6, Problem 32

For c>0 f(x) is defined and infinitely differentiable everywhere. For c=0 f is undefined at x=0, and for c<0 f is undefined for x<=sqrt(-c) and x>+-sqrt(-c).
Find f' an f'':
f'_c(x) = (2x)/(x^2+c),
f''_c(x) = 2*(c-x^2)/(x^2+c)^2.
1. For c<0:f' is negative for xlt-sqrt(-c), f decreases. f' is positive for xgtsqrt(-c), f increases.f'' is always negative, f is concave downward on (-oo,-sqrt(-c)) and on (sqrt(-c),+oo).
2. For c=0: (f(x)=2ln|x| )f'(x)=2/x is negative for x<0, f decreases, and positive for x>0, f increases.f''(x) = -2/x^2 is always negative, f is concave downward on (-oo,0) and on (0,+oo).
3. For c>0:f' is negative for c<0, f decreases, f' is positive for x>0, f increases. At x=0 f'(x)=0 and this is a minimum.f'' has roots at x=+-sqrt(c). F'' is negative for xlt-sqrt(c) and f is concave downward,F'' is positive for x on (-sqrt(c),+sqrt(c)) and f is concave upward,F'' is negative for xgtsqrt(c) and f is concave downward.So x=+-sqrt(c) are inflection points.

The only transitional value of c is zero.Please look at the graph here: https://www.desmos.com/calculator/89vayoctfv(the green graphs are for c>0, red for c<0 and blue for c=0)

How does The Hammurabi Code document represent its own culture?

This document can tell historians a great deal about the culture of ancient Mesopotamia. Laws represent the priorities of a society, which are, essentially, cultural. We can see, for example, that the security of one's property was important, as many of Hammurabi's laws are aimed at protecting it, including this one:

If any one is committing a robbery and is caught, then he shall be put to death.

But we can also see that Hammurabi's society viewed private property within a different cultural framework than our own, because if the robber mentioned in the above law was not caught, the public would be responsible for compensating the victim for his loss. We can also see, by looking at the laws, that family was important, and that in Babylonian culture, the home was highly patriarchal:

If a man's wife be surprised [having an affair] with another man, both shall be tied and thrown into the water, but the husband may pardon his wife and the king his slaves.
If a son strike his father, his hands shall be hewn off.

We can also see the nature of justice in Babylonian culture in the famous "eye for an eye" and "tooth for a tooth" laws that define justice in retributory terms. The code also tells us much about the various class relations within Babylonian society as well as the nature of slavery and gender relations. There are dozens of laws governing each of these aspects in the code.
https://avalon.law.yale.edu/ancient/hamframe.asp

What is the original source of “I am no bird; and no net ensnares me: I am a free human being with an independent will” from Charlotte Bronte's Jane Eyre?

This quote truly characterizes Jane Eyre; she demonstrates throughout the narrative of Charlotte Bronte's novel that she is a "free human being with an independent will."
Having been orphaned in her childhood, Jane must live with her uncle's wife, Mrs. Sarah Reed, who is very cruel to her and allows her spoiled children to taunt her. When her cousin John abuses her one day as she reads History of British Birds, Jane falls and hurts her head. Because she is hurt, Jane cries out and she fights back against John; as punishment the cruel aunt sends her to the "Red Room," the room in which her uncle has died. Little Jane is horrified in this room as she believes that she sees a ghost, but no one will let her out. Jane never forgets this experience and strengthens herself from it.
The headmaster of Lowood School comes to Gateshead Hall to meet with Jane; he questions her in a cruel manner. Nevertheless, the intrepid child replies bravely. When Mr. Brocklehurst inquires if she likes the Psalms, the candid and truthful girl bravely replies, “No sir.”
At Lowood School, Jane makes friends with a lovely girl named Helen Burns. Soon after they become friends, Helen is beaten by one of the teachers. When Jane talks to the long-suffering girl, Helen tells her, 

“Love your enemies; bless them that curse you; do good to them that hate you and spitefully use you.”

         Helen does not agree, saying that she could not possibly bless Mrs. Reed.
Having completed her studies at Lowood and taught there for a while, Jane Eyre is hired at Thornfield Hall, where she will work as the governess for Mr. Rochester's ward. There she develops a warm relationship with her employer. However, when it appears that he will marry, Jane feels that she must resign, telling him that she is "no bird" that can be ensnared. "I am a free human being with an independent will which I now exert...."
But Jane does not leave in Chapter 23 after she says these words, because Mr. Rochester proposes to her. Later, however, Jane discovers that Rochester is already married--to an insane woman. She departs then even though she has nowhere to go.
It is a starving and destitute Jane Eyre who unknowingly collapses at the home of her cousins. She does not expect charity and is glad when she is offered a position. 
When Jane receives her inheritance from her uncle, she divides her inheritance of £20,000 among her newfound relatives.  But because she will not be "ensnared" in marriage with St. John Rivers, whom she does not love, he becomes upset with her.
Jane tells Diana and Mary Rivers that she is going on a journey “to see or hear news of a friend about whom I had for some time been uneasy.” After she reaches Thornfield, she sees a "blackened ruin," so she stops at the Rochester Arms Inn and learns of the fire. She is told that Mr. Rochester now lives at his manor home, Ferndean. She flies freely to her one love, Edward Rochester.

This quote comes from Chapter 23 of Jane Eyre, a novel by Charlotte Brontë. Jane says this in response to Rochester, who tells her to stop struggling "like a frantic bird." Jane responds that rather than being a bird, she has no net. She is free and can exercise her free will to leave Rochester, which she then chooses to do. The metaphor of a bird runs throughout this passage, as Rochester likens her to a bird, and Jane refuses to characterize herself as a creature who is locked in a cage. Rochester thinks of a bird as wild, while Jane sees a bird as caged. In this instance, Jane can exercise her free will, which makes her very different than Bertha, Rochester's wife who is locked away in the third floor of Thornfield, Rochester's house.