Please provide a critical analysis of W. Somerset Maugham's short story "Salvatore."

The author frames the story such that we are well aware of the narrator's presence. In this way, we are reminded of the oral tradition, the style of old-fashioned storytelling. What is special about this narrator is that they seem to be somewhat unsure about the outcome of this storytelling: "I wonder if I can do it." This tactic really grabs the attention of the reader; we are eager to see what the narrator so earnestly wishes to accomplish and if they are able.
At the very end of the story, the narrator says the ultimate purpose of this tale is to sketch a picture of "Goodness. Just goodness." Did it work? Was the author able to do it? Moreover, what is "goodness"?
Salvatore's life is far from perfect. A number of events thwart his goals and disorient him: being drafted into the military, falling ill, losing his first love, and essentially committing to a life unlike the one he imagined for himself. Yet Salvatore seems to understand the futility of allotting blame for these unfortunate events. He seems to acknowledge that a life is simply comprised of unexpected twists and turns. In short, he bears no bitterness about what many would consider bitter circumstances. As a result, he can rejoice in the beauty of his children and the small pleasures of life. When all is said and done, Salvatore seems happy, and the reader can feel happy for him. The author has made us feel the core of "goodness" which runs through Salvatore and how it resulted in a satisfying life, if not a perfect one.
Ostensibly the author considers "goodness" to be of great importance. So what does goodness look like? Salvatore is at times scared, sick, uncertain, rejected, and child-like, yet none of these qualities diminish him in our eyes. How is this? It is because Salvatore possesses "a quality which is the rarest, the most precious and the loveliest that anyone can have." Salvatore loves deeply and is kind and fair even in the face of adversity and pain:

Often his rheumatism prevented him from doing anything at all and then he would lie about the beach, smoking cigarettes, with a pleasant word for everyone notwithstanding the pain that racked his limbs.

This determination to be kind, loving, and "pleasant" regardless of the moment's circumstances, this kind of perseverance, is "goodness."

In his short story "Salvatore," Maugham starts out by saying, "I wonder if I can do it." The reader is unsure what Maugham is trying to do as the author draws a portrait of a man named Salvatore who faces a series of disappointments in his life. While serving in the military in China, Salvatore falls ill. Consequently, the woman he wants to marry refuses to marry him because she is afraid he will not be strong enough to work.
Rather than wallow in self-pity, Salvatore agrees to marry Assunta, a woman he claims is "as ugly as the devil," and he then faces life with determination and "the most beautiful manners I [the author] had ever seen in my life." Though he does not live the life he imagined, Salvatore comports himself with goodwill and makes the most of his marriage, his job as a fisherman, and his children. In the end, the author states that his task was to see if he could hold the attention of the reader long enough to tell the tale of a good man who possesses an extremely rare quality that the author describes as "Goodness, just goodness."
Maugham's story has the style of a parable, a didactic tale that is meant to teach a lesson. His character, Salvatore, is not dynamic; he is static and shows no change as he continually faces life with a cheerful acceptance and integrity. Maugham holds Salvatore up to the reader as an example of pure radiance and goodness and as someone who should be emulated in dealing with the trials and tribulations of life. 

Although the title character of the short story "Salvatore" doesn't experience the life he expects for himself, he ends up making the most of it and lives gracefully. At the end it turns out that the whole point of telling Salvatore's story was to see if the narrator could hold the reader's attention simply by relating a tale of goodness. In this way, W. Somerset Maugham presents the story as a sort of moral lesson rather than a plot dealing with conflict and a character who undergoes change.

Who is Henrietta Lacks and why is she immortal?

Born Loretta Pleasant in August 1920, the “immortal” Henrietta Lacks was a Virginian woman who received cancer treatment at Johns Hopkins University in the 1950s.
During her treatment, doctors conducted a biopsy of Lacks’ tumor from which they extracted cervical cancer cells. Without her knowledge or consent, the doctors then studied these cells, noting how they divided at a rapid rate and survived much longer than previously studied cancer cells. Because of this unique observation, her cells became known as “immortal.”
Researcher George Gey later extracted more cells from Lacks’ body after her death during an autopsy—again without her family’s knowledge or consent. Her cells were then used in subsequent studies and experiments, eventually becoming the standard for numerous types of biomedical research.
Lacks’ family was unaware of this until the 1970s, after which scientists had produced nearly 20 tons of her cells. Thus, Lacks became immortal in the sense that her genetic material lived on long after her death, replicated in labs all over the globe.
This brings up issues of ethical consent practices and whether it is okay to violate/ignore consent if the information gleaned from research will be inestimably valuable, as HeLa cells led to numerous breakthroughs in medical science.

College Algebra, Chapter 4, 4.2, Section 4.2, Problem 4

Determine which of the following statements couldn't possibly be true about the polynomial function $P$?
a.) $P$ has degree 3, two local maxima, and two local minima.
b.) $P$ has degree 3, and no local maxima or minima.
c.) $P$ has degree 4, one local maximum, and no local minima.

Statement (a) is not true, since the number of local extrema should be $n-1$. where $n$ is the degree of the polynomial. In this case, the degree of the polynomial is 3 and as its local extrema should not be greater than 2.

Why does Achilles tell Patroclus to limit his efforts?

Achilles refused to help the Greeks assault Troy because he was mad at Agamemnon. The gods sympathized with him, so they enabled Hector and the Trojans to push the Greeks back all the way to their ships. This troubled Patroclus, so he begged Achilles to lend him his armor and let him join the Greeks on the battlefield. Achilles consented, but he told Patroclus to limit his efforts to defending the Greek ships; he did not want his friend to join the Greeks as they continued to push toward Troy. One reason for this is that Achilles did not want the Greeks to be defeated, but he also did not want them to prove victorious without his help.
When Patroclus went out on the battlefield, everyone thought he was Achilles since he was wearing Achilles' armor. This emboldened the Greeks and struck fear into the hearts of the Trojans. The Greeks successfully defended the ships, and they began to push the Trojans back toward Troy. Unfortunately, Patroclus did not listen to Achilles; he remained for the assault, and Hector eventually slew him.

Single Variable Calculus, Chapter 4, 4.5, Section 4.5, Problem 22

Use the guidelines of curve sketching to sketch the curve. $\displaystyle y = \sqrt{x^2+x} -x $

The guidelines of Curve Sketching
A. Domain.
We know that $f(x)$ contains square root function that is defined only for positive values of $x$. Hence, $x^2 + x \geq 0 \Longrightarrow x(x+1) \Longrightarrow x \geq 0$ or $x \leq -1$. Therefore, the domain is $(-\infty, -1]\bigcup[0, \infty)$

B. Intercepts.
Solving for $y$-intercept, when $x=0$,
$y = \sqrt{0^2 + 0} - 0 = 0$
Solving for $x$-intercept, when $y=0$

$
\begin{equation}
\begin{aligned}
0 & = \sqrt{x^2 + x } - x\\
\\
\sqrt{x^2+x} &= x\\
\\
x^2 + x & = x^2\\
\\
x &= 0
\end{aligned}
\end{equation}
$



C. Symmetry.
The function is not symmetric to either $y$-axis or origin by using symmetry test.


D. Asymptotes.
The function has no vertical asymptotes
For the horizontal asymptotes

$
\begin{equation}
\begin{aligned}
\lim_{x \to \pm\infty} \left(\sqrt{x^2+x} - x \right) &= \lim_{x \to \pm\infty} \left( \sqrt{x^2+x} - x \right) \cdot \left( \frac{\sqrt{x^2+x}+x}{\sqrt{x^2+x}+x} \right) && \Longleftarrow \text{(By multiplying the conjugate)}\\
\\
&= \lim_{x \to \pm\infty}\frac{x^2 + x - x^2}{\sqrt{x^2 + x} +x }\\
\\
&= \lim_{x \to \pm\infty} \frac{x}{\sqrt{x^2+x}+x} && \Longleftarrow \left(\text{by dividing to } \frac{1}{x}\right)\\
\\
&= \lim_{x \to \pm\infty}\frac{1}{\sqrt{1 + \frac{1}{x} }} + 1\\
\\
&= \frac{1}{2}
\end{aligned}
\end{equation}
$

Therefore, the horizontal asymptote is $\displaystyle y = \frac{1}{2}$

E. Intervals of Increase or Decrease.
If we take the derivative of $f(x)$, By using Chain Rule,

$
\begin{equation}
\begin{aligned}
y' &= \frac{1}{2} (x^2 + x)^{\frac{-1}{2}} (1x+1) -1 \\
\\
y' &= \frac{2x+1}{2\sqrt{x^2 + x}} - 1
\end{aligned}
\end{equation}
$

When $y' = 0$,
$\displaystyle 0 = \frac{2x+1}{2(x^2+x)^{\frac{1}{2}}} -1$
We don't have critical numbers.

So the intervals of increase or decrease are...

$
\begin{array}{|c|c|c|}
\hline\\
\text{Interval} & f'(x) & f\\
\hline\\
x < -1 & - & \text{decreasing on } (-\infty, -1)\\
\hline\\
x > 0 & + & \text{increasing on } (0, \infty)\\
\hline
\end{array}
$



F. Local Maximum and Minimum Values.
We have no local maximum and minimum.

G. Concavity and Points of Inflection.

$
\begin{equation}
\begin{aligned}
\text{if } f'(x) &= \frac{2x+1}{2\sqrt{x^2 + x }} - 1 \qquad \text{, then by using Quotient Rule and Chain Rule,}\\
\\
f''(x) &= \frac{(2\sqrt{x^2+x})(2) - (2x+1)\left(2 \left( \frac{2x+1}{2\sqrt{x^2+x}}\right) \right) }{(2\sqrt{x^2+x})^2}\\
\\
f''(x) &= \frac{4\sqrt{x^2 + x} - \frac{(2x+1)^2}{\sqrt{x^2+x}} }{(2\sqrt{x^2+x})^2} = \frac{\frac{4x^2+4x-4x^2-4x-1}{\sqrt{x^2+x}}}{4(x^2+x)}\\
\\
f''(x) &= \frac{-1}{4(x^2+)^{\frac{3}{2}}}
\end{aligned}
\end{equation}
$


when $f''(x) = 0$
$\displaystyle 0 = \frac{-1}{4(x^2+x)^{\frac{3}{2}}}$
$f''(x) = 0$ does not exist. Therefore, we don't have inflection point.
Thus, the concavity in the domain of $f$ is...


$
\begin{array}{|c|c|c|}
\hline\\
\text{Interval} & f''(x) & \text{Concavity}\\
\hline\\
x < -1 & - & \text{Downward}\\
\hline\\
x > 0 & - & \text{Downward}\\
\hline
\end{array}
$


H. Sketch the Graph.

Why are public order and crime control necessary in our society?

The simple answer to this question is that without public order and crime control, there wouldn't be a society worthy of the name. Of its very nature, society can only function if there is some semblance of order, some minimum level of stability in existence that allows people to go about their daily lives. That means that we need to have rules, laws, and regulations in place to provide us with the maximum degree of freedom necessary to live a vaguely tolerable life.
The greatest single threat to such order and stability is crime. Crime undermines those rules and laws that shape our lives and which, if devised and applied correctly, can enhance our personal freedoms. This helps to explain why dictatorships, which of their very nature are antithetical to freedom, are in actual fact little more than gigantic criminal enterprises.
Dictators, like all criminals, greatly inhibit our freedom to live the kind of lives we want to lead. The laws that they set down are actually violations of law, a higher law that says we are free human beings endowed with inalienable rights and liberties. Dictatorships, then, despite their propaganda, do not really provide public order and crime control; they simply nationalize crime on a monumental scale. In doing so, they destroy civil society—which, in order to thrive, must be separated from the state as much as possible.

Public order and controlling crime are essential for a functioning society. When people become fearful because they perceive something to be unsafe, the society will not function smoothly. Fear can inhibit economic growth and may lead to people looking to move to safer areas.
There is a very recent example that can be used to support this. In Milwaukee, about a month ago, there was a great deal of unrest that was tied to a police shooting. Several businesses were burned and property was vandalized. This led to a growing fear that businesses wouldn’t invest in this neighborhood, and that other people might stop coming to do business in the area. Eventually, the police restored order with the help of community activists, religious leaders, and the citizens of the area. A curfew was established for people who were 17 and younger, and a greater police presence also existed in the neighborhood. Community members urged people to act peacefully instead of violently. Things have calmed down in this area. While the issues leading to this disturbance need to be addressed, law and order have returned, and the people of this area are getting back to a more normal routine.
There have been other situations that have occurred that have put people on edge. Several years ago, a shooter was randomly targeting people in the Washington, D.C. and the Phoenix areas. People were afraid to go out and do their normal routines. Once the individuals responsible for these actions were caught, life returned to normal.
It is necessary to control crime and maintain public order for society to function smoothly.
https://www.jsonline.com/story/news/crime/2016/08/15/sherman-park-unrest-decades-making/88806222/?from=global&sessionKey=&autologin=

https://www.jsonline.com/story/news/crime/2016/08/20/night-conflict-chaos-and-courage-sherman-park/88994022/?from=global&sessionKey=&autologin=

https://www.jsonline.com/story/news/education/2016/08/27/borsuk-sherman-park-know/89429692/?from=global&sessionKey=&autologin=

In "Lamb to the Slaughter," the characters are a collection of stereotypes and cliches who behave more like puppets than real human beings. Mary is the "little woman," Patrick is the "cheating husband," and the police are the "blundering detectives." List the ways in which the stereotypes are developed through the actions and the comments of the characters. Discuss how Mary uses her "little woman" image as a protective covering after the murder.

The characters of Roald Dahl’s dark 1953 short story “Lamb to the Slaughter” can be seen as somewhat flat, stereotyped caricatures rather than round, fully developed characters.
Mary, for example, plays the part of the bored, doting Eisenhower era housewife. She eagerly awaits her husband Patrick’s return home from work, putting aside her sewing and greeting him with a kiss and a drink. She’s quick to wait on him, offering to make him another drink, fetch his slippers, and make him dinner. Mary also provides a clichéd image of the glowing pregnant mother.
Patrick seems to be a stereotypical cheating husband. He acts surly, downing whiskey as he works up the nerve to admit his affair to his pregnant wife. Patrick is matter of fact and shows little guilt, saying, “I hope you won’t blame me too much.” Mary acts as if she's in shock, not believing her husband’s words and offering to start making dinner. Ironically, she does not seem angry even as “without any pause she swung the big frozen leg of lamb,” shattering her husband’s skull and killing him.
The police who respond to Mary’s call serve as caricatures of blundering detectives. While they question Mary, they always treat their murdered coworker’s wife kindly, delicately. Mary uses the detectives’ belief in gender stereotypes against them in concealing her crime. A detective comments, “Get the weapon, and you’ve got the man,” revealing an underlying bias that the murderer is likely male. Mary uses her housewife role to con the detectives into destroying the murder weapon—the very leg of lamb on which they dine. The story ends with Mary giggling to herself, literally getting the last laugh.    

Which quotes best describe Squealer's traits and importance in George Orwell's Animal Farm?

Squealer is described as a clever speaker. At the beginning of the book, he is painted in the following way: 




"He was a brilliant talker, and when he was arguing some difficult point he had a way of skipping from side to side and whisking his tail which was somehow very persuasive. The others said of Squealer that he could turn black into white" (page 6).

Squealer is so good at convincing others of his point of view that he can literally make black into white and make things that aren't true appear to be true. His importance is that he keeps the animals in line and maintains the pigs' top position in the hierarchy through his speeches. 
Squealer later uses his considerable powers of persuasion to tell the other animals that the pigs are justified in drinking all the farm's milk and eating the windfall apples. He says:




"Milk and apples (this has been proved by Science, comrades) contain substances absolutely necessary to the well-being of a pig. We pigs are brainworkers. The whole management and organisation of this farm depend on us" (page 14).

Squealer convinces the other animals to allow the pigs to eat all the best food because it's in the other animals' interest to do so. He makes the pigs' selfishness seem like altruism, and he backs up his arguments with pseudoscience. Whenever the other animals are even thinking about disagreeing with him, he cleverly asks them, "Surely, comrades, you do not want Jones back?" (page 22). He equates disagreeing with him to bringing back the old regime with Jones, and he frightens the others into agreeing with him. 

Who is grandfather in Chains?

Grandfather is a fairly minor character in this book. He is the old man who works the Tea Water Pump, and Curzon calls him "grandfather" when he is there with Isabel in chapter 13. Isabel mistakenly thinks that the relationship is real, but then she learns that a lot of people refer to him as "grandfather." This is because he is one of the oldest slaves in the area. He is described as a man "with stone-gray hair and skin the color of the night sky." Isabel feels an immediate kinship with the old man because he has a scar that reminds her of her own father.
Despite being a minor character, he does play a vital role in the story. It is his advice that provides Isabel with a catalyst that propels her into action in order to secure her own freedom from the Locktons and slavery.

You must choose your own side, find your road through the valley of darkness that will lead you to the river Jordan . . . Everything that stands between you and freedom is the river Jordan

I need a detailed note on the structure of English syllables.

To answer this question, we should first establish what constitutes a syllable. A syllable is generally described as a “building block” of language, a slightly unscientific explanation that can lead to confusion with morphemes (the smallest possible grammatical unit of language) and phonemes (the smallest elements of sound that distinguish words from each other). Children learn that a syllable is a “beat”: words can contain one or multiple syllables. For example, “printing” contains two: “print” and “ing.” Not all syllables are created equal, as becomes obvious from a study of their structure in English.
Syllables in English are broken down in linguistics into two key parts: the onset and the rhyme. Within the "rhyme" section, we see two further subsections: the nucleus and the coda.
Effectively, the "onset" of any syllable consists of the consonant or consonants that come before the "rhyme." The "nucleus" of the rhyme is almost always a vowel, except when a consonant expresses a vowel, as /y/ does in "Flynn." The “coda” is anything following the vowel.
Returning to “print”, we find all the elements of a syllable: “pr” is the onset, “i” is the nucleus, and “nt” is the coda. “Ing,” however, only has the rhyme and does not have an onset. Syllables like “be” have an onset and nucleus without a coda. “A” or “I” have only a nucleus.

Why was A Discourse and View of Virginia written?

William Berkeley's 1663 treatise, A Discourse and View of Virginia, had four purposes. First, it sought to encourage Virginia farmers to diversify their economy by increasing the production of what Berkeley labels "commodities," including "Silk, Flax, Hemp, Pitch, Pot-ashes and Iron." Second, he condemned the ubiquitous growing of tobacco. Berkeley argued tobacco had become monolithic, impacting every aspect of colonial life. It was used as a cash crop, a mode of currency, and a method for applying credit and debit. Berkeley used a barrage of complaints against the crop, calling it a "vicious weed."
Third, Berkeley hoped that through economic diversification and less emphasis on tobacco, the colonies would be able to export their goods not only to the English, but also to the rest of the world. He goes on to say that because Virginia farmers deal only in tobacco they are at the mercy of English merchants who can "give us what they please for it." Finally, Berkeley asked the king to increase the tariff on tobacco and give part of the money back to the colony "to resist the Indians."
Although Berkeley was twice governor of the Virginia Colony and had the full support of the English crown for his program of diversification, he ultimately failed and was challenged by other colonists during Bacon's Rebellion. Moreover, the English government denied Berkeley's proposal to return tax money to the colonists. This habit by the English king would eventually lead to the American Revolution.
http://nationalhumanitiescenter.org/pds/amerbegin/permanence/text5/BerkeleyVirginia.pdf

Calculus of a Single Variable, Chapter 6, 6.1, Section 6.1, Problem 49

The general solution of a differential equation in a form of y’ =f(x,y) can be 'evaluated using direct integration. The derivative of y denoted as y' can be written as(dy)/(dx) then y'= f(x,y) can be expressed as (dy)/(dx)= f(x,y) .
That is form of the given problem:(dy)/(dx)=xsqrt(x-6) .
We may apply the variable separable differential in which we follow N(y) dy = M(x) dx .
Cross-multiply dx to the right side: dy=xsqrt(x-6)dx .
Apply direct integration on both sides: intdy=int xsqrt(x-6)dx .
For the left side, we apply basic integration property:
int (dy)=y
For the right side, we may apply u-substitution by letting: u = x-6 or x = u+6 then dx = du .
intxsqrt(x-6)dx=int (u+6)sqrt(u)du
=int (u+6)u^(1/2)du
=int(u^(3/2)+6u^(1/2))du
Apply the basic integration property: int (u+v) dx= int (u) dx + int (v) dx .
int u^(3/2)du+ int 6u^(1/2)du
Apply the Power Rule for integration : int x^n= x^(n+1)/(n+1)+C .
int u^(3/2)du+ int 6u^(1/2)du=u^((3/2+1))/(3/2+1)+ 6u^((1/2+1))/(1/2+1)+C
=u^(5/2)/((5/2))+ 6u^(3/2)/((3/2))+C
=u^(5/2)*(2/5)+ 6u^(3/2)*(2/3)+C
=(2u^(5/2))/5+ 4u^(3/2)+C
Plug-in u = x-6 , we get:
intxsqrt(x-6)dx=(2(x-6)^(5/2))/5+ 4(x-6)^(3/2)+C
Combining the results, we get the general solution for the differential equation:
y=(2(x-6)^(5/2))/5+ 4(x-6)^(3/2)+C

Would anything be lost if the gravediggers in act 5, scene 1 were omitted?

Any answer to this question is always going to be subjective, but I would argue for the scene's retention; the reason being that it serves to highlight Hamlet's growing preoccupation with death.
Earlier in the play, Hamlet teasingly suggests to Claudius that the worms which feast upon a king's corpse can easily pass through a fish, and then into the digestive system of a beggar. And we see a similar theme here, only the gravediggers show an even more irreverent attitude towards death than Hamlet. Their badinage, painful puns, and witty wordplay add a humorous gloss to what really ought to be a deeply solemn theme. However mighty we may think ourselves, we will one day all suffer the same fate—high or low, rich or poor, king or beggar. This is what Hamlet was driving at when he played his mind games with Claudius after killing Polonius.
The gravediggers, like Hamlet, have a profound sense of the fundamental absurdity of human existence. In the face of what they regard as a meaningless universe, they feel they have no choice but to make merry; for tomorrow, they too may die. The gravediggers' gallows humor sets up Hamlet perfectly, allowing him to take up Yorick's skull in his hands and embark upon another of his great soliloquies, articulating with great eloquence the same insights expressed earlier by the gravediggers, albeit with considerably less refinement.

What were the most important ideas in the book?

Replete with vivid recollections of growing up in a poor, working-class Appalachian community, Vance’s memoir offers a broad sociological analysis of the problems common to Appalachian communities that keep their residents mired in poverty and hopelessness. Among these problems are periods of long-term economic recession brought about by deindustrialization that fosters multi-generational welfare dependency, poly-substance abuse and addiction, chronic poor health, violence, familial dysfunction, sexism, racism, and an overall aversion to ask for help when help is needed. Using this as a basis for extrapolation, the veteran and Yale Law School alumnus further attempts to identify national trends that are negatively affecting working-class whites.
Since its 2016 publication, some critics also have hailed Vance’s memoir for its insights into Trump’s overriding appeal to “hillbilly” and other working-class voters.

What happens when Coates takes Samori to the movies?

Between the World and Me was published in 2015 by the famous contemporary African American journalist and author Ta-Nehisi Coates. The book came to be in the form a letter to Coates' then-fifteen year old son Samori. The narrative of the book/letter is essentially Coates being straightforward in relating his own experience of being black in America, including his youth in 1980s Baltimore, and losing a friend who became a fatal victim of police brutality.
Some time after Coates moved his family to New York City, he took an almost five year old Samori to a screening of the movie Howl's Moving Castle. A white woman became impatient with waiting for Samori to move off of an escalator, and pushed the boy. Coates perceived that this is not something the woman would have done if she were not in the primarily white Upper West Side, and Samori were not a black boy. When Coates spoke to the woman harshly in defense of his son, a white man "spoke up in her defense," and he and Coates almost got into a fight. The white man threatened Coates with, "I could have you arrested!"
The quote below, taken from an article adapted from Coates' book before it was released (link below), demonstrates how shaken up Coates was by the incident:

I came home shook. It was a mix of shame for having gone back to the law of the streets, and rage—“I could have you arrested!” Which is to say: “I could take your body."
I have told this story many times, not out of bravado, but out of a need for absolution. But more than any shame I felt, my greatest regret was that in seeking to defend you I was, in fact, endangering you.
“I could have you arrested,” he said. Which is to say: “One of your son’s earliest memories will be watching the men who sodomized Abner Louima and choked Anthony Baez cuff, club, tase, and break you.” I had forgotten the rules, an error as dangerous on the Upper West Side of Manhattan as on the West Side of Baltimore. One must be without error out here. Walk in single file. Work quietly. Pack an extra No. 2 pencil. Make no mistakes.
https://www.theatlantic.com/politics/archive/2015/07/tanehisi-coates-between-the-world-and-me/397619/

Should important decisions be made by parents for teenage children?

This is something that will vary by household.  Every situation is unique, and every culture has its own approach to growing up.  We usually view growing up as a gradual release of responsibility.  This means that at some point along the way the parents will relinquish some responsibility to the children.  When that happens depends on the parents and the children.
Children need to learn how to make decisions on their own.  If they do not learn how to make small decisions, and then larger ones, they will not be successful adults.  The rise of “helicopter parenting” in our culture has brought attention to parents who try to protect their children from all possible harm and make all decisions for them, but parents making decisions for their children is nothing new.  Again, it depends on the culture and the time period.
Legally, parents have the right to make decisions for their children while they are still minors and under 18.  However, responsible parents will teach their children how to make good decisions from a young age.  Teenagers often have other influences in their lives that lead them to lose perspective.  Parents sometimes need to intervene and make better decisions.  The teens may not realize until later that their parents saved them from disaster.
https://cca-ct.org/legalresources/legalresources_teenrights/legal-rights-info-for-teens-2/

https://www.cnn.com/2016/03/30/health/the-80s-latchkey-kid-helicopter-parent/

What are the various methods for macro-environmental analysis?

One method for macro-environmental analysis is called the "PESTLE" method. This is essentially a framework through which to explore the broad environment surrounding an organization. PESTLE stands for Political, Economic, Socio-cultural, Technological, Legal, and Environmental. It's a relatively simple method: you analyze each of these individual areas and how they relate to the organization, and come up with a broader plan that incorporates these various factors. 
For example:
1) Political: What political factors might affect your organization? What are the government's beliefs and policies?
2) Economic: What are the current economic conditions in the area? Is the economy growing or shrinking? What are interest rates like?
3) Socio-cultural: What is the social climate like? What are some demographics that might affect the organization?
4) Technological: What technology is available and how can it be used? This means not only digital/ internet tools but also manufacturing and distribution tools.
5) Legal: The laws in any country are constantly changing. What are the legal factors that might help or hinder the organization? Are there new or changing laws that might have an effect?
6) Environmental: An organization's physical location and its relationship to the environment can also affect the organization. What is the climate like? What are the local waste disposal practices?
Another method, called STEEPLE, integrates the components of PESTLE with one additional factor: Ethics. Ethics can be complex, since something that is legal is not always ethical and something that is ethical is not always legal. In today's world, it is much easier for people to align with companies they ethically support, and it is important for organizations to consider their ethical profile.
All of these can be run through a SWOT analysis, which refers to an organization's Strengths, Weaknesses, Opportunities, and Threats. Any one finding from a PESTLE/ STEEPLE analysis can fall into any of these four categories. A new legal ruling might be an opportunity or a threat; a piece of technology might be a strength or a weakness.
https://pestleanalysis.com/difference-swot-pest-steep-steeple-analysis/

https://pestleanalysis.com/pestle-analysis-business-environmental-analysis/

Who or what is the protagonist and antagonist of the story, "The Lottery"?

The protagonist is the most prominent, or central, character in a story. The protagonist of the short story "The Lottery" is Tessie, but she is a representative of the whole village. All the villagers, just like Tessie, are equally bound to, and affected by, the lottery. They all have the same chance as Tessie of being picked as "winners," which entails that each villager lives, albeit obliviously, with the terrifying thought of death in the back of their minds.
While Tessie is the selected villager in this particular celebration of the lottery, the reality is that it could have been any of them, by rule of probability. Therefore, the whole village is truly the protagonist of the story but, in this particular version of the lottery, the protagonist would be Tessie because she stands out even further by being the selected one to die.
This being said, the antagonist is the opponent of the protagonist. It is the person, place, force of nature, spiritual intervention, or thing that prevents the protagonist from accomplishing his or her purpose in the story.
From the very moment that Tess enters the story, she has had a problem with the lottery being conducted. She was doing her dishes, and had to stop her duties as a housewife, because of the lottery.

"Wouldn't have me leave m'dishes in the sink, now, would you. Joe?,

When her family is picked, she realizes that the end is coming.
"You didn't give him time
enough to take any paper he wanted. I saw you. It wasn't fair!"
When her name is finally pulled, she knows her death is impending. Therefore, the fact that the lottery brings death, and thus the end to all the purpose of anyone who is selected, makes it the antagonist of the story.

College Algebra, Chapter 10, 10.4, Section 10.4, Problem 36

An archer normally hits the target with probability of $0.6$. She hires a new coach for a series of special lessons. After the lessons, she hits the target in five out of eight attempts.

a.) Find the probability that she would have hit five or more out of the eight attempts before her lessons with the new coach.

b.) Did the new coaching appear to make a difference? (Consider the coaching effective if the probability in part (a) is $0.05$ or less.)

Recall that the formula for the binomial probability is given by

$C(n,r) p^r q^{n-r}$

a.) In this case, where the archer has not hire a coach yet, the probability of success is $p=0.60$ while the probability of failure is $q=1-p=0.40$. Thus, the probability that the archer hits the target five or more eight attempts is equal to sum of the probability that the archer hits exactly $5,6,7$ and $8$ of her attempts. Thus, we have


$
\begin{equation}
\begin{aligned}

=& C(8,5) (0.60)^5 (0.40)^{8-5} +C(8,6) (0.60)^6 (0.40)^{8-6} + C(8,7) (0.60)^7 (0.40)^{8-7} + C(8,8) (0.60)^8 (0.40)^{8-8}
\\
\\
=& 0.2787 + 0.2090 + 0.0896 + 0.0168
\\
\\
=& 0.5491

\end{aligned}
\end{equation}
$



b.) After hiring a new coach, the probability of success is $\displaystyle p= \frac{5}{8} = 0.625$. This gives the probability of failure $q=1-p=0.375$. Thus, the probability in this case is


$
\begin{equation}
\begin{aligned}

=& C(8,5) (0.625)^5 (0.375)^{8-5} +C(8,6) (0.625)^6 (0.375)^{8-6} + C(8,7) (0.625)^7 (0.375)^{8-7} + C(8,8) (0.625)^8 (0.375)^{8-8}
\\
\\
=& 0.2816+0.2347+0.1118+0.0233
\\
\\
=& 0.6514


\end{aligned}
\end{equation}
$



It shows that the coaching is effective since probability that the archer hits her target in the given case is increased by $0.6514 - 0.5941 = 0.0573$.

What symbolism is in "Easter 1916"?

An early symbol in the poem appears in the first stanza: it is "the fire at the club." This represents the comfortable middle-class world people like him live in, with their "polite meaningless words" and genteel eighteenth-century houses. This world and its occupants are a contrast to the Irish freedom fighters—whose sacrifice causes a terrible and beautiful world to be born.
An important symbol in the poem is the stone in the "midst" of the stream that appears in the second stanza. This stone represents the Irish freedom fighters, unmoved by the changing times: steadfast and purposeful. They are directly contrasted to images that symbolize fleeting, transitory moments, such as clouds and horses racing by. While the stone stays the same, these other symbols are shown in all their changeableness. The clouds, for example, are first "tumbling" clouds and then appear as the "shadow" of a cloud reflected in the stream.

The clearest examples of symbolism in W. B. Yeats's poem can be found in the final two stanzas. Yeats uses natural imagery and an extended simile comparing "hearts with one purpose alone" to a stone which "trouble[s] the living stream," or the onward passage of time and the natural order of things. The stone symbolizes the stony resolve of these people who are so dedicated to the cause of Irish independence, but its position at the bottom of the "living stream" also represents the fact that these people are now removed from the action of what is happening. The next stanza, which references several heroes of the Irish independence movement who lost their lives to it, makes clear that this unmoving stone "in the midst of all" that still lives "minute by minute" symbolizes these dead soldiers, wedded to their purpose even in death. They are, after all, soldiers of "summer and winter" (compare Thomas Paine's "the winter soldier" and "the summer soldier") and their hearts have become stones wedded to their purpose through "sacrifice."
Another, more straightforward instance of symbolism can be found in the final stanza describing "wherever green is worn." Green is a color strongly associated with Ireland and here symbolizes Ireland and the Irish.

What would be some good points to discuss in an essay on the theme "fair is foul and foul is fair" as it concerns Macbeth and Frankenstein?

Your general themes are appearance versus reality and good versus evil. Frankenstein and Macbeth approach these themes quite differently, so you might want to structure your essay to compare and contrast them.
Macbeth shows the transformation of an admirable character into an evil one through a combination of the blandishments of the three weird sisters and his own ambition. Over the course of the play, Macbeth degenerates from a "fair" hero whose ambition, bravery, and energy have caused him to be a powerful and admired supporter of King Duncan into a "foul" tyrant and murderer. Although Macbeth himself changes over the course of the play, readers are not asked to think about the nature of our own moral judgments. We are expected to share a moral stance that regards murder and treachery as evil. In the play, fair becomes foul and Macbeth's own perceptions distort.
In Frankenstein, we are confronted with the dilemma of whether, our perception of fair, as seen in the educated European Victor, and foul, as exemplified by the monster, should be reversed. We need to consider whether the fair and civilized scientist is in fact more foul than his monster, who appears hideous on the surface, but is really as much a mistreated innocent as a source of evil. The novel also asks us to question whether we should blame mistreated outcasts for lashing out at society or whether the society that has mistreated them is really the "foul" entity that is morally culpable.

Calculus of a Single Variable, Chapter 8, 8.8, Section 8.8, Problem 11

Integral is improper if we have to take limit in order to calculate it. This can happen if we have infinite values of integration or if the interval if integration contains point(s) where the function is not defined. The latter is the case here because the function we are integrating is not defined for x=1.
Because this point is within the interior of the interval of integration (not at the endpoint) we first must write this integral as a sum of two integrals.
int_0^2 1/(x-1)^2 dx=int_0^1 1/(x-1)^2dx+int_1^2 1/(x-1)^2dx=
Substitute u=x-1 => du=dx. Since u=x-1 all bounds of integration become lower by 1.
int_-1^0 1/u^2 du+int_0^1 1/u^2 du=-1/u|_-1^0-1/u|_0^1=
lim_(u to 0^-) -1/u+1/-1-1/1+lim_(u to 0^+) 1/u=
Notice the use of directional limits (from the left for the first and from the right for the second integral).
-(-infty)-2+infty=infty
As we can see the integral diverges.
The image below shows the graph of the function and area under it corresponding to the value of the integral. Asymptotes of the graph are x-axis and line x=1. The other image (the red one) shows the graph of the function f(u)=1/u. There we see why the two directional limits have different values.

How does the novel The Outsiders show readers that being a hero is more than simply being brave?

Bravery is certainly a quality displayed by heroes. However, in The Outsiders, there are many instances when characters display heroic qualities other than bravery. Loyalty is one such quality. The boys consider each other as brothers. For example, when Ponyboy wants to run away after Darry hits him, he runs to get Johnny. Johnny asks no questions. He simply goes along with Ponyboy. Another example of loyalty occurs when Ponyboy and Johnny go to Dally for help. Dally provides them with money and tells them how to find a place to hide. He safeguards their secret and provides assistance because he is loyal.
Another quality shown by the boys is selflessness. One such example is seen in the hospital. As Two-Bit and Ponyboy are visiting Dally, Dally expresses the need to win the rumble against the Socs. Upset upon hearing the latest news of Johnny's state, Dally asks Two-Bit for his blade. Two-Bit's blade is his "prize possession," yet he hands it to Dally without hesitating. Darry also displays selflessness by giving up college to take care of his brothers. He puts the needs of his brothers ahead of his own.

S.E. Hinton illustrates how characters who are considered heroes in the novel are more than just brave individuals. Characters like Darry, Dally, Johnny, and Ponyboy selflessly help others. Each of these characters sacrifices something for the benefit of other people. Darry sacrifices an athletic scholarship and a college education to keep his family together, while Johnny and Ponyboy risk their lives saving children from the burning church. Dally is considered a hero because he not only helps Ponyboy and Johnny hide from the police but also saves Johnny's life by dragging him from the burning building. In each instance, the characters put other people's needs in front of their own. Although each of the characters are brave, Hinton suggests that a hero is also someone who sacrifices something for the benefit of others. Darry, Dally, Ponyboy, and Johnny are all selfless individuals who help others even when it does not benefit them.

Why does Golding have the boys reenact the pig hunt? What mood does it create? What does it show?

In chapter 7, the boys form a hunting expedition and search for the beast throughout the island. When a boar suddenly appears out of the forest, Ralph throws his spear at the charging boar and successfully hits it in the nose. Jack and the hunters quickly gather around Ralph as he attempts to tell the boys how he successfully struck the boar. Jack then instructs the boys to make a ring and Robert begins acting like a pig. The boys proceed to poke and stab Robert as he starts to scream for them to stop. The frenzy of the group heightens as they strike Robert and chant, "Kill the pig! Cut his throat! Kill the pig! Bash him in!" (Golding, 88). Fortunately, Jack ends the violent game and suggests that they use a littlun to act as the pig next time.
Golding provides a description of the boys reenacting the hunt to illustrate their mindset and bloodthirsty, savage nature. Even as they pretend to hunt Robert, they act like brutal barbarians and demonstrate no sympathy towards him. Golding creates a mood of hysteria, suspense, and aggression throughout the reenactment, which reveals that the boys have completely descended into savagery.

Why does Pony Boy remind Cherry that they both watch the same sunset?

In S.E. Hinton's novel The Outsiders, Ponyboy and Cherry talk about sunsets in Chapter Three. But Ponyboy doesn't remind Cherry that they both watch the sunsets, it's part of his thoughts after he talks with her. Cherry and Ponyboy talk about why their groups are so different (the Greasers and the Socs) and they come to the conclusion that it's about feelings. The Socs are cold and don't show their emotions, and the Greasers show their emotions too much. But in that conversation, they find out that they have things in common, as well. Ponyboy and Cherry both like to watch sunsets. Cherry shares that she thinks Ponyboy watches sunsets. She recognizes his sensitivity, and that's what she bases her assumption on. She also shares that she used to watch them, but then she got too busy for that. Here is the quote from Chapter Three where Ponyboy is thinking about the similarities between the Greasers and the Socs.

It seemed funny to me that the sunset she saw from her patio and, the one I saw from the back steps was the same one. Maybe the two different worlds we lived in weren't so different. We saw the same sunset.

You see here that Ponyboy is beginning to change his thinking regarding the Socs. Before, he thought they were as different from the Greasers as night and day. After the conversation with Cherry, he's thinking that they may have more in common than they previously thought.

An airplane in Australia is flying at a constant altitude of 2 miles and a constant speed of 600 miles per hour on a straight course that will take it directly over a kangaroo on the ground. How fast is the angle of elevation of the kangaroo's line of sight increasing when the distance from the kangaroo to the plane is 3 miles? Give your answer in radians per minute.

Hello!
Denote the elevation angle as alpha(t) (in radians, t is in hours). Denote the known speed as V and the (unknown) horizontal distance between the airplane and the kangaroo that corresponds to t=0 as L. Then the horizontal distance at any time t is equal to L - Vt.
This way the tangent of alpha(t) is  2/(L - Vt), so  alpha(t) = arctan(2/(L - Vt)).
The increase of the angle of elevation is the derivative of alpha(t), and we are interested of its value for t such that the height 2mi, the horizontal distance L - Vt and the distance 3mi form a right triangle. In other words, L - Vt = sqrt(3^2-2^2) = sqrt(5) (mi).
Find the derivative:
d/dt(alpha(t)) = 1/(1+(2/(L - Vt))^2)*(2V)/((L - Vt)^2) =(2V)/((L - Vt)^2+4).
When L - Vt = sqrt(5) it will be (2V)/9 approx 133 (radians per hour). In radians per minute it will be 60 times less, about 2.2. This is the answer.

Describe the characters of Newjack: Guarding Sing Sing.

Your question is about the characters in Ted Conover's Newjack: Guarding Sing Sing. Newjack is the true story of Conover's time at Sing Sing prison, where he was a guard.
Conover himself is the primary character; the experience of being a guard at Sing Sing is told from his point of view. Conover is an experienced journalist with a history of involving himself in situations in order to write about them from an insider's perspective. He decided to train as a prison guard and work at Sing Sing when he was unable to get journalistic access to the prison.
Conover is transformed by his time as a prison guard. He says:

Prison got into your skin, or under it. If you stayed long enough, some of it probably seeped into your soul.

Conover seems humbled by the experience, especially when he sees that you can't tell what a person's character is from their appearance. Some people he expects to be in prison for white-collar type crimes are actually there for violent crimes, for example. 
Conover narrates with precision, showcasing his meticulous nature. He wants the reader to see the world he lived in for almost a year. His attention to detail and careful reflection are strong characteristics. He says, describing keys from the prison:

The pewter-colored cell key was the biggest, its shaft as thick as a Mont Blanc pen . . .

Conover changes throughout the narrative and questions his own goodness when he feels an unwilling thrill as an inmate is beaten.
Other prominent characters include the following:
Mama Cradle, the overweight correctional officer. Cradle is a tough person but has the best of intentions for the staff and prisoners alike. Cradle is forced to balance the needs of the inmates and the corrections officers along with the demands of the state.
Officer Smith, a fellow correctional officer who Conover admires. He sees Smith as a person who's able to see the humanity in prisoners and act accordingly. A major theme throughout the book is how prisoners are dehumanized, and Smith is someone who showcases the best of what correctional officers can aspire to be.
Dieter, an ex-marine who Conover rooms with during training. Conover says of him that they were fundamentally different. Dieter used substances, disliked women and liberals, and woke up early, whereas Conover had opposite habits and beliefs. 
Toussaint is a gang member who is questioned by the COs of Sing Sing after a physical incident. His reflections on gang membership cause Conover to reflect on the nature of gangs, the conditions that cause them to exist, and the people in them.
Sergeant Wickersham is an abusive man with a troubled past. He was once held hostage during a prison riot, which may help explain his violent disposition.
Most of the characters in Newjack are described with a few personal details that reflect their place in the prison system. They are both affected by and described by their jobs and positions at Sing Sing. Conover's character is the one most in focus because, of course, the book is based on his own experience and written from his perspective.
https://archive.nytimes.com/www.nytimes.com/books/00/05/14/reviews/000514.14bergnet.html?mcubz=0

What is the climax of the story "The Most Dangerous Game"?

The climax in the plot of a short story is the highest point of interest. In other words, the reader should be at a point in the story where suspense has built up to an inevitable crisis. In Richard Connell's short story the climax is when Rainsford decides to jump into the ocean in order to avoid General Zaroff, who will most certainly kill Rainsford if he catches him. After trying every hunting trick he knows, including the Malay man-catcher and Burmese tiger pit, Rainsford finds himself on the edge of a cliff across from Zaroff's chateau. The general is being led by his pack of dogs toward Rainsford when the American leaps:

Twenty feet below him the sea rumbled and hissed. Rainsford hesitated. He heard the hounds. The he leaped far out into the sea....

Connell uses an ellipsis here to indicate that it is unknown whether Rainsford survives the jump or not. The falling action, which follows the climax, involves Zaroff going back to his chateau, dining and reading. When he goes to bed he discovers Rainsford, who has survived the swim (foreshadowed earlier in the story when Rainsford falls off his yacht and swims to the island), in his bedroom. They fight and, in the resolution of the conflict between the two men, Rainsford kills the general and sleeps in his bed.
Some might argue that the climax actually occurs when Rainsford reappears in Zaroff's bedroom; though there's a case to be made for this interpretation, the fact that the fight itself isn't described in detail leaves the scene reading more like traditional falling action. The reader's anticipation is greatest in the scene where Rainsford jumps off the cliff; thus I would argue that this scene, not the one in which Rainsford reappears, is better identified as the climax.

The climax of any story is the high point of the story.  The moments leading up to the climax are all part of the rising action, and anything after the climax is falling action and resolution.  The climax of "The Most Dangerous Game" is when Rainsford kills Ivan and escapes from Zaroff by jumping off the cliff.  This is by far the most tense and suspenseful part of the story, and the moments after this are not nearly as heart pounding.  When Rainsford jumps, the story is at its peak in terms of momentum.  
After this climactic moment in the story, Rainsford makes his way back to Zaroff's house.  Once there, he waits for Zaroff to return.  The story concludes with Rainsford killing Zaroff and sleeping soundly in the man's bed.  I have seen some interpretations that support this final scene as the climax, but very little detail appears in the scene itself.  The author hints that a fight ensues, but no explanation is given.  

The general made one of his deepest bows. "I see," he said. "Splendid! One of us is to furnish a repast for the hounds. The other will sleep in this very excellent bed. On guard, Rainsford." . . .
He had never slept in a better bed, Rainsford decided.

As you can see, Zaroff readies himself for a fight, and the next thing the reader gets is the information that Raisford slept really well.  We have no idea how intense the fight was.  Compared the cliff jumping sequence, the bedroom confrontation is much less climactic.  I would categorize the bedroom confrontation as the story's falling action.  

Where in the preamble to the Declaration of Independence does it talk about separation of powers or government with branches?

Separation of powers is not a concept that is discussed in the Preamble to the Declaration, (or elsewhere in the document.) Generally, the Declaration is an assertion of principles and a list of grievances against King George. Their focus is on the alleged abuses they have suffered as British subjects, not how government might be structured in such a way as to avoid these abuses. Their complaints were related to the imperial relationship between the colonies and the Crown and Parliament. They argued that the King (after spending years arguing against the usurpations of Parliament) had violated their rights as Englishmen. The idea of separation of powers was well-established in the Anglo-American world--the famous French philosopher Montesquieu had based his defense of the concept on the English constitution--but Jefferson and the authors of the Declaration did not assert it as a principle in the Preamble or elsewhere. To see what late eighteenth-century Americans thought about the importance of separation of powers, one might turn to the various state constitutions, which established the principle after the Declaration, or the Federalist Papers, specifically Federalist 51, which discusses and defends the system separation of powers in the Constitution. 

Why do people choose to eat a vegetarian diet?

Let me begin by stating that there are different levels of vegetarian diets.  For this answer, I'll provide reasons to be on a 100% vegetarian diet.  
It's healthier.  In some cases this is absolutely true.  In some cases this is not true.  For example, most meats are complete proteins.  This means that they contain all 9 essential amino acids.  A vegetarian can still eat a diet that contains all 9 essential amino acids; however, the person must be much more intentional about mixing and matching foods so that all 9 of those amino acids are consumed. A vegetarian diet that does not contain all 9 of these amino acids might not be healthier than a diet that contains at least some meat. 

For moral reasons.  Some people don't like or don't agree with the killing of animals in order to eat them.  Being a vegetarian means that their personal diet does not contribute to further killing of animals. 
Lower risk of disease.  Vegetarians tend to have a lower risk for things like heart disease, diabetes, high blood pressure, obesity, and stroke.  This is likely because a vegetarian is consuming fewer foods that are high in cholesterol and saturated fats. 
Potential to live a longer life.  Studies exist that show vegetarians typically live longer than non-vegetarians.  
http://veg.ca/go-veg/the-7-day-veggie-challenge/top-ten-reasons-to-go-vegetarian/

https://www.accessdata.fda.gov/scripts/InteractiveNutritionFactsLabel/protein.html

https://www.downtoearth.org/go-veggie/top-10-reasons

In Romeo and Juliet, do people have control over their own lives?

An important distinction to make is the difference between control and choice. From a Western, 21st century perspective one might equate making choices about the direction or path of life with exercising control. Being free to choose who to marry or what career to pursue is valued in Western culture and the idea of lacking options can seem like a restraint. However, in the setting of Romeo and Juliet, namely the 12th century, the societal expectations of personal control would have been perceived very different. Free choice was not a value as highly regarded as it is in Western, capitalist society today. Relational ties, such as family, were more highly regarded and would have been seen as just as important if not more important than a marriage or a livelihood. Romeo and Juliet got to make many choices throughout their lives, the ultimate of which being the choice to take their own lives. Some scholars argue that Shakespeare’s prologue sets the expectation that their fate is determined and no choice they make will change the outcome. Despite the outcome being identical to what is predicted in the prologue, choices are made throughout the story which could have changed the outcome along the way without the reader being aware.

Romeo and Juliet doesn't show people having the kind of control over their own lives to which we are accustomed in the twenty-first century. Both of the lovers are forced to act secretly, because their families are bitterly feuding. As Juliet points out, Romeo could easily be killed if one her male relatives found him at her balcony. Neither one dares to say openly that they are in love with the other. Further, Juliet has very few options when her father decides she will marry Paris. A young woman was expected to obey her father and marry in accordance with what was best for her family, not for love. Juliet doesn't feel she can openly defy her father's desires.  
To marry at all, the young lovers have to do so secretly. Juliet has to feign death to avoid having to marry Paris. 
Yet, the two lovers do exercise some control over their lives. They do marry, albeit secretly, and they both commit suicide when they think the other is dead. 

why is the sun the primary gravitational force in the solar system?

It is not correct to say that the Sun is a force. Gravity is a force of attraction between any two bodies that have mass. The gravitational attraction to the Sun is far greater than the attraction to any other body in the solar system. To explain this, consider the equation for the force of gravitational attraction between two objects:
F = (Gm_1m_2)/r^2
Here F is the force of gravitational attraction. Note that this force acts equally on both bodies. We often think of Earth and planets being attracted by the Sun, but force of gravity on the Sun from the Earth is equal to the force on the Earth from the Sun. G is the gravitational constant, a number that is known and can be looked up in a table. The variables on which the force depends are m_1 , m_2 , and r , the masses of the two bodies and the distance between them.
The Sun’s mass of about 2 X 10^30 kg is by far the greatest mass of any object in the solar system. It is about a thousand times as great as the mass of Jupiter, the next most massive object. Thus, the force of attraction between the sun and most other objects is generally greater than the force between other pairs of objects.
Less massive objects that are close together, so that r is small, may still be strongly attracted. This is why the moon and the satellites of other planets revolve around their respective planets. For these satellites, the closeness of their planets leads to a stronger attraction to the planet than to the distant Sun. Still, the Sun’s mass attracts all of the planets, asteroids, and comets in the solar system so strongly that all of them revolve around the Sun, and the entire solar system is thus organized around the Sun.

Single Variable Calculus, Chapter 8, 8.2, Section 8.2, Problem 26

Determine the integral $\displaystyle \int^{\frac{\pi}{4}}_0 \sec^4 \theta \tan^4 \theta d \theta$



$
\begin{equation}
\begin{aligned}

\int^{\frac{\pi}{4}}_0 \sec^4 \theta \tan^4 \theta d \theta =& \int^{\frac{\pi}{4}}_0 \sec^2 \theta \sec^2 \theta \tan^4 \theta d \theta
\qquad \text{Apply Trigonometric Identity } \sec^2 \theta = \tan^2 \theta + 1 \text{ for } \sec^2 \theta
\\
\\
\int^{\frac{\pi}{4}}_0 \sec^4 \theta \tan^4 \theta d \theta =& \int^{\frac{\pi}{4}}_0 (\tan^2 \theta + 1) \tan^4 \theta \sec^2 \theta d \theta
\\
\\
\int^{\frac{\pi}{4}}_0 \sec^4 \theta \tan^4 \theta d \theta =& \int^{\frac{\pi}{4}}_0 (\tan^6 \theta + \tan^4 \theta) \sec^2 \theta d \theta

\end{aligned}
\end{equation}
$


Let $u = \tan \theta$, then $du = \sec^2 \theta d \theta$. When $\displaystyle \theta = 0, u = 0, \theta = \frac{\pi}{4}, u =1 $. Therefore,


$
\begin{equation}
\begin{aligned}

\int^{\frac{\pi}{4}}_0 (\tan^6 \theta + \tan^4 \theta) \sec^2 \theta d \theta =& \int^1_0 (u^6 + u^4) du
\\
\\
\int^{\frac{\pi}{4}}_0 (\tan^6 \theta + \tan^4 \theta) \sec^2 \theta d \theta =& \left[ \frac{u^{6 + 1}}{6 + 1} + \frac{u^{4 + 1}}{4 + 1} \right]^1_0
\\
\\
\int^{\frac{\pi}{4}}_0 (\tan^6 \theta + \tan^4 \theta) \sec^2 \theta d \theta =& \left[ \frac{u^7}{7} + \frac{u^5}{5} \right]^1_0
\\
\\
\int^{\frac{\pi}{4}}_0 (\tan^6 \theta + \tan^4 \theta) \sec^2 \theta d \theta =& \frac{(1)^7}{7} + \frac{(1)^5}{5} - \frac{(0)^7}{7} - \frac{(0)^5}{5}
\\
\\
\int^{\frac{\pi}{4}}_0 (\tan^6 \theta + \tan^4 \theta) \sec^2 \theta d \theta =& \frac{1}{7} + \frac{1}{5}
\\
\\
\int^{\frac{\pi}{4}}_0 (\tan^6 \theta + \tan^4 \theta) \sec^2 \theta d \theta =& \frac{5 + 7}{35}
\\
\\
\int^{\frac{\pi}{4}}_0 (\tan^6 \theta + \tan^4 \theta) \sec^2 \theta d \theta =& \frac{12}{35}

\end{aligned}
\end{equation}
$

Who is the one with the most fault in Romeo and Juliet's deaths?

Pretty much every character contributed to Romeo and Juliet's deaths in one way or another. Many believe that Romeo and Juliet themselves are the most responsible for their deaths. They committed suicide, therefore they are to blame.
However, in my opinion, the answer is not so clear-cut. Romeo and Juliet were too young and too distraught to make rational decisions. Even though they ultimately committed suicide, their suicides were the result of a chain of very unfortunate events.
I think the biggest blame should fall on the two families and their feud. The rivalry, hate, and anger between these two families was what caused Romeo and Juliet to believe that they couldn't be together in the first place.
Also to blame are Mercutio and Tybalt. Their fight escalated an otherwise almost stable situation. Tybalt killed Mercutio while dueling with Benvolio, and Romeo then killed Tybalt. Romeo was banished as a result. This set off a chain of events which was too fast and unpredictable for Romeo and Juliet to fight or control.
Finally, timing, although not a character, is a huge contributing factor to Romeo and Juliet's deaths. A misunderstanding caused Romeo to think that Juliet was actually dead when in reality she was only unconscious from the Friar's potion. All Romeo needed was for Friar Laurence to contact Romeo earlier or for Juliet to wake up a few minutes before he took the poison.

Who hits Luis with a blackjack in Tangerine?

The narrator of Tangerine, Paul Fisher, has an older brother called Erik. Erik's the blue-eyed high-school football star who can do wrong in his parents' eyes. But he always seems to go out of his way to make life difficult for his kid brother. For instance, when Paul's hanging out with his friend Tino one day, Erik punches Tino in the face, knocking him unconscious. When he hears about this, Tino's cousin Luis goes looking for Erik to confront him. He arrives at the football field, ready for a showdown. But Erik's not prepared to waste his valuable time arguing with Luis, so he instructs his friend, the thuggish Arthur Bauer, to take care of things. Arthur does as he is bid and whacks Luis across the side of his head with a blackjack. The attack doesn't kill Luis straight away, but he dies from a brain aneurysm just over a week later.

Beginning Algebra With Applications, Chapter 5, 5.1, Section 5.1, Problem 32

The following table shows average lengths of fetuses for selected stages of prenatal development in humans.

$\begin{array}{c|cccc}
\text{Month of pregnancy} & 2 & 4 & 6 & 8 \\
\hline\\
\text{Length, in inches} & 1 & 7 & 12 & 16
\end{array} $

a. What is the average rate of change per month in the length of a fetus from the sixth month of pregnancy to the eighth month of pregnancy?


$
\begin{equation}
\begin{aligned}

\text{average rate of change} =& \frac{\text{length of a fetus in eighth month - length of fetus in sixth month}}{8-6}
\\
\\
=& \frac{16-12}{8-6}
\\
\\
=& \frac{4}{2}
\\
\\
=& 2 \text{ inches}

\end{aligned}
\end{equation}
$



The average rate of change per month is 2 inches.

b. Find the average rate of change per month in the length of a fetus from the second month of pregnancy to the fourth month of pregnancy. Is this greater than or less than the average rate of change per month from the sixth month to the eighth month?


$
\begin{equation}
\begin{aligned}

\text{average rate of change} =& \frac{\text{length of the fetus in fourth month - length of fetus in second month}}{4-2}
\\
\\
=& \frac{7-1}{4-2}
\\
\\
=& \frac{6}{2}
\\
\\
=& 3 \text{ inches}

\end{aligned}
\end{equation}
$



The average rate of change per month from fourth month of pregnancy to the second month of pregnancy is 3 inches. And it is greater than the average rate if change per month from the sixth month to the eighth month.

Single Variable Calculus, Chapter 6, 6.3, Section 6.3, Problem 28

Use the Midpoint Rule with $n = 5$ to estimate the volume of the region shown in the figure below, if the region is rotated about the $y$-axis.

*Refer to the figure in the book.*

By using Midpoint Rule with $n = 5$, we can determine the thickness of the approximately rectangles as...

$\displaystyle \Delta x = \frac{12 - 2}{5} = 2$ thus, the midpoints are $\displaystyle \left( \frac{2 + 4}{2} \right) = 3, \left( \frac{4 + 6}{2} \right) = 5, \left( \frac{6 + 8}{2} \right) = 7, \left( \frac{8 + 10}{2} \right) = 9, \left( \frac{10 + 12}{2} \right) = 11$

Notice that the distance of these approximating rectangles at $y$-axis is $x$. If you revolve, this length to about the $y$-axis, you'll have a circumference of $2 \pi x$ and the total volume is equal to the product of the circumference and the total area of the curve. So..


$
\begin{equation}
\begin{aligned}

V =& \int^{12}_2 2 \pi x f(x) \Delta x
\\
\\
\approx & 2 \pi [3 f(3) + 5f(5) + 7f(7) + 9 f(9) + 11f(11)] \cdot 2
\\
\\
\approx & 2 \pi [3(2) + 5 (4) + 7(4) + 9(2) + 11(1)] \cdot 2
\\
\\
\approx & 4 \pi [83]
\\
\\
\approx & 332 \pi \text{ cubic units}

\end{aligned}
\end{equation}
$

What is the central conflict of "Sredni Vashtar" by Saki? Who took part in it? Was there a resolution to the conflict?

The main conflict in "Sredni Vashtar" is between the protagonist Conradin and his cousin Mrs. De Ropp, the antagonist. For Conradin,

[Mrs. De Ropp] represented those three-fifths of the world that are necessary and disagreeable and real.

His cousin and guardian, Mrs. De Ropp seems to delight in the fact that Conradin is a sickly child who cannot do the things that ordinary boys can, for then she can impose her will upon him. Fortunately for Conradin, he has an imagination that is "rampant under the spur of loneliness"; indeed, it is this creativity which keeps the boy alive longer than the doctor has predicted.
Each day, Conradin's goal is to enjoy himself and thwart the Woman's, as he calls her, attempts to spoil his pleasure. He does this by avoiding the gardens where a window can easily open and from which scoldings issue forth. Instead, Conradin directs his attention to a certain old tool-shed that is almost hidden behind overgrown shrubbery. Inside this old shed, Conradin has found a haven, "something that took on the varying aspects of a playroom and a cathedral." There are multitudes of imaginary figures, issuing from Conradin's reading and his own imagination. In a far corner, however, there are two living creatures: a Houdan hen upon which Conradin lavishes much attention as well as his devoted affection, which has no other outlet. Also, in a far corner Conradin has a large ferret which the butcher boy has smuggled in for him. This sharp-fanged "polecat" incites fear in Conradin, but he views it as a mysterious little deity and names it Sredni Vashtar.
After the "Woman," as Conradin thinks of her, discovers that he has housed the little hen in the tool-shed, she removes the beloved hen and sells it. Happily, she informs Conradin that the hen is gone because it was not good for him to "be pottering down there in all weathers." After she says these words,

[With] her short-sighted eyes she peered at Conradin, waiting for an outbreak of rage and sorrow, which she was ready to rebuke with a flow of excellent precepts and reasoning.

However, Conradin remains stoic, even when she troubles herself to make toast for tea time.

"I thought you liked toast," she exclaimed, with an injured air, observing that he did not touch it.
"Sometimes," said Conradin.

Later, however, in his suffering of the loss of the only creature that he has had to love, Conradin prays privately to Sredni Vashtar, "Do one thing for me." Feeling that the god should know what he means, Conradin mentions nothing; he only chokes back a sob as he glances at the empty corner where his hen used to be. The next night and every night afterwards, Conradin prays to Sredni Vashtar.Then one day, the Woman informs Conradin that she has noticed that he still goes to the tool-shed. When Mrs. De Ropp goes out to the shed, Conradin imagines that she will open the cage and peer in with her myopic eyes. "And Conradin fervently breathed his prayer for the last time" as he watches out a window.
After some time, Conradin begins to despair. A maid passes under the window on her way to make tea inside. Then,

...out through that doorway came a long, low, yellow-and-brown beast, with eyes a-blink at the waning daylight, and dark wet stains around the fur of jaws and throat. Conradin dropped on his knees.

"Tea is ready," the surly maid calls, then asks, "Where is the mistress?" Conradin simply replies that she has gone to the tool-shed. This time the toast tastes delicious to Conradin, and he delights in it. 
After a while, Conradin hears the maid scream. Then another asks,

"Whoever will break it to the poor child? I couldn't for the life of me!" exclaimed a shrill voice.

And while the servants debated the matter among themselves, Conradin simply made himself another piece of victory toast.

How does Du Bois' idea of double-consciousness show the reproduction of racialized domination?

DuBois describes double-consciousness as follows:

After the Egyptian and Indian, the Greek and Roman, the Teuton and Mongolian, the Negro is a sort of seventh son, born with a veil, and gifted with second-sight in this American world,—a world which yields him no true self-consciousness, but only lets him see himself through the revelation of the other world. It is a peculiar sensation, this double-consciousness, this sense of always looking at one’s self through the eyes of others, of measuring one’s soul by the tape of a world that looks on in amused contempt and pity. One ever feels his two-ness,—an American, a Negro; two souls, two thoughts, two unreconciled strivings; two warring ideals in one dark body, whose dogged strength alone keeps it from being torn asunder.

"Double-consciousness" is the inability to be oneself, to live a life completely dedicated to authenticity, because one is constantly aware—hyper-aware—of the perceptions of others. The "veil" is a metaphor that refers to the way in which black people are not seen, but perceived. This tendency to be perceived helps one to anticipate the expectations and anxieties of others but makes it very difficult to achieve self-awareness. The inability to be self-aware and to form an identity that is completely distinct from racism is "the reproduction of racialised [sic] domination of which you speak." One is dominated, or under the control, of others when one's identity is indistinct from someone else's perception.
Furthermore, there is the dichotomy between being "an American," a product of a particular culture and devotee to the ideals of a great nation, and "a Negro," a figure of contempt, reviled in the culture but also the source of the nation's great advantage in wealth.
https://www.bartleby.com/114/

Single Variable Calculus, Chapter 8, 8.2, Section 8.2, Problem 42

Determine the integral $\displaystyle \int^{\frac{\pi}{3}}_{\frac{\pi}{6}} \csc^3 x dx$

Using Integration by parts

$\int \csc^3 x dx = \int udv$

where


$
\begin{equation}
\begin{aligned}

dv =& \csc^2 x dx
\\
\\
v =& - \cot x
\\
\\
u =& \csc x
\\
\\
du =& - \csc x \cot x dx

\end{aligned}
\end{equation}
$


then


$
\begin{equation}
\begin{aligned}

\int \csc^3 x dx =& \int u dv
\\
\\
\int \csc^3 x dx =& uv - \int vdu
\\
\\
\int \csc^3 x dx =& - \csc x \cot x - \int - \cot x \cdot - \csc x \cot x dx
\\
\\
\int \csc^3 x dx =& - \csc x \cot x - \int \csc x \cot^2 x dx
\qquad \text{Apply Trigonometric Identity } \csc^2 x = 1 + \cot^2 x \text{ for } \cot^2 x
\\
\\
\int \csc^3 x dx =& - \csc x \cot x - \int \csc x (\csc^2 x - 1) dx
\\
\\
\int \csc^3 x dx =& - \csc x \cot x - \left( \int (\csc^3 x) - \csc x) dx \right)
\\
\\
\int \csc^3 x dx =& - \csc x \cot x - \int \csc^3 x dx + \int \csc x dx
\qquad \text{Combine like terms}


\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}

\int \csc^3 x dx + \int \csc^3 x dx =& - \csc x \cot x + \int \csc x dx
\\
\\
2 \int \csc^3 x dx =& - \csc x \cot x + \int \csc x dx
\\
\\
\int \csc^3 x dx =& \frac{- \csc x \cot x + \int \csc x dx}{2}
\\
\\
\int \csc^3 x dx =& \frac{-1}{2} \csc x \cot x + \frac{1}{2} \int \csc x dx
\\
\\
\int \csc^3 x dx =& \frac{-1}{2} \csc x \cot x + \frac{1}{2} (- \ln (\csc x + \cot x)) + c
\\
\\
\int \csc^3 x dx =& \frac{-1}{2} \csc x \cot x - \frac{1}{2} \ln (\csc x + \cot x) + c


\end{aligned}
\end{equation}
$


Evaluating the limit from $\displaystyle \frac{\pi }{6} \text{ to } \frac{\pi}{3}$


$
\begin{equation}
\begin{aligned}

\int^{\frac{\pi}{3}}_{\frac{\pi}{6}} \csc^3 x dx =& \left[ \frac{-1}{2} \csc x \cot x - \frac{1}{2} \ln (\csc x + \cot x) \right]^{\frac{\pi}{3}}_{\frac{\pi}{6}}
\\
\\
\int^{\frac{\pi}{3}}_{\frac{\pi}{6}} \csc^3 x dx =& \frac{-1}{2} \csc \left( \frac{\pi}{3} \right) \cot \left( \frac{\pi}{3} \right) - \frac{1}{2} \ln \left( \csc \left( \frac{\pi}{3} \right) + \cot \left( \frac{\pi}{3} \right) \right) + \frac{1}{2} \csc \left( \frac{\pi}{6} \right) \cot \left( \frac{\pi}{6} \right) + \frac{1}{2} \ln \left( \csc \left( \frac{\pi}{6} \right) + \cot \left( \frac{\pi}{6} \right) \right)
\\
\\
\int^{\frac{\pi}{3}}_{\frac{\pi}{6}} \csc^3 x dx =& \frac{-1}{\cancel{2}} \left( \frac{\cancel{2} \sqrt{3}}{3} \right) \left( \frac{\sqrt{3}}{3} \right) - \frac{1}{2} \ln \left( \frac{2 \sqrt{3}}{3} + \frac{\sqrt{3}}{3} \right) + \frac{1}{\cancel{2}} (\cancel{2}) (\sqrt{3}) + \frac{1}{2} \ln (2 + \sqrt{3})
\\
\\
\int^{\frac{\pi}{3}}_{\frac{\pi}{6}} \csc^3 x dx =& \frac{-3}{9} - \frac{1}{2} \ln \left( \frac{\cancel{3} \sqrt{3}}{\cancel{3}} \right) + \sqrt{3} + \frac{1}{2} \ln (2 + \sqrt{3})
\\
\\
\int^{\frac{\pi}{3}}_{\frac{\pi}{6}} \csc^3 x dx =& \frac{-1}{3} - \frac{1}{2} \ln (\sqrt{3}) + \sqrt{3} + \frac{1}{2} \ln (2 + \sqrt{3})

\end{aligned}
\end{equation}
$

Precalculus, Chapter 7, 7.4, Section 7.4, Problem 25

[x^2+12x+12]/[x^3-4x]=[x^2+12x+12]/[x(x+2)(x-2)]
[x^2+12x+12]/(x^3-4x)=A/x+B/(x+2)+C/(x-2)

Multiply through by the LCD x^3+4x.
x^2+12x+12=A(x^2-4)+Bx(x-2)+Cx(x+2)
x^2+12x+12=Ax^2-4A+Bx^2-2Bx+Cx^2+2Cx
x^2+12x+12=(A+B+C)x^2+(-2B+2C)x+(-4A)

Equate coefficient of like terms. Then solve for A, B, and C.
1=A+B+C
12=-2B+2C
12=-4A

A=-3

1=A+B+C
1=-3+B+C
4=B+C

Solve for B and C using the elimination method.
4=B+C
12=-2B+2C
Multiply the first equation by 2. Then solve using the elimination method.
8=2B+2C
12=-2B+2C
_________________
20=4C
C=5

1=A+B+C
1=-3+B+5
B=-1

A=-3, B=-1, C=5

(x^2+12x+12)/(x^3-4x)=-3/x-1/(x+2)+5/(x-2)

How did the jailed suffragists protest the arrests they saw as illegal, and what was the result of their action?

The jailed British suffragists of the early twentieth century were famous for going on hunger strikes to protest their arrests. They simply refused to eat. This upset the jail authorities. The women were then force fed in often brutal and barbaric ways. Since this method was normally used only on people unable (not unwilling) to feed themselves, the feedings garnered much negative publicity and helped gain sympathy for the suffragettes.
Some British newspapers, such as the Illustrated London News, focused on this unpleasant topic. In the link below, a very prominent suffragist named Sylvia Pankhurst described her experience with force feeding, offering a number of gruesome details:




Then I felt a steel instrument pressing against my gums, cutting into the flesh, forcing its way in. Then it gradually prised my jaws apart as they turned a screw. It felt like having my teeth drawn; but I resisted—I resisted. I held my poor bleeding gums down on the steel with all my strength. Soon they were trying to force the india-rubber tube down my throat.




I was struggling wildly, trying to tighten the muscles and to keep my throat closed up. They got the tube down, I suppose, though I was unconscious of anything but a mad revolt of struggling, for at last I heard them say, "That's all"; and I vomited as the tube came up.




Pankhurst noted that the procedure was not only painful, but degrading, humiliating, and psychologically draining. Overall, the publicity helped the suffragist cause in the court of public appeal.

x=t+1 , y=t^2+3t Find all points (if any) of horizontal and vertical tangency to the curve.

Parametric curve (x(t),y(t)) has a horizontal tangent if its slope dy/dx is zero i.e. when dy/dt=0 and dx/dt!=0
It has a vertical tangent, if its slope approaches infinity i.e. dx/dt=0 and dy/dt!=0
Given parametric equations are:
x=t+1
y=t^2+3t
dx/dt=1
dy/dt=2t+3
For Horizontal tangents,
dy/dt=0
2t+3=0
=>2t=-3
=>t=-3/2
Corresponding point on the curve can be found by plugging in the value of t in the equations,
x=-3/2+1=-1/2
y=(-3/2)^2+3(-3/2)
y=9/4-9/2
y=(9-18)/4=-9/4
Horizontal tangent is at the point (-1/2,-9/4)
For vertical tangents,
dx/dt=0
However dx/dt=1!=0
So there are no vertical tangents.

Single Variable Calculus, Chapter 3, 3.3, Section 3.3, Problem 93

Find the values of $a$ and $b$ such that the line $2x+y = b$ is tangent to the parabola $y = ax^2$ when $x=2$

If the line is tangent to the curve at some point. It means that the first derivative of the
curve is equal t the slope of the line and by inspection, the slope of the line is -2 using the
general equation of the line $y = mx + b $ where $m$ is the slope.

Taking the first derivative of the curve we get

$
\begin{equation}
\begin{aligned}
y &= ax^2\\
\\
y' &= 2ax && \text{;when } x = 2\\
\\
y' &= 2a(2)\\
\\
y' &= 4a && \text{;equating this to the slope of the line}\\
\\
-2 &= 4a\\
\\
a &= \frac{-1}{2}
\end{aligned}
\end{equation}
$


To find the value of $b$, we equate both equations since they have a point of intersection


$
\begin{equation}
\begin{aligned}
2x + y &= b \\
\\
y &= -2x + b \quad ; \text{when } x=2 \qquad y = -2(2)+b \qquad = -4 +b\\
\\
y &= ax^2 \qquad ; \text{when } x = 2 \qquad y = a(2)^2 \qquad =4a\\
\\
4a &= -4 + b \qquad \text{Substituting the value of } a\\
\\
4\left(\frac{-1}{2}\right) &= -4+b \qquad \text{Solve for } b\\
\\
b &= 2
\end{aligned}
\end{equation}
$


Therefore the required values are $\displaystyle a = -\frac{1}{2}$ and $b = 2$

Why did the policeman on his nightly beat slow down halfway on a certain block?

In "After Twenty Years," the cop is patrolling a certain area where most of the shops are typically closed at that particular time of night. He slows down when he sees a man standing near one of the shops. It appears as if the cop is simply being cautious upon encountering a man in front of a closed shop. Before the cop speaks, the man offers an explanation as to why he is there at that particular time. He explains that twenty years ago, he and his friend were having dinner when they determined they would meet at the same location in twenty years.
While it appears that the cop is doing his job by slowing down when he encounters the man, the cop is actually the man's friend from twenty years ago. When he sees the man at that location, he knows it must be his old friend. Not wishing to arrest his old friend, he continues along his beat and has another officer arrest the man that is wanted by the Chicago police.

Judge whether Jing-mei or her mother had Jing-mei's best interests in mind.

When trying to judge whether Jing-Mei or her mother had Jing-Mei's best interest at heart it is important to remember that "Two Kinds" is being told through a limited first person perspective. Meaning, as a reader, you know what Jing-Mei is thinking about the situation, but you are never given any insight as to what her mother might be thinking.
Jing-Mei's mother had a tough life back in China, which leads the reader to believe that the mother is only pushing Jing-Mei to be a prodigy because she wants to make sure that her daughter doesn't have to suffer. But from Jing-Mei's perspective, her mother pursues this goal with unrelenting pressure which has the opposite effect on her daughter. Instead of being a successful prodigy, Jing-Mei distances herself from her mother, and doesn't truly find herself until she herself becomes an adult.
While Jing-Mei's mother is trying to make her daughter successful, Jing-Mei is doing anything within her power to remain true to herself. Jing-Mei is rebelling against her mother, because she doesn't want her mother to control everything about her life.
The answer to whether Jing-Mei or her mother have Jing-Mei's best interests at heart, depends on whose perspective you are viewing the situation from. Since "Two Kinds" depicts Jing-Mei's transition into adulthood, it is easy to side with Jing-Mei in this situation.

At first glance, it seems that Jing-Mei's mother is more concerned about what other people think about her daughter than how her daughter actually feels. The constant struggle to create a child prodigy seems to be a very coldhearted process. Jing-Mei is repeatedly compared to other children and forced to develop all sorts of talents; she is encouraged to become the Chinese Shirley Temple and master the piano.
Looking deeper, however, we see that Jing-Mei's mother does, in fact, have her daughter's best interests at heart. Given her own traumatic background in China, the mother simply wants the best for her daughter and hopes to give Jing-mei the opportunities that she herself never had.
In contrast, Jing-Mei does not realize that her mother is planning for the future. Instead, she focuses on the short term. Specifically, she dislikes being forced to be a prodigy. It is only in adulthood that she realizes what her mother was trying to achieve. 
Accordingly, both Jing-Mei and her mother can be said to have Jing-Mei's best interests at heart. They are simply approaching this subject from different angles.

why did the french and indian war affect the british

"The French and Indian War" is a term only really used in the United States. It refers to only part of a broader conflict, the Seven Years' War, in which Britain, along with much of Europe, was embroiled from 1756-63. Remember that at this point in time, America did not exist as a nation, so the French and Indian War, or the North American front of the wider conflict, was really a war between French and British colonists, a reflection of the European conflict between France and Britain. It affected the British because British colonists and their Native American allies were the primary combatants against French colonists in their dispute over land. At this point in time, these people were British citizens.
In terms of mainland Britain, it also affected the British at home because the wars overseas had to be financed and were very expensive. Indeed, the huge amount of money the British government had apportioned to defending its North American colonies was highlighted as a reason against revolution in the United States, the argument being that Britain had helped the colonists defend their territories, at great cost to itself, and deserved their loyalty. The huge tax hikes that followed the Seven Years' War, which caused such agitation in the colonies, were in large part a result of expenditure in North America: Britain's national debt was now enormous and the government was seeking to recover it. So, this war affected Britain's economy significantly, and also contributed to the loss of the North American colonies it had spent so much money in defending.

In A Retrieved Reformation. How can you tell that Jimmy Valentine and any other characters never expected to complete jail time?

Jimmy Valentine was an exception. The other prisoners did not expect to be "sprung" from prison before their sentences were served; but Jimmy had a lot of connections on the outside. The text explains this in part and leaves more to the reader's imagination.

He had expected to stay only about three months, at the longest. When a man with as many friends on the outside as Jimmy Valentine had is received in the “stir” it is hardly worth while to cut his hair.

Jimmy is an exceptional person. For one thing, he makes lots of money in his illegal profession, and no doubt he is generous to politicians and other important people. For another thing, he is exceptionally intelligent, which explains why he is so successful as a criminal. The other men in "stir" are not like him. Jimmy has a charming personality. This also explains why he has so many "friends on the outside." Everybody likes Jimmy. They call him "Jimmy" rather than Jim because they like him. Even the warden likes him.

“Now, Valentine,” said the warden, “you'll go out in the morning. Brace up, and make a man of yourself. You're not a bad fellow at heart. Stop cracking safes, and live straight.”

When Jimmy goes to the place where he keeps a room, the building-owner Mike Dolan greets him cordially.

“Sorry we couldn't make it sooner, Jimmy, me boy,” said Mike. “But we had that protest from Springfield to buck against, and the governor nearly balked. Feeling all right?”

Dolan is one of Jimmy's many "friends on the outside." He represents a whole wide circle of underworld figures, shady politicians, and others who can do such favors as getting a criminal pardoned. 
Jimmy's brains and personality are great assets. But he comes to realize that he can use his personal assets to better advantage by going straight rather than remaining a career criminal. He is getting too well known to many people such as Mike Dolan and Ben Price, the detective. Jimmy decides to move to an entirely different area of operations where he is unknown. There he falls in love and his whole life changes. He is even more successful as an honest businessman than he was as a safecracker.
 
 

How is isolation shown in Frozen?

Frozen (2013) revolves around the isolation of two sisters, Anna and Elsa. While these two princesses are best of friends as young children, Elsa, who has magical powers that she struggles to control, withdraws from the world, essentially locking herself in her bedroom. When their parents die in a shipwreck, their isolation deepens.
One way to trace the theme of isolation throughout the film is through its soundtrack. The hit song “Do You Want to Build a Snowman?” appears in the film during a montage that reveals the progression of Anna and Elsa’s isolation. As the line “It doesn’t have to be a snowman” suggests, the titular question is not so much about building a snowman as it is a sister’s plea for companionship. When Elsa’s coronation day arrives and the castle is opened for guests, Anna celebrates that “for the first time in forever / I won’t be alone.”
Although popular culture has embraced “Let It Go” as a song about (female) empowerment, it is also a song about isolation. Consider the extreme long shots of Elsa as she climbs further and further up the mountain and away from everyone else. It is about her embracing her powers, but sadly it’s also about her withdrawing from her sister and the people that she is to rule. We see her embracing her identity, but it's from a great distance against a backdrop of snow. Even from the viewer, Elsa’s isolation deepens, as she becomes harder and harder to see—from this perspective, her visual transformation takes on a new significance. Fittingly, it is later in the film, also against a snowy backdrop, that this isolation is ended by true love’s kiss. In this late moment, it is their reunion that ends the snowstorm—the recurring symbol of isolation—and their isolation itself.

Is burning a chemical or physical change? Explain your answer.

Burning is a chemical change because it has a chemical reaction and results in a new substance. A physical change does not cause the substance to change. For example, melting ice is a physical change because in the liquid state, water is made up of 2 parts hydrogen and one part oxygenm just as it is in the solid state. The only change is the state of matter from a solid to a liquid.
Baking a cake, represents a chemical change however, because we have taken the sugar, flour, eggs, etc. and chemically altered them. They are no longer separate substances, but have now merged and formed a new substance.
Other sources: chem4kids.com

Burning is a chemical change since it is a reaction between substances, usually including oxygen and usually accompanied by the generation of heat and light in the form of flame. The rate or at which the reactants combine is high, in part because of the nature of the chemical reaction itself and in part because more energy is generated than can escape into the surrounding medium, with the result that the temperature of the reactants is raised to accelerate the reaction even more. A familiar example is a lighted match.Properly ignited, the heat from the flame raises the temperature of a nearby layer of the matchstick and of oxygen in the air, and the wood and oxygen react in.When equilibrium between the total heat energies of the reactants and the total heat energies of the products is reached, combustion stops.The emission of light in the flame results from the presence of excited particles'usually charged atoms,molecules and electrons.

Burning, or combustion, is a chemical change, and one of the most dramatic to observe. A chemical change happens when the molecular structure of a substance changes in a way that cannot be reversed. When a substance burns, its molecular bonds are broken down, and it becomes a different substance. When one burns carbon compounds, for example, new chemicals are produced—including (depending on the amount of oxygen present) carbon dioxide and carbon monoxide. When wood is burned, it is reduced to ash, and gases escape. The fact that combustion gives off heat and light in addition to changing the chemical composition of the fuel is another indicator that it is a chemical change. Also, (as mentioned above) unlike a physical change, a chemical change cannot be undone. If water freezes, it can be thawed, and, conversely, running water can be frozen. If a piece of firewood burns into ashes, these ashes cannot be reformed into wood.
http://eschooltoday.com/science/states-and-behaviour-of-matter/what-is-a-chemical-change.html

http://www.chem4kids.com/files/matter_chemphys.html

Single Variable Calculus, Chapter 3, 3.2, Section 3.2, Problem 28

a.) Illustrate the graph of $f(x) = \sqrt{6 - x}$







b.) Sketch the graph of $f'$ using the graph from part (a)







c.) Find $f'(x)$ using the definition of a derivative. State the domains of $f$ and $f'$.

Using the definition of derivative


$
\begin{equation}
\begin{aligned}

\qquad f'(x) =& \lim_{h \to 0} \frac{f(t + h) = f(t)}{h}
&&
\\
\\
\qquad f'(x) =& \lim_{h \to 0} \frac{\sqrt{6 - (x + h)} - \sqrt{ 6 -x}}{h}
&& \text{Substitute $f(x + h)$ and $f(x)$}
\\
\\
\qquad f'(x) =& \lim_{h \to 0} \frac{\sqrt{6 - x - h} - \sqrt{ 6 -x}}{h} \cdot \frac{\sqrt{6 - x - h} + \sqrt{ 6 -x}}{\sqrt{6 - x - h} + \sqrt{ 6 -x}}
&& \text{Multiply both numerator and denominator by $(\sqrt{6 - x - h} + \sqrt{ 6 -x})$}
\\
\\
\qquad f'(x) =& \lim_{h \to 0} \frac{6 - x - h - \cancel{\sqrt{(6 - x - h) + (6 -x)}} + \cancel{\sqrt{(6 - x - h) + (6 -x)}} - (6 -x )}{h(\sqrt{6 - x - h} + \sqrt{ 6 -x})}
&& \text{Combine like terms}
\\
\\
\qquad f'(x) =& \lim_{h \to 0} \frac{\cancel{6} - \cancel{x} - h - \cancel{6} + \cancel{x}}{h(\sqrt{6 - x - h} + \sqrt{ 6 -x})}
&& \text{}
\\
\\
\qquad f'(x) =& \lim_{h \to 0} \frac{-\cancel{h}}{\cancel{h}(\sqrt{6 - x - h} + \sqrt{ 6 -x})}
&& \text{Cancel out like terms}
\\
\\
f'(x) =& \lim_{h \to 0} \left( \frac{-1}{\sqrt{6 - x - h} + \sqrt{6 - x}} \right) = \frac{-1}{\sqrt{6 - x - 0} + \sqrt{6 - x}} = \frac{-1}{\sqrt{6 - x} + \sqrt{ 6 - x}}
&& \text{Evaluate the limit}
&&
\\
\\
f'(x) =& \frac{-1}{2 \sqrt{6 -x}}
&&

\end{aligned}
\end{equation}
$


Both $f(x)$ and $f'(x)$ are root functions that are continuous for every positive values of $x$. However, the square root is placed in the denominator of $f'(x)$ making the function defined only for $6 - x > 0$.

$
\begin{array}{cc}
\text{For } f(x) \qquad & \text{For } f'(x) \\
6 - x \geq 0 \qquad & 6 - x > 0 \\
\, \, \, \, \, x \leq 6 \qquad & \, \, \, \, \, x < 6
\end{array}
$


Therefore, the domain of $f(x)$ is $(-\infty, 6]$ while the domain of $f'(x)$ is $(-\infty, 6)$

d.) Graph $f'$ and compare with your sketch in part (b)

What aesthetic features are used in The Great Gatsby to demonstrate the theme "buying love through wealth"?

For all his phenomenal wealth, Gatsby is a deeply insecure man. This is largely due to his humble background, not to mention his past involvement with organized crime. Despite being fantastically rich, he's not one of society's elite and never will be. But because he's so blinded by love for Daisy, he thinks that at some point she'll be so impressed by his opulent displays of wealth that she'll eventually give in and leave Tom to be with him.
Yet she doesn't. Why? Because even in the midst of the Jazz Age, with American society becoming more fluid, less hierarchical, blood still counts. Daisy may weep over Jay's gorgeous collection of fancy shirts, but she's not about to leave Tom and move in with Gatsby any time soon. For all her shallowness, Daisy's still a social snob. She'll gladly attend Jay's legendary parties, partake of his generous hospitality, but what she won't do is be with him on a permanent basis; won't step outside her East Egg comfort zone. And so Gatsby's attempts to buy her love are all in vain.

The theme is demonstrated largely through Gatsby's attempt to appear as lavishly wealthy as possible because he is, of course, obsessed with the prospect of Daisy coming back to him. Since the original bone of contention in their relationship was him not having enough money, he throws extravagant parties with outrageous amounts of money spent on decadent food, drink and entertainment. Gatsby cares nothing for the celebrations themselves, he simply wants to appear as wealthy as possible.
There is no dignity or subtlety whatsoever in Gatsby's approach, and he often seems to be making a great fool of himself. The epigraph at the beginning of the novel brings this in particular to mind. By "wearing the gold hat," Gatsby believes that he needn't have shame or subtlety. As long as he spends enough money, he believes he will have his love.

Gatsby wants to buy Daisy's love through impressing her with his great wealth. He throws his vast parties in the hopes that she will one day show up and be awed. At the opening of chapter three, in a long sequence, Nick describes the preparations for theses parties, showing the vast amounts spent on them. His lyrical description makes the parties seem alluring, beautiful, and vital. I won't quote the entire sequence (to get the full effect, however, you need to read the whole thing), but here is an example:

On buffet tables, garnished with glistening hors d’oeuvre, spiced baked hams crowded against salads of harlequin designs and pastry pigs and turkeys bewitched to a dark gold. In the main hall a bar with a real brass rail was set up, and stocked with gins and liquors and with cordials so long forgotten that most of his female guests were too young to know one from another.

When Gatsby reunites with Daisy for the first time in five years, he is anxious to walk with her (and Nick) over to his mansion next door and show it off to her. He wants to impress her with his belongings. He shows her room after room. Finally, they end up in his bedroom. Gatsby displays his vast number of shirts and begins to toss them out in an beautiful array of colors:

While we admired he brought more and the soft rich heap mounted higher—shirts with stripes and scrolls and plaids in coral and apple-green and lavender and faint orange with monograms of Indian blue.

The imagery around Gatsby's lifestyle is lovely, aesthetically appealing, if also at times faintly garish, but it isn't enough to win Daisy.

What specific advice would Atticus Finch from To Kill a Mockingbird give to Brother from The Scarlet Ibis, and how would Brother react to it?

In a lot of ways, Brother and Atticus are similar characters. They are both patient and hard-working individuals, and neither of them is willing to give up on a situation that the rest of the world sees as a lost cause. Brother refuses to give up on Doodle, and Atticus refuses to give up on Tom Robinson. I think the following quote is likely a piece of advice that Atticus would give Doodle.

"First of all," he said, "if you can learn a simple trick, Scout [Brother], you'll get along a lot better with all kinds of folks. You never really understand a person until you consider things from his point of view . . . until you climb into his skin and walk around in it."

Obviously, Atticus is telling Scout this pearl of wisdom, but it would also apply to Brother. By viewing things from Doodle's perspective, Brother would likely have further patience to handle Doodle's abilities and reactions to situations. Brother is already incredibly patient with Doodle, but he does every now and again fail to consider what Doodle might be feeling. This is most evident when they are running home, and Brother fails to recognize the terror in Doodle's cries. Brother runs off, and Doodle is tragically killed.
I do honestly think that Brother would take the advice quite well. It's advice that he would be craving from an adult since all of the other adults in his life seem to have more or less given up on what potential Doodle might have.

Single Variable Calculus, Chapter 3, 3.4, Section 3.4, Problem 47

Find the limit $\displaystyle \lim\limits_{x \to \pi/4} \left( \frac{1 - \tan x}{\sin x - \cos x}\right)$

$
\begin{equation}
\begin{aligned}
\lim\limits_{x \to \pi/4} \left( \frac{1 - \tan x}{\sin x - \cos x}\right) &= \lim\limits_{x \to \pi/4} \left( \frac{1-\frac{\sin x}{\cos x}}{\sin x - \cos x}\right)\\
\\
&= \lim\limits_{x \to \pi/4} \frac{\cos x - \sin x}{\sin x - \cos x} \left( \frac{1}{\cos x} \right)\\
\\
&= \lim\limits_{x \to \pi/4} \frac{-\cancel{(\sin x - \cos x)}}{\cancel{(\sin x - \cos x)}} \left( \frac{1}{\cos x}\right)\\
\\
& = \lim\limits_{x \to \pi/4} \frac{-1}{\cos x}\\
\\
& = \frac{-1}{\cos \frac{\pi}{4}}\\
\\
& = \frac{-1}{\frac{\sqrt{2}}{2}} = \frac{-2}{\sqrt{2}} && \text{(By rationalizing the denominator)}\\
\\
& = \frac{-2}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}}\\
\\
& = \frac{-\cancel{2}\sqrt{2}}{\cancel{2}} \\
\\
& = - \sqrt{2}
\end{aligned}
\end{equation}
$