int 6/sqrt(10x-x^2) dx Find the indefinite integral

int6/sqrt(10x-x^2)dx
Take the constant out ,
=6int1/sqrt(10x-x^2)dx
Let's rewrite the denominator by completing the square,
=6int1/(sqrt(-(x-5)^2+25))dx
Now apply integral substitution: u=x-5
du=1dx
=6int1/sqrt(-u^2+25)dx
=6int1/sqrt(5^2-u^2)du
Again apply integral substitution: u=5sin(v)
=>du=5cos(v)dv
=6int(1/sqrt(5^2-5^2sin^2(v)))5cos(v)dv
=6int(5cos(v))/(sqrt(5^2)sqrt(1-sin^2(v)))dv
Use the trigonometric identity: cos^2(x)=1-sin^2(x)
=6int(5cos(v))/(5sqrt(cos^2(v)))dv
=6int(5cos(v))/(5cos(v))dv , assuming cos(v)>=0
=6int1dv
=6v 
substitute back v=arcsin(u/5) and u=(x-5)  
=6arcsin((x-5)/5)
Add a constant C to the solution,
=6arcsin((x-5)/5)+C
 

In Miriam Toews' A Complicated Kindness, Nomi talks with her old friend Sheridan, whose “dad had been excommunicated” and whose mother had “gone nuts” and ultimately killed herself. Nomi’s mom thought “Sheridan’s dad should have left town to save his mom the pain of having to pretend he was dead” (37). How does this statement relate to Nomi’s family situation?

The statement relates to what's happening in Nomi's family because it explains why Trudie chose to leave her husband and Nomi. It also explains why every other member of her family chooses to leave. Living in such an oppressive community is difficult and causes them to feel shame and judgement.
Nomi's mother has an affair and is threatened by her affair partner, Mr. Quiring. She wants to end it, so he makes up lies about her and condemns her to the local religious authority. Rather than live with that judgement, Nomi's mother does what she believes Sheridan's father should have done—she leaves. This removes her from the community and, to her mind, helps keep her family safe from judgement.
However, her leaving doesn't stop them from being judged. It only stops Nomi and her father from being judged on Nomi's mother's actions. Nomi is ultimately shunned, and her father leaves rather than ignore her. Nomi is the only one left because her sister, mother, and father are gone.

In the small town of East Village depicted in Miriam Toews' novel A Complicated Kindness, conformity is the rule and the expectation. A strict Mennonite community where certain traditions and customs are expected could be claustrophobic for some, and the youth of Toews' story are among those who chafe at the restrictions and customs to which they are expected to adhere. Nomi, the novel's young protagonist and narrator, is committed to maintaining the unity of her family. Nomi's older sister, Natasha, or Tash, is of an age where she can exercise her freedom to leave, and she promptly does with her boyfriend. The goal of family unity destroyed, Nomi can only wonder, somewhat rhetorically, why her parents failed so miserably:

"Why was Tash so intent on derailing our chances and sabotaging our plans to be together for goddam ever and why the hell couldn't my parents see what was happening and rein that girl in."

Tash, however, needed to escape and did. The strictures of the Mennonite community are too much for her to endure, so she leaves with Ian, her boyfriend, for the more carefree lifestyle of California. Furthermore, Nomi's mother is chafing to conform and senses that she is failing in that regard, which, as we learn, prompts her departure, leaving only Nomi and her father, Ray.
Which brings us to Nomi's observation regarding her mother's comment about Sheridan's father, that "...Sheridan's dad should have left town to save his mom the pain of having to pretend he was dead." Sheridan's father is not one of the town's more upstanding citizens, having been, Nomi points out, "excommunicated" from the Mennonite Church. In short, both Sheridan and Nomi are members of dysfunctional families, and efforts at adapting one's temperament and ambitions to the restrictions of this community's lifestyle are doomed to fail. Much better, the quote suggests, for the more dysfunctional among us to disappear than to try to fit in where conformity is highly unlikely to prevail, with the strains on those to whom we are closest that entails.

Explain the political and religious environment in Europe during the 16th and 17th centuries. How were these events represented in art, literature, and political thinking?

The sixteenth century saw Europe in the throes of the Reformation, while the seventeenth century saw Europe make great strides in the realm of science, politics, philosophy, and technology.
First, we will discuss the Reformation, which began with the publication of Martin Luther's 95 theses in Germany. His ideas about the religious purification of the Catholic Church were met with resistance from the leaders of the church. Luther was eventually excommunicated, but his daring ideas about God and religion spread throughout Europe. 
Inspired by Luther's boldness, the Frenchman John Calvin founded Calvinism, a branch of the Christian faith which championed the theology of predestination. In Switzerland, Ulrich Zwingli spearheaded the Swiss Reformation while King Henry VIII began his own church in England (albeit for self-serving reasons). At the time, King Henry VIII wanted to marry his mistress Anne Boleyn, but the Catholic Church refused to allow him to annul his marriage to the Catholic Queen Catherine.
King Henry's response was to sever all ties with the Catholic Church; it was he who founded the Church of England. After his death, the Catholic Queen Mary (daughter of Queen Catherine) reigned during a short period known as the Counter-Reformation in Europe. Although Jesuit theologians pushed back against the efforts of Luther, Zwingli, and Calvin, they could not stem the tide of Protestantism. Northern Europe became largely Protestant in the sixteenth and seventeenth centuries.  
In England, the Protestant tradition continued with King Henry VIII's daughter Elizabeth; her reign began around 1559. Elizabeth presided over the golden age of the English Renaissance, which saw tremendous works of literature produced by acclaimed authors as William Shakespeare, Christopher Marlowe, John Milton, and Edmund Spencer. At this time, it must be noted that Reformation artists largely rejected the iconographic nature of Catholic art. 
During Elizabeth's reign, famous English explorers such as Sir Walter Raleigh and Sir Francis Drake sailed the seas, traded with foreign powers, and founded colonies. In the sixteenth century, the works of Italian masters Michelangelo, Leonardo da Vinci, and Raphael exemplified the clarity and meticulous precision of the classical tradition.
The High Renaissance period saw the revival of humanism and a renewed reverence for the Greek and Roman classical traditions in architecture, sculpture, and painting. Quite simply, late Renaissance art in the sixteenth century was inspired by the humanist ideals of naturalism and authenticity. Naturalists did not try to hide the blemishes of the human body; instead, these were accepted and celebrated.
In the seventeenth century, men like Newton, Descartes, Galileo, and Kepler spearheaded the Scientific Revolution. Galileo introduced his famous laws of motion, Kepler introduced his laws of planetary motion, and Newton introduced his law of universal gravitation. The seventeenth century also came to be known as the Age of Reason. During this time, Thomas Hobbes and John Locke developed modern political thought. Hobbes wrote Leviathan, and Locke wrote Two Treatises of Government; the works of both men greatly influenced the French and American revolutions.
Locke's works are classified as Restoration-era literature. Other Restoration works you may recognize are John Bunyan's Pilgrim's Progress, John Milton's Paradise Lost, and John Dryden's Absalom and Achitophel. The religious and political developments of the seventeenth century greatly influenced the art and literature of the time. Increased focus on themes such as democracy versus monarchy were common, and new ideas like empiricism increased in importance: Restoration literature.
Also, read about the characteristics of Restoration-style art.
https://www.artyfactory.com/art_appreciation/art_movements/italian-renaissance/italian-renaissance-art-humanism.html

https://www.history.com/topics/reformation

https://www.radford.edu/rbarris/art216upd2012/Raphael%20and%20Leonardo%20S11.html

What analysis would you give for the following quotes: " 'tis too much! by far too much. I do not deserve it. oh! why is not everybody as happy" and "her petticoat, six inches deep in mud"?

Louisa Hurst, Mr. Bingley's married sister, remarks on the appearance of Elizabeth Bennet's petticoat when Elizabeth arrives at Netherfield to check on her sister's health. Elizabeth has walked some three miles to get there rather than take the carriage, a more proper mode of transit for young women. Louisa laughs at Elizabeth, mocking her behind her back for her untidy appearance. Louisa and her sister, Caroline, think Elizabeth's behavior is shocking and improper, while their brother thinks that she looked quite healthy and well when she arrived. He applauds her affection for Jane. Louisa and Caroline care a great deal more about appearances and what is proper, and they care less about sisterly love and affection. Their relationship seems to be predicated on shared shallowness rather than common depth of feeling (as Elizabeth's and Jane's relationship is). This scene does a good job of showing the difference—as if we didn't already know—between the Bennet sisters and the Bingley sisters.
The other line is spoken by Jane Bennet after she has received and accepted Mr. Bingley's marriage proposal. This quotation shows her plainspoken sweetness by conveying three things: she's thrilled to be engaged to the man she truly loves, she feels unworthy of experiencing so much happiness, and she wishes that everyone in the world could feel as happy as she does. We see Jane's loving nature, her humility, and her goodwill toward humanity, all wrapped up in a line. This is her character in a nutshell.

What are some metaphors in Othello?

A metaphor is a comparison that does not use the words "like" or "as."
In act 1, scene 1, Iago tries to incite Brabantio to fury over the elopement of Othello and Desdemona by telling him,

an old black ram is tupping your white ewe

In this instance, Iago is comparing the Othello to a black ram and Desdemona to a white female sheep. The animal metaphors are Iago's way of trying to make the union between the newlyweds seem sordid and bestial.
By act 4, scene 2, Othello has been worked into a frenzy, through Iago's manipulations, into thinking Desdemona has been sleeping with Cassio. He uses heightened language that reflects his emotional distress as he addresses Desdemona. He likens her to a weed, saying, "O thou weed." He then likens her white skin to the light paper in a book and her body to a "goodly book," asking if such pure paper (Desdemona's flesh) were made to become a whore:

Was this fair paper, this most goodly book,
Made to write “whore” upon?

In act 5, scene 2, Emilia is very angry that Othello has killed Desdemona. Emila says,


Oh, the more angel she,
And you the blacker devil!

Here, she uses a metaphor to compare Desdemona to an angel and another one to compare Othello to the devil, playing on traditional (and racist) notions of angels as wearing white and devils as black, again a reference to race as well as Emilia's opinion of their respective characters.

In act I, scene 1, Iago tells Roderigo to yell with great abandon at Desdemona's father's house to waken him. He says, "Do, with like timorous accent and dire yell/ As when, by night and negligence, the fire/ Is spied in populous cities." Using a metaphor, Iago compares the yell Roderigo is supposed to make to the yell people make to warn others of fire in cities. In other words, Roderigo is supposed to make a very loud and powerful yell.
Later, in act II, scene I, Iago, describing women, says to Emilia, "You are pictures out of door, bells in your parlors, wild-cats in your kitchens, saints in your injuries, devils being offended, players in your housewifery, and housewives in your beds." In this speech, Iago uses a series of metaphors, or comparisons. He likens women to pictures (or pretty compositions) when they are outside and to bells that make a lot of noise inside. He compares women to wild cats when in their kitchens, to saints when they are injured, and to devils when they are offended. When they are doing chores, they are "players" who do not take things seriously, and they are tarts in bed. This series of metaphors describing women is far from complimentary and could be considered misogynistic. 
In act II, scene 3, Othello says to Desdemona, "The purchase made, the fruits are to ensue: That profit’s yet to come ’tween me and you." In this speech, Othello compares his marriage to a sale. Now that he has purchased Desdemona, he can enjoy what he has purchased, which means his ability to sleep with Desdemona. He clearly treats her like goods that he has bought and can treat any way he wishes.

Was the snake dead in the poem "The Snake" by D.H. Lawrence?

The snake in Lawrence's poem is very much alive when we first encounter it. The snake is before the speaker at the water trough, sipping the water; it "sipped with his straight mouth" and forced the speaker to wait "like a second comer" for the use of the water trough himself. The snake in this poem has no time to spare for human supremacy but makes use of the water trough as he pleases.
Later in the poem, the speaker feels that he should kill the snake, although he does not want to. However, when he throws something at the snake—"I think I did not hit him"—the snake withdraws into a "dreadful hole" still alive, and the speaker feels grateful in reality that he did not kill the snake, "one of the Lords of life," because he had not really wanted to kill it in the first place and only made aggressive overtures towards it because he felt he should.

College Algebra, Chapter 5, 5.5, Section 5.5, Problem 26

Determine the temperature after 10 min and illustrate by graphing the temperature function. Suppose that a kettle full of water is brought to a boil in a room with temperature $20^{\circ} C$ . After 15 the temperature of the water has decreased from $100^{\circ} C$ to $75^{\circ} C$.




Recall the formula for radioactive decay

$m(t) = m_0 e^{-rt}$ in which $\displaystyle r = \frac{\ln 2}{h}$

where

$m(t)$ = mass remaining at time $t$

$m_0$ = initial mass

$r$ = rate of decay

$t$ = time

Based from the given, we can see that



$
\begin{equation}
\begin{aligned}

Ts =& 20^{\circ} C
\\
\\
T(15) =& 75^{\circ} C
\\
\\
D_0 =& 100^{\circ}C - 20^\circ C = 80^\circ C

\end{aligned}
\end{equation}
$


So,


$
\begin{equation}
\begin{aligned}

75 =& 20 + 80 e^{-k(15)}
&& \text{Subtract each side by } 20
\\
\\
55 =& 80 e^{-k (15)}
&& \text{Divide each side by } 80
\\
\\
\frac{55}{80} =& e^{-15 k}
&& \text{Take $\ln$ of each side}
\\
\\
\ln \left( \frac{55}{80} \right) =& -15 k
&& \text{Recall } \ln e = 1
\\
\\
k =& - \frac{\displaystyle \ln \left( \frac{55}{80} \right) }{15}
&& \text{Divide each side by } -15
\\
\\
k =& 0.0250
&&

\end{aligned}
\end{equation}
$



Therefore, the temperature function will be

$T(t) = 20 + 80 e^{-0.0250 t}$

The temperature after another 10 min is $t = 25$ min, so


$
\begin{equation}
\begin{aligned}

T(25) =& 20 + 80 e^{-0.025 (25)}
\\
\\
T(25) =& 62.84^{\circ} C

\end{aligned}
\end{equation}
$


Hence, the graph is

What are the similarities between the Creature and Captain Walton?

The creature and Captain Walton are both characters who tend to feel things very deeply, and they have both been significantly affected by the life and history of Victor Frankenstein.  The creature began his life, he says, as a benevolent and kind being who took great pleasure in nature and humanity.  Captain Walton likewise began as a highly sensitive and emotional being -- he'd wanted to be a poet, though he had no training or education -- and he is very much alive to the beauties of nature, especially as he travels north and is greatly affected by the polar scenes around him. 
In addition, both the creature and Captain Walton are highly persistent individuals who will go to the furthest lengths to achieve their goals.  For the creature, that meant acquiring a mate, and, when that pursuit proved impossible, he turned Frankenstein himself into a companion of sorts by rendering his maker utterly alone and desirous of revenge.  For Captain Walton, he braves death in order to seek the pole and discover the secret of the compass and so forth.  Both are dedicated to their pursuits, whatever those may be.

In The Grapes of Wrath, what is the significance of animal imagery?

In Steinbeck's wonderful novel The Grapes of Wrath, the author frequently uses animals as symbols for the state of well-being of the family members; there are many examples of this throughout the novel, and the animals more often than not symbolize struggle.
One example can be found in the cat that lives at the Joad farm. When Tom returns home from a stint in prison, he finds that the farm is almost entirely abandoned apart from the cat. The cat refuses to go near Tom, for it has become entirely independent in its means of survival. It can no longer rely on others—for it had surely stopped receiving food once the people left—and thus it's forced back to pursue its primal nature as it turns "directly to one of the little piles of rabbit entrails on the ground."
Another example of animals acting as symbolism for the Joad family's struggles is the dog that gets run over by the truck. After a gruesome and painful death, Pa admits that there was no true way to be able to feed the dog. The dog's death is cruel, unexpected, and wholly grotesque, yet the death ends the struggles that the dog would have faced. In a sense, the dog shows the desperation of the family while also symbolizing the cruel, dangerous nature of the outside world.

Please explain to me the meaning of the quote, "Freedom and slavery are mental states."

This is something Mahatma Gandhi said and its context is:

The moment the slave resolves that he will no longer be a slave, his fetters fall. He frees himself and shows the way to others. Freedom and slavery are mental states. Therefore, the first thing is to say to yourself; ‘I shall no longer accept the role of a slave. I shall not obey orders as such, but shall disobey them when they are in conflict with my conscience.’

Gandhi was the leader of the Indian movement for independence from British rule. He advocated the use of non-violent techniques and he strongly influenced Martin Luther King, Jr.'s leadership of the Civil Rights movement in the U.S.
A person's physical context may have little or nothing to do with their psychological context. Humans have the opportunity to choose responses to others, including those who would be oppressive. All the authority in the world cannot stop each individual from making this choice. People can obey oppressive authority or we can respectfully choose not to obey it. 
There are many good historical examples of individuals making this choice. For example, resistance against Hitler and the Nazis rose quickly in Europe and a significant number of people chose not to obey the Nazis. In the U.S., those who ran the "Underground Railroad" and thus freed slaves opted to break laws both in the north and the south in order to set people free.
Later, during the Civil Rights movement in the U.S., Rosa Parks continued to sit where she was on a bus despite a driver ordering her to the back. She did not act oppressed; she acted as though she had the freedom and ultimately her actions in concert with the actions of others, won that freedom. 
 
In China, Nien Cheng was imprisoned during the Cultural Revolution but she chose how she responded to her captors. For example, instead of reading Mao's Little Red Book, she would reconstruct in her mind poetry she had learned as a young person. Her mind was free even if her body was captive. 
The human mind is powerful and can transcend the worst of circumstances. Human beings have to keep remembering that there is a choice: we can cooperate with oppression or choose to be free. That is what Gandhi meant. 
https://en.wikipedia.org/wiki/Mahatma_Gandhi

https://en.wikipedia.org/wiki/Rosa_Parks

What characteristics of Wilfred Owen's poetry changed after his experience in the war?

The main characteristics of Owen's poetry show the results of the poet's own trauma, both physical and emotional, while serving in World War I. Owen was wounded multiple times and experienced what was then called "shell shock" and is now known as Post-Traumatic Stress Disorder (PTSD). The poetry for which he is principally known today was written in the last year of his life and published only after his death. Poems such as "Dulce et Decorum est" and "Strange Meeting" express the horror of the battlefield and the senselessness of war.
British soldiers, like their American allies who joined them in the last two years of the war, had been encouraged to enlist based on a need to safeguard freedom and democratic values. The actual experience of the war was disillusioning to most of these men. The casualties were enormous, and new methods of warfare such as the use of poison gas made conditions even more horrific than in previous wars. There were incompetent battlefield commanders who made tactical blunders, sending waves of troops against entrenched enemy positions and causing a massive number of deaths and injuries. As in the American Civil War fifty years earlier, the firepower and accuracy of the weaponry had gone beyond what battlefield tacticians were able to deal with. The European commanders had learned little in the period from the middle of the nineteenth century to the Great War.
The horrifying conditions in the field made Owen and millions of others feel they had been tricked by their country into serving in a useless, futile cause. "Dulce et Decorum est" derives its title from a line of the Latin poet Horace, meaning "it is sweet and fitting to die for one's country" (dulce et decorum est pro patria mori). Owen quotes it ironically, saying that given the condition of men gassed on the battlefield, if the leaders could see this, they never would have told men to fight and die for the homeland. In "Strange Meeting" the speaker encounters a dead soldier who talks to him and finally reveals that "I am the enemy you killed." The poem "Disabled" tells of a hospital ward in which men who have been maimed in battle are suffering, without hope of any kind.
Owen himself was killed in battle only a week before the Armistice in 1918. His fate was thus similar to that of Paul, the disillusioned German soldier in the novel All Quiet on the Western Front, who is killed shortly before the war's end.

Answer the following: A) The narrator of "Our Society at Cranford" by Elizabeth Gaskell is (a) second person limited (b) first person limited (c) third person limited (d) third person omniscient B) The tone of Matthew Arnold's poem "Dover Beach" is (a) happy (b) secretive (c) dark and bleak (d) excited C) In "The Windhover," by Gerard Manley Hopkins, the line "/dom of daylights' dauphin, dapple-dawn-drawn Falcon..." has (a) alliteration (b) onomatopoeia (c) anaphora (d) personification D) a portmanteau word is (a) a word made up of two words (b) a suitcase (c) a synonym for alliteration (d) personification

The student's question specifies the text of "Our Society at Cranford" by Elizabeth Gaskell. For purposes of discussion, it will be presumed that the assigned text was Chapter 1 of Gaskell's classic of 19th Century literature, Cranford, which is titled "Our Society." Cranford had its origins in a series of short stories written incrementally that were subsequently formed into a single novel. That opening chapter, "Our Society," as the title suggests, provides a descriptive narrative of the fictional town of Cranford in Gaskell's native England. One need not read too far into this chapter to identify the form of narrative the author employed in her story. On the second page of Chapter 1, Gaskell's narrator, Mary Smith, states:

"I can testify to a magnificent family red silk umbrella, under which a gentle little spinster, left alone of many brothers and sisters, used to patter to church on rainy days. Have you any red silk umbrellas in London? We had a tradition of the first that had ever been seen in Cranford. . ."

The use of the words "I" and "We" clearly suggest that the author of the novel in question employed first-person limited narration. In general, first-person limited narration is used by authors wishing to tell a story form the narrator's perspective. The "limited" element suggests that the narrator is able only to provide observations and suggestions, but cannot, logically, see inside the minds of the other characters, thereby "limiting" the first-person perspective. Mary Smith is not a god or a seer capable of reading minds, therefore the form of narration used is first-person limited.
The second question posed by the student regards the tone of Matthew Arnold's poem "Dover Beach."  Unlike Gaskell's opening chapter, in which a perfunctory reading of the opening passages suffices to identify the type of narration employed, Arnold's poem requires a thorough reading in order to identify the tone. And, that tone is decidedly dark and melancholy, evident in the author's use of phrases and words such as "eternal note of sadness," "Of human misery," "the melancholy, long, withdrawing roar," and ""And we are here as on a a darkling plain."  One could be forgiven for rushing to judgment with regard to Arnold's tone. "Dover Beach" begins with a somewhat calming demeanor, noting that "The sea is calm tonight," and that "the moon lies fair Upon the straights," and so on. By the end of the first stanza, however, the tone has taken an unambiguous turn from serenity to sadness. The answer to the question, then, is "C," "dark and bleak." Spend enough time in England, and one cannot help but appreciate the poem's tone.
If one were forced to categorize the full text of Gerard Manley Hopkin's "The Windhover," it would present a more challenging case than with Arnold's poem. The reason for the difficulty of answering would be that it does not include option (e) All of the above. Alliteration, onomatopoeia, anaphora and personification can all be said to exist in "The Windhover." As the student specifies only one line, however, the task is rendered considerably more simple. That line reads as follows: "dom of daylight's dauphin, dapple-dawn-drawn Falcon . . ." That's it; neither the text immediately before nor that which follows are included in the student's question. For that reason, the answer is (a) alliteration. The phrase clearly fits within the definition of "alliteration" because of its repetitive use of the letter "d" for each word in that line except for "of" and "Falcon." As the definition of "alliteration" is precisely that--the repeated use of the same consonant at the beginning of adjacent or closely-connected words--alliteration is clearly the proper answer.
The student's final question, 'what is the definition of "portmanteau",' can be answered as (a) "a word made up of two words." 

Single Variable Calculus, Chapter 2, 2.5, Section 2.5, Problem 27

Explain using theorems of continuity why the function $F(x) = \sqrt{x} \sin x$ is continuous at every number in its domain. State the domain

We can rewrite
$\quad F(x) = g(x) + h(x)$ where $g(x) = \sqrt{x}$ and $h(x) = \sin x$
Both of the functions $g(x) = \sqrt{x}$ and $h(x) = \sin x$ are examples of the functions that are continuous on every number on its domain. $h(x) = \sin x$
has a domain of $(-\infty, \infty)$.

However, $g(x) = \sqrt{x}$ is defined only for its domain $[0, \infty)$,

Therefore,
$\quad$ The domain of $F(x)$ is $[0, \infty)$

What smells affected Isabel? In other words, what smells reminded her of something?

Isabel smells a lot of different things throughout Chains.  Anderson does a nice job of hitting that sense for readers.  It's the second part of the question that greatly focuses this question.  The smell has to trigger some kind of memory in Isabel.  
The first time that a smell triggers a memory for Isabel is in chapter nine.  She has been asked to wait upon Master Lockton and his friends while they discuss how to best bribe Patriot soldiers.  Isabel is asked to bring the men some jam at one point.  As the men begin spreading the apricot jam, Isabel tells readers that the smell of apricots reminds her of the orchards near Miss Mary's house.  That's a nice memory for Isabel.  
The smell of rose-scented soap is not a nice memory for Isabel though.  That smell reminds her of Madam Lockton.  
Near the end of the book, Isabel tells us that the smell of fresh-cut hay reminds her of home.  

Why do the patients in the hospital cause John to shudder when he looks at them?

The hospital patients in Brave New World cause John to react this way due to the clinical, unemotional setting in which they rapidly head toward death under the influence of soma. Death is treated casually and cheerfully in this world, while John's limited experiences and emotional development, combined with his exposure to intense emotions and tragic moving death scenes via the works of Shakespeare, inspire in him high expectations of what his mother's death should entail. John wants to vividly feel love for her and heavily experience the impending loss: an ideal completely at odds with the scene unfolding around him in which Delta children are desensitized to death at a young age so that they will never fear or be moved by it. This childhood indoctrination is repugnant to John, as is the matter-of-fact manner in which the children and nurse accept his mother's passing.

Wilfred Owen tells of "horror" in his poem "Dulce Et Decorum Est." Explain what he means by this "horror."

Although the word "horror" is absent from the poem, Wilfred Owen describes the horror of war through a series of images.
In the first stanza, a group of fellow soldiers are returning from battle. They are emotionally and physically exhausted. Many of these soldiers have lost their boots, and as a result, their feet are bleeding. This is already a depressing scenario, but there is more to come in Stanza Two.
Stanza Two is when the "horror" begins. As the soldiers are making their way home, gas shells explode all around them. The men frantically pull on their gas masks, but one man is seen "yelling out and stumbling." Owen doesn't tell us whether the soldier is missing his mask or is simply too slow in pulling his mask on. In this stanza, the poet talks about the soldier "drowning" under a "green sea." The green color very likely refers to chlorine gas, which was used during World War One (the setting of the poem).
The third stanza describes the soldier's excruciating death from gas poisoning:

In all my dreams before my helpless sight,
He plunges at me, guttering, choking, drowning. 

The "horror" comes from both the manner of the soldier's death as well as its reoccurring image in the form of flashbacks in the poet's mind. The poet is forever haunted by this disturbing imagery. He will never be free from the terror of such a moment as long as he lives. Essentially, the "horror" is replayed in his mind over and over again.


...watch the white eyes writhing in his face, 
His hanging face, like a devil’s sick of sin; 
If you could hear, at every jolt, the blood 
Come gargling from the froth-corrupted lungs, 
Obscene as cancer, bitter as the cud 
Of vile, incurable sores on innocent tongues--

During World War One, soldiers who were exposed to chlorine gas died very painful deaths. The poison gas caused burning eyes, vomiting, intense stomach pain, severe headaches, and "incurable sores" on tongues. In other words, the last stanza perfectly describes the "horror" of such a death. Eventual demise comes from what is called asphyxiation or suffocation.
 
The poet portrays war as a thing of horror. He explains that too many people quote the phrase Dulce et decorum est Pro patria mori (It is sweet and fitting to die for one’s country) without truly understanding the consequences of war. Through a series of disturbing images, the poet reinforces the human suffering that has been caused by war.
 

 
http://www.vlib.us/medical/gaswar/chlorine.htm

How was "Sinners in the Hands of an Angry God" effective and ineffective? How would you react?

"Sinners in the Hands of an Angry God" was outrageously effective in regard to the mindset of the Great Awakening. In fact, the sermon is often cited by theologians and historians as the most important of that period. Edwards is said to have been interrupted several times during his sermon by moaning congregation members, begging him to tell them what to do in order to be saved. The sermon was largely effective due to the sheer outrage in Edwards's tone and his imagery of hell. Edwards was condemning the air of hypocrisy, the going-through-the-motions brand of Christianity that had festered before the Great Awakening took place. The sermon marked a stroke of rhetorical genius, essentially saying, "If this is what you believe, this is what's waiting for you." Furthermore, the beat and dynamic rhythm of the speech likely struck fear into the hearts of the audience. Edwards brilliantly simulated the shock and cacophony of hell by sporadically adjusting his tone. In regards to how it was ineffective, the only way that it could be considered as such is outside the world of Christianity. To everyone who held the same literal belief in an afterlife of punishment, the sermon made an incredibly lasting impression. As for myself, though my religious beliefs are certainly different from Edwards, the sermon would have made quite an impression on me even without inspiring fear of an eternal hell.

Edwards's famous sermon was incredibly effective if the immediate reaction of his audience is anything to go by. It's no exaggeration to say that many of his auditors were absolutely terrified at his lurid, detailed descriptions of the terrible fate that awaits sinners in the raging flames of hell. It's no wonder that a number of audience members actually fainted in horror.
Even those who managed to remain upright throughout the entire course of Edwards's sermon would have been given much food for thought. Edwards intended to make people think deeply about their lifestyles, whether they were behaving as God-fearing Christians should. He wanted nothing less than to change people's lives for the better, and there's no doubt that many people did indeed heed his word and set themselves on a different path in life.
However, what Edwards had to say wasn't universally accepted. Although just about everyone in America at that time believed in God, not everyone believed that he was the kind of wrathful, vengeful law-giver as presented in the Old Testament. Nor did they believe that hell was a literal place reserved for sinners. That being the case, Edwards's hellfire and brimstone rhetoric would have had no effect on large swathes of the population.
As for myself, Edwards's sermon would've had no effect on me either as his religious beliefs were radically different to mine. (And that's putting it mildly.) Nevertheless, I would still have appreciated his famous sermon as a tour de force of rhetorical brilliance. And that is why, over 250 years later, "Sinners in the Hands of an Angry God" is still pored over, studied, and examined by countless individuals over whom Edwards's Calvinist theology holds no sway.

Accounts of the reception of Edwards's sermon that day in 1741 maintain that some in the congregation cried out, some fainted, and some wept. In the short term, it is plausible to assume it shook people up and made them reexamine the ways they were living and thinking about their afterlife. In that way, it could be deemed effective.
It could be said that Edwards's sermon, perhaps a centerpiece of the Great Awakening in the 1730s and 40s, did little to staunch the flow of people abandoning the vestiges of Puritan thought present in his theology. In that way, it was ineffective. As more people came to the colonies, many for reasons unrelated to religious freedom, what came with them were other ways of worship and attitudes toward the role of religion. The Enlightenment greatly influenced the rise of rational thought, and Deism became a more comfortable way for some to think about God.
The last part of your question is more difficult to answer; it's not easy for a person of the 21st century to fully understand the outlook of a person who would have attended this sermon. Since you asked, though, I would say the sermon would be a turn off for me.

What does Piggy like about himself in the novel Lord of the Flies?

Piggy is the novel's most intelligent character who is continually ridiculed by the other boys because of his weight, asthma, and whiny attitude. Although Piggy struggles to become friends with the boys, he considers himself to be Ralph's biggest supporter. Throughout the novel, Ralph does not consider Piggy a "friend," but he does defend Piggy when others attempt to bully him. As the novel progresses, Ralph loses respect from the majority of the boys, but Piggy remains loyal. In Chapter 8, Ralph and Piggy are discussing how their makeshift society has broken down, and Ralph asks Piggy what makes things break apart. Golding writes, "When he understood how far Ralph had gone toward accepting him he flushed pinkly with pride" (140). Piggy likes the fact that Ralph has begun to rely upon him and views him favorably. Piggy is proud that he was the first boy to follow Ralph and remains loyal to the chief. Piggy also believes that he has good ideas. Piggy recognizes the fact that he is intelligent. When the other boys agree with his ideas, he feels a sense of pride. In Chapter 8, Piggy mentions that they should move the signal fire from the mountain to the platform. When everyone agrees, Piggy feels satisfied and proud of his contribution.

How did the sun look when it came out after the rain stopped?

The sun looks marvelous to the children who have never seen it before. The narrator likens it to many things. It looks like "blazing bronze" against a sky that looks to the children like a blue tile. It feels like a warm iron on their faces. They compare it to the sunlamps they have known almost all their lives and think it is much better than those. They stare up at it, amazed at its yellowness.
Bradbury tries to capture and convey how children who never remember having seen the sun experience it. They have no context so can only compare it to the things they know from the tunnels they have lived in most of their lives: they compare it to items such as irons. They seemed to be primarily amazed by its vividly bright colors, as they have lived so long in a gray universe.

In "The Stolen Party" by Liliana Heker, how do expectations related to one's gender affect the characters' actions? What cultural values are revealed by the characters' actions that are dictated by gender expectations?

In the story, gender-related expectations seem to affect the actions of some characters. For example, the magician chooses to call upon a boy to participate in one of his tricks. When the boy becomes frightened and loses his hold of the monkey, the magician chides him for his "unmanly" behavior. The boy is perplexed by the magician's meaning, so the magician explains that "unmanly" conduct is "sissy" behavior. Essentially, a sissy is a boy or man who exhibits cowardly or effeminate behavior.
The magician initially chooses the boy because of his expectation that a boy would be more adept at handling a monkey. When the boy becomes frightened, however, he unintentionally invalidates the Hispanic cultural value of machismo, where males are expected to be dominant, active, and fearless. This type of machismo also fuels the independent and competitive spirit of males in Hispanic culture, where the greatest offense against manhood is the failure to act like a man.
We can see this in the story when the boys proclaim their collective desire for Rosaura to join their team for the game of charades. The boys are focused on winning; they are naturally competitive. Any possible embarrassment in having a girl on the team is subordinate to the desire to win. Success is seen as the result of male competence, and it is a measure of masculine worth in Hispanic culture. In contrast, females in Hispanic culture are expected to be submissive, patient, and yielding in nature. Although there are other girls at the party, Rosaura is the only one who dares to challenge the prevailing social norms. She wins the sack race and is far ahead of the competition during the game of tag. Additionally, the boys clamor for her to be on their team.
On the other hand, the girl with the bow exemplifies all that is expected of females in Hispanic culture. At surface level, she personifies all that is feminine and attractive in a young girl. However, her attitude towards Rosaura demonstrates her deep insecurity; to her, Rosaura represents an anomaly in the existing order of things. Yet, because of prevailing social expectations, females in Hispanic culture must avoid revealing their aggressive tendencies to others. So, the girl with the bow uses a passive-aggressive strategy to obliterate what she sees as a threat to her comfortable world; her veiled aggression takes the form of social exclusiveness. She uses her words and attitudes to convey to Rosaura the latter's social and material deficiencies.
This method of excluding female competitors from a social circle is a form of feminine violence. It is only practiced because females believe that they have little recourse in destroying potential threats to their social position. The girl with the bow sees Rosaura as a threat because Rosaura's outward appearance matches her own, despite the fact that Rosaura is merely the housekeeper's daughter. On the surface, Rosaura looks no different from the girl with the bow. However, the latter interprets Rosaura's confidence and self-possession as ambition, and she sets out to put Rosaura in her place.
In all, gender expectations are based on cultural values. From the examples above, it is clear that gender expectations that are fueled by rigid cultural values often result in dysfunctional forms of coping. 
 
 

What would be an example of a scenario or conversation between a therapist who is treating someone who has histrionic personality disorder with a psychodynamic approach?

Since DSM-III (Diagnostic and Statistical Manual of Mental Disorders, Third Edition), hysterical personality disorder has been known as histrionic personality disorder. Individuals who suffer from this disorder enjoy being the center of attention. In fact, they thrive on being dramatic or provocative in their behavior, all for the purpose of gaining the attention they crave from others. The psychodynamic approach would address self-esteem issues resulting from past conflicts or emotionally-stifling experiences. A therapist using such an approach may seek to address the patient's incomplete resolution of the oral or Oedipal stage. Freud stated that infants should get adequate and regular oral stimulus at this early stage, whether it's through breastfeeding or the bottle. He believed that infants who lacked adequate and regular stimulation at the oral stage would be at a disadvantage; they could not then advance to the next developmental stage (the anal stage). Essentially, a patient who was neglected at this stage in life would mature into an adult who seeks constant validation of his/her worth from others. Such an individual may also be a good manipulator, intent only upon securing the praise and adulation he/she desires.
Psychodynamic therapy would focus on how the patient's unconscious processes affected his/her actions. Therapists who use this approach believe that a thorough and honest evaluation of past conflicts or undesirable experiences would help patients understand how the past affects the present. The idea is that, once patients receive clarity or insight about unresolved, past conflicts, they will be able to live happier and more constructive lives.
So, a possible scenario surrounding such an approach to histrionic personality disorder is:
1) Brief therapy sessions with one major focus for each of the sessions, rather than traditional, longer sessions where the patient freely discusses any and all topics he desires. Sessions may range from between 25-40 sessions.
2) In the first or second sessions, the therapist brainstorms with the patient and discusses what the central topic will constitute. Doing this allows the therapist to address the patient's most pressing issues during therapy sessions. At this early stage of the therapy process, the therapist can help the patient identify the main issues and map out a goal for the sessions.
3) Sessions may incorporate different therapeutic techniques to achieve the main goals of the treatment. For example, the therapist may use what is called dream analysis (favored by many who advocate the psychodynamic approach). During initial sessions, the therapist may ask the patient to write down the recent dreams he/she has had. Usually, these dreams are challenging to the patient in the sense that they are frightening or disturbing in nature. After the patient writes down these dreams, the therapist will help the patient interpret the dreams. Here, the therapist hopes to uncover the disguised, latent content of the patient's dream, so he can help the patient process his repressed feelings.
4) In other sessions, the therapist may use transference analysis to help the patient understand his unconscious habits. For example, the patient may experience difficulty in relating to women. The therapist can help the patient uncover the reasons for this. Perhaps, the patient had a very difficult relationship with his own mother. So, he relates to women today in the same way that he related to his mother in the past. Transference analysis can help this patient discover why he finds it difficult to communicate clearly and effectively with women.
5) In some sessions, the therapist may use the Core Conflictual Relationship Theme (CCRT) to address how childhood experiences continue to affect the patient today. Most importantly, the therapist will address how and why the patient is unaware of these influences. The above is an example of a likely scenario between a therapist and a patient in psychodynamic-structured therapy sessions.
https://psychcentral.com/disorders/histrionic-personality-disorder/

https://www.ncbi.nlm.nih.gov/books/NBK64952/

Explain how race impacts the novel Monster.

Race plays a decisive role in the novel, but it is not necessarily front and center throughout the story. The only time the unsaid prejudices are brought up is when O’Brien, Steve’s lawyer, tells him his race could make people think he is automatically guilty. O’Brien says that despite reminding the jury that Steve is supposed to be presumed innocent, she believes that he is considered guilty by many of them,

Well, frankly, nothing is happening that speaks to your being innocent. Half of those jurors, no matter what they said when we questioned them when we picked the jury, believed you were guilty the moment they laid eyes on you. You’re young, you’re black, and you’re on trial. What else do they need to know?

When O’Brien says “frankly” she means it—this is the only time race is explicitly mentioned in the text as a means by which people view Steve. Otherwise, it goes unspoken but acknowledged in other ways. For instance, when Petrocelli, the prosecutor calls both Steve and King “monsters” during the opening statement. The use of the word “monster” is something that sticks to Steve because it implies that he isn’t human.
The use of language to dehumanize African Americans is a practice nearly as old as America itself. While the argument could be made that Petrocelli would refer to white murders, in the same way, history bears out that it would be unlikely. The truth is that race plays a significant role in not only Steve’s trial but also how he is linked to and portrayed by the case. The prosecution links Steve to King and Evans, who committed the murder because he is black and looks like them. The prosecutor uses that to link Steve to the others in the mind of the Jury.
Race also affects how Steve’s defense is built. Steve makes his case by establishing doubt that he was even there or involved, the other part is built on presenting Steve as an upstanding young man—to try and erase the innate prejudice of the jury. Steve’s defense seeks to distance him from King, while the prosecutors use race to tie him to King.

Race impacts the characters in Monster—especially Steve—because it is something that has a major effect on how people see him.
After jury selection, Steve's lawyer tells him that half the people they could have selected for the jury would have already believed him guilty. One of the reasons he gives for this is that Steve is black. If he was white, they'd be less likely to automatically assume he took part in the crime. His race is a characteristic that makes the trial more difficult for him because many are predisposed to see him as a criminal—before they know anything about him.
It isn't only the potential jurors who find Steve suspicious. His lawyer is also unsure as to whether or not his own client is innocent. Part of the reason that he distrusts him is likely the same reason he gave Steve about the difficulty of selecting a jury.

In Walter Dean Myers's novel Monster, Steve Harmon, a young African American male, is put on trial for murder after a botched robbery leads to the death of a store owner. Throughout Monster, Steve Harmon is looked at as a monster, for many members of the jury—as well as the prosecution team—consider him to be directly involved with the murder. While the prosecution suggests that Steve participated as a look-out man during the robbery and is therefore guilty by association, Steve continues to claim that he is innocent.
Race plays an important role in Monster in the form of bias and prejudice. Steve runs into more problems proving his innocence because of his race. In one of his first interactions with his lawyer, Steve is told,

Half of those jurors, no matter what they said when we questioned them when we picked the jury, believed you were guilty the moment they laid eyes on you. You’re young, you’re Black, and you’re on trial. What else do they need to know?

Steve, therefore, faces higher stakes than many other young men would. Despite the fact that Steve knows King, Cruz, and Bobo only as acquaintances, the jury's (and prosecution's) racial prejudice makes Steve seem directly connected to the murder.
Even though Steve is a kind, mild-mannered young man whose sole interest is cinema, he is looked at as a criminal and a monster solely because of his race. Myers's gripping novel aims to show the reader how racial inequality still exists in this country, particularly in the American justice system.

How does Sam create music in the wilderness?

Sam has shown himself remarkably adept at surviving all by himself in the Catskill Mountains. He can do all sorts of things: hunt, fish, build a tent out of evergreen hemlock branches, and even identify wild onions. He struggles to build himself a fire, but on the whole he's still a pretty resourceful young man.
When the unusual figure of Bando arrives on the scene, Sam starts to learn even more about how to survive in the wilderness. Bando helps Sam make a raft, which they then use to drift downstream to catch fish. He also gives the young man a useful lesson in how to make jam out of sugar. But man does not live on bread alone, as they say—nor jam, for that matter—and even up in the mountains it's important not to neglect the higher things of life such as music. Thankfully, Bando is on hand to teach Sam how to make his very own musical instrument: a little wooden whistle hewn from a willow branch. From such an unlikely source Sam is able to make sweet music in the wilderness.

What does Francis get for Christmas? (4 things)

We learn that Aunt Alexandra's grandson Francis is deposited with her every Christmas and that Scout doesn't like him. She writes that he:

enjoyed everything I disapproved of, and disliked my ingenuous diversions.

There is, however, some pathos about Francis, whose parents don't seem much interested in him. We learn that his parents don't spend Christmas with him.

Henry and his wife deposited Francis at his grandparents’ every Christmas, then pursued their own pleasures.

Scout is therefore forced to spend time with Francis during Christmas at Finch's Landing, the old Finch ancestral estate. When she asks him what he got for Christmas, Francis tells her he got what he asked for: "a pair of knee-pants, a red leather booksack, five shirts and an untied bow tie." It's hard to imagine any boy, even Francis, asking for nothing but clothes. This must be what his indifferent parents purchased for him.
The contrast in their presents reflect the contrasts in their situations. While Scout tells Francis about her air gun (Jem gets one too) and Jem's chemistry set, Francis may be exhibiting jealousy when he says the chemistry set must be a toy, which she denies, and when he asks her what use her plan to make invisible ink is.
Later, Francis taunts her by insulting Atticus, leading to a fist fight.

In chapter 9, the Finch family gathers together to celebrate Christmas at Finch’s Landing, and Scout is forced to hang out with her preppy, arrogant cousin, Francis Hancock. After exchanging presents, Scout is forced to entertain Francis, and the two relatives begin discussing what they received for Christmas. When Scout asks Francis what he got for Christmas, Francis tells her: "a pair of knee-pants, a red leather booksack, five shirts and an untied bow tie" (Lee, 83). Scout responds by lying to her cousin and says, "That's nice" (Lee, 83). Scout then tells Francis that she and Jem received air rifles and Jem got a chemistry set. Scout proceeds to tell Francis that Jem plans on making some invisible ink with his chemistry set that she will use to write Dill a letter. Scout mentions that speaking to Francis gives her the sensation of "settling slowly to the bottom of the ocean," and the two relatives end up getting into a fight after Scout punches Francis in the face.

Intermediate Algebra, Chapter 3, 3.2, Section 3.2, Problem 46

Determine the slope of of the line $x + 3y = -6$ and sketch the graph.

The intercepts can be used as the two different points needed to find the slope. So

$x$-intercepts


$
\begin{equation}
\begin{aligned}

x + 3y =& -6
&& \text{Given equation}
\\
x + 3(0) =& -6
&& \text{To find the $x$-intercepts, we let $y=0$ and solve for $x$}
\\
x =& -6
&&

\end{aligned}
\end{equation}
$


The $x$-intercept is $-6$.


$y$-intercepts


$
\begin{equation}
\begin{aligned}

x + 3y =& -6
&& \text{Given equation}
\\
0 + 3y =& -6
&& \text{To find the $y$-intercepts, we let $x=0$ and solve for $y$}
\\
y =& -2
&& \text{Divide each side by $3$}

\end{aligned}
\end{equation}
$


The $y$-intercept is $-2$.

Thus, the points are $(-6,0)$ and $(0,-2)$.

Using the two points in slope formula


$
\begin{equation}
\begin{aligned}

m = \frac{y_2 - y_1}{x_2 - x_1} =& \frac{-2-0}{0- (-6)}
&& \text{Substitute } (x_1, y_1) = (-6,0) \text{ and } (x_2, y_2) = (0,-2)
\\
\\
=& \frac{-2}{6}
&& \text{Simplify}
\\
\\
=& - \frac{1}{3}


\end{aligned}
\end{equation}
$

Single Variable Calculus, Chapter 7, 7.3-1, Section 7.3-1, Problem 66

Determine the equation of the tangent line to the curve $y = e^{-x}$ that is perpendicular to the line $2x - y = 8$

Since the tangent line is perpendicular to the tangent line, its slope is equal to the negative reciprocal of the perpendicular line. So..

$M_T = - \frac{1}{M_N}$

Solving for $M_N$


$
\begin{equation}
\begin{aligned}

& zx - y = 8
\\
& y = 2x - 8

\end{aligned}
\end{equation}
$


By observation, $M_N = 2$, hence, $\displaystyle M_T = -\frac{1}{2}$

Also, recall that the first derivative is equal to the slope of the tangent line at the curve, so..


$
\begin{equation}
\begin{aligned}

\text{if } y =& e^{-x}, \text{then}
\\
\\
y' =& e^{-x} (-1)

\end{aligned}
\end{equation}
$


Thus,


$
\begin{equation}
\begin{aligned}

\frac{-1}{2} =& -e^{-x}
\\
\\
\frac{1}{2} =& \frac{1}{e^x}
\\
\\
e^x =& 2

\end{aligned}
\end{equation}
$


Taking the natural logarithm of both sides..


$
\begin{equation}
\begin{aligned}

x (ln e) =& ln (2)
\\
\\
x(1) =& ln (2)
\\
\\
x =& ln (2)

\end{aligned}
\end{equation}
$


So when $x = ln(2)$, then...


$
\begin{equation}
\begin{aligned}

y =& e^{-x} = \frac{1}{e^x}
\\
\\
y =& \frac{1}{e^{e^{ln2}}} = \frac{1}{2}

\end{aligned}
\end{equation}
$


Therefore, by using point slope form, the equation of the tangent line is..


$
\begin{equation}
\begin{aligned}

y - y_1 =& m(x - x_1)
\\
\\
y - \frac{1}{2} =& \frac{-1}{2} (x - ln(2))
\\
\\
y =& \frac{-1}{2} x + \frac{ln (2)}{2} + \frac{1}{2}
\\
\\
y =& \frac{-x}{2} + \frac{ln(2) + 1}{2}



\end{aligned}
\end{equation}
$

How did the carpetbaggers feel about the Thirteenth Amendment?

The carpetbaggers were people from the North who moved to the South during Reconstruction. They came to the South to help with the rebuilding of the South. They were negatively portrayed by some southerners as greedy northerners who tried to profit from Reconstruction. The word carpetbagger describes a person who came to a new region with a scraggly suitcase that had few possessions in it.
The carpetbaggers supported the Thirteenth Amendment. This amendment abolished slavery. Since the carpetbaggers were from the North, and since the North was fighting to end slavery, they would have been very supportive of an amendment to end slavery. They wanted to go to the South to help rebuild the area. They hoped to economically redevelop the South. They also hoped to bring about reforms or changes to the South. Many carpetbaggers were professionals from the middle class that wanted to make a difference in rebuilding the South.
https://www.history.com/topics/american-civil-war/carpetbaggers-and-scalawags

Calculate the number of atoms and volume of 1 gallon of helium gas at stp.

Hello!
STP means standard temperature and pressure. Denote the temperature as T (in Kelvin) and the pressure as P. They may be different for different standards.
The formula we need is  PV = nRT, where V is the volume of a gas, n is the number of moles and R is the ideal gas constant, about 8.3 J/(mol*K). The volume is also given, it is 1 gallon approx 3.8*10^(-3) m^3.
From all this data we can find the quantity of helium in moles:  n = (PV)/(RT). The number of atoms in each mole is a constant called Avogadro's constant, N_A approx6*10^(23) (mol)^(-1), so the number of atoms is n*N_A = (PV)/(RT)*N_A.
Let T = 273 K and P = 10^5 Pa, then the number of atoms is about
(10^5*3.8*10^(-3)*6*10^(23)) / (8.3*273) approx 0.01*10^(25) = 10^23.
This is the answer.

How is the theme of Fahrenheit 451 shaped by a literary element or device?

Though many literary elements and devices are used throughout Ray Bradbury's Fahrenheit 451, two are most prevalent. Irony is used in the sense that the protagonist, Montag, is a fireman. One would normally expect that to mean his job is to put out fires; instead, he is tasked with starting them. In a sense, Bildungsroman (coming-of-age) is also employed throughout the story, though not in the traditional sense.
Before we get into the story, let us look at the definitions of the two literary devices listed above (provided here by the Ohio Department of Education and UC Berkeley):

Irony: "An irony of situation is when an event occurs that directly contradicts expectations."
Bildungsroman: "[T]racing the spiritual, moral, psychological, or social development and growth of the main character usually from childhood to maturity."

Very early in the story, Montag talks with a neighbor about his profession. This conversation gives a backstory for Montag, describing his role as a fireman and where he is currently at in his life. His neighbor, Clarisse McClellan, mirrors the reader in that she is ignorant as to what a fireman does (within the context of this story):

...then Clarisse McClellan said:"Do you mind if I ask? How long've you worked at being a fireman?""Since I was twenty, ten years ago.""Do you ever read any of the books you burn?"He laughed. "That's against the law!""Oh. Of course.""It's fine work. Monday burn Millay, Wednesday Whitman, Friday Faulkner, burn 'em to ashes, then burn the ashes. That's our official slogan."

These few lines act as a form of exposition, telling the reader a great deal about Montag's life in a relatively short amount of time. He is thirty years old and has worked as a fireman for the past ten years. This requires him to burn books, which are outlawed. Bradbury's use of alliteration in the last part of the quote helps showcase the monotonous routine of his work: Monday, he burns books; Wednesday, he burns books; Friday, he again burns books. The reader is also shown that Montag is at least aware of those three authors's names, though it is implied that he has not read any of them. This passage showcases the first use of irony in the story. In real life, firemen are tasked with putting out fires and saving people. Firemen in Fahrenheit 451, however, have the opposite job of starting fires, burning books, then "burn[ing] the ashes." This contradicts the reader's expectations of what constitutes a fireman.
In addition to irony, Bildungsroman is also used throughout the story—though admittedly, not in the traditional sense (i.e., "from childhood to maturity"). The previous passage clearly shows Montag is not a child. However, his discussion with Clarisse suggests that he missed out on the early inquisitive years that make up one's adolescence and help to form individuality. After meeting this new neighbor, Montag's mind awakens, and he begins his journey toward moral and psychological growth; he begins to read and collect books, questions the practice of burning books, and faces the figurative 'firing squad' for his newfound beliefs. He goes from ignorantly burning books because he is told to do so (much like a child told to clean his room, eat his vegetables, etc.), to forming his own beliefs about the importance of books and knowledge.
For further study on how Bildungsroman is shown throughout the story, you might investigate the specific ways in which Montag's lack of world/general knowledge early in the story mirrors that of a child. Then, you might compare that with his transformation later in the story to showcase his development and growth as a character.

The phoenix is a literary device that Bradbury uses to shape his theme of rebirth and renewal. It is one of the symbols of the firefighters because it represents rising up again from a fire. Montag, like the other firefighters, wears the "phoenix disc" on his chest to show he is impervious to the fires he helps to set. He was once proud of this symbol, just as he was once proud of his job.
But the phoenix has a wider meaning as a general symbol of renewal, change, and rebirth. The bird that can be reborn from the flames ironically changes for Montag from a symbol of book-burning to a symbol of his transformation into a person who wants to preserve books and the knowledge they contain.
At the end of the novel, Montag has joined an underground group living on the edges of society and working to save what he, as a firefighter, once sought to destroy. As Montag joins this renegade group, the phoenix comes to represent the message he is working to spread. As Granger says,

"There was a silly damn bird called a Phoenix back before Christ: every few hundred years he built a pyre and burned himself up. He must have been first cousin to Man. But every time he burnt himself up he sprang out of the ashes, he got himself born all over again. And it looks like we're doing the same thing, over and over, but we've got one damn thing the Phoenix never had. We know the damn silly thing we just did. We know all the damn silly things we've done for a thousand years, and as long as we know that and always have it around where we can see it, some day we'll stop making the goddam funeral pyres and jumping into the middle of them. We pick up a few more people that remember, every generation."

Are there any advantages of social stratification?

Most societies have some form of stratification. A few societies are egalitarian, meaning that they strongly emphasize the equal status of all members and employ “leveling mechanisms” to prevent people from trying to gain superiority over others. This system tends to work only in small groups. A stratum is a layer or level, so stratification refers to the arrangement of the levels. Economic and political stratification are intertwined with social stratification.
The most important advantage of stratification is that it facilitates social organization and governance. Within the social group, having one or more acknowledged leaders leads to greater efficiency in decision-making, in contrast to egalitarian systems that rely on achieving consensus among the entire group. Without some orderly arrangement of positions, anarchy or chaos might ensue, ultimately leading to violent conflict within the group.
Another advantage is that the group’s members have clear expectations of appropriate behavior. This is especially true in a “closed” stratified society, in which people gain their positions by birthright or family connections. In an “open” system, in contrast, statuses are achieved; while clear divisions exist, anyone could, in theory, take the required steps to move up the levels. In reality, however, individuals have unequal opportunities to gain status, and people of high status are protected (through social support, inheritance, etc.) from losing it, so it is common for generations to maintain their status.

Whether or not there are any advantages to social stratification really depends on who you are and where you fall in that system. By its very nature, social stratification limits access to power, prestige, and privilege by systemically oppressing and exploiting particular groups of people. Though complex societies rely on the differentiation of labor, there does not necessarily need to be a differential distribution of wealth based on irrelevant characteristics like race, gender, ethnicity, bodily ability, religion, health status, or socioeconomic background. 
I would say that there are advantages to social stratification for those who fall into the preferential categories and higher ranks of stratification. Though there may exist advantages in access to power, prestige, and privilege, they are not justified in a system of social stratification. Where there are systemic advantages, there are also disadvantages. For example, in the United States, there persists a racial and ethnically based system of social stratification which gives preferential access to health, wealth, and education to white people, while placing People of Color in a cycle of poverty. For every one white person who does well in the United States, there is a handful of People of Color who have been denied the opportunity and resources for achievement.

Why is District 12 surrounded by fences?

In chapter 1 of the first book in the Hunger Games trilogy, protagonist Katniss Everdeen states that the fence, which is meant to be electrified but generally isn't, is there to keep the predators that live in the woods out. These predators are described as "wild dogs, lone cougars and bears," as well as "flesh-eaters."
As you read the trilogy, however, it becomes apparent that the fence is about a lot more than that. It is one of the myriad ways by which the powers that be in the Capitol attempt to control the lives of those who live in the districts. The fence is designed to restrict the movements of residents of District 12 and prevent them from hunting.
Hunting for Katniss and her close friend Gale Hawthorne is a lifeline and an invaluable source of both food and money. In the early stages of the trilogy, authorities largely turn a blind eye to this hunting activity (largely because the Peacekeepers enjoy the spoils of Katniss and Gale's hunting), but as the rebellion begins and the authorities clamp down on activities in the district, it gets harder and harder for residents of District 12 to hunt.
The electricity in the fence is later turned on, which the author uses to showcase the stricter rules and harsher penalties that residents of District 12 are faced with as the story progresses.

In The Hunger Games, District 12 is surrounded by fences. The narrator of the story, Katniss Everdeen, lives in District 12. According to her, "Separating the Meadow from the woods, in fact enclosing all of District 12, is a high chain-link fence topped with barbed-wire loops." Katniss shares with us that the fences are there to keep predators such as wild dogs and bears out of the district. Another result of the fences is that the people of District 12 are more easily kept within their district.
While the fences are supposed to be electrified, Katniss finds that they are usually not supplied with electricity. She knows to listen for a hum to determine whether or not the fence is electrified. Katniss is one of the District 12 residents that often ventures beyond the fence into the woods to hunt. While this is against the rules, the Peacekeepers are typically quite forgiving of this activity because "they’re as hungry for fresh meat as anybody is."

What is the drive of the Otis family from the railway station to Canterville Chase like?

The drive from the railway station in Ascot to Canterville Chase is initially uneventful and peaceful. Members of the Otis family are able to delight in happy pastoral scenes that correspond with their own high spirits. The first leg of the seven mile journey from Ascot to Canterville Chase is restful and uneventful.
The Otis family is able to revel in the pleasant summer weather; as the family drives through the forest, its senses are teased by the redolent (fragrant) scent of pinewood. Along the way, the Otis family enjoys glimpses of pheasants, squirrels, and rabbits. The wood-pigeon's sweet song also contributes greatly to the pleasantness of the journey.
On the second leg of the journey, however, as the family enters the avenue of Canterville Chase, the atmosphere changes. Clouds gather ominously, and a flight of rooks mysteriously fly over the sky. Soon, raindrops begin falling even before the Otis family reaches the house on Canterville Chase.
So, the Otis family enjoys a pleasant drive until it reaches the avenue of Canterville Chase. There, the weather suddenly changes, and rain comes upon the unsuspecting family. Nevertheless, the family is able to reach the house safely, without any untoward incidents to mar its journey.

College Algebra, Chapter 7, 7.3, Section 7.3, Problem 10

Determine the inverse of the matrix $\left[ \begin{array}{cc}
3 & 4 \\
7 & 9
\end{array} \right]$ if it exists.

First, let's add the identity matrix to the right of our matrix

$\left[ \begin{array}{cc}
3 & 4 \\
7 & 9
\end{array} \right]$

By using Gauss-Jordan Elimination

$\displaystyle \frac{1}{3} R_1$

$\left[ \begin{array}{cc|cc}
1 & \displaystyle \frac{4}{3} & \displaystyle \frac{1}{3} & 0 \\
7 & 9 & 0 & 1
\end{array} \right]$

$\displaystyle R_2 - 7 R_1 \to R_2$

$\left[ \begin{array}{cc|cc}
1 & \displaystyle \frac{4}{3} & \displaystyle \frac{1}{3} & 0 \\
0 & \displaystyle \frac{-1}{3} & \displaystyle \frac{-7}{3} & 1
\end{array} \right]$

$\displaystyle -3 R_2$

$\left[ \begin{array}{cc|cc}
1 & \displaystyle \frac{4}{3} & \displaystyle \frac{1}{3} & 0 \\
0 & 1 & 7 & -3
\end{array} \right]$

$\displaystyle R_1 - \frac{4}{3} R_2 \to R_1$

$\left[ \begin{array}{cc|cc}
1 & 0 & -9 & 4 \\
0 & 1 & 7 & -3
\end{array} \right]$

The inverse matrix can now be found in the right half of our reduced row-echelon matrix. So the inverse matrix is

$\left[ \begin{array}{cc}
-9 & 4 \\
7 & -3
\end{array} \right]$

Single Variable Calculus, Chapter 3, 3.8, Section 3.8, Problem 36

At what rate is cart $B$ moving toward $Q$ at the moment when cart $A$ is 5ft from $Q$?



We know that $L_A + L_B = 39$, if we take the derivative with respect to time
we will get $\displaystyle \frac{dL_A}{dt} + \frac{dL_B}{dt} = 0$ so,
$\displaystyle \frac{dL_A}{dt} = - \frac{dL_B}{dt} \qquad \Longleftarrow \text{ Equation 1}$
Also, by using Pythagorean Theorem in both triangle we obtain $L_A^2 = 12^2 + X_A^2$ and $L_B^2 = 12^2 + X_B^2$

Taking the derivative with respect to time,

$
\begin{equation}
\begin{aligned}
\cancel{2} L_A \frac{dL_A}{dt} &= \cancel{2}X_A \frac{dX_A}{dt} & \text{and} && \cancel{2}L_B \frac{dL_B}{dt} &= \cancel{2}X_B\frac{dX_B}{dt}\\
\\
\frac{dL_A}{dt} &= \frac{X_A}{L_A} \frac{dX_A}{dt} &&& \frac{dL_B}{dt} &= \frac{X_B}{L_B} \frac{dX_B}{dt}
\end{aligned}
\end{equation}
$


Substituting these values in Equation 1
$\displaystyle \frac{X_A}{L_A} \frac{dX_A}{dt} = - \left( \frac{X_B}{L_B} \frac{dX_B}{dt} \right)$

We have,
$\displaystyle \frac{dX_B}{dt} = - \frac{L_B X_A}{L_A X_B} \frac{dX_A}{dt}$; but $L_B = 39 - L_A$
$\displaystyle \frac{dX_B}{dt} = - \frac{(39-L_A) x_A}{L_A X_B}\frac{dX_A}{dt} \qquad \Longleftarrow \text{ Equation 2}$

Using the equations we in obtain Pythagorean Theorem, we know that when $X_A = 5$,
$L_A = \sqrt{5^2 + 12^2} = 13$
Hence,
$X_B = \sqrt{(39-L_A)^2-12^2} = \sqrt{(39-13)^2 - 12^2} = \sqrt{532}$

Now, plugging all values in Equation 2 we have,

$
\begin{equation}
\begin{aligned}
\frac{dX_B}{dt} &= \frac{-(39,13)(5)}{13(\sqrt{532})} (2)\\
\\
\frac{dX_B}{dt} &= -0.8671 \frac{\text{ft}}{s}
\end{aligned}
\end{equation}
$

This means that as cart $A$ is being pulled away from $Q$. the distance of cart $B$ to $Q$ is decreasing at a rate $\displaystyle 0.8671 \frac{\text{ft}}{s}$

Who are the main characters in the beginning of the story?

Said to be inspired by Nathaniel Hawthorne's "Young Goodman Brown," Stephen King's 1994 short story published in The New Yorker "The Man in the Black Suit" opens with the narrator, Gary, a man in his 90s, preparing to write into his diary a terrifying and vivid memory of an event during his childhood in western Maine.
In the memory from 1914, it is himself at age nine as well as his mother, Loretta, and father, Albion, living on a farm in a sparsely populated rural area. His only brother, Dan, has been dead for a year, killed by a bee sting. He has a Scottie dog named Candy Bill. The only other character who appears in the story is the man in the black suit, who is the incarnation of the devil.

What is a time Crooks feels frustration, anger, relief, loneliness, fear, and humiliation in the book Of Mice and Men?

At the beginning of chapter 4, Lennie enters Crooks's room, which initially upsets and frustrates Crooks. Crooks tells Lennie, "You got no right to come in my room. This here's my room. Nobody got any right in here but me" (Steinbeck, 33). Crooks then begins to bully Lennie by telling him that George might not return. After Lennie becomes extremely angry and threatening, Crooks realizes his mistake and reveals the cause of his pessimistic nature. Crooks laments his difficult situation and reveals his loneliness by saying,

"S'pose you didn't have nobody. S'pose you couldn't go into the bunkhouse and play rummy 'cause you was black. How'd you like that? S'pose you had to sit out here an' read books. Sure you could play horseshoes till it got dark, but then you got to read books. Books ain't no good. A guy needs somebody to be near him . . . A guy goes nuts if he ain't got nobody. Don't make no difference who the guy is, long's he's with you. I tell ya . . . I tell ya a guy gets too lonely an' he gets sick" (Steinbeck, 36).

When Candy enters Crooks's room, he begins talking about their plan to buy their own piece of property and leave the ranch for good. After Candy tells Crooks that they already have the money, Crooks experiences a feeling of relief and hope in the possibility that he might be able to join the men. Crooks tells Candy,

"If you . . . guys would want a hand to work for nothing—just his keep, why I'd come an' lend a hand. I ain't so crippled I can't work like a son-of-a-bitch if I want to" (Steinbeck, 37).

Curley's wife then enters Crooks's room and laughs after hearing about their dream of one day leaving the ranch. After she begins messing with Lennie, Crooks displays his anger and frustration by saying,

"I had enough . . . You got no rights comin' in a colored man's room. You got no rights messing around in here at all. Now you jus' get out, an' get out quick. If you don't, I'm gonna ast the boss not to ever let you come in the barn no more" (Steinbeck, 39).

Immediately after being chastised, Curley's wife threatens to have Crooks lynched. Crooks becomes helpless, afraid, and humiliated by Curley's wife. Steinbeck writes,

Crooks had reduced himself to nothing. There was no personality, no ego—nothing to arouse either like or dislike. He said, "Yes, ma'am," and his voice was toneless (39).

College Algebra, Chapter 5, Review Exercise, Section Review Exercise, Problem 18

Determine the domain of the function $g(x) = \log (2 + x - x^2)$
If the given is a Logarithmic Function, then we want

$
\begin{equation}
\begin{aligned}
2 + x - x^2 &> 0 && \text{Model}\\
\\
x^2 - x - 2 &< 0 && \text{Multiply both sides by } -1\\
\\
(x+1)(x-2) &< 0 && \text{Factor}
\end{aligned}
\end{equation}
$

The factors on the left hand side are $x + 1$ and $x - 2$, these factors are 0 when $x$ is $-1$ and $2$ respectively. These numbers divide the number line
into intervals
$(-\infty,-1)(-1,2)(2,\infty)$
By testing some points in the interval,


Thus $(x + 1)(x-2) < 0$ at interval $(-1,2)$. Therefore, the domain of $g$ is $(-1,2)$

What do you admire or dislike about Rainsford?

While Rainsford may be foolish to go so near the side of the boat (an event that causes his fall into the water and eventual capture by Zaroff), there are quite a number of things about Rainsford in Connell's "The Most Dangerous Game" that make this world-renowned hunter admirable.
Perhaps what I admire most is that even though Rainsford loves to hunt, he has no desire to compromise his moral code by hunting humans. Even though he is on an island under circumstances that would never allow anyone to know if he were to join Zaroff, it never occurs to him. His integrity is not governed by whether or not someone is watching, but by his unshakable sense of what he knows to be right.

“Tonight,” said the general, “we will hunt—you and I.”
Rainsford shook his head. “No, general,” he said. “I will not hunt.”

Another thing that I admire about Rainsford is his ability to think creatively even while running for his life. While running, he is able to come up with unusual methods not only to protect himself (like climbing the tree), he also adopts methods of defense to remove threats against him (such as Ivan) and engages in unique offensive tactics.

“Rainsford,” called the general, “if you are within sound of my voice, as I suppose you are, let me congratulate you. Not many men know how to make a Malay mancatcher."

Finally, though Rainsford initially experiences a moment of panic, he is able to work past it to do whatever he can to protect himself and survive.
Ironically, while Zaroff looks to find the "most dangerous game" in capturing and hunting unfortunate sailors, Rainsford's abilities to adapt and strategize make him the most dangerous game.

What does the mother compare her life to?

In "Mother to Son", the mother compares her life to a splintered and dilapidated stairway:


It’s had tacks in it,
And splinters,
And boards torn up

A stairway is a means of getting somewhere or, literally, of moving up in the world. So, the mother could be comparing her life here, metaphorically, to a splintered and dilapidated stairway to suggest that her path in life has been a difficult one. The "tacks" and "splinters" and the ripped up "boards" could represent the obstacles that she has had to overcome. The description of the stairway also implies poverty, especially when compounded with the word "Bare" two lines later, so perhaps the mother's life has been difficult because she has been poor, and the obstacles that she has had to overcome are the obstacles that poverty imposes.

The speaker (the mother) then continues the metaphor and says that, on the "landin's" and while "turnin' corners," she has had nobody else to guide her. She has had to find her own way. This is implied by the lines,


And sometimes goin’ in the dark
Where there ain’t been no light.

The absence of light here could suggest that she has had nobody to guide her, as a light might guide somebody through the darkness. She has had to turn corners in her life, and find doorways in her life, without the guidance that most might expect somewhere along the way.

The mother compares her life to a staircase filled with nails, broken boards, and missing boards. For her, life has not been easy. She sees her life as a struggle upwards, fighting against injustice, discrimination, and despair. In the poem, she states "I'se been a-climbin' on, / And reachin' landin's, / And turnin' corners, / And sometimes goin' in the dark / Where there ain't been no light." She has been met with dead-ends, anxiety, and the unknown. However, even with all of this struggle and pain, she keeps going, because that's all she knows how to do. To keep going in the face of all of this shows her strength of character and her belief that if she just keeps climbing, life will be better for her and her son. She tells him, "So, boy, don't you turn back. / Don't you set down on the steps. / 'Cause you finds / it's kinder hard. / Don't you fall now— / For I'se still goin', honey, / I'se still climbin'" and extends the metaphor of the stair and her life to show her son that she can still keep going and he can, too.

Who is called the Queen of Courtesy in the poem "Pearl" and why?

In the Middle English in which the poem was written, cortayse has much broader connotations than the modern-day "courtesy." The word is related to "court," as in a royal court, and in the context of the poem represents the very highest nobility, dignity, graciousness, and benevolence. All of these qualities and more are exemplified by the Queen of Courtesy, the Virgin Mary herself.
But courtesy is much more than good manners; it is the grace of God Himself. According to Medieval Christian theology, the Virgin Mary, in her capacity as the Queen of Courtesy, is instrumental in the distribution of God's grace. Through her, this most wondrous of heavenly gifts is bestowed. The grieving father's deceased daughter is the recipient of such gifts; she has become part of the community of grace. The child's gift of grace was entirely undeserved, as was her father's tragic loss.

Identify and explain an overarching theme found in Roger Williams's work.

An overarching theme in Roger Williams's work is religious freedom. He wrote about this in several works, including his famous The Bloudy Tenent of Persecution, for Cause of Conscience and his work The Bloudy Tenent Yet More Bloudy.
In Bloudy Tenent of Persecution, written in 1644, Williams calls for the separation of church and state, using the Bible to support his argument. He argued for the religious freedom of the various Protestant sects and argued for Catholics, Jews, Muslims and other "heretical" groups to be left free to worship as they wished. He based this assertion of religious freedom on Jesus's teaching that God would ultimately judge who was and was not righteous. If the state judged and persecuted people for their faith, the state usurped God's role. The state could, through poor decisions, harm the good "wheat" of the truly faithful followers of Christ.
Williams stated that the Bible condemned kings like Nebuchadnezzar who forced Jews to worship the gods of the state against their conscience. He quoted Paul to argue that the state should use only spiritual, not physical, weapons to convince unbelievers. Williams also thought the beast in Revelation was the symbol of state churches.
Williams wrote:
It is the will and command of God that, since the coming of his Son the Lord Jesus, a permission of the most Paganish, Jewish, Turkish, or anti-christian consciences and worships be granted to all men in all nations and countries : and they are only to be fought against with that sword which is only, in soul matters, able to conquer: to wit, the sword of God's Spirit, the word of God.
After he was attacked for arguing in favor of the separation of church and state, he repeated and elaborated on his arguments in The Bloudy Tenent Yet More Bloudy.
His arguments for religious freedom clearly found favor in the the United States, where freedom of religion was enshrined in the Constitution. Nevertheless, his ideas were radical for a time when church and state were tightly tied together and when the monarch was considered God's representative on earth.

What is the meaning behind the proverb "not all that glitters is gold"?

At it‘s most basic level, this quote expresses the idea that something’s appearance is not necessarily a true representation of what it really is. In other words, things are not always what they appear to be.
A deeper analysis would show that this proverb also implies that something’s appeal (glitter) in fact may be hiding a negative or unpleasant reality (not gold after all). Gold is used here because we associate this precious metal with a high level of value. Though something else may mimic the glittering of gold, it doesn’t mean that it will hold that same value.
This can be applied to actual objects (such as fake Gucci glasses), people (someone who is handsome but then is discovered to be a liar or cruel to others), or even situations (a job promotion that seemed great but comes with far too much work).
In order to truly appreciate this proverb, one must realize that not only must they understand what phrase means, but also the lesson it is conveying. The warning “not all that glitters is gold” implies that a person much look deeper than the surface and not make assumptions based on first appearances. Critically analyze the situation or object/person and don’t make hasty decisions about them. In this way, one can appreciate both the meaning and lesson of this proverb.

The popular English expression "Not all that glitters is gold" is used to mean that sometimes things that look valuable, attractive, or promising turn out to be anything but. At an extremely literal level, one example of this can be found in iron pyrite, otherwise known as fool's gold, which is a mineral that at first glance may be mistaken for actual gold but, upon closer examination, is relatively worthless. An interpersonal example might be if you met someone who was extremely attractive and seemed superficially nice and interesting, only to find out upon spending more time with them that they were actually cruel and boring. Beauty on the outside is not the same as beauty on the inside.
To think of examples from your own life, try to remember a time when you had high expectations for something based on cursory knowledge of what it was only to dig deeper and be disappointed, or a time when you've been tricked by something's outward appearance. We've all been there!

What is Johnny's reaction when the nurse tells him that his mother is at the hospital to see him?

Readers are informed very early on in the book that Johnny's home life is not good and that his relationship with his parents is terrible. His father beats him, and his mother either ignores him completely or screams at him.

His father was always beating him up, and his mother ignored him, except when she was hacked off at something, and then you could hear her yelling at him clear down at our house.

Johnny's parents show no love for him, and that is confirmed again for readers in chapter 6. Dally, Johnny, and Ponyboy are all talking, and Dally is informing Johnny and Ponyboy of some recent news. Johnny asks if his parents have asked about him, and Dally flatly states that they have not. The news is not surprising, but Johnny is still hurt.

"My parents," Johnny repeated doggedly, "did they ask about me?"
"No," snapped Dally, "they didn't. Blast it, Johnny, what do they matter?"

Once Johnny is in the hospital, his mother does come and try to see him; however, Johnny knows that she isn't there for any kind of good reason. Johnny flatly denies his mother access to him. He tells the nurse that he does not want to see his mother. Johnny believes that she has only come to berate him for one reason or another.

"I said I don't want to see her." His voice was rising. "She's probably come to tell me about all the trouble I'm causing her and about how glad her and the old man'll be when I'm dead. Well, tell her to leave me alone. For once"—his voice broke—"for once just to leave me alone."

Johnny is so enraged and upset by the entire situation that he passes out.

Johnny has a terrible relationship with his callous mother and does not want to see her when she visits him in the hospital.
In chapter 8, Johnny Cade is lying incapacitated in his hospital bed when the nurse informs him that his mother has arrived to visit him. Johnny reacts by telling the nurse that he does not want to see her. Johnny mentions that his mother has probably come to visit him so that she can tell him how much trouble he is causing the family. Johnny then tells the nurse to tell his mother to leave him alone for once. As Pony and Two-Bit are leaving the hospital, they see Johnny's mother arguing with the nurse about her right to see her son. When she spots Pony and Two-Bit, she blames them for Johnny's injuries. Two-Bit responds by telling Johnny's mother,

No wonder he hates your guts (Hinton, 105).

Ponyboy feels sorry for Johnny and shoves Two-Bit along before he can cuss out Johnny's mother.

Single Variable Calculus, Chapter 8, 8.2, Section 8.2, Problem 68

Prove that $\displaystyle \int^\pi_{-\pi} \sin (mx) \sin (nx) dx = \left\{
\begin{array}{c}
0 & \text{if} & m \neq n\\
\pi & \text{if} & m = n
\end{array}\right.
$


where $m$ and $n$ are positive integers.
If we use the sum and difference angles formula for cosine, we get


$
\begin{equation}
\begin{aligned}
\cos (mx - nx) &= \cos (mx) \cos (nx) - \sin (mx) \sin (nx) \qquad \text{and}\\
\\
\cos (mx + nx) &= \cos (mx) \cos (nx) + \sin (mx) \sin (nx)
\end{aligned}
\end{equation}
$

Then, $\cos (mx - nx) - \cos(mx+nx) = \cos (mx) \cos (nx) - \sin (mx) \sin (nx) - \cos (mx) \cos (nx) + \sin (mx) \sin (nx) = 2 \sin (mx) \sin (nx)$

Therefore,
$\displaystyle \int^\pi_{-\pi} \sin (mx)\sin(nx)dx = \int^\pi_{-\pi}\left[ \frac{\cos(mx-nx)-\cos(mx+nx)}{2} \right]dx$

if $m \neq n$

$
\begin{equation}
\begin{aligned}
\int^\pi_{-\pi} \sin (mx)\sin(nx)dx &= \frac{1}{2} \left[ \frac{\sin(mx-nx)}{(m-n)} - \frac{\sin(mx+nx)}{(m+n)} \right]^\pi_{-\pi}\\
\\
\int^\pi_{-\pi} \sin (mx)\sin(nx)dx &= \frac{1}{2} \left(\left[ \frac{\sin(m\pi - n \pi)}{(m-n)} - \frac{\sin(m\pi+n\pi)}{(m+n)} \right] - \left[ \frac{\sin(m(-\pi) - n(-\pi))}{(m-n)} - \frac{\sin(m(-\pi) + n (-\pi))}{(m+n)} \right] \right)\\
\\
&= 0
\end{aligned}
\end{equation}
$


if $m =n$,

$
\begin{equation}
\begin{aligned}
\int^\pi_{-\pi} \sin (mx) \sin(nx) dx &= \int^\pi_{-\pi} \left[ \frac{\cos (mx - mx) - \cos (mx + mx)}{2} \right] dx\\
\\
&= \frac{1}{2} \int^\pi_{-\pi} [\cos(0) - \cos(2mx)] dx\\
\\
&= \frac{1}{2} \int^\pi_{-\pi} [ 1 - \cos(mx)] dx\\
\\
&= \frac{1}{2} \left[ x - \frac{\sin(2mx)}{2m} \right]^\pi_{-\pi}\\
\\
&= \frac{1}{2} \left( \left[ \pi - \frac{\sin(2m\pi)}{m} \right] - \left[ (-\pi) - \frac{\sin(2m(-\pi))}{2m} \right] \right)\\
\\
&= \frac{1}{2} [ \pi + \pi]\\
\\
&= \frac{2\pi}{2} \\
\\
&= \pi
\end{aligned}
\end{equation}
$

What is a summary of Alfred Noyes' poem "Song of the Wooden-Legged Fiddler"?

Alfred Noyes wrote "Song of the Wooden-Legged Fiddler" in 1805. It is the tale (song) of a youngster who ran away to sea, to "fight like a sailor for country and king" (19). The poem is five stanzas, with seven lines in each. At the end of each stanza is a one-line chorus, which echoes the last line of the stanza.
In the first stanza, the singer speaks about his life as a boy. He lived in a cottage in the West, but had a restless spirit that forever called him to sea:

But I knew no peace and I took no rest
Though the roses nigh smothered my snug little nest;
          For the smell of the sea
          Was much rarer to me,
And the life of a sailor was all my joy (3-7)

The boy has a "snug" home, described as a picture-perfect cottage, surrounded by roses. However, it was not the flowers that he smelled that overwhelmed him, but the rare smell of the salty ocean water.
In the second stanza, the narrator tells of his mother's wishes for him:

My mother she wept, and she begged me to stay... (9)

He notes that she wanted to keep him close to home, tied to "her apron-string" (10), to help with the hay—we can assume with its harvest. (Hay is the crop of a season's growth of grass that is harvested before it goes to seed.) The singer relents to his mother's wishes for the cutting of the hay, but sneaks out and runs off the following spring.

On a night of delight in the following spring,
                With a pair of stout shoon
                And a seafaring tune
     And a bundle and stick in the light of the moon,
                Down the long road
                To Portsmouth I strode... (13-18)

He takes a pair of strong shoes ("shoon"), and he whistles a sea chantey, having packed a few belongings in a piece of cloth (like a kerchief), carried on the end of a stick—walking to Portsmouth to follow his dream. We can infer this is some distance if his home does not afford him the smell of the sea.
In the third stanza, the sailor is returning home, though the sea still calls him away. The memories of sailing the Spanish Main—chasing French and Spanish frigates—are still fresh in his mind. Perhaps the most poignant line is found in this section of the song:

For at heart an old sailor is always a boy... (25)

This is the line that reminds the listener, even until the end of the song, that the ocean's call never loses its power as the boy grows into a man, and eventually an aged sailor who can no longer make his living on the sea.
The listener (or reader) can believe that a sailor's heart never ages and the draw of the profession never fades: even after all of his experiences, the sea still calls to him like a mythical siren. The smells of gunpowder (for the canon) and pitch (tar to waterproof the ship) are still in his nose. His heart will belong to the sea (he notes) until he cannot tell the difference between either of them—and even when (as he looks out over the ship's side) he cannot distinguish the "grin o' the guns from a glint o' the sea" (27). At this point he will lack the mental capacity to tell the difference between the legendary Nelson and some other jack-tar like himself.
The fourth stanza lets the listener know that the sailor is no longer young:

Ay! Now that I'm old I'm as bold as the best... (32)

By now he has lost his leg—a wooden peg has taken its place; and he is as bald as an egg. Even in light of these drastic changes, his love of the sea has not diminished:

The smell of the sea
              Is like victuals to me... (37-38)

In other words, living on the ocean is as necessary to him as food ("victuals"). Even in his grave, he is certain he will still be calling "Ahoy!" When his body is "ready to rest" (die), he echoes the sentiment he shared earlier:

At heart an old sailor is always a boy. (41)

Interestingly, while he recalls whistling a sea song when he left home, his story has become a sea chantey, based upon his life rather than another sailor's, as he has lived the life he was called to so many years before. It would also seem that his choice was true to his heart and he has no regrets—other than, perhaps, having to leave his life on the sea because he can no longer sail. For the boy's heart in him is still passionately in love with the sea.

Intermediate Algebra, Chapter 2, 2.1, Section 2.1, Problem 22

Solve the equation $5(x + 3) + 4x - 5 = 4 - 2x$, and check your solution. If applicable, tell whether the equation is an identity or contradiction.


$
\begin{equation}
\begin{aligned}

5(x + 3) + 4x - 5 =& 4 - 2x
&& \text{Given equation}
\\
5x + 15 + 4x - 5 =& 4 - 2x
&& \text{Distributive property}
\\
9x + 10 =& 4 - 2x
&& \text{Combine like terms}
\\
9x + 2x =& 4 - 10
&& \text{Add $(2x-10)$ from each side}
\\
11x =& -6
&& \text{Combine like terms}
\\
\frac{11x}{11} =& \frac{-6}{11}
&& \text{Divide both sides by $11$}
\\
x =& \frac{-6}{11}
&&

\end{aligned}
\end{equation}
$


Checking:


$
\begin{equation}
\begin{aligned}

5 \left( \frac{-6}{11} + 3 \right) + 4 \left( \frac{-6}{11} \right) - 5 =& 4 - 2 \left( \frac{-6}{11} \right)
&& \text{Substitute } x = \frac{-6}{11}
\\
\\
5 \left( \frac{27}{11} \right) + 4 \left( \frac{-6}{11} \right) - 5 =& 4 - 2 \left( \frac{-6}{11} \right)
&& \text{Add inside the parentheses}
\\
\\
\frac{135}{11} - \frac{24}{11} - 5 =& 4 + \frac{12}{11}
&& \text{Multiply}
\\
\\
\frac{56}{11} =& \frac{56}{11}
&& \text{True}

\end{aligned}
\end{equation}
$

How to prove Abigail is immoral and unchristian? What will be the quotation to support it (quotation must be related with the relationship between sexual behavior and reputation)

Abigail Williams is by definition an immoral individual throughout the play. She not only engages in an affair with John Proctor, but continues to tempt him while they are alone, threatens to kill the other girls if they do not follow her lead, and falsely accuses innocent citizens of witchcraft. When Reverend Parris and the adults leave Betty's room in Act One, Mary Warren begs Abigail to tell the truth and Betty mentions that Abigail drank blood to put a curse on Elizabeth Proctor. Abigail responds by saying,

"Now look you. All of you. We danced. And Tituba conjured Ruth Putnam’s dead sisters. And that is all. And mark this. Let either of you breathe a word, or the edge of a word, about the other things, and I will come to you in the black of some terrible night and I will bring a pointy reckoning that will shudder you. And you know I can do it; I saw Indians smash my dear parents’ heads on the pillow next to mine, and I have seen some reddish work done at night, and I can make you wish you had never seen the sun go down!" (Miller, 30).

After threatening the girls, John Proctor arrives and Abigail reveals her emotions for him. She proceeds to tempt John Proctor by saying,

"I have a sense for heat, John, and yours has drawn me to my window, and I have seen you looking up, burning in your loneliness. Do you tell me you’ve never looked up at my window?" (Miller, 32).

In Act Two, Mary Warren says that she saved Elizabeth's life in court after Abigail falsely accused her of witchcraft. Elizabeth, who is an innocent Christian, understands Abigail's motives to remove her in order to get to John. Elizabeth tells John,

"She wants me dead. I knew all week it would come to this!" (Miller, 56).

Abigail's unrestrained sexual appetite, her violent temper, and her manipulative personality illustrate that she is an immoral individual.

How does Mr. Darcy fall in love with Elizabeth? What aspects of her character does he fall for, and where is this shown in the novel?

Mr. Darcy fell in love with Elizabeth gradually but intensely. The first time he is shown to be attracted to her is in chapter 6, where he notices the "beautiful expression of her dark eyes." At this point, he has been eavesdropping on her conversations, which are having an impact on him. Though Darcy tries to appear indifferent to Elizabeth, his eavesdropping betrays his desire to get to know her better. In spite of his pride and "critical eye" he must admit to himself that she has a "light and pleasing" figure and manners that show an "easy playfulness." Even when she appears at Netherfield having walked through muddy puddles to reach Jane in chapter 8, he notices that her eyes were "brightened by the exercise." By chapter 11, he is thoroughly impressed by Elizabeth's personality, conversation, wit, and liveliness—so much so that "he began to feel the danger of paying Elizabeth too much attention." In chapter 34, he finally declares his ardent love for her.

Even Darcy himself struggles to answer this question. In chapter 60, Elizabeth asks Darcy to explain how, when, or why he fell in love with her:

she wanted Mr. Darcy to account for his having ever fallen in love with her. “How could you begin? . . . what could set you off in the first place?”

At this point in the novel, Elizabeth has already agreed to marry Mr. Darcy. Neither Elizabeth nor Mr. Darcy greatly enjoyed each other's company early in the book. Mr. Darcy, however, steadily grows in admiration of Elizabeth. He proposes to her, for the first time, midway through the novel. She refuses this first proposal, shocked that he would ever consider such a match, but she learns to appreciate and love Mr. Darcy as they continue to interact in the second half of the book. He responds to Elizabeth's question:

I cannot fix on the hour, or the spot, or the look, or the words, which laid the foundation. It is too long ago. I was in the middle before I knew that I had begun.

She then recounts their initial observations of one another and early feelings toward each other. At first, he had refused an opportunity to dance with her with his infamous line,

She is tolerable, but not handsome enough to tempt me (chapter 3).

Clearly, Darcy does not fall in love with Elizabeth simply for her appearance. She also doubts that he could have fallen in love with her early manners and actions:

my behaviour to you was at least always bordering on the uncivil, and I never spoke to you without rather wishing to give you pain than not. Now be sincere; did you admire me for my impertinence? (chapter 60)

Impertinence refers to disrespect or discourtesy. In our modern language, we might call impertinence an extreme form of sassiness. Darcy takes this negative word, impertinence, and rephrases it in a positive manner:

For the liveliness of your mind, I did (chapter 60).

He tells her that he appreciated her clever words (or, perhaps, her well-planned sass). Additionally, he mentions the "affectionate behavior" that Elizabeth showed Jane when she got ill and was forced to stay at the Bingley's house until she got better. Mr. Darcy learned to look past mere physical appearance. Yes, it does seem that Mr. Darcy grew to think that Elizabeth is beautiful as time progressed. In a conversation with Miss Bingley he announces,

I have been meditating on the very great pleasure which a pair of fine eyes in the face of a pretty woman can bestow.

When she asks him whose eyes captured his attention, he responds:

Miss Elizabeth Bennet (chapter 6).

However, it isn't Elizabeth's physical beauty alone that draws his love and affection. Darcy admits to appreciating Elizabeth's active mind and her passionate concern for her friends and family. Her love and concern for others is seen not only when Elizabeth cares for her sister Jane when she got ill, but is also seen when Elizabeth goes to visit her friend Charlotte Lucas after Charlotte marries an irksome husband for money and comfort rather than love.