How and why does the rebellion happen in Animal Farm?

The Rebellion occurs because Mr. Jones starts drinking heavily after losing a lawsuit. Because of his drinking, he neglects the farm, sometimes spending days at a time doing nothing but sitting in a chair, reading the paper, drinking, and feeding Moses. As a result of his lack of supervision, his farm hands do little work, and the farm goes to wrack and ruin: the fields are weedy, the roofs are left unrepaired, and the animals are underfed.
Things come to a head when Mr. Jones celebrates Midsummer's Eve, gets drunk, doesn't come back until a day later, and then promptly falls asleep. His workers haven't been bothering to feed the animals. Finally, the animals get so hungry that they break into the store shed and start feeding themselves. When Mr. Jones and his men arrive and try to whip them out of the shed, the frustrated animals fight back and run the humans off the farm.
The animals had been secretly preparing for the rebellion they expected to someday take place, but they are surprised at how quickly and spontaneously it happens.

The origins of the Rebellion lie in Chapter One, when Old Major makes his speech about the evils of mankind and the necessity of overthrowing their master. Even though Old Major dies three days later, the animals are so inspired by what he told them that they begin making their preparations for the Rebellion straightaway.
The Rebellion doesn't quite go to plan, however, as we see in Chapter Two. In fact, it happens much sooner than expected. When Mr. Jones forgets to feed the animals, they become very agitated and angry. As a result, they seize their chance for freedom by attacking the humans. Their attack is successful and they evict all of the humans from the farm, including Mr. Jones.
With the humans gone, the animals waste no time in taking over the management of the farm. To consolidate their victory, the animals rename the farm from Manor Farm to Animal Farm.

How does Shakespeare build suspense in act 1 of Romeo and Juliet?

The opening prologue of the play does a nice job of setting the stage with tension and suspense. The third and fourth lines of the prologue alert readers to the fact that the general setting involves two warring families.

From ancient grudge break to new mutiny,Where civil blood makes civil hands unclean.

He uses words like "grudge," "mutiny," and "blood." All of those are not pleasant or happy words. Shakespeare ups the suspense in the next four lines by telling readers exactly what is going to happen to the two young lovers. We know from the beginning that they are going to die.

A pair of star-cross'd lovers take their life;

This is incredibly suspenseful because we immediately start wondering why and how and a whole host of other questions regarding these deaths.
After the prologue, Shakespeare continues to set the stage for a suspenseful play by having the opening scene be a violent scene. He has the Capulets and Montagues throwing insults at each other until the situation escalates and turns to actual violence.
Scene 2 shows audiences that Paris is trying to marry Juliet. Audiences know that the play is titled Romeo and Juliet and Paris is not part of that title. Shakespeare has introduced a possible love triangle quite early. All of this serves to raise the suspense level for audience members.

Define ignoble, specious, ersatz, debacle, collateral, and demean.

Below are definitions for the following words: ignoble, specious, ersatz, debacle, collateral, and demean.
ignobleadjective
1. not honorable either in purpose or in character. "The brother had ignoble feelings of desire for his sister-in-law." 2. of low origin or status. "The ignoble beggar continued to peddle his wares."
Synonyms: dishonorable, degenerate, sordid, low

specious

adjective
1. plausible on the surface, but actually wrong. "The banker provided a specious explanation as to why their loan was denied." 2. misleading in appearance. "The theme park gives their attractions a specious appearance of originality."Synonyms: false, misleading, deceptive
 
ersatz
adjective
1. not genuine, a knock-off. "The aspiring actress wore a coat of tacky ersatz fur."
Synonyms: fake, substitute, faux
 
debacle 
noun
1. a sudden, ungraceful failure. "The media flocked to report on the politician's latest personal debacle."
Synonyms: fiasco, mess, failure
 
collateral
noun
1. security pledged for the payment of a debt. "The pawn shop held the title of his car as collateral. They would hold it as security in the event that he was unable to complete the payment plan for his purchase." 2. a side branch, as of a vessel or nerve.
Synonyms: Assurance, pledge, secondary
 
demean
verb
1. to speak extremely poorly of. "The mayor demeaned his opponent during the debate." 2. to do something that shames oneself. "As a professional musician, he found the singing of campfire songs demeaning."
Synonyms: decry, belittle, humiliate

The following sentence is ambiguous. Provide two explanations which illustrate the different meanings of the sentence: "Please make sure you take the right turn at the intersection."

The primary reason this sentence is ambiguous is because of the unclear placement and use of the word "right." In the English language, the word "right" can mean two very different things.
The first meaning of "right" relates to truth. To do something the "right" way is to do it correctly or as it was intended to be done. 
The second meaning of "right" is directional. It indicates which side one should physically move toward: "right" as opposed to "left."
Thus, the first meaning of the sentence instructs "you" to make the correct turn at the intersection. The second meaning of the sentence instructs "you" to turn right literally onto a particular street. 
Unfortunately, with this sentence standing alone, we don't have any context that could help us determine what meaning is actually intended. Thus, the sentence is a poorly constructed one as it leaves too much to interpretation.

How was Odysseus brave?

Odysseus is the archetype of an epic hero. He has immortal ancestors, he has completed a quest, and he has superhuman intellect. However, Odysseus is still human. Be that as it may, it seems Odysseus never lets his human worries get the best of him. His courage and valor are his legacies, as told in the Iliad and the Odyssey.
Odysseus goes to war, a tale told in the epic poem the Iliad. While he is not a central character of this narrative, he leaves his wife and son behind to honor his homeland in battle. It's even been said that he is the brains behind the famous Trojan Horse trick. While these moments implicitly speak of bravery, a trait all soldiers must embody to survive, Odysseus shines in the sequel epic, the Odyssey.
Here are some key moments from his journey that highlight Odysseus's moments of courage and strength.

After losing many of his men to the Cicones on the island of Ismarus, Zeus foils their course, setting them off track for nine days. Odysseus never panics, keeps his men calm, and sails on.
On the island of the Lotus Eaters, Odysseus's men eat the lotus and refuse to leave. Odysseus drags them to the ship, ties them down, and remains on his course toward Ithaca.
In one of the most famous stories by far, Odysseus is trapped in the cyclops Polyphemus's cave and watches many of his men get eaten alive. He keeps his nerve and devises a plan to escape. It works, and he defeats the cyclops by blinding him.
The men arrive on Circe's island. Circe, a sorceress who is known for causing trouble, turns Odysseus's men into pigs. With the help of Hermes, Odysseus faces Circe and gets his men back.
Next, Odysseus travels to the Underworld to receive his prophecy from Tiresias. He must face a horde of the dead, which includes his long-lost friends who died in battle and his recently deceased mother.
Odysseus is warned about the singing Sirens who cause men to crash their ships. Odysseus covers his men's ears with wax and himself listens to their sweet songs while tied to the mast. He survives the trap and carries on toward home.
With few men left, Odysseus must face Scylla, a hideous six-headed monster, and Charybdis, a man-eating whirlpool. It seems that this is the moment Odysseus lets fear into his heart as he watches his men get snatched up by Scylla, but once again, his bravery shines through as he moves his ship forward into the unknown.

Odysseus faces many other treacherous moments on his ten-year voyage home, such as his men eating Helios's cattle and dying in a storm, getting trapped on Calypso's island for almost eight years, and of course, returning to Ithaca to face over one hundred suitors who have overtaken his home. Through it all, Odysseus keeps his cool, uses his keen wit, and returns to his wife and son at the epic's end.
At the end of the day, Odysseus never gives up. He never lets fear get the best of him and pushes on through trials and tribulations to return to his family. He faces everything from monsters to gods and does so with death lurking around every corner. On top of it all, he fights for ten years and travels home for another ten. If that isn't bravery, I don't know what is!

Odysseus shows many acts of bravery in Homer's epic poem the Odyssey. First, he shows bravery when he tricks Polyphemus, the Cyclops, and gouges out his eye. This is an act of bravery. It will also cost him because Polyphemus was the son of Poseidon, the god of the sea. He also showed bravery in sailing into Hades, which is also known as the land of the dead. He encounters his mother there, who was alive when he left Ithaca.
Odysseus does not plug his ears when passing the island of the Sirens but has his men tie him to the ship's mast. The men had ear protection in order to not hear the song of the Sirens, but Odysseus bravely faced the temptation. He also cunningly made a provision for himself so that he would not succumb to it (being tied to the mast).
Odysseus shows bravery in bypassing Scylla. This was a multiheaded monster he faced on his journey back to Ithaca.
He also showed bravery when he faced the suitors who were in his home when he returned to Ithaca. Once more he has to fight, this time for what was rightfully his, and he shows bravery in facing great odds.

Odysseus is the cunning hero of Homer's Iliad as well as the main character and hero in his Odyssey.
Although he has a central part in both epic poems and fights bravely in the war with Troy (narrated in the Iliad), I assume you are referring to his actions in the Odyssey.
Odysseus is continuously proving his bravery, resourcefulness, and cleverness throughout the Odyssey. He encounters Polyphemus, the one-eyed Cyclops who keeps him and his men as prisoners and eats them one by one. With nerves of steel and a great deal of bravery, Odysseus manages to trick him and blind him. allowing him and his men to escape.
Further on, he encounters Circe, a sorceress who turns his men into pigs. Well aware of the danger she poses because of her magical abilities, he confronts anyway her to save his men.
He also faces the sirens head on: rather than being scared, he asks his men to tie him to the mast in order to be able to listen to the sirens' song without desperately chasing it.
However, I think his most significant act of bravery is his communion with the dead in order to learn his fate, an extraordinary feat which is presented as extremely dangerous for living humans.
Odysseus demonstrates bravery continuously; this, coupled with intelligence and resourcefulness finally allows him to finally return home to Penelope after twenty years.

Single Variable Calculus, Chapter 3, 3.2, Section 3.2, Problem 16

Suppose that $f(x) = x^3$





a.) Estimate the values of $f'(0)$, $\displaystyle f'\left(\frac{1}{2}\right)$, $f'(1)$, $f'(2)$ and $f'(3)$
using the graph of $f$

b.) Use symmetry to deduce the values of $\displaystyle f'\left(-\frac{1}{2}\right)$, $f'(-1)$, $f(-2)$ and $f'(-3)$

c.) Use the values from parts(a) and (b) to graph $f'$

d.) Guess a formula for $f'(x)$

e.) Use the definition of a derivative to prove that your guess in part(d) is correct.



a.) Referring to the graph, $f'(0) \approx 0$, $\displaystyle f'\left(\frac{1}{2}\right) \approx 0.5$, $f'(1) \approx 4$,
$f'(2) \approx 11$ and $f'(3) \approx 25$

b.) By symmetry across the $x$-axis, it looks like the slopes are all the same or each sides of they $y$-axis
$\displaystyle f'\left(-\frac{1}{2}\right) \approx 0.5$, $f'(-1) \approx 4$, $f'(-2) \approx 11$ and $f'(-3) \approx 25$.

c.)



d.) Based from the symmetrical values of slopes across $y$-axis, we can form a formula for $f'(x)$ as $f'(x) = nx^2$; for $n > 0$
where $n$ could be any positive constant.


e.) Based from the definition of derivative,


$\quad \displaystyle f'(x) = \lim\limits_{h \to 0} \frac{f(x+h)-f(x)}{h} \qquad \text{ where } f(x) = x^3$


$
\begin{equation}
\begin{aligned}
f'(x) &= \lim\limits_{h \to 0} \frac{(x+3)^3-x^3}{h}\\
f'(x) &= \lim\limits_{h \to 0} \frac{\cancel{x^3}+3x^2+h3xh^2+h^3-\cancel{x^3}}{h}\\
f'(x) &= \lim\limits_{h \to 0} \frac{\cancel{h}(3x^2+3xh+h^2)}{\cancel{h}}\\
f'(x) &= \lim\limits_{h \to 0} (3x^2+3xh+h^2)\\
f'(x) &= 3x^2+3x(0) + (0)^2\\
f'(x) &= 3x^2
\end{aligned}
\end{equation}
$



It shows that part(d) and part(c) resembles each other.

Why does Rainsford agree to be hunted?

Sangor Rainsford only agrees to be hunted because if he does not, he will be turned over to Ivan, who will undoubtedly torture and kill him.
While General Zaroff talks with Rainsford at dinner, he mentions the lack of enthusiasm for hunting that he had until he created his "dangerous game." But now, he complains, this "ennui" [boredom] seems to be returning because the hunting the night before was not exciting. 

"The fellow lost his head. He made a straight trail that offered no problems at all. . . . It's most annoying."

Since Rainsford recalls having heard the pistol shot, he is well aware of the outcome of that hunt. So, when Zaroff suggests that he and Rainsford hunt that night, Rainsford shakes his head in dissent. "No, general, . . . I will not hunt." Zaroff shrugs his shoulders and replies that the choice is Rainsford's, adding,

"But may I not venture to suggest that you will find my idea of sport more diverting than Ivan's."

Rainsford recalls the general's description of Ivan as once having served as "official knouter" to the Great White Czar." (He issued whippings to criminals.) According to Zaroff, Ivan "has his own ideas of sport." General Zaroff also has mentioned that the others who have been on the island have invariably chosen the hunt. So, since not agreeing to the hunt as suggested by Zaroff means a prolonged and brutal death, Rainsford decides to be hunted by Zaroff. As an accomplished hunter himself, Rainsford figures that he may be able to outwit Zaroff. 

What's an analysis of Don Juan Tenorio?

Zorrilla's Don Juan Tenorio is a Romantic transformation, or re-think, of the basic Don Juan story. It follows the basic outlines of the narrative used by others in the previous two hundred plus years, but it adds important elements and changes the overall thrust of the play and its moral.
Part I of the play contains the five-act structure of a complete drama. Don Juan is presented, from the start, as the legendary seducer who, as in Mozart's operatic version of 1787, keeps a list of the women he has seduced. But in Zorrilla's version, Don Juan is shown in opposition to another man, Don Luis, who seemingly wishes to compete with Don Juan in "immoral" attempts and makes a wager with him to this effect.
Zorrilla's point here seems to be that other men envy Don Juan and wish to be like him to beat him at his own game. In this regard, Zorrilla is a prototypical Romantic writer. The tendency of nineteenth-century literature is to exalt characters who are individualistic rebels and who defy the norms of society and the laws of man and God. In versions of the Don Juan story predating the nineteenth century, this view of the character may have been expressed but not explicitly—partly because of censorship and partly because artists themselves had not yet adopted the defiant and anti-religious mindset that would later characterize the Romantic period.
In this wager between Don Juan and Don Luis, it's not at all surprising that Juan comes out on top, though the outcome ends up being Juan's undoing. Don Juan is meant to be seen as both despicable and admirable. Through a ruse he gains entry to the apartments of Doña Ana, the betrothed of Don Luis. That his other seduction attempt of the night takes a different turn is evidence of Don Juan's dual-sided character, which, in keeping with the Romantic ethos, is a combination of good and bad, unlike the mostly good-for-nothing seducer of Tirso de Molina's and Moliere's treatments in the seventeenth-century.
Don Juan becomes overwhelmed with the purity and beauty of Doña Ines, a novice, or nun trainee, who is the daughter of the Commander of Seville, Don Gonzalo. It's as if his previously diabolical nature now has the potential to become angelic, and he waxes rhapsodic over Ines, declaring his great love for her. This, however, precipitates tragedy: it is as if Don Juan's ability genuinely to love a woman results, ironically, in his destruction. Or, Zorrilla's message is, conversely, that one's past will always catch up with one. Don Luis wants revenge for Juan's having seduced Luis's fiancee Ana, and Don Gonzalo disbelieves, unsurprisingly, that Juan has "honorable" intentions towards his daughter Ines. Don Juan, then, is forced to kill both Gonzalo and Luis.
This development differs from the similar point in the previous versions of the story. The chief plot device in de Molina, Moliere, and in Mozart's opera is the killing of the Commander alone, whose ghost, in the form of a statue, then exacts vengeance upon Don Juan. By having two killings, Zorrilla is, arguably, representing the good and evil sides of Don Juan and of human nature. Don Luis confronts Don Juan and duels with him in order to avenge one of Juan's typical, ruthless seductions. However, it's Don Juan's "conversion" to one who is actually capable of loving a woman that forces him into conflict with Don Gonzalo. Juan is forced to flee from Spain, and Ines dies of grief, setting the stage for Part II in which the supernatural phase of the story takes place.
We can see that Zorrilla's Don Juan is similar to other literary characters of the age, such as Heathcliff in Emily Bronte's Wuthering Heights and Julien Sorel in Stendhal's Le Rouge et le Noir. He has at least as much in common with these characters as with the Don Juan of Byron's epic poem, since, though one can see Byron's general influence on Zorrilla, Byron's Don Juan character and treatment of the story differ so much from the traditional version that there would have been little in them for Zorrilla to take as direct points of departure. Zorrilla prefers to stick to the basic outline of the legend and most of the literary versions. Probably, the most immediate antecedent for Zorrilla's version is Mozart's opera, which fired the imagination of the Romantic generation. Mozart's hero-villain has been interpreted by various commentators and writers (such as E.T.A. Hoffmann) as the prototype of the Romantic rebel, who, though on the surface he appears a cynical, manipulative seducer, is actually a kind of existential superhero who restlessly searches for the ultimate woman with whom he can bond. This is exactly the way I would interpret Zorrilla's Don Juan. In Ines he finds this idea, ultimate partner; she is the one who remains chaste, and rather than relinquish her, Don Juan confronts her father and kills him. Though at this point the reader, or audience, has no way of anticipating the outcome, in Part II it leads to Don Juan's salvation. As in the earlier versions, the animated statue of the Commander intends to drag Don Juan to hell, but the ghost of Ines intervenes and redeems him. The ending also has something in common with that of Goethe's Faust and its verse that "the eternal feminine leads us on high."
In summary, Zorrilla's treatment of the story is a Romantic re-think, an interpretation not grounded in the concepts of sin and guilt but in the dual, or multi-faceted nature, of human beings, who contain within themselves both good and evil. Don Juan makes the choice, unexpectedly, and perhaps unrealistically, to abandon his life style of seduction and crime when he encounters Ines. Both his flaws, and the better qualities within him, lead him to this, and the resulting tragedy of his killing both Gonzalo and Luis has the effect of both destroying and saving Don Juan. It is a typical Romantic juxtaposition of opposites, one in which the complexities and unexpected qualities of human nature are to be celebrated, and are the elements that enable man to strive towards the divine and the eternal, as the Romantic artist so often has him do.

How does the "Star-Spangled Banner" elicit feelings of love and pride for one's country through both its words and instrumental pieces?

The context of the "Star-Spangled Banner" is that it was written by Francis Scott Key during the War of 1812 about the British bombardment of Fort McHenry during the Battle of Baltimore. The American flag that remained during the battle, which ended in an American victory, inspired Key to write a poem called "Defence of Fort M'Henry." Though the poem is four stanzas in length, only the first stanza was used for the song.
The lyrics of the song celebrate the American flag, which was not really a symbol of the country until the War of 1812. That war, considered the second war of American independence, made the United States definitively free from British rule. The lyrics present vivid imagery, including the "dawn's early light." Even then, the "broad stripes and bright stars" remain visible. The flag is a symbol of American permanence and strength in the wake of attack. As the flag survives the battle, so too will the United States survive. The lyrics use a great deal of alliteration—the repetition of initial sounds—such as "the rocket's red glare," enhancing their poetic quality. 
The music was set to the tune of "The Anacreontic Song" by English composer John Stafford Smith. As the range of the music is one octave and one fifth, it is considered a difficult song to sing. It requires vocal training to hit all the notes. The instrumental version, often played by military bands, is often considered very rousing. In 1917, John Philips Sousa and others made an official arrangement for the army and navy. This version was harmonized by Walter Damrosch and arranged by Sousa, making it exciting and expertly arranged.
https://amhistory.si.edu/starspangledbanner/symbols-of-a-new-nation.aspx

What was the social impact of the automobile for teenagers?

The automobile had tremendous social impact on the lives of millions of teenagers. Previously restricted in their mobility by their dependence on adults, mainly parents, for transportation, the introduction of the automobile provided teenagers their own (assuming they were/are able to secure use of a vehicle) form of transportation that greatly exceeded the geographical limitations associated with the use of bicycles and walking. Teenagers were able to socialize at each other's homes, at malls, at diners, or at any other location without reliance on parents for transportation—reliance that often precluded certain types of activities, such as smoking and drinking.
The use of automobiles also impacted the social lives of teenagers by enabling them to interact within the confines of their vehicles while occasionally simultaneously interacting with friends and others either standing nearby or in vehicles of their own. "Cruising" became a common pastime, with teenagers using their cars to enhance their social status by emphasizing their independence. In short, the introduction of the automobile had a very profound, if occasionally disturbing impact on the social lives of teenagers.

How did urban industrialization affect Americans’ lives outside of work?

During the late nineteenth and early twentieth century, urban growth was spurred by industrial growth as new technological developments, industries, and business practices combined to create what is now called the Second Industrial Revolution or, alternatively, the Gilded Age. Societal change accompanied these developments, especially as cities grew to meet new labor demands. For the first time in US history, more people lived in cities than in rural areas, as both men and women flocked to cities to fill factory jobs. Immigrants also contributed to this migration, creating diverse cities in which many immigrants clustered into communities or neighborhoods such as Little Italy and Chinatown. These waves of immigrants were also met with backlash and challenges; they faced anti-immigrant sentiment, low wages, and crowded living conditions in tenements.
Contrary to popular belief, the average standard of living rose for most Americans during this time period. Goods could be mass produced in factories, making them cheaper and more affordable. Previously, many Americans had made their own clothes and household items, but with the rise of industrialization, more Americans could afford to buy consumer products. Finally, in part due to the reduced need to make one's own goods and food, Americans had more leisure time. Pastimes such as baseball became popular, and in the twentieth century, the radio and the automobile would become symbols of American freedom, leisure, and consumerism.
For more info, please go to the following website: https://www.gilderlehrman.org/history-now/gilded-age

How does Hans Christian Anderson make us feel sympathetic toward the little girl in the short story "The Little Match Girl"?

First, Andersen establishes a brutal setting for her: "It was dreadfully cold; it was snowing fast, and was almost dark."  To make matters worse, she is bareheaded and barefooted, having lost her excessively large slippers running across a street to escape the carriages that "were passing terribly fast."  Now, her feet are "red and blue with cold."  As if these descriptions of the dreadful cold, the terrible speed of the frightening carriages, and the painful visual imagery of her frozen feet are not enough, the narrator tells us, "Poor little girl!  Shivering with cold and hunger she crept along, a perfect picture of misery." 
Not only is the child rendered terribly sympathetic by word choices such as these, she also begins to smell savory roasted goose from a house she is passing, contrasting painfully with her hunger and need.  She huddles against a wall, and, to warm herself, she lights her matches one by one, imagining the feast inside the home, the beautifully trimmed Christmas tree, and, finally—lighting an entire bundle so the vision will not fade—her grandmother, "the only person who had loved her."  The child goes to God in the arms of her grandmother, with "neither hunger nor cold, nor care."  She is found smiling—and dead—in the morning.
Thus, Andersen elicits our sympathy with the harsh winter setting, the child's abject poverty, careful word choice, vivid description and imagery, and the juxtaposition of the child's reality with her fantasy.  Even the fact that he chooses a child as the main character elicits more sympathy than would an adult protagonist.

How has Bill Gates shown utilitarianism in business?

As the developer of such products as Microsoft Windows, Bill Gates has contributed much to the forces that have changed society over the last four decades. Few technologies have been as transformative, meeting the needs of more people, than those marketed by Microsoft. In this sense, the career of Bill Gates would be in line with the principles of utilitarianism, at least for those who accept that the profit motive and the desire to do the greatest amount of good are not mutually exclusive. It is in the philanthropic work that Gates has done, however, that we see a profoundly utilitarian approach, at least in philosophy. The Bill and Melinda Gates Foundation has sought to use the resources and global exposure Gates can provide to attack very large problems—disease in Africa, education reform in the United States, and sustainable farming practices. While some of these measures, especially his influence on education, have met with some controversy, there is no arguing that he has chosen to use his enormous wealth to attempt to do good for the most possible people. In this sense, his philanthropic work is utilitarian in nature.
https://www.gatesfoundation.org/

Bill Gates's products use a great definition of utilitarianism. Utilitarianism, as described by Jeremy Bentham and John Stewart Mill, can be defined as seeking the greatest good for the greatest number of people. Gates's Windows operating systems have been around for over twenty years and they continue to be some of the most common computer operating systems in the world. Microsoft has branched into the gaming world as well, but it mainly is rooted in computers for business and personal use. By creating this system, Gates has allowed millions of workers to be trained in the use of a single operating system that is user-friendly and nearly universal. Computer programmers design specific programs that will be compatible with the operating system, thus creating more jobs for more people. Gates, as a result of this, has become quite rich. In the process of helping other people understand and use technology, Gates has expanded his own wealth.

Calculus of a Single Variable, Chapter 5, 5.7, Section 5.7, Problem 38

To evaluate the given integral: int 2/sqrt(-x^2+4x)dx , we may apply the basic integration property: int c*f(x)dx= c int f(x)dx .
The integral becomes:
2 int dx/sqrt(-x^2+4x)
We complete the square for the expression (-x^2+4x) .
Completing the square:
For the first step, factor out (-1): (-x^2+4x) = (-1)(x^2-4x) or -(x^2-4x)
The x^2 -4x or x^-4x+0 resembles the ax^2+bx+c where:
a=1 , b =-4 and c=0 .
To complete the square, we add and subtract (-b/(2a))^2 .
Using a=1 and b=-4 , we get:
(-b/(2a))^2 =(-(-4)/(2(1)))^2
=(4/2)^2
= 2^2
=4
Add and subtract 4 inside the (x^2-4x) :
-(x^2-4x+4 -4)
Distribute the negative sign on -4 to rewrite it as:
-(x^2-4x+4) +4
Factor the perfect square trinomial: x^2-4x+4 = (x-2)^2 .
-(x-2)^2 +4

For the original problem, we let: -x^2+4x=-(x-2)^2 +4 :
2 int dx/sqrt(-x^2+4x)=2 int dx/sqrt(-(x-2)^2+4)
It can also be rewritten as:
2 int dx/sqrt(-(x-2)^2 +2^2) =2 int dx/sqrt(2^2 -(x-2)^2)
The integral part resembles the integral formula:
int (du)/sqrt(a^2-u^2) = arcsin(u/a)+C .
Applying the formula, we get:
2 int dx/sqrt(2^2 -(x-2)^2) =2 *(arcsin (x-2)/2) +C
Then the indefinite integral :
int 2/sqrt(-x^2+4x)dx = 2arcsin((x-2)/2)+C

Calculus of a Single Variable, Chapter 9, 9.2, Section 9.2, Problem 12

sum_(n=1)^oo n/sqrt(n^2+1)
To verify if the series diverges, apply the nth-Term Test for Divergence.
It states that if the limit of a_n is not zero, or does not exist, then the sum diverges.

lim_(n->oo) a_n!=0 or lim_(n->oo) a_n =DNE
:. sum a_n diverges

Applying this, the limit of the term of the series as n approaches infinity is:
lim_(n->oo) a_n
=lim_(n->oo) n/sqrt(n^2+1)
=lim_(n->oo) n/sqrt(n^2(1+1/n^2))
=lim_(n->oo) n/(nsqrt(1+1/n^2))
=lim_(n->oo) 1/sqrt(1+1/n^2)
=(lim_(n->oo)1)/(lim_(n->oo)sqrt(1+1/n^2))
=1/sqrt(0+1)
=1
The limit of the series is not zero. Therefore, by the nth-Term Test forDivergence, the series diverges.

Suppose a firm finds that the marginal product of capital is 60 and the marginal product of labor is 20. If the price of capital is $6 and the price of labor is $2.50, how should the firm adjust its mix of capital and labor? What will be the result?

The idea in question here is that money in the firm is finite, and therefore the budget must be maximized with what it currently has. Therefore, if you spend an extra dollar on capital, you must spend a dollar less on labor. We want to calculate marginal benefit of each expenditure by dividing marginal product by price.
For capital, Marginal Benefit = 60/6, or 10, and for labor, Marginal benefit = 20/2.5, or 8. Therefore, for each dollar spent on capital, the company gains 10 units of production, and for each dollar spent on labor, the firm gains 8 units of production.
Extrapolating this using the principle in question, if you move a dollar from labor to capital, you will gain 10 units of production but lose 8 at the same time, therefore totaling a net positive of 2 units. Therefore, you will want to move funds to capital until you begin to see diminishing returns from reducing labor.

First, we can find the firm's marginal benefit per additional dollar that it spends on both factors of production: capital and labor.
To find the marginal benefit of a factor of production, take its marginal product, or MP, and divide it by its price, or P.
For capital, this is equivalent to the calculation 60/$6 = 10 units of product per additional dollar spent.
Similarly, for labor, this is equivalent to 20/$2.50 = 8 units of product per additional dollar spent.
We have now found that the firm has a rationale to become more capital-heavy, since its money is more productive when fed into its capital holdings. Usually, as a firm acts on such insight and feeds more money into the more effective factor of production, the firm will discover new efficiencies, and its ratio MP/P for each factor of production will equilibrate (tend toward equality).

In this example, you are attempting to minimize the amount the firm spends on labor and capital by mixing it appropriately. In order to accurately identify how much of each item—labor and capital—to utilize, you need to know the amount of units given to you, such as a total budget for labor and capital.
If, for example, we were given $100 for this project, you could make a budget to determine the most effective use of your finances. You need to employ both capital and labor to make your machinery work and can't simply throw all of your resources into one arena, but by analyzing the cost per unit of production, you can see where the most value for your money lies.
In this example, each dollar of capital gives you 10 units of production, and each dollar of labor gives you 8 units of production (60/$6 and 20/$2.50, respectively). Knowing this, you find that—when mixing labor and capital—capital will give you 25% more production than labor.

Based on Economics (Tregarthen and Rittenberg), if we spend $1 more on capital, we must spend $1 less on labor.
Since the marginal product of capital is 60, and the price of capital is $6, the marginal benefit of $1 spent on capital is Marginal Product of Capital/ Price of Capital= 60/6= 10.
So, the firm will gain 10 units of output by spending an additional $1 on capital.
Then, we are told that the marginal product of labor is 20 and the price of labor is $2.50. The marginal disadvantage of $1 less spent on labor would be Marginal Product of Labor/ Price of Labor= 20/2.50= 8.
The firm would lose 8 units of output from spending $1 less on labor.
To compare, MPC/P > MPL/P
 60/6 > 20/2.50
So, the company achieves a net gain of 2 units of output if it transfers $1 from labor to capital. It will continue to transfer funds as long as it gains more output from the additional capital than it loses in output by reducing labor. Essentially, the company will increase in output and be capital-intensive for a period of time.

why do you think Lawrence uses words like "dreamily " or "drunken" here?

The words "dreamily" and "drunken," used alliteratively by Lawrence to describe the way the snake looks at him after it "drank" at his trough, serve to emphasize the overall mood of the poem, which drowsily evokes the hot Sicilian afternoon. The alliteration in these words continues throughout the stanza: the snake is "thrice adream" as he begins to "draw" his length away. The "dr" sound itself is drowsy, dreamy; Lawrence also uses alliteration on "s" in this poem—"slowly," "softly," "silently," "slack"—to create a soft, dream-like atmosphere.
These words also personify the snake: throughout the poem, Lawrence does this, describing the snake as "him" rather than "it" and suggesting that he has more right to drink at the trough than the speaker, "like a second-comer," does. The snake is at first drinking "as cattle do," but as the speaker continues to watch, the snake becomes "like a guest" and then "like a god." The "drunken" dreamy aspect of the snake, then, is partly reflected in the speaker himself, who seems half-hypnotized by the snake, "honoured" by his presence.

Calculus of a Single Variable, Chapter 5, 5.7, Section 5.7, Problem 4

Recall that the indefinite integral is denoted as:
int f(x) dx =F(x)+C
There properties and basic formulas of integration we can apply to simply certain function.
For the problem int (12)/(1+9x^2)dx
we apply the int cf(x)dx = c int f(x)dx to become:
12 int 1/(1+9x^2)dx
Then apply the basic inverse trigonometric function formula:
int (du)/(a^2+u^2) = 1/a arctan(u/a)+C
By comparison with the basic formula and the given problem, we can let:
a^2 =1
u^2=9x^2 or (3x)^2
then du = 3 dx
To satisfy the given formula, we need to multiply the integral by 3/3 to
be able to match du = 3 dx .

The integral value will note change since multiplying by 3/3 is the same as multiplying by 1. Note: 3/3= 1 and 3/3 = 3*(1/3)
Then 12 int 1/(1+9x^2)dx * 3/3
= 12 int 1/(1+9x^2)dx * 3 * 1/3
= 12 (1/3)int 1*3/(1+9x^2)dx
=4 int (3 dx)/(1+9x^2)
The int (3 dx)/(1+9x^2) is now similar to int (du)/(a^2+u^2) where:
du =3dx , a^2 =1 and u^2 = 9x^2 or (3x)^2
then a=1 and u =3x .

Plug-in a=1 and u = 3x in 1/a arctan(u/a)+C , we get:
4* int (3 dx)/(1+9x^2) = 4* 1/1 arctan((3x)/1)+C
=4 arctan(3x)+C

What are some symbols related to themes of sin, revenge, and reputation in The Scarlet Letter?

At the beginning of chapter 1, entitled "The Prison Door," the narrator says,

The founders of a new colony, whatever Utopia of human virtue and happiness they might originally project, have invariably recognized it among their earliest practical necessities to allot a portion of the virgin soil as a cemetery, and another portion as the site of a prison.

Thus, the Puritans built a cemetery and a prison because they knew, no matter how much they hoped it could be otherwise, that people would inevitably do two things: they would die and they would commit crimes. Just as a cemetery can be symbolic of death, the prison is symbolic of our criminal (and, for the Puritans, sinful) natures; since sins were crimes to them, the prison becomes a symbol of sin.
The imaginary circle that constantly surrounds Hester and Pearl when they are near other people, the circle into which others typically do not venture, could be seen as symbolic of their reputation as sinful beings. It is a physical representation of the feelings many people experience: they want to keep their distance from Hester and her daughter, as though their sinfulness might infect others who come near to them. The narrator says,

Mother and daughter stood together in the same circle of seclusion from human society . . .

Because of their sinful reputations, they are physically set apart.
The character of Chillingworth, himself, could be considered a symbol of revenge. His obsession with taking his revenge on Hester's co-sinner overwhelms him, and he changes from someone who was once good to a person that others associate with the devil. The narrator says,

At first, his expression had been calm, meditative, scholar-like. Now, there was something ugly and evil in his face, which they had not previously noticed, and which grew still the more obvious to sight, the oftener they looked upon him. According to the vulgar idea, the fire in his laboratory had been brought from the lower regions, and was fed with infernal fuel; and so, as might be expected, his visage was getting sooty with the smoke.

Chillingworth's physical and moral declension shows how revenge ravages a person, stripping them of their humanity.

The scarlet A that Hester Prynne wears is at first a symbol of her transgression in the eyes of her Puritan community; it is said to stand for "adultery." However, after years of living humbly in their judgment, there are those who begin to say that Hester's A has come to symbolize "able" as she comforts the sick and performs other acts of charity. In these ways, Hester's letter symbolizes both sin and reputation.
Revenge is symbolized in the subject of the representational tapestry hanging in the shared living space of Arthur Dimmesdale and Roger Chillingworth. Chillingworth correctly surmises that Dimmesdale is the father of Pearl, and as Hester's legal husband, he would like to exact covert revenge against the pastor. The tapestry depicts David's shame over his adultery with Bathsheba. Chillingworth enjoys seeing Dimmesdale suffer, and the fact that Dimmesdale has a constant visual reminder in their shared home symbolizes his desire for revenge.

Calculus of a Single Variable, Chapter 3, 3.2, Section 3.2, Problem 2

The Rolle's theorem is applicable to the given function, only if the function is continuous and differentiable over the interval, and f(a) = f(b). Since all trigonometric functions are continuous and differentiable on R, hence, the given function is continuous and differentiable on interval. Now, you need to check if f(pi) = f(3pi).
f(pi) = cot (pi/2) = 0
f(3pi) = cot(3pi/2) = 0
Since all the three conditions are valid, you may apply Rolle's theorem:
f'(c)(b-a) = 0
Replacing 3pi for b and pi for a, yields:
f'(c)(3pi-pi) = 0
You need to evaluate f'(c), using chain rule:
f'(c) = (cot(c/2))' = -1/(2sin^2(c/2))
Replacing the found values in equation f'(c)(3pi-pi) = 0.
-2pi/(2sin^2(c/2)) != 0
Hence, in this case, there is no valid value of c for Rolle's theorem to be applied.

When did Sula and Nel's friendship end?

The catalyst for the break between Nel and Sula occurs when Sula goes to bed with Nel's husband, Jude. Jude initially isn't physically attracted to Sula but sees how she could engage a man's mind. He's intrigued by the challenge that Sula seems to represent, which contrasts with Nel's more malleable character. Nel walks in on Jude and Sula having sex and, initially, registers incredulity at what she sees. After they notice that Nel has entered the room, Sula sits up in bed, leaving her nude body exposed. She doesn't look at her shocked friend but instead casually examines her fingernail.
Both Sula and Nel are products of the Bottom, the ironically-named black community in the town's valley. Nel, who is lighter-skinned, grew up with a mother who believed that she could gain favor with white people by distinguishing herself and her daughter as "a better breed" of black folks. Nel witnesses this one day, as a child, when her mother smiles obsequiously at a white man who insults her. Sula, who is darker, is the daughter of Hanna, a beautiful woman known for having many relationships with men. The Peace family, particularly its women, are known for existing on the margins of an already ostracized community.
Despite these contrasts in their backgrounds and their characters, I wouldn't agree with the previous educator's assessment that it's "amazing" that the girls became friends. They grew up learning different ways to cope with oppression. The friendship between the girls is cemented when Sula staves off a pack of boy bullies by slicing off the tip of her finger, warning them that, if she's willing to do such a thing to herself, what might she do to them? Arguably, Sula's decision to sleep with Jude is a similar act. It, too, bears the mark of mutilation and severance. The purpose, in both instances, was to protect Nel, to let her know that Sula would protect her right to exist. It's not until the end of the novel, after Sula has died, that Nel understands her friend and the things she tried to do for her. Sula's transgressive act of "taking" Nel's husband had nothing to do with wanting Jude and everything to do with getting Nel to see which bonds would really help her to flourish.

Sula and Nel's friendship has more than its fair share of ups and downs. But it is amazing that they ever became friends in the first place when considering their radically different upbringings. In any case, as Morrison is anxious to point out, friendship is a complex business, involving good times and bad times: this includes love and hate, loyalty and betrayal. Betrayal is what finally puts an end to Sula and Nel's friendship.
Sula has a different attitude when it comes to forming sexual relationships, one that puts her outside the bounds of so-called respectable society. Nel, on the other hand, subscribes to the social role accorded to her as a young African American woman from a good family. The friends' respective worldviews are diametrically opposite to one another, and it is their eventual collision that leads to the breakdown of their friendship. When Sula returns to her hometown after a lengthy absence, she hooks up with Nel's husband and begins an affair with him. Unsurprisingly, Nel is infuriated by this and severs all connections with her former friend.

College Algebra, Chapter 4, 4.6, Section 4.6, Problem 64

Find the intercepts and asymptotes of the rational function $\displaystyle r(x) = \frac{x^3 - x^2}{x^3 - 3x - 2}$ and then sketch its graph.

We first factor $r$, so $\displaystyle r(x) = \frac{x^2 (x - 1)}{x^3 - 3x - 2}$

Use synthetic Division to factor the denominator, then by trial and error







Thus, $\displaystyle r(x) = \frac{x^2 (x - 1)}{(x - 2)(x^2 + 2x + 1)} = \frac{x^2 (x - 1)}{(x - 2)(x + 1)^2}$

The $x$-intercepts are the zeros of the numerator $x = 0$ and $x = 1$.

To find the $y$-intercept, we set $x = 0$ then

$\displaystyle r(0) = \frac{(0)^2 (0-1)}{(0 -2)(0 + 1)^2} = 0$

the $y$-intercept is .

The vertical asymptotes occur where the denominator is , that is, where the function is undefined. Hence the lines $x = 2$ and $x = -1$ are the vertical asymptotes.

We need to know whether $y \to \infty$ or $y \to - \infty$ on each side of each vertical asymptote. We use test values to determine the sign of $y$ for $x$- values near the vertical asymptotes. For instance, as $x \to 2^+$, we use a test value close to and to the right of $2$ (say $x = 2.1$) to check whether $y$ is positive or negative to the right of $x = 2$.

$\displaystyle y = \frac{(2.1)^2 [(2.1) - 1]}{[(2. 1) - 2] [(2.1) + 1]^2}$ whose sign is $\displaystyle \frac{(+)(+)}{(+)(+)}$ (positive)

So $y \to \infty$ as $x \to 2^+$. On the other hand, as $x \to 2^-$, we use a test value close to and to the left of $2$ (say $x = 1.9$), to obtain

$\displaystyle y = \frac{(1.9)^2 [(1.9) - 1]}{[(1.9) - 2][(1.9) + 1]^2}$ whose sign is $\displaystyle \frac{(+)(+)}{(-)(+)}$ (negative)

So $y \to -\infty$ as $x \to 2^-$. The other entries in the following table are calculated similarly

$\begin{array}{|c|c|c|c|c|}
\hline\\
\text{As } x \to & 2^+ & 2^- & -1^+ & -1^- \\
\hline\\
\text{Sign of } \frac{(x^2) (x - 1)}{(x -2 ) (x + 1)^2} & \frac{(+)(+)}{(+)(+)} & \frac{(+)(+)}{(-)(+)} & \frac{(+)(+)}{(-)(+)} & \frac{(+)(-)}{(-)(+)} \\
\hline\\
y \to & \infty & - \infty & \infty & \infty\\
\hline
\end{array} $

Horizontal Asymptote. Since the degree of the numerator is equal to the degree of the denominator, then the horizontal asymptote $\displaystyle = \frac{\text{leading coefficient of the numerator}}{\text{leading coefficient of the denominator}} = \frac{1}{1}$. Thus, the line $y = 1$ is the horizontal asymptote .

Is Imagery evident in Brave New World?

Yes, Huxley relies heavily on imagery to describe both the World State and the Indian Reservation. Imagery is description that uses the five senses of sight, sound, touch, smell, and taste. To effectively convey an alternate universe, as Huxley does, it is important that readers are able to imagine it clearly. Huxley therefore gives us what we need to visualize living in the New World State, where everything is clean, bright, new, and sterile—but sometimes not much fun. He doesn't just tell us about how the babies are conditioned, for example, but shows it to us with the vivid use of imagery. For instance, right before a group of babies is about to be conditioned to hate nature through use of a loud siren and electric shock, Huxley sets the scene in full detail:

The Director opened a door. They were in a large bare room, very bright and sunny; for the whole of the southern wall was a single window. Half a dozen nurses, trousered and jacketed in the regulation white viscose-linen uniform, their hair aseptically hidden under white caps, were engaged in setting out bowls of roses in a long row across the floor. Big bowls, packed tight with blossom. Thousands of petals, ripe-blown and silkily smooth, like the cheeks of innumerable little cherubs ...

We can easily visualize the bright, clean setting, the nurses in white, and the beautiful rose blossoms set in bowls, which sets up a sharp contrast to the way the babies will soon be treated.
Likewise, a religious ceremony at the Indian Reservation is described using vivid imagery:

Then the old man lifted his hand and, startingly, terrifyingly, there was absolute silence. The drums stopped beating, life seemed to have come to an end. The old man pointed towards the two hatchways that gave entrance to the lower world. And slowly, raised by invisible hands from below, there emerged from the one a painted image of an eagle, from the other that of a man, naked, and nailed to a cross. They hung there, seemingly self-sustained, as though watching. The old man clapped his hands. Naked but for a white cotton breech-cloth, a boy of about eighteen stepped out of the crowd and stood before him, his hands crossed over his chest, his head bowed.

The detailed description highlights the contrasts between the two worlds, which will collide in John the Savage when he comes to the World State.

How did Daniel formerly look at stealing food, and why has his attitude changed?

While serving as a member of Rosh's gang, Daniel was regularly called upon to participate in acts of robbery against unsuspecting travelers. Even though many of these travelers were Jews like themselves, Rosh is such a fanatical zealot that he thinks that the end justifies the means. The revolutionaries need a regular supply of food and valuables to survive and continue their fight with the Romans.
Daniel wants to impress the charismatic zealot leader, so initially goes along with the robberies enthusiastically. However, he quickly develops pangs of guilt after one of the old men the gang rob reminds him of his beloved grandfather. Gradually, Daniel becomes disillusioned with Rosh's methods. He joined up with the zealots to fight Romans, not steal from his own people. This is the beginning of what will eventually become an irreparable breach between Daniel and Rosh.

College Algebra, Chapter 2, 2.2, Section 2.2, Problem 66

Show that the equation $x^2 + y^2 -2x - 2y = 2$ represents a circle. Find the center and radius of the circle.


$
\begin{equation}
\begin{aligned}

x^2 + y^2 - 2x - 2y =& 2
&& \text{Model}
\\
\\
(x^2 - 2x + \underline{}) + (y^2 - 2y + \underline{ }) =& 2
&& \text{Group terms}
\\
\\
(x^2 - 2x + 1) + (y^2 - 2y + 1) =& 2 + 1 + 1
&& \text{Complete the square: add } \left( \frac{-2}{2} \right)^2 = 1, \text{ twice}
\\
\\
(x - 1)^2 + (y - 1)^2 =& 4
&& \text{Perfect Square}

\end{aligned}
\end{equation}
$


Recall that the general equation for the circle with
circle $(h,k)$ and radius $r$ is..

$(x - h)^2 + (y - k)^2 = r^2$

By observation,

The center is at $(1, 1)$ and the radius is 2.

I need help with a two-part assignment. 1. Does Socrates teach anything of his own in the Euthyphro? What textual proof can you offer to support your point? 2. Explain and summarize the 2nd definition of piety and Socrates’s response to that definition.

The first question is itself somewhat problematic. If you read the Euthyphro, you will note that the method of the dialogue seems to be one of offering up a series of questions and tentative solutions. The tentative solutions are then examined and rejected. Thus while Socrates examines many different definitions of piety, he does not set forth any single definition as dogma. The dialogue ends with an aporia, as can be seen in the final statement "Then we must begin again and ask, What is piety?" Of the ideas examined, of course, many are original. One of the most interesting aspects of the dialogue is that it probably is the first example of a Greek text to use the term "ousia" to mean "essence". Although the nature of piety itself is not resolved in the dialogue, one can answer that the distinction between essence and "not-essence" (accident) is established and not refuted; thus Socrates could be said to teach philosophical method in his call for definitions to reflect the ousia of what is being defined. 
The second definition of piety is that it is what is pleasing to the gods. Socrates refutes this with the observation that different things please different gods. For example, chastity pleases Artemis but not Aphrodite. 
https://plato.stanford.edu/entries/plato-ethics-shorter/

A pilot wishes to fly a plane due north relative to the ground. The airspeed of the plane is 200 km/h and the wind is blowing from the west to east at 90 km/h. In what direction should the plane head? What is the ground speed of the plane?

Since the wind is blowing to the east, a plane headed due north will drift off coarse toward the east.Hence, to compensate for this crosswind, the plane must head west of due north. We must use addition of velocity vectors to relate the plane relative to the ground v_(pG)^(->) , the plane relative to the air v_(pA)^(->) , and the air relative to the ground v_(AG)^(->) .
The three velocities are related by the velocity vector addition formula.
eq. (1) :-> v_(ac)^(->)=v_(ab)^(->)+v_(bc)^(->)
We want to know the ground speed of the plane which is v_(pG)^(->) . Therefore let a=p , c=G , and b=A in eq. (1) .
v_(pG)^(->)=v_(pA)^(->)+v_(AG)^(->)
This makes the velocity addition diagram that is given below. From the diagram you can tell that the sine of the angle theta equals the ratio of two of the vectors.
sin(theta)=v_(AG)^(->)/v_(pA)^(->)=(90 (km)/h)/(200 (km)/h)=9/20
Therefore the plane must travel relative to the air,
theta=sin^-1(9/20)~~27^@ west of north.
We can now use the Pythagorean theorem to find the magnitude of v_(pG)^(->) .
|v_(pG)^(->)|=sqrt(|v_(pA)^(->)|^2+|v_(AG)^(->)|^2)
v_(pG)^(->)=sqrt((200 (km)/h)^2+(90 (km)/h))^2=180 (km)/h
http://hyperphysics.phy-astr.gsu.edu/hbase/airpw.html

x = y+2, x=y^2 Find the x and y moments of inertia and center of mass for the laminas of uniform density p bounded by the graphs of the equations.

First lets find the bounds of integration. When looking at the graph the furthest that the lamina is bounded on the y-axis is where the curves interest. Lets find those points.
y+2=y^2
0=(y+1)(y-2)
Therefore the y bounds are y=-1 and y=2. Then we will integrate between the furthest right curve (x=y) and the furthest left curve.
The center of Mass is:
(x_(cm),y_(cm))=(M_y/M, M_x/M)
Where the moments of mass are defined as:
M_x=int int_A rho(x,y)*y dy dx
M_y=int int_A rho(x,y)*x dy dx
The total mass is defined as:
M=int int_A rho(x,y)dy dx
First, lets find the total mass.
M=int^2_-1 [int^(x=y+2)_(x=y^2) rho dx] dy
M=rho int^2_-1 [(y+2)-(y^2)] dy
M=rho [(1/2)y^2+2y-(1/3)y^3]|^2_-1
M=9/2 rho
Now lets find the x moment of mass.
M=int^2_-1 y*[int^(x=y+2)_(x=y^2) rho dx] dy
M=rho int^2_-1 y*[(y+2)-(y^2)] dy
M=rho int^2_-1 (y^2+2y-y^3) dy
M=rho ((1/3)y^3+y^2-(1/4)y^4)|^2_-1
M_x=9/4 rho
Now the y moment of mass.
M=int^2_-1 [int^(x=y+2)_(x=y^2) rho x dx] dy
M=rho/2 int^2_-1 [x^2|^(y+2)_(y^2)] dy
M=rho/2 int^2_-1 (y^2+4y+4-y^4) dy
M=rho/2((1/3)y^3+2y^2+4y-(1/5)y^5)|^2_-1
M_y=36/5 rho
Therefore the center of mass is:
(x_(cm),y_(cm))=(M_y/M, M_x/M)=((36/5 rho)/(9/2 rho),(9/4 rho)/(9/2 rho))=(8/5,1/2)
The moments of inerita or the second moments of the lamina are:
I_x=int int_A rho(x,y)*y^2 dy dx
I_y=int int_A rho(x,y)*x^2 dy dx
I won't solve these integrals step by step since they are very similar to the others, but you will find that:
I_x=63/20 rho
I_y=423/28 rho

The narrator's tone is best described as what?

Charlotte Perkins Gilman's "The Yellow Wallpaper" is a classic example of narrative driven action--all the elements of the story spring from the unnamed woman's entries in her journal, over the course of her treatment for "nervous exhaustion."
This narrator is an excellent example of what is called an "unreliable narrator"--over the course of the story, we begin to realize that the author is going, or has been for some time, mad, due her confinement in one room, in order to recover from her illness. Tone in a piece of literature indicates how the author feels about what they are writing about, and/or to whom they are writing, and in this story, the narrator stands in explicitly for the author. This story is famous in part because something very similar happened to Perkins Gilman--she suffered from "nervous exhaustion," was prescribed "the rest cure" (confinement to bed for a period of several months, with no stimulation, especially not reading or writing) and she suffered a nervous breakdown from the "cure." Perkins Gilman wrote this story explicitly to expose her suffering, and that of other women in similar situations, and the first thing she did after writing it was send it to the doctor who had treated her, Dr. S. Weir Mitchell, and "convince him of the error of his ways" (Thrailkill 2002, p. 528).
With these facts mind, we can see the tone of the story develop from a determined cheerfulness in the beginning, when the narrator describes the "ancestral hall" she and her family are renting for the summer as "The most beautiful place!" with "a delicious garden!" as the narrator is determined to do what the authoritative men in her life deem best, despite her own misgivings.
As the story develops, the hints of trouble from the opening become more ominous--the narrator is forced to hide her writing from anyone, as it violates her treatment, and she becomes increasingly paranoid, even suspecting her sister-in-law of spying on her. And the terrible wallpaper of the room to which the narrator is confined--"I never saw a worse paper in my life"--takes on a terrifying life of its own as it color-"dull yet lurid orange in some places, a sickly sulphur tint in others...smouldering, unclean"-- and patterns--"dull enough to confuse the eye in following, pronounced enough to constantly irritate, and provoke study, and when you follow the lame, uncertain curves for a little distance they suddenly commit suicide—plunge off at outrageous angles, destroy themselves in unheard-of contradictions"--infiltrate the narrator's mind.
By the time we come to the long climax of the story, the narrator is in a full blow pyschotic break, seeing a woman/women trapped in the yellow wallpaper, whose heads "the pattern strangles...off and turns them upside-down, and makes their eyes white!" and finally, coming to believe that the woman in the wallpaper is herself. In an ironic turn, the woman desperate to escape the awful room she's been confined to for months, becomes determined to remain there, locking out her husband and staying where she "can creep smoothly on the floor, and [her] shoulder just fits in that long smooch around the wall, so [she] cannot lose [her] way."

Given this tension and these twists, what can we say of the narrator's tone. Firstly, there is passion, passion in exposing the dreadful circumstances of 19th century women who were profoundly mistreated by doctors for issues we recognize today as medical (depression, anxiety), and urgency, in trying to reach the men who dictated this treatment. There is also despair, for the narrator is essentially a prisoner, and she knows it; as well, the narrator's marriage to her doctor husband is breaking down and she is parted for her newborn infant for the sake of her health. Finally there is determination to see the challenges through, both Perkins Gilman's challenge to the medical world, and the narrator's determination to tear down the terrible wallpaper so that she, and no other woman, can be trapped by it again.

The narrator's tone can best be described as pessimistic, sad, disparaging, and sarcastic.
In the story, the narrator is a wife and mother who is very obviously depressed. She is discouraged that her husband, John, is not more supportive of her. John's masculine tendency is to focus on the empirical. The narrator and her husband's differing worldviews foster much of the conflict in the story.
The narrator states that John is "practical in the extreme." Her husband and brother, both physicians in good standing, determine that she suffers from a "slight hysterical tendency." For her part, the narrator feels that the men in her life are wrong. She feels marginalized by their sterile diagnosis. The narrator believes that she would feel better if she were given "congenial work, with excitement and change." However, she does not define what she means by this. She only knows that her ennui is exacerbated by John's complete and utter lack of sympathy.
The narrator is angry with her husband, and it is apparent in her sarcastic comments.

John is away all day, and even some nights when his cases are serious.
I am glad my case is not serious!

In the story, the narrator manifests persistent symptoms of depression: she is anxious, pessimistic, and guilt-ridden. Her words are often a mass of contradictions. She laments that she cannot spend time with her baby and yet maintains that the baby makes her nervous. Similarly, she complains that she is denied the opportunity to write but also asserts that she gets "pretty tired" when she tries. The narrator's depressed state makes her an unreliable storyteller. Her tone, however, is clearly pessimistic, sad, and disparaging.

How has the study of global business affected you as a business employee or manager? Why?

The study of global business should affect employees or managers of businesses quite profoundly. Studying the interaction of companies and governments across international boundaries or even within blocs such as the European Union is essential for remaining competitive in an increasingly globalized framework. Knowledge and understanding of the vagaries of international trade agreements and uncertainties that accompany developments such as the pending exit by Great Britain from the European Union will help managers to better navigate the oft-times complicated networks that constitute international business arrangements today.
The phrase “global business” includes a vast array of activities involving potentially dozens of foreign countries. Each one of the countries provides a unique challenge with respect to the laws and regulations governing business, to say nothing of the multitude of challenges posed by the various cultures and social customs involved. Moreover, as recent developments in Spain and in Great Britain illustrate (the movement for independence by the region of Catalonia in Spain and the potential break from Great Britain of Scotland over the issues of nationalism and perceptions of E.U. membership), the study of global business is a life-long enterprise. Business owners or managers who fail to adequately follow trends and developments in countries to which they rely for markets and/or materials will almost certainly fail in the highly competitive environment in which most operate.
From the perspective of employees, the study of global business is important because of the stake these individuals have in the decisions of their managers and in the specifics of each foreign country in which their company does business. Employees may not take the time to follow international business trends themselves, but they should know that it is imperative that their own financial well-being is closely tied to the ability of others to understand what is going on beyond their borders. Employees of a particular company might benefit from overseas markets to which that company exports goods or services, or they may suffer from unfavorable comparisons of wage and benefit structures (i.e., they may lose their jobs to outsourcing). Either way, they are impacted by developments in global business—developments that can only be understood through the study of foreign markets, cultures, and political structures. Finally, employees are impacted by the trade agreements in which their governments become engaged and by the sanctions their government might impose upon certain foreign governments for any number of reasons.

Who is Eli Rochert?

Jodi Picoult's Second Glance, set in Comtosook, Vermont, is centered in the atmosphere of conflict between a group of Abenaki Native Americans and a developer called Redhook Group that wants to build a strip mall on the group's burial ground. When supernatural occurrences start getting in the way of the construction workers building the mall, Redhook Group brings in Ross Wakeman to figure out what's going on. 
In the story, Eli Rochert is one of multiple side characters that Ross gets involved in his investigation. Eli is a police officer who happens to be half Abenaki. He was divorced by his wife, and in his dreams he now sees a woman that he has never met before. This woman turns out to be Ross's sister, Shelby.

What would happen if cheetahs were removed from the ecosystem?

This is an interesting question. It is difficult to estimate the effect of the loss of any given species on an ecosystem because of its inherent complexity. Ecosystems are dynamic structures, complete with all sorts of feedback mechanisms, so it is hard to judge the impact of a specific change.
In the case of the cheetah, it is even more difficult to say. For one, cheetahs inhabit a variety of ecosystems, each with unique characteristics. There are various subspecies of cheetah. So the cheetah's disappearance would have differing effects in each case. In general terms, however, the cheetah is a predator and hunter at the top of the food chain, so its disappearance would impact its prey and so on down the line. It is usually the case that the disappearance of animals and organisms that are more widespread in the ecosystem and food chain have the greatest impact.
Sadly, cheetahs are already disappearing. They are vulnerable and even on the verge of being endangered world-wide. Their numbers have dwindled due to a number of factors: poaching, illegal pet trade, habitat loss, etc. They also have unique genetic characteristics and suffer from inbreeding, which has made them vulnerable to disease.

College Algebra, Chapter 4, 4.4, Section 4.4, Problem 102

Suppose that a rectangular box with a volume of $2\sqrt{2}\text{ft}^3$ has a square base as shown in the figure. The diagonal
of the box is $1\text{ft}$ longer than each side of the base.
a.) If the base has sides of length $x$ feet, show that $x^6 - 2x^5 - x^4 + 8 = 0$
b.) Show that two different boxes satisfy the given conditions. Find the dimensions in each case.

a.) If the value of the box is $2\sqrt{2}\text{ft}^3$, then
$2\sqrt{2}=x^2 y$ Equation 1
Hence, by using Pythagorean Theorem,



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


By substituting Equation 2 and Equation 1, we get

$
\begin{equation}
\begin{aligned}
2\sqrt{2} &= x^2 \left( \sqrt{(x+1)^2 - 2x^2 }\right) && \text{Model}\\
\\
8 &= x^4 \left[ (x+1)^2 - 2x^2 \right] && \text{Square both sides}\\
\\
8 &= x^4 \left[ x^2 + 2x+1 -2x^2 \right] && \text{Expand}\\
\\
8 &= x^4 \left[ -x^2 + 2x + 1 \right] && \text{Combine like terms}\\
\\
8 &= -x^6 + 2x^5 + x^4
\end{aligned}
\end{equation}
$

Thus,
$x^6 - 2x^5 - x^4 + 8 = 0$

What use are a book, a camera, and a knife to the diver ?

In Adrienne Rich's poem "Diving into the Wreck," the three items in your question—the book, the camera, and the knife—are all mentioned at the beginning of the poem. The first part of the opening stanza reads:

First having read the book of myths,
and loaded the camera,
and checked the edge of the knife-blade,
I put on the body-armor of black rubber
the absurd flippers
the grave and awkward mask. (lines 1–6)

In these lines, the three items are all part of the speaker's preparation for her "dive." She has "read the book of myths," so she is informed of all of the falsehoods and origin stories that she apparently needs to successfully complete her mission. The camera is "loaded," indicating that the speaker plans to take pictures as evidence of something during her dive. She also has sharpened "the edge of the knife-blade." This suggests that she is expecting to have to defend herself or to cut something loose. Her "body-armor" supports the former idea. At the end of the stanza, the speaker asserts that she must undertake her mission "alone."
After describing her experience exploring the wreck in vivid detail, the speaker returns to those three items in the closing stanza:

We are, I am, you are
by cowardice or courage
the one who find our way
back to this scene
carrying a knife, a camera
a book of myths
in which
our names do not appear. (87–94)

The poem has emphasized that the speaker and anyone else who would brave the wreck must do so alone. Here, she reiterates that one who would dive would have to "find [her] own way." Those brave people would carry the same three pieces of equipment, but here, the speaker puts a twist on the description that we saw in stanza one. This book is one "in which / our names do not appear." This implies that the speaker can explore the wreck after reading the book of myths, and she can discover the truth, but she will still not be part of the "official history." As a feminist poet, Rich often writes about the oppression of women or gender inequality in society. This poem does it rather subtly, but this sentiment that closes the poem suggests the inferior placement of women in society throughout history.

In what ways can the time period in which Emily Grierson from "A Rose for Emily" lived in help support the fact that she is guilty for murdering Homer Barron?

Emily Grierson grew up in the antebellum South, a time period before the Civil War in which slavery was legal and prestigious families owned valuable plantations. Because Emily hails from a wealthy, aristocratic family, she is revered by her community members, particularly the older citizens of Jefferson, who identify with the Old South. At a time when women had few rights, Emily Grierson was the exception because of her revered family name. When Emily begins courting Homer Barron following her father's death, the community of Jefferson discourages her from dating a northerner. Emily also becomes aware that Homer Barron has no plans of getting married and visits a local pharmacy to purchase arsenic. When the pharmacist tells Emily that the law requires her to tell him why she is purchasing poison, Emily simply stares at the man. Since the pharmacist is aware of Emily's social status, he politely gives her the arsenic without asking any more questions. In the Old South, it would have been considered rude to reject a woman with such a revered last name.
Homer Barron then mysteriously disappears, and there is an awful smell permeating from Emily's home. One could easily ask Emily about Homer Barron and look into the cause of the permeating smell, but it would have been considered inappropriate given the time period. The citizens of the Old South refuse to question Emily and inquire about the odor coming from her home. Their actions correspond to how men treated women of a certain social status in the Old South. Since Emily is fully aware that men will not question her, she proceeds to murder Homer Barron. Emily has the motivation and is protected by the unwritten social laws of the time period to get away with murder.

What are Kevin's fears in Freak the Mighty?

Kevin ("Freak") doesn't fear anything in Freak the Mighty.  He has a birth defect that leaves him with a leg brace and crutches. Others judge and stare, but he isn't bothered by it in the slightest.  He ignores the comments and looks.  Kevin is confident enough to be who he truly is.  He may be physically small, but he is enormous in smarts.  He loves to read and learns an amazing amount of new and wonderful vocabulary.  He even creates his own dictionary.  Kevin is a genuine boy who is tough, feisty, and quite funny.  "Freak" is willing to share his intelligence with his new friend, Max, and he feels good about doing so.  Together they go on many fun-filled adventures, helping others along the way and enjoying life as different but kindred individuals.  Kevin is very aware of his looming illness and maybe that is why he doesn't have any true fears.  He is hopeful of getting a robotic transplant to extend his life.  But he knows his time is limited and is making the best of every day.  Living each day as if it were his last...as if each day were a gift.

When Curley enters the bunkhouse at the end of section three, he is already upset. Why?

Towards the end of chapter three, Curley bursts into the bunkhouse looking for his wife. When the men tell Curley that they haven't seen his wife, he inquires about Slim's whereabouts before running out of the bunkhouse to look for him. It is evident that Curley is upset because he is under the impression that his wife may be fooling around with Slim. Curley is a suspicious, insecure man, who does not trust his wife. The fact that she is continually flirting with the workers and is the only female on the ranch heightens Curley's insecurities. When Slim returns to the bunkhouse with Curley close behind him, he is irritated with Curley, who is apologetic. Carlson proceeds to ridicule Curley for being scared of Slim, and Curley goes on to pick a fight with Lennie, which turns out to be a terrible idea.

Curley bursts into the bunkhouse looking for his wife. He can't find her and that makes him even angrier than he already is. He know what she's like; he knows her reputation, and he's very insecure about his relationship with her. He always imagines that she's cheating on him, so when he barges his way into the bunkhouse and she's not there, his suspicions get out of hand. Worse still, there's no sign of Slim, either. Curley fears the worst and heads off angrily to the barn, expecting to find his wife alone with Slim.
But Curley doesn't find anything suspicious going on in the barn. In any case, he's no match for Slim, but his blood's still up when he returns to the bunkhouse. He wants to give someone a good hiding. Carlson and Candy taunt Curley over his cowardice; he feels his manhood being impugned and desperately needs to prove his masculine credentials. So he unwisely picks a fight with Lennie, ending up with a crushed hand for his trouble. Curley is reduced to a broken, whimpering mess, his already fractured sense of manhood further compromised.

How does Locke’s interpretation of the social contract differ from Hobbes’s interpretation?

The differences are fundamental and relate to their respective understandings of what a social contract is for. Locke, like most social contract thinkers, looks upon the arrangement as a means of keeping governmental power in check. For Hobbes, on the other hand, a social contract is a way of keeping the innate greed and selfishness of human beings in check. Locke believes that the people should ultimately control the government; for Hobbes it is the other way around.
Another key difference lies in their respective views concerning natural rights. Locke believes human beings to be endowed with certain innate rights. Locke is no more sentimental than Hobbes when it comes to the purposes of government. It exists to protect our rights, the most important of which is the right to own property.
Hobbes believes that human beings are fundamentally selfish and always look out for themselves. Accordingly, we have no natural rights to speak of in the Lockean sense. In the barbarous state of nature, our natural right consist of grabbing whatever we can lay our hands on. This right is dangerous and needs to be given up when we enter into a contract with an all-powerful sovereign, who keeps all citizens under control.
For Locke, the government can only exercise its authority with the just consent of the governed. As we have seen, it exists purely and solely to protect our natural rights. However, if the government should fail to do so, then, under the right circumstances, we have the right to change it. It is not surprising that Locke's political thought was so influential on American revolutionaries, who put his ideas into practice in their war with the British.
Such a notion is completely unthinkable to Hobbes. He does concede that we do still retain the right to self-defense, however. However, beyond that, we have no right to overthrow the sovereign power. If we are foolish enough to challenge the sovereign, chaos, war, and bloodshed will ensue. Moreover, in the event of success, we would have to replace the old sovereign with a new one. If the new sovereign power were limited, then, according to Hobbes, it would not be truly sovereign. On the other hand, if the new sovereign does have absolute power, it is formally identical to the old sovereign. Overthrowing the old sovereign merely allowed for the possibility of anarchy and disorder.
https://www.the-philosophy.com/hobbes-vs-locke

How does the speaker feel about the grain the mouse steals?

The answer to your question about how the speaker feels about the mouse stealing grain is found in these lines:

A daimen icker in a thrave'S a sma' request;I'll get a blessin wi' the lave,An' never miss't.

Here, the speaker identifies the theft as one ear out of twenty-four, which he considers a small crime. The speaker is sure that what is left is more than enough for himself.
Elsewhere in the poem, the speaker regrets how his plow has disturbed the mouse's nest. He recognizes how much labor that represents for the mouse and acknowledges that with the cold winter coming, there is no green grass left for it to build a new nest with.
Overall, the speaker feels that the mouse is better off than he himself is, because the mouse lives only in the present, while the speaker can both look backward with regret and forward with fear of what may come.

How does Julius Caesar connect, extend, and/or challenge the perspectives offered on fortune and luck in The Prince?

The action of Julius Caesar can definitely be seen as connected to the principles stated by Machiavelli not only in chapter 25 of The Prince, but also elsewhere in the book. Machiavelli indicates that a leader has to understand the spirit of the times and the direction in which events will move based upon it. The defeat of the conspirators against Caesar is at least partly due to misunderstanding of the feelings of the Roman population—they do not have their finger on the pulse of the population. Brutus and the others are clueless about Caesar's genuine popularity with the "plebs," as well as the devotion Antony can elicit. Unlike Antony, Brutus and the others have no grasp of mass psychology. They are caught off guard by the riot that begins after Antony's oration. The crowd's response is like the uncontrolled torrent of a river, which Machiavelli likens to fortune. In contrast to what Machiavelli recommends, the conspirators have no idea of how to react to this force. Brutus, despite his ideals, lacks the virtù (which, in Machiavelli's usage, means "strength" as well "virtue") needed for leadership.
The other central point about Brutus in particular is that he is actually (as Antony states ironically) "an honorable man." In chapter 18 of The Prince, Machiavelli discusses when it is expedient for a leader not to be honest. He is not so much advocating for lying as much as describing the actions of princes that have made them successful. Alexander VI, he says, hardly ever took any kind of action without being deceptive. Brutus and the other conspirators, even Cassius, are too honest. In their idealistic way they extol "liberty, freedom, and enfranchisement," but seem unaware that the people are not motivated by this. Instead, they are motivated by a visceral loyalty to Caesar and their emotional connection to him. Through history we have seen this scenario acted out again and again, including in our own time. A leader can be valued on an irrational level by people because they like the way he talks, even if the things he says make no sense. Brutus makes sense in his speech to the crowd—and they seem to recognize this at first—but ultimately, his appeal to the intellect falls on deaf ears.

What were Meg’s feelings about her father, brother, and Calvin after escaping from IT? Do think she should have felt this way? Why?

After they escape, Meg feels angry at her father and Calvin for not seeming to share her urgency to go back and save Charles Wallace from Camazotz. She is especially angry at her father for leaving Charles Wallace behind.
Some of Meg's intense anger and hostility come from the evil effects of having been on Camazotz. Although she fought off the attempts of IT to control her mind, some of its evil has infected her. As Aunt Beast says:

The Black Thing burns unless it is counteracted properly.

Meg is also an adolescent girl who idealized her father and is now having to come to terms with the idea that he is not perfect and all-powerful. She is angry that he can't simply solve all her problems and save Charles Wallace.
While feelings are feelings, and therefore not able to be delineated as things you "should" or "shouldn't" feel, the novel makes clear that Meg's response is unfair. Her father and Calvin want to rescue Charles Wallace as much as she does. They are trying as hard as she is, but the answers aren't easy. Meg has become temporarily less trusting because of her experience of evil on Camazotz.

A fruiterer had the same number of apples, pears and oranges at first. After 98 oranges, some apples and pears were sold, there were 392 fruits left. There were thrice as many apples as pears left. The number of oranges left was 35 fewer than the number of apples left. How many pears were sold?

For the stated word problem, we need to use variable to represent the unknown counts per each fruit. We may let:
o = original number of oranges
a= original number of apples
p = original number of pears.
 To set-up an equation, we translate the given conditions in the problem.
Condition 1: A fruiterer had the same number of apples, pears and oranges at first.
 This implies that we can equate them as o =a=p .
Condition 2:After 98 oranges, some apples and pears were sold, there were 392 fruits left. 
We may let:
unsold oranges = o'
unsold apples = a'
unsold pears = p'
 It indicates that the  sum of the remaining number of fruits = 392 such that: sold oranges =98
o' +a' +p' = 392
Condition 3: There were thrice as many apples as pears left
This means that a' =3p' or p' =(a')/3
Condition 4: The number of oranges left was 35 fewer than the number of apples left.
o' = a' -35
Using  a'=3p' , we get: o'=3p'-35
Applying condition 3: a' = 3p' and condition 4: o' = 3p'-35 on condition 2:
3p'-35 +3p' +p' = 392
7p'-35=392
7p'=392+35
7p'=427
p' =427/7
p'=61 as the number of "unsold pears".   
 
Plug-in p' =61 on o'=3p'-35 , we get:
o' = 3(61)-35
o' =148 as number of unsold oranges
With sold oranges = 98 and unsold oranges=148 then
original number of oranges: o= 246 .
Applying  o=a=p , we can determine that we also have:
246 original number of pears and 61 unsold pears.
Then,
sold pears: 246-61 =185   [FINAL ANSWER]
In addition, the other unsold apples and oranges are:
Plug-in p' =61 on a'=3p' , we get:
a'=3*61=183 as number of unsold apples
 
then sold apples: 246-83=63
Here is the tally.
Number of sold fruits: 63 apples, 185 pears, and 98 oranges
Number of unsold fruits: 183 apples, 61 pears, and 148 oranges
 

Did Romeo have flaws?

Romeo does have flaws. He is in love with being in love and lives too much in the moment. Whatever emotion he is experiencing at a particular moment becomes the be-all and end-all of his life. Like many adolescents, he can't seem to think even a few days ahead of the all-important now.
This flaw first emerges, rather comically, in his love for Rosaline. When she won't return his love, he moons around, worrying his father. When his friends suggest a visit to the Capulet ball, he agrees unwillingly to go. He says there is no possible way he could ever think of any other girl in the world other than Rosaline. However, he has hardly been at the Capulet's two minutes when he falls helplessly, hopelessly in love with Juliet. Rosaline is utterly forgotten.
This impulsive trend continues. Not only does Romeo now consider Juliet every woman in the world—along with better than the sun and all the stars in the sky put together—he wants to marry her the next day and won't rest until this happens. A more sensible person might say, "let's slow down and get to know each other better," but that is not Romeo's way.
This leads to Romeo's destruction when he finds Juliet seemingly dead. Rather than take time to reflect and try to think through a sensible plan of action, he acts out of the emotion of the moment and kills himself. Ironically, Juliet isn't even dead.
Romeo takes to an extreme the concept of love at first sight and acting immediately on one's desires. The friar warns him to slow down and not let his passion burn too bright, but Romeo is not structured to listen to that kind of advice.

Romeo's main flaw in Romeo and Juliet is his tendency to be unrealistically romantic. We can see from how he talks about his previous love, Rosaline, that he idealizes women and loves to wallow in his own misery. When he's talking to Benvolio about Rosaline in Act 1, Scene 1, compares losing Rosaline to going blind. Benvolio also mentions to Romeo's parents earlier in that same scene that Romeo has been wandering in the woods weeping every day since being rejected by Rosaline. His temperament is clearly dramatic, and Shakespeare intends us to draw the conclusion that Romeo is not ready for love at this point. When he later meets Juliet, she begins to make him act more practically, just as Romeo inspires Juliet to be more romantic. She quips at him that he kisses "by th' book," meaning that he is being very conventional in his courtship. She also makes him vow to marry her before she will exchange vows of love with him in the balcony scene. In this way, the two lovers help each other overcome their flaws, forming a complementary relationship. 

What was the advice of the priest to the boy?

As the title of the story implies, the little boy Joji draws cats. In fact, he really loves drawing cats. He loves it so much that he devotes every spare moment to his one and only hobby. Unfortunately, this doesn't make him much use around the family farm, and his parents have reluctantly concluded that Joji will never grow up to be a farmer.
So they take him to the local temple; perhaps he can train for the priesthood instead? The priest at the temple is only too happy to instruct Joji. Soon, however, he realizes that Joji's not cut out to be a priest. It's the same old problem: the boy just won't stop drawing cats. The priest, then, tells Joji that he'll never be a priest and advises him to leave the temple and return home to his family.

What does the grandmother say to the Misfit to try to convince him not to kill her? Does the conversation alter his viewpoint in any way?

The grandmother tries to appeal to the Misfit's nonexistent sense of morals by claiming to see in him his "good blood" and by asserting that she "knows" he "come[s] from nice people." She delivers these appeals in a panic, desperate in her knowledge that she is likely not going to survive these moments. After all, by this point in the story, her family have not survived this encounter with the Misfit and his gang, so her last resort is to encourage the Misfit to get in touch with his good side and allow her to live. She even says to him, "You're one of my own children!" as a way to get some sympathy, as she believes that if she identifies with a mother figure, surely the Misfit with show her some mercy.
These attempts to get some mercy from the Misfit fail utterly. The Misfit clearly has no regard for mothers nor for the children of mothers. Not only is the Misfit unconvinced and unaltered in his viewpoint, he is scornful and mocking of the Grandmother's last gasps. The story finishes with these lines, leaving the reader with no uncertainty as to the Misfit's absolute lack of emotion and morality:

"She would of been a good woman," The Misfit said, "if it had been somebody there to shoot her every minute of her life.'"
"Some fun!" Bobby Lee said.
"Shut up, Bobby Lee," the Misfit said. "It's no real pleasure in life."

In an attempt to convince the Misfit not to kill her, the grandmother repeatedly asserts that the Misfit is "a good man" and that he isn't "common." The irony of this statement is that the Misfit is clearly an outlaw bent on murdering the entire family, and the grandmother's statement that he's "a good man" does nothing to stop his murderous rampage or change his evil intentions. Indeed, as the grandmother continues to assert that the Misfit is good, the criminal casually orders his henchmen to begin killing the grandmother's family. As such, the grandmother's statements seem to be her attempt to convince herself that she is not about to be killed, despite mounting evidence to the contrary. These attempts grow increasingly pathetic, as it becomes clear that the Misfit is determined to stick to his original plan and kill the grandmother and her entire family.  

Beginning Algebra With Applications, Chapter 5, Review Exercises, Section Review Exercises, Problem 26

Determine the equation of the line through the points whose coordinates are $(4,14)$ and $(-8,-1)$.

We let $(x_1, y_1) = (4,14)$ and $(x_2, y_2) = (-8,-1)$

Using Slope of the line Formula,


$
\begin{equation}
\begin{aligned}

m =& \frac{y_2 - y_1}{x_2 - x_1}
\\
\\
m =& \frac{-1-14}{-8-14}
\\
\\
m =& \frac{-15}{-12}
\\
\\
m =& \frac{5}{4}


\end{aligned}
\end{equation}
$


Using the point slope form, where $\displaystyle m = \frac{5}{4}$ and $(x_1, y_1) = (4,14)$



$
\begin{equation}
\begin{aligned}

y - y_1 =& m(x - x_1)
&&
\\
\\
y - 14 =& \frac{5}{4}(x-4)
&& \text{Substitute } m = \frac{5}{4} \text{ and } (x_1, y_1) = (4,19)
\\
\\
y-14 =& \frac{5}{4}x - 5
&& \text{Apply Distributive Property}
\\
\\
y =& \frac{5}{4}x + 9
&& \text{Add } 14

\end{aligned}
\end{equation}
$

What are some examples of kidney diseases, and what variables influence how they function?

The kidneys are a pair of vital organs that remove toxins, waste, and extra water from your blood.  After substances are filtered out of blood, they travel through the ureter to the bladder for storage until they can be passed through urine.
Diseases that progressively damage the kidneys and impair their ability to function are referred to as Chronic Kidney Disease (CKD).  If the kidneys are malformed during fetal development, they won't function as efficiently as fully formed kidneys.  Genetic diseases, such polycystic kidney disease, can impair kidney function because it damages the organ's tissue.  Lupus, an immune disorder, can reduce kidney function by causing inflammation in the kidney's filtration system.  This is referred to as lupus nephritis.   Kidney stones are accumulations of minerals that can become lodged in renal tissue, causing damage.  Individuals with diabetes often experience hypertension which can decrease the functioning capabilities of the kidney.  It is unclear why, but occurrence of diabetes varies depending on a persons' ethnicity. 
If a person's kidney disease progresses to the point where the damage is irreversible, they may experience kidney failure. At this point, they may like dialysis or transplantation, to help their body remove toxins and waste from their blood stream.
https://www.kidney.org/atoz/content/about-chronic-kidney-disease

https://www.lupus.org/resources/how-lupus-affects-the-renal-kidney-system

College Algebra, Chapter 2, 2.1, Section 2.1, Problem 46

Show that the triangle with vertices $A(6,-7), B(11,-3)$, and $C(2,-2)$ is a right triangle by using the converse of the Pythagorean Theorem. Find the area of the triangle.

By using distance formula,

$
\begin{equation}
\begin{aligned}
d_{AB} &= \sqrt{(-3-(-7))^2 + (11-6)^2} &&& d_{AC} &= \sqrt{(-2-(-7))^2 + (2-6)^2}\\
\\
d_{AB} &= \sqrt{4^2 + 5^2} &&& d_{AC} &= \sqrt{5^2 + (-4)^2}\\
\\
d_{AB} &= \sqrt{16+25} &&& d_{AC} &= \sqrt{25+16}\\
\\
d_{AB} &= \sqrt{41} \text{ units} &&& d_{AC} &= \sqrt{41} \text{ units}\\
\\
\\
d_{BC} &= \sqrt{(-2-(-3))^2 + (2-11)^2}\\
\\
d_{BC} &= \sqrt{1^2 + (-9)^2}\\
\\
d_{BC} &= \sqrt{1+81}\\
\\
d_{BC} &= \sqrt{82} \text{ units}
\end{aligned}
\end{equation}
$

Next, by using the converse of the Pythagorean Theorem if the sides $\sqrt{82}$, $\sqrt{41}$ and $\sqrt{41}$ forms a right triangle.

$
\begin{equation}
\begin{aligned}
(\sqrt{82})^2 &= (\sqrt{41})^2 + (\sqrt{41})^2\\
\\
82 &= 41+41\\
\\
82 &= 82
\end{aligned}
\end{equation}
$

Since both sides are equal, then the three sides form a right triangle.
Thus, the area is $\displaystyle A = \frac{1}{2} bh = \frac{1}{2} (\sqrt{41}) (\sqrt{41}) = 20.5$ square units

What brave thing does Atticus do in chapter 10?

In Chapter 10, Atticus does something that Jem and Scout believe is completely out of character--he shoots and kills a rabid dog.

In an earlier scene, Scout and Jem ironically complain to Miss Maudie that their father is old and boring. Miss Maudie responds by saying, "You'd be surprised [...] there's some life in him yet." Atticus lives up to her praises by swiftly taking down the rabid dog with one shot from a rifle when it begins charging up the street at him. Even the Sheriff, Heck Tate, is too poor of a shot to take down the dog.
After the dog is killed, Miss Maudie says, "I think maybe [Atticus] put his gun down when he realized that God had given him an unfair advantage over most living things. I guess he decided he wouldn't shoot till he had to, and he had to today." Jem and Scout learn a pivotal lesson about their father here: real bravery is using stepping up when nobody else will.

SOURCES:
https://cleveracademy.vn/wp-content/uploads/2016/10/To-Kill-a-Mockingbird.pdf

In chapter 10, Jem notices a sick dog staggering down the middle of the street and runs to tell Calpurnia about it. When Calpurnia sees the sick dog, she immediately recognizes that the dog has rabies. Calpurnia instructs the children to stay inside and calls the operator to inform the community that a rabid dog is walking through town. When Sheriff Tate and Atticus arrive on the scene, Sheriff Tate gives his rifle to Atticus and asks him to shoot the rabid dog. While the other citizens are safely behind closed doors, Atticus courageously stands in the middle of the street aiming his rifle at the rabid dog. Atticus demonstrates his bravery by shooting the dog while it walks in his direction. After Atticus kills the dangerous animal, Jem is speechless, and Scout is astonished at her father's marksmanship abilities. The fact that Atticus never told his children that he was a talented marksman also reveals his humility.

Calculus of a Single Variable, Chapter 9, 9.5, Section 9.5, Problem 7

To determine the convergence or divergence of the series sum_(n=1)^oo (-1)^n/3^n , we may apply the Ratio Test.
In Ratio test, we determine the limit as:
lim_(n-gtoo)|a_(n+1)/a_n| = L
Then, we follow the conditions:
a) L lt1 then the series converges absolutely
b) Lgt1 then the series diverges
c) L=1 or does not exist then the test is inconclusive.The series may be divergent, conditionally convergent, or absolutely convergent.
For the given series sum_(n=1)^oo (-1)^n/3^n , we have a_n =(-1)^n/3^n .
Then, a_(n+1) =(-1)^(n+1)/3^(n+1) .
We set up the limit as:
lim_(n-gtoo) | [(-1)^(n+1)/3^(n+1)]/[(-1)^n/3^n]|
To simplify the function, we flip the bottom and proceed to multiplication:
| [(-1)^(n+1)/3^(n+1)]/[(-1)^n/3^n]| =| (-1)^(n+1)/3^(n+1) *3^n/(-1)^n|
Apply the Law of Exponent: x^(n+m) = x^n*x^m . It becomes:
| ((-1)^n (-1)^1)/(3^n *3^1)*3^n/(-1)^n|
Cancel out common factors (-1)^n and (3^n) .
| (-1)^1/ 3^1 |
Simplify:
| (-1)^1/ 3^1 | =| (-1)/ 3 |
= |-1/3|
=1/3
Applying |[(-1)^(n+1)/3^(n+1)]/[(-1)^n/3^n]|= 1/3 , we get:
lim_(n-gtoo) | [(-1)^(n+1)/3^(n+1)]/[(-1)^n/3^n]|=lim_(n-gtoo) 1/3
lim_(n-gtoo) 1/3 = 1/3
The limit value L=1/3 satisfies the condition: L lt1 .
Therefore, the series converges absolutely.

What are some adjectives and examples to describe the relationship between Ruth and Beatrice in Paul Zindel's The Effect of Gamma Rays on Man-in-the-Moon Marigolds?

Paul Zindel's play contains a powerful central metaphor in the title and to what it refers. The experiment Tillie conducts to determine if radiation creates mutations in marigolds symbolizes the effect that negative energy and dysfunction has on her own family. The impact of negative emotions like anger, regret, and cruelty strongly affect the family unit.
The relationship between Beatrice and her daughter Ruth is particularly problematic. The outgoing Ruth shows some promise of being socially accepted—unlike Tillie, whose shyness prevents her from engaging with people. Beatrice thinks of herself as attractive and outgoing, but people in her community mock her behind her back and suggest she is mentally ill. This creates a problem with Ruth seeing her mother as a role model. Like Betty, Ruth is very aware of other peoples' opinions of her and is vulnerable to them.
An example is that people have been known to call Beatrice "Betty the Loon," and this remark is overheard by Ruth at school. Ruth repeats it to insult her mother when the two are arguing over the science fair. Ruth's illness makes her dependent on others, though. This causes her to feel resentment, and she may be worrying she'll turn out like her mother, as her condition makes her vulnerable to taunting like Betty was. Some adjectives to describe their relationship might include problematic, toxic, complicated, dysfunctional, dependent, antagonistic, intense, and volatile.

What is Malcolm Gladwell's argument in the book Outliers? How can I write a five-paragraph essay on it?

Malcolm Gladwell argues that the reality behind any success story is very different from the long-held assumptions that many people possess around the notion of success. Success involves a highly complex set of circumstances, argues Gladwell, and though luck and hard work can often contribute to success, other conditions must also be met for a success story to take place.
When formulating your own thesis statement about success, make sure your argument is debatable; re-stating Gladwell's argument as your own will not work for a five-paragraph argumentative essay. Some ideas you might consider exploring in your own argument include the role of race and/or class, whether or not education is as important as people make it out to be, or even the potential of a role model's ability to impact a person's chances of success. Plenty of evidence around these issues is available to you in Gladwell's book.
Once you formulate an original and debatable thesis statement, create a brief outline of your three body paragraphs. Each of these paragraphs must start with a topic sentence that addresses some aspect of your overarching thesis statement; each topic sentence should also summarize the argument contained in that particular body paragraph. Every sentence in the paragraph must connect back to the topic sentence. Once you have your outline ready, look for quotes that support your ideas. Paraphrase them so that you know you understand the quotes you are using as evidence, and organize your quotes so that you have two to three quotes per body paragraph.
Finally, write your conclusion and introductory paragraphs. Many writers struggle when they try to write their introductions before their body paragraphs; writing the introduction after the body paragraphs ensures that you know what you are introducing and streamlines the whole process. Your conclusion can make a point about your essay that leaves your reader with a final interesting thought—but be careful not to end your essay with a new argument or angle to your argument.

The main argument of the book is the idea that successful people are made, not born. Gladwell analyzes the lives and habits of numerous successful individuals from different fields and professions to analyze what has made them successful. In the end, he came to the conclusion that the majority of success is earned, not inborn, even if there is a certain amount of luck or fair fortune that plays a part in their success.
Gladwell coins the concept of the “10,000 hour” expert—the idea that if you spend 10,000 hours on any activity, you will become an expert on it. In the end, he reasons that if you become an expert in a marketable area, you will be successful by putting forth the necessary effort. You can apply this to an essay by analyzing the aspects of success that he discusses—the small amount of luck that takes place, the selection of a marketable skill, and the dedication to honing one’s trade.

Outliers by Malcolm Gladwell is a book that attempts to demythologize the notion of the extraordinary individual by showing the structural factors behind individual success. He argues that individual success stories can be explained by a combination of hidden advantages, cultural advantages, and extensive practice.
A five-paragraph essay consists of an introductory paragraph asserting a thesis, three body paragraphs, each supporting some aspect of the thesis, and a concluding paragraph showing how the body paragraphs confirm the thesis set out in the introduction.


Introduction: Summarize the overall argument of the book concerning "outliers" being explicable through a combination of external preconditions and extended practice.

Body Paragraph 1: Discuss the structural advantages that contribute to success, such as the birth dates of Canadian hockey players.

Body Paragraph 2: Discuss the cultural legacies which can affect success or failure.

Body Paragraph 3: Summarize Gladwell's account of how a minimum of 10,000 hours of practice affects success.

Conclusion: Conclude by showing how the three factors covered in the body paragraphs can explain the success of outliers.

Outliers is a study of extraordinarily successful people. In very simple terms, its author, Malcolm Gladwell, is attempting to explain why these people have been able to achieve as much as they have. His argument is that very successful people are not born that way, but rather made by hard work. This is the famous "10,000 hour" concept that he introduces; only through 10,000 hours of practice, training, hard work in short, can people achieve that level of success. But at the same time, and this is the most important argument of the book, people have to have the means to put in this kind of effort. Brilliant athletes, musicians, and inventors have to have supportive parents and live in societies that support this kind of effort. One can't spend 10,000 hours practicing on guitar if one is hungry, after all. This is Gladwell's thesis in his words:

People don't rise from nothing. We do owe something to parenting and patronage. The people who stand before kings may look like they did it all themselves. But in fact they are invariably the beneficiaries of hidden advantages and extraordinary opportunities and cultural legacies that allow them to learn and work hard and make sense of the world in ways that others cannot. 

One way to go about writing about it (i.e. coming up with three body paragraphs) would be to look at some of the specific examples he uses (Bill Gates, the Canadian hockey players, the Beatles, or Robert Oppenheimer) of people who have been recognized as "outliers." Focus on the ways that he uses them to illustrate his thesis. You might also use some "negative" examples, such as Chris Langen, the man with a 195 IQ who works on a ranch and has not achieved the fame and success of someone like Oppenheimer or Einstein. He did not have the encouragement or have the same family support and education that these men had.
https://books.google.com/books/about/Outliers.html?id=3NSImqqnxnkC&printsec=frontcover&source=kp_read_button