Beginning Algebra With Applications, Chapter 5, 5.2, Section 5.2, Problem 104

Graph $x + 2y = 4$ by using $x$- and $y$-intercepts

$x$-intercept:


$
\begin{equation}
\begin{aligned}

x + 2y =& 4
&& \text{Given equation}
\\
x + 2(0) =& 4
&& \text{To find the $x$-intercept, let } y = 0
\\
x =& 4
&&

\end{aligned}
\end{equation}
$


The $x$-intercept is $(4,0)$

$y$-intercept:


$
\begin{equation}
\begin{aligned}

x + 2y =& 4
&& \text{Given equation}
\\
0 + 2y =& 4
&& \text{To find the $y$-intercept, let } x=0
\\
2y =& 4
&& \text{Divide by } 2
\\
y =& 2
&&

\end{aligned}
\end{equation}
$



The $y$-intercept is $(0,2)$

Graph the ordered pairs $(4,0)$ and $(0,2)$. Draw a straight line through the points.

What company did Bill Gates start?

Bill Gates started Microsoft with Paul Allen in 1975 when a company called Altair (makers of micro-computers) became interested in some software the two college students were writing. Originally Micro-Soft, the name was inspired by this first project, creating SOFTware for MICRO-computers. 
Before Microsoft, Gates and Allen had already created a successful software used to analyze traffic patterns in Seattle. They would have started a company together then, but Gates' parents wanted him to finish school first.
Microsoft is now the leading provider of personal computer operating systems (Windows), as well as programs that do word processing (Word), manage email (Outlook), and create spreadsheets (Excel), presentations (PowerPoint), and databases (Access). The company has also branched out to games and gaming systems (Xbox), Smartwatches (Band), computer accessories, mobile devices, and more.
The company generates billions of dollars in revenue and is a household name in the United States.

Intermediate Algebra, Chapter 3, Review Exercises, Section Review Exercises, Problem 18

Determine the slope of the given graph below:



We can see from the graph that the line passes through $(2,0)$ and $(0,2)$. If we let $(x_1, y_1) = (2,0)$
and $(x_2, y_2) = (0,2)$, then the slope is
$\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - 0}{0 - 2} = \frac{2}{-2} = -1$

dy/dx = 5 - 8x Solve the differential equation

(dy)/dx=5-8x
This differential equation is separable since it has a form

N(y) (dy)/dx=M(x)
And, it can be re-written as

N(y) dy = M(x) dx
So separating the variables, the equation becomes
dy=(5-8x)dx
Integrating both sides, it result to
int dy = int (5-8x)dx
y + C_1 = 5x - (8x^2)/2 + C_2
y+ C_1 = 5x - 4x^2 + C_2
Isolating the y, it becomes
y = 5x - 4x^2 + C_2 -C_1
Since C2 and C1 are constants, it can be expressed as a single constant C.
y=5x-4x^2+C
y=-4x^2 + 5x + C
Therefore, the general solution of the given differential equation is y=-4x^2 + 5x + C .

'Quality' by John Galsworthy is indeed the story of Mr. Gessler's triumph over crushing adversities. Discuss.

“Quality” tells the story of Mr. Gessler, a German shoemaker.  Although Mr. Gessler makes the best boots in London, his business is failing because he is unable to compete with the big companies around him. These companies, we learn, earn their customers not through quality but advertising. Mr. Gessler is ultimately triumphant in that he is able to establish his own conditions for success; what matters most to Gessler is that he produces quality boots, and in this regard he succeeds.
Gessler views making boots as an art during a time in which the world around him is increasingly shaped by the buying and selling of commodities. Mr. Gessler refuses to give into modern business practices. Whereas his competitors depend on advertisement, Gessler’s approach is minimalist in nature:

There was no sign upon it other than the name of Gessler Brothers; and in the window a few pairs of boots. He made only what was ordered, and what he made never failed to fit.

Mr. Gessler tells the narrator that “Dose big virms ‘ave no self-respect.” Ultimately, Gessler’s triumph is that of an artist who respects himself and his work. Mr. Gessler makes a quality product—it is so high quality, in fact, that the narrator claims it lasts forever. But Mr. Gessler is less concerned with selling more boots and making a profit than he is making a work of art, and in this regard he succeeds on his own terms.

Mr. Gessler is a German shoemaker who makes quality boots in London around the turn of the twentieth century. He buys the best leather and handcrafts the boots himself. But he can't make ends meet. Competitors advertise, which the Gesslers do not. People buy the lower-quality boots from other sellers, who more aggressively market. Mr. Gessler, however, refuses to compromise. He makes his boots the old-fashioned, high-quality way. He slowly starves to death, works night and day, and sometimes goes without a fire.
These are crushing adversities, and in the end, they kill Mr. Gessler. However, he triumphs in that he never compromises quality. His craft comes before his profit. He holds onto his integrity by doing his work in the old-fashioned way, the best way.
The story can be understood in the context of William Morris and the Arts and Crafts movement. Morris argued in favor of craftsmen. As factory-made goods displaced what was handcrafted, workers became alienated from their work. After all, rather than handcrafting items, they were simply running the machines that made them—but advertising allowed these inferior products to sell. This story criticizes a society that puts hype and profit ahead of quality workmanship. It implies that better supports were needed for people like Mr. Gessler, if only in the form of people noticing and buying from him, and mourns the passing of such craftsmen.

Why does Scot's ability to read and write annoy her teacher, Miss Caroline?

Miss Caroline is a young, new, inexperienced teacher. She is inexperienced in the classroom and in the ways of Maycomb. She is insecure about her authority. Scout unwittingly undermines her authority by trying to explain to her some details of the Maycomb social hierarchy. On top of that, Scout has the audacity to already know how to read.
Scout's reading skills annoy Miss Caroline because she has rigid, preconceived notions about how a child is supposed to learn to read correctly. Scout messes up her system by coming in with independent knowledge. Miss Caroline fears that Scout has been taught incorrectly and tells her not to read independently at home with Atticus.
At home, Atticus tells Scout to be diplomatic and tactful and to go along with authority. She may continue to read as she has, but she shouldn't upset Miss Caroline by letting her know this.

Miss Caroline Fisher is a weak, inexperienced teacher. As such, she appears insecure in her abilities. So when Scout shows up for her first day at school, and is clearly able to read and write, Miss Caroline gets quite indignant. Atticus must've taught her, she thinks. And Miss Caroline feels rather put out as she seems to think it somehow undermines her authority as a teacher.
The unpleasant episode with Miss Caroline illustrates once more the warped nature of life in Maycomb. It's perfectly fine for Burris Ewell to turn up for the first day of school and then stay away for the rest of term. But for a child to come to school with the ability to read and write is somehow a problem. Clearly, it's more important to follow strict, inflexible rules than to educate children properly. Miss Caroline is one of many adult authority figures in the story whose actions make little sense to those of us not familiar with the strange customs, laws, and conventions that govern the lives of the citizens of Maycomb.

What is bebop?

Bebop is a type of modern jazz that was popular between 1940 and 1955. Bebop musicians essentially added to the traditional 7-chord harmonies with improvised chords from the 12-note chromatic scale.
The stunning chord progressions were revolutionary for their time. Traditional jazz artists decried the destruction of the jazz form, but others praised the often abrupt melodic progressions in bebop. Because of its nontraditional melodic structure and rhythmic complexity, bebop was more suited to listening than dancing.
Important bebop performers of the time included Dizzy Gillespie, Charlie Parker, and Thelonious Monk. A bebop band was usually small, and the only music instruments were the trumpet, saxophone, drums, piano, and bass. Bebop musicians were such nonconformists; they modified Count Basie's popular rhythm section and came up with their own distinctive rhythms. For more, please refer to the links below.
https://www.britannica.com/art/bebop

https://www.jazzinamerica.org/JazzResources/StyleSheets/10

What is one important similarity between the British colonies in the Chesapeake region and the British colonies in New England in the period from 1607 to 1754?

Both regions made money from shipping--New England was a supplier of timber and fish while the Chesapeake was known for its tobacco. The shipping industry would turn Boston and Baltimore into major colonial cities. Both regions also had slavery before the American Revolution. Slavery would eventually prove to be more important to the Chesapeake region as it needed manpower to grow tobacco. Many in New England also used slaves as house servants.
Both regions would be hard-hit by disease and starvation. The early Pilgrims were nearly wiped out during their first winter in the New World. The settlers of Jamestown faced starvation and malaria. Both regions also had problems with Native Americans. Virginia settlers fought against the Powhatan Confederacy and New England settlers fought King Philip's War against Metacom. Both of these wars were rooted in European encroachment on native lands.
While the regions were quite different in terms of the nature of settlement and the purpose of colonization, hardship and commerce were two things that New England and the Chesapeake region had in common.

One important similarity between the British colonies in the Chesapeake region and those of New England was the fact that both nearly failed. Britain's first colony on Roanoke Island (1587–1590) had disappeared, so establishing a viable colony in North America was a formidable task.
In 1607, the first settlers reached Chesapeake Bay and founded Jamestown. Many of them had expected to find gold and become rich as the Spanish had done in Central and South America. Few colonists had the survival skills that they needed. Only 38 of 105 settlers survived the first year. By 1610, the colonists were prepared to give up and return to Britain. But ships carrying supplies arrived and the colony was saved.
In 1620, the Pilgrims landed in what eventually became Massachusetts. The Mayflower had tried to land in Virginia but went off course, and that was their first problem. Almost half died during the first New England winter. Then Squanto, a local Indian, taught them how to grow maize and catch fish. The survival skills he taught the Pilgrims were invaluable. Thankful Pilgrims then held the first Thanksgiving.

The British had colonies throughout North America, including those in the New England and the Chesapeake regions. There were some similarities of the colonies in both of these regions. One similarity was the jobs. The main jobs of the people in the New England region included manufacturing, fishing, lumbering, and shipping. There also was some farming in the New England colonies. In the Chesapeake colonies closer to New England there was more manufacturing and trade. In those colonies further to the south, there was more farming due to the fertile soil and a mild climate.
Another similarity is that these colonies were founded, in part, by people who wanted to practice their religion freely. While there was more religious tolerance in the Chesapeake colonies, people came to these regions to escape religious persecution in Europe. The colonies in both regions also faced hardships when they were first established. These hardships included dealing with harsh winters and diseases.
There were similarities between the New England and the Chesapeake colonies.

The New England and Chesapeake colonies had many differences.  They did, however, share some similarities.  
Both were settled by British citizens who adhered to a Christian faith.  The Pilgrims were Separatists, and they settled in Massachusetts.  Puritans later settled in New England.  The Chesapeake colonists were mostly members of the Church of England.
Colonists in both regions built towns filled with houses, stores, and institutions.  Cities such as Boston and Williamsburg were built.  Commerce was important in both regions, and goods were shipped from England to sell in colonial shops.  Colonists from both New England and the Chesapeake region established towns and cities near bays and the Atlantic Ocean.  This allowed cities and towns to be easily accessible by ship.
Colonists from both regions farmed to maintain food supplies.  Farming was more prevalent in the Chesapeake region due to the fertile soil and longer growing season.  New England colonists farmed, but their long winters and rocky soil sometimes made growing crops difficult.
Disease was a hardship that colonists from both regions faced.  Diseases often spread through towns and cities.  Disease killed many early settlers in both Jamestown and Plymouth Colony.
https://www.nps.gov/jame/learn/historyculture/jamestown-and-plymouth-compare-and-contrast.htm

What is the tone in chapter 28 of To Kill A Mockingbird?

This is the chapter in which Jem and Scout are attacked as they cross the dark schoolyard on their way home from the pageant. The tone is ominous. It is a tone of slowly building tension and confusion. Even after the attack happens, the tension and confusion do not completely dissipate. They continue until the end of the chapter, when we find out from Mr. Heck Tate that Bob Ewell attacked the children, and that Bob Ewell has been stabbed dead.
The ominous tone is created against a homey backdrop. There is humor in the first few pages of the chapter, when Mrs. Merriweather narrates her overblown pageant about Maycomb County, and Scout blunders onto the stage, late, in her ham costume. Before the children even get to the pageant, Harper Lee has already given us clues this will be a scary evening.  
On the way to the school, walking by the old Radley place, Jem and Scout discuss how they used to be scared of Boo Radley and haints. Scout, in her narration, adds, "Haints, Hot Steams, incantations, secret signs, had vanished with our years as mist with sunrise." Yet, the next moment she tells Jem to "Cut it out" when he talks about haints. A moment later, she trips on a tree root (foreshadowing what will happen later). There is some discussion about how remote the old oak tree is from all buildings except the Radley place, and how dark it is under the tree. Cecil Jacobs then jumps out and scares Jem and Scout. This is the classic "decoy" jump scare that sets us up for the real thing later. 
After the pageant, the two children begin to walk home across the schoolyard by themselves. Tension and confusion are taken up a notch because Scout, who is narrating the story, is still in her ham costume and can't see out of it. Jem is leading her. Then the tension builds rapidly as the children begin to hear someone following them. There are many little phrases in this section to give us a clue that something is not right:
"I felt [Jem's] fingers press the top of my costume, too hard, it seemed."
"'Be quiet,' he said, and I knew he was not joking."
"This was the stillness before a thunderstorm."
"'Aw, it's just Halloween got you. . . ' I said it more to convince myself than Jem, for sure enough, as we began walking, I heard what he was talking about."
And so on. 
When the actual attack comes, Scout (and by extension, the reader) still cannot really tell what is going on.  
After the attack, as she makes her way back to the house, following the mysterious man who is carrying Jem's body, Scout still does not know what really happened. (It will take the next few chapters for everyone to sort out the logistics of what happened.) When she first returns to the house, her question is, "Is Jem dead?" The adults in the house are just as confused as Scout. Aunt Alexandra is so distracted that she hands Scout her overalls to put on (Aunt Alexandra hates Scout's overalls, and prefers she wear dresses).  
The confusion, and hence the tension of not knowing exactly what happened, continues until the very end of the chapter. People come and go, including the doctor and Heck Tate. When Heck Tate gets there, he takes his time revealing the identity of the man under the tree. This keeps the ominous tone going until the very last line of the chapter.

If Washington Irving's A History of New York is a parody, can we assume his history contains facts?

Understanding that a parody is, by definition, a humorous exaggeration or an imitation (with similarities to farce or satire), a work like Washington Irving's A History of New York is likely to contain very few actual facts.
Following the excursions and observances of the fictional Diedrich Knickerbocker, A History of New York takes aim at the Dutch-American settlers in New York during the early 1800s. Through the voice of Knickerbocker, Irving manipulates, exaggerates, or completely disregards any true facts in favor of a satirical parody. Real-life figures such as Thomas Jefferson are parodied (Jefferson becomes satirized as William the Testy), and the general mannerisms and behavior of the Dutch settlers are not taken seriously to any degree. Certainly, among other things, A History of New York offers some factual basis on how things were, but as the facts become filtered through the parody, they become wholly unreliable and unrecognizable.

What does Tom condemn?

Tom is an arrogant, intolerant man. His comments in the book frequently demonstrate his thorough contempt for African Americans and other minorities, as well as other people he deems inferior because of their social class (Myrtle's Wilson's husband, for example). These prejudices color his most thorough condemnation: the affair between Gatsby and Daisy. He describes their affair as an instance of what he perceives as society's decline:

I suppose the latest thing is to sit back and let Mr. Nobody from Nowhere make love to your wife. Well, if that's the idea, you can count me out. . . . Nowadays people begin by sneering at family life and family institutions, and next they'll throw everything overboard and have intermarriage between black and white.

Note that his condemnation is not simply an accusation of infidelity. Tom himself has been carrying on an affair with Myrtle Wilson. Rather it is that Gatsby is a "Nobody" from "Nowhere" who is clearly inferior in Tom's mind. The affair is evidence, in a way that Tom's own dalliance is not, of the decline of society. The conversation that led to this condemnation began by Tom questioning Gatsby's time at Oxford and culminates with Gatsby telling Tom that Daisy never loved him. Tom has already condemned Gatsby's alleged associations with the gangster Meyer Wolfsheim. So his hatred for Gatsby goes beyond his anger that the man has had an affair with his wife. Gatsby represents much of what Tom hates in the world and is, in Tom's eyes, beneath him.

Tom Buchanan condemns several things and people throughout the novel The Great Gatsby. In chapter 1, Tom goes on a rant condemning civilization and the influence of other races. Tom's racist personality is revealed as he tells Nick, Daisy, and Jordan that colored people are ruining civilization. Tom urges his guests to read "The Rise of the Colored Empires," which explores how other races are attempting to suppress the "white race."
In chapter 7, Tom Buchanan also condemns Jay Gatsby's illegal business ventures. Tom exposes Jay Gatsby as a bootlegger in front of Daisy, Jordan, and Nick during their visit to New York City. Tom condemns Gatsby for being in business with Meyer Wolfsheim and selling grain alcohol over the counter at drug stores. Tom also condemns the fact that Gatsby allowed his friend, Walter Chase, to go to jail for a month. Tom then proceeds to criticize Gatsby for his false identity and manufactured personality before everyone leaves the city.

How does Dorian Gray's outlook on the world change throughout the novel?

Dorian Gray's view of the world changes dramatically as the novel progresses. At first, he is pleased to sell his soul, in order that all of his sins and signs of aging show up on his portrait, while his own body remains young and unblemished. He indulges himself freely in decadence, believing he won't have to pay a price for it. This seems a good bargain to him.
As time goes by, however, Dorian begins to see the limitations in a life of hedonism. The trade off he has made no longer seems so good. He increasingly doesn't want to face who he is and what he has done. His body might not show his dissipation, but his actions weigh on his memory. Wanting to forget, he tries to throw himself ever more into the sensual world, to barricade himself in it. He wonders,

"To cure the soul by means of the senses, and the senses by means of the soul!" How the words rang in his ears! His soul, certainly, was sick to death. Was it true that the senses could cure it?

By the end of the novel, however, he is sickened by his life and by the horrible monster he sees in the portrait of himself. He no longer wants to face that person: the real him. He learns his deal with the devil has been an error. He stabs the portrait but because it is him, he dies, taking on its grotesque form, while the picture converts back to the young Dorian.

At the start of the novel, Wilde presents Dorian Gray to the reader as an extraordinary-looking and impressionable young man. At the start, Basil, an artist, makes a fuss over Dorian, unworried about the effect such attentions might have on him because Dorian is not at all spoiled by his beauty. Dorian's outlook on the world is still innocent. It is only when Lord Henry meets Dorian and speaks with him frankly about the value of beauty in the world of pleasure-seeking Lord Henry inhabits that things change.
Dorian begins to transform into an amoral hedonist only after he learns that he has power thanks to his beauty and youth. At this point, his outlook on the world becomes a self-centered one, and he looks at individuals he meets as objects to be used for his own entertainment and enjoyment.

Throughout the novel, Dorian Gray's outlook on the world changes fairly drastically.  At the beginning of the story, Dorian is young and easily influenced.  He is beautiful, which makes him the perfect subject of a portrait by artist Basil.  Basil uses Dorian as a muse, and introduces him to Lord Henry.  Under Lord Henry's influence, Dorian learns that he can get away with a lot because of his beauty, and he also begins to feel that life is meant to be lived by taking what you want.  
This hedonistic world view causes Dorian to make a declaration that he would sell his soul to stay young and beautiful forever.  Dorian later learns that his fate has been tied to Basil's portrait of Dorian, leaving Dorian free to explore a world of excess and pleasure with no physical repercussions.   Dorian, throughout the rest of the novel, becomes increasingly hedonistic and arrogant, and he is constantly finding new ways to entertain himself.  He believes that the world owes him constant entertainment.

Why is the Declaration of Independence still applicable today?

The Declaration of Independence is still applicable today in that it states who should be in charge of the American government—the American people. It says the government derives its power "from the consent of the governed." It also states the government is necessary to provide for the people's "inalienable rights," which according to Jefferson are life, liberty, and the pursuit of happiness. The rhetoric in the Declaration of Independence has been used by American politicians as well as leaders in other countries who wish to create their own forms of self-government.  
The Declaration of Independence is also important in that it gives a list of wrongs committed by Britain against the American colonies. Without this list, the American colonists are only tax-dodgers. This list shows the colonists have legitimate complaints.  
Finally, the Declaration of Independence gives the American people a right to revolution.  A passage states "the people have the right to alter or to abolish that government, and to establish a new government," which means that if the government infringes on life, liberty, and/ or the pursuit of happiness, people have an inalienable right to change the government or establish a new one. The next passage begins with the word "prudence," however, meaning the people should take this responsibility seriously and not flippantly alter the government on a whim.  
http://www.let.rug.nl/usa/documents/1776-1785/the-final-text-of-the-declaration-of-independence-july-4-1776.php

College Algebra, Chapter 5, 5.3, Section 5.3, Problem 50

Combine the expression $\displaystyle \ln (a + b) + \ln (a - b) - 2 \ln c$, using the Laws of Logarithm


$
\begin{equation}
\begin{aligned}

\ln (a + b) + \ln (a - b) - 2 \ln c =& \ln (a + b) + \ln (a - b) - \ln c^2
&& \text{Law of Logarithm } \log_a (A^C) = C \log_a A
\\
\\
\ln (a + b) + \ln (a - b) - 2 \ln c =& \ln (a + b)(a - b) - \ln c^2
&& \text{Law of Logarithm } \log_a (AB) = \log_a A + \log_a B
\\
\\
\ln (a + b) + \ln (a - b) - 2 \ln c =& \ln \left[ \frac{(a + b)(a - b)}{c^2} \right]
&& \text{Law of Logarithm } \log_a \left( \frac{A}{B} \right) = \log_a A - \log_a B
\\
\\
\ln (a + b) + \ln (a - b) - 2 \ln c =& \ln \left( \frac{a^2 - b^2}{c^2} \right)
&& \text{Special Product } (A - B)(A + B) = (A^2 - B^2)

\end{aligned}
\end{equation}
$

What punishment was given to Gulliver by the king of Lilliput?

In chapter 7, Gulliver learns that Flimnap, Skyresh Bolgolam, and other politicians have drafted articles of impeachment for committing treason and other capital crimes against Lilliput. The articles against Gulliver accuse him of "maliciously" and "traitorously" discharging urine within the precincts of the royal palace, not following the emperor's orders to destroy the entire Blefuscuan fleet, and secretly attempting to aid and assist the country of Blefuscu. Gulliver then learns that the Lilliputian emperor has accepted the articles and crimes levied against him. The Lilliputian emperor also met with his council and decided to "mercifully" blind Gulliver and gradually starve him to death as punishment for his crimes. Swift uses the emperor's terrible punishment and description as being merciful and generous to satirize how the English politicians portrayed the cruel King George I. Fortunately, Gulliver is able to escape Lilliput before the emperor can enact his brutal punishment.

Gulliver has been accused by a number of scheming Lilliputian politicians and courtiers of treason. Gulliver thought he was doing the right thing by not seizing the entire Blefuscan fleet, but, being a naive, trusting soul, he never reckoned on the chronic deviousness of Lilliputian court lackeys. He is also accused of passing water in public, which, given Gulliver's enormous size in relation to the Lilliputians, is a serious charge indeed.
The Emperor, a fool as well as an ingrate, succumbs to the influence of the smears and innuendos whispered in his ear by his slippery subordinates. He decides to punish Gulliver "humanely" by making him blind and allowing him to starve to death. This way he will save on his upkeep. Gulliver gets wind of this dastardly plan and immediately takes off for Blefuscu.

What is the conflict in Sonnet 130?

Sonnet 130 doesn't present or discuss a traditional conflict; rather, it satirizes typical romantic poetry of the time, specifically the kind that used hyperbolic language to describe a subject's beauty. Shakespeare pokes fun at this common poetic method by doing the opposite: describing the "mistress" in the poem by comparing her appearance, breath, and voice unfavorably to traditionally beautiful things like roses, snow, music, and goddesses:

My mistress' eyes are nothing like the sun;
Coral is far more red than her lips' red;
If snow be white, why then her breasts are dun;
If hairs be wires, black wires grow on her head.
I have seen roses damasked, red and white,
But no such roses see I in her cheeks;
And in some perfumes is there more delight
Than in the breath that from my mistress reeks.
I love to hear her speak, yet well I know
That music hath a far more pleasing sound;
I grant I never saw a goddess go;
My mistress, when she walks, treads on the ground.


The woman Shakespeare describes has lips that are not particularly red, skin that isn't snow-white, cheeks that aren't rosy, breath that is not sweet, and a voice that is not musical. The sonnet ends on a favorable note, however:



And yet, by heaven, I think my love as rare
As any she belied with false compare.



It could be said that the conflict in the sonnet is that the woman being described does not measure up to these elevated standards of beauty, but Shakespeare presents the idea in a clearly satirical way.

Why does Ponyboy not like being in the country?

Pony initially dreams of residing in the country, away from the big town and threatening rival gangs. Ponyboy envisions the country as a tranquil environment where he would have enough leisure time to lay down beneath a tree, read a book, or draw a picture. In Pony's daydream, he would own a healthy yellow dog, and Sodapop would finally get Mickey Mouse back. Unfortunately, Pony's dreams of the country do not resemble the reality of rural life. When Ponyboy and Johnny flee the town after Bob Sheldon's murder, they hide out in an abandoned church in Windrixville, which is a rural area. In Windrixville, Pony discovers that his appearance makes him an outsider. He is also forced to remain in the abandoned church, and he eventually gets homesick. Despite the natural beauty of the countryside, Ponyboy despises being confined in the abandoned church and eating baloney sandwiches every day. The fact that Johnny is the only person with him has a significant impact on Pony's emotions. He begins to miss his brothers and the rest of the Greaser crew. Overall, Pony comes to hate his time in the country, where he is considered an outsider and forced to remain in the confines of the abandoned church.

Ponyboy has a fantasy about how wonderful the country would be. In his imagination, the country is full of natural beauty; it is a place where "clouds are pink and meadowlarks are singing." However, when the circumstances surrounding Bob's murder force Ponyboy to run away to the country to hide, he realizes that his own appearance contrasts with the appearance of country boys. The greaser style—long greased hair, worn jeans, and leather jacket—that Ponyboy has used to help him assimilate into the culture of his neighborhood and school gang now actually works against him in the country because he doesn't look or dress like the farm boys. In order to hide, he will have to get rid of the outward identifiers that for so long have made him feel like a member of a group. Once again, Ponyboy finds himself an "outsider."

Calculus of a Single Variable, Chapter 8, 8.3, Section 8.3, Problem 11

To solve the indefinite integral, we follow int f(x) dx = F(x) +C
where:
f(x) as the integrand function
F(x) as the antiderivative of f(x)
C as the constant of integration.
For the given integral problem: int x sin^2(x) dx, we may apply integration by parts: int u *dv = uv - int v *du .
We may let:
u = x then du =1 dx or dx
dv= sin^2(x) dx then v = x/2 - sin(2x)/4
Note: From the table of integrals, we have int sin^2(ax) dx = x/2 - sin(2ax)/(4a) . We apply this on v =int dv =intsin^2(x) dx where a =1 .
Applying the formula for integration by parts, we have:
int x sin^2(x) dx= x*(x/2 - sin(2x)/4 ) - int (x/2 - sin(2x)/4 ) dx
=x^2/2 - (xsin(2x))/4 - int (x/2 - sin(2x)/4 ) dx
For the integral: int (x/2 - sin(2x)/4 ) dx , we may apply the basic integration property: : int (u-v) dx = int (u) dx - int (v) dx .

int (x/2 - sin(2x)/4 ) dx =int (x/2) dx -int sin(2x)/4 ) dx
= 1/2 int x dx - 1/4 int sin(2x) dx .

Apply the Power rule for integration:
int x^n dx = x^(n+1)/(n+1) +c
1/2 int x dx = 1/2*x^(1+1)/(1+1)
= 1/2* x^2/2
= x^2/4
Apply the basic integration formula for sine function: int sin(u) du = -cos(u) +C .
Let: u =2x then du = 2 dx or (du)/2 = dx .
1/4 int sin(2x) dx = 1/4 int sin(u) * (du)/2
= 1/4 *1/2 int sin(u) du
= 1/8 (-cos(u))
= -cos(u)/8
Plug-in u = 2x on -cos(u)/8 , we get: 1/4 int sin(2x) dx =-cos(2x)/8 .
Combining the results, we get:
int (x/2 - sin(2x)/4 ) dx =x^2/4 - (-cos(2x)/8) +C
=x^2/4+ cos(2x)/8 +C
Then, the complete indefinite integral will be:
int x sin^2(x) dx=x^2/2 - (xsin(2x))/4 - int (x/2 - sin(2x)/4 ) dx
=x^2/2 - (xsin(2x))/4 -(x^2/4+ cos(2x)/8) +C
=x^2/2 - (xsin(2x))/4 - x^2/4 - cos(2x)/8 +C
= (x^2)/4- (xsin(2x))/4- cos(2x)/8 +C

College Algebra, Chapter 1, 1.3, Section 1.3, Problem 90

Suppose that a flagpole is secured on opposite sides by two guy wires, each of which is $5 ft$ longer than the pole. The distance between the points where the wires are fixed to the ground is equal to the length of one guy wire. What is the height of the flagpole to the nearest inch?

Let $h$ be the height of the pole







By Pythagorean Theorem,


$
\begin{equation}
\begin{aligned}

a^2 + b^2 =& c^2
&&
\\
\\
h^2 + \left( \frac{h + 5}{2} \right)^2 =& (h + 5)^2
&& \text{Model}
\\
\\
h^2 + \frac{h^2 + 10 h + 25}{4} =& h^2 + 10 h + 25
&& \text{Expand}
\\
\\
4h^2 + h^2 + 10h + 25 =& 4h^2 + 40h + 100
&& \text{Multiply both sides by 4}
\\
\\
4h^2 - 4h^2 + h^2 - 40h + 10h - 100 + 25 =& 0
&& \text{Combine like terms}
\\
\\
h^2 - 30h - 75 =& 0
&& \text{Simplify}
\\
\\
h^2 - 30h =& 75
&& \text{Add 75}
\\
\\
h^2 - 30h + 225 =& 75 + 225
&& \text{Complete the square: add } \left( \frac{-30}{2} \right)^2 = 225
\\
\\
(h - 15)^2 =& 300
&& \text{Perfect Square}
\\
\\
h - 15 =& \pm \sqrt{300}
&& \text{Take the square root}
\\
\\
h =& 15 \pm 10 \sqrt{3}
&& \text{Add 15}
\\
\\
h =& 15 + 10 \sqrt{3} \text{ and } h = 15 - 10 \sqrt{3}
&& \text{Solve for } h
\\
\\
h =& 15 + 10 \sqrt{3} ft
&& \text{Choose } h > 0
\\
\\
h =& (15 + 10 \sqrt{3}) ft \left( \frac{12 in}{1ft} \right) = 387.85 in = 388 in
&& \text{Convert $ft$ into inches}

\end{aligned}
\end{equation}
$

What are all the literary devices and their purposes in the first two pages of, The Road, by Cormac McCarthy?

The first two pages of Cormac McCarthy's The Road, as an introduction to the story of the man and the boy, also introduce us to the minimalist style that characterizes the novel. The characters are never named and are only referred to as the man and the boy or by the pronouns "he" and "him," which we see from the very first sentence.
Another feature of the writing style that we see in the first two pages is repetition. This repetition works to create and reiterate the mood of the novel, which reflects the state of the world in which it is set. For example, McCarthy repeats the words "dark," "darkness," and "gray," which all point to the post-apocalyptic setting. These words are contrasted with the repetition of the word "light" as the man waits for the approaching sunrise. However, in this world, even the sun does not provide much brightness to the gloomy atmosphere.
The first couple of pages also include similes. McCarthy describes the approaching darkness each night as "Like the onset of some cold glaucoma dimming away the world." This implies that the problem is with the viewer and not with the world around him, which is actually the case. One of the paragraphs on the first two pages is a fairly detailed account of the man's dream, which includes simile and imagery and is also symbolic. In the man's dream, he is led by the boy into a cave. He and the boy are described as "Like pilgrims in a fable" (a simile), which makes it seem like the experience is not quite real. Imagery is used to describe "the black and ancient lake." The lake houses is depicted as a monster, whose eyes are described with a simile comparing them to "the eggs of spiders." After the dream is described, the man looks around the landscape, so McCarthy uses more imagery to describe the scene, characterized by "ash."
Overall, the first two pages introduce us to the two characters, the setting, and McCarthy's writing style through his use of repetition, imagery, and figurative language.

Is it possible to prepare for extreme stress while working as a first responder?

Yes, it is possible for first responders to prepare for extremely stressful situations. In fact, such occupations as police officers, firefighters, Emergency Medical Technicians (EMTs), and others train hard precisely to prepare for extremely stressful situations.
Professions such as those listed above are inherently stressful. Confronting armed suspects, or suspects who may or not be armed but who are encountered in a particularly tense environment, is extremely stressful, as is entering a burning building or attending to victims of a shooting while the shooter remains in the area. All of these are routine scenarios for which first responders prepare. 
Stress cannot be eliminated from inherently stressful scenarios, such as a terrorist attack or natural disaster. And, it is the exceedingly rare individual who is immune to the kind of stresses that can diminish the mental capacities of untrained individuals. That is why first responders train and train and train. They train because that is the only way they can be ready to respond to extremely stressful situations. That is why law enforcement academies include live fire ranges where recruits are subjected to different types of scenarios that require split-second decisions on whether to discharge their firearms. It is the reason firefighters attempt to recreate the most realistic training scenarios possible--so that prospective and active personnel will know how to respond if and when the scenarios depicted actually occur. And, it is why EMTs are incorporated into training exercises that involve large numbers of individuals who are enlisted into the exercises to act as "victims" of a shooting, airplane disaster, large-scale automotive accidents, and other possible contingencies. 
There is a problem with the training regimens described above, however. That problem is budgetary. Training costs money, and the more specialized the training, or the more elite the unit, the higher the costs. Plus, training takes time—time not spent on the street patrolling, for instance. Consequently, not every department with first responders is as well-prepared as circumstances may dictate. This, however, is a bit of a digression. First responders can be prepared for extreme stress. That preparedness comes from training in real-life scenarios, including on mock-ups of actual city streets or buildings into which first responders will likely have to enter under difficult circumstances. Pay a visit to a modern law enforcement academy, or the one operated by the United States Secret Service or the Federal Bureau of Investigation, and you will observe recruits and others being subjected to real-life, extremely stressful scenarios in fake towns designed to simulate the kinds of situations they may have to face during the course of their careers.
https://www.fbi.gov/services/training-academy

Present a character sketch of Mani from Rabindranath Tagore's "The Lost Jewels" based on the statement, "Mani did not understand Bhusan, that's true."

Mani is described as a selfish woman who only takes from her husband, Bhusan, rather than giving anything in return. The story also describes her as viewing her husband as "a mere machine for turning out her Dacca muslins and her bangles—so perfect a machine, indeed, that never for a single day did she need to oil its wheels." As the story progresses, Tagore also notes that Mani is not overly talkative or social. She tries to avoid interacting with her neighbors and seems unaffected by her isolation. Another notable fact about her character is that she never appears older than sixteen, even after many years had passed. Tagore uses this suspension of youth as a metaphor for Mani's frozen heart.
Tagore also describes Mani as a character who is efficient and dedicated to her work. She does not hire more servants than necessary and she is not "distracted by love." In light of the statement, "Mani did not understand Bhusan, that's true," it is easy to see that her relationship with Bhusan is strained. While he adores her, Mani's selfish character keeps her from being a loving partner and she does not return his affections. For his part, Bhusan's weakness leads him to spoil Mani, which prevents her from growing as a person and as a wife. The statement also serves to illustrate the emotional differences between husband and wife. While Mani does not understand Bhusan's gentle nature, it is clear that he is equally oblivious to her callousness.
https://archive.org/stream/TheLostJewels/The%20Lost%20Jewels_djvu.txt

What does "thee" mean?

"Thee" is an archaic English object pronoun used between a person of higher class and one of lower class, between an older and younger person, or between two people of the same status and age who are on good terms with each other. It is equivalent to French “you” and harks back to a time when English, like French and German, had more than one set of pronouns, with one being formal and the other informal. In modern English, the old formal “you” is both the subject and the object pronoun. With thee/thou, the “thou” form is used when the person addressed is the subject of a sentence—“thou art a villain”—whereas “thee” is used for the object, such as “I will not come with thee.” In some texts we can see “thee” being used as an insult towards a person, such as a king, who should warrant a formal pronoun.

Is the US an empire?

Yes, the United States of America is an empire. All empires throughout history have had immense lands, vast trade networks, and influence in international policy. The United States controls a large portion of the North American continent, as well as islands in the Pacific such as Hawaii and American Samoa. The US controls much of the world's trade—the New York Stock Exchange is the largest stock exchange in the world, and its rises and falls influence trade in Europe and Asia. American culture also helps drive foreign markets, as American multinational corporations such as McDonald's and Disney are considered international brands.
The US is also a key player in international foreign policy. The US is expected to take the lead role in fighting ISIS. The UN is based in the United States, and American troops made up the majority of NATO-led missions in Bosnia and the Middle East. American-made munitions are considered the standard for many armies. The US is also one of the leaders in combating weapons of mass destruction and nuclear proliferation. The US is not only an empire, but, due to its political, cultural, and economic influence, one of the largest empires in world history.  

Single Variable Calculus, Chapter 3, 3.6, Section 3.6, Problem 44

Use implicit differentiation to show that $\displaystyle y' = \frac{p}{q} x ^{(p/q) - 1}$ suppose that if $y = x^{p/q}$, then $y^q = x^p$.

Using Power Rule and implicit differentiation.


$
\begin{equation}
\begin{aligned}

y^q =& x^p
\\
\\
qy^{q - 1} \frac{dy}{dx} =& px^{p - 1}
\\
\\
\frac{dy}{dx} =& \frac{px^{p - 1}}{qy^{q - 1}}
\\
\\
\text{but } y =& x^{p/q}, \text{ so }
\\
\\
\frac{dy}{dx} =& \frac{px ^{p - 1}}{q [ (x^{p/q})^{q - 1}]}
\qquad \qquad \text{ Using the Property of Exponent }
\\
\\
\frac{dy}{dx} =& \frac{p}{q} \frac{\displaystyle \left[ \frac{x^p}{x} \right]}{\displaystyle \left[ \frac{\displaystyle \left( \frac{x^{p/q}}{x} \right)^q}{(x^{p/q})} \right]}
\\
\\
\frac{dy}{dx} =& \frac{p}{q} \frac{\cancel{x^p} (x^{p/q})}{x \cancel{(x^p)}}
\\
\\
\frac{dy}{dx} =& \frac{p}{q} \frac{x^{p/q}}{x}
\\
\\
\frac{dy}{dx} =& \frac{p}{q} x^{p/q - 1}
\end{aligned}
\end{equation}
$

College Algebra, Chapter 7, 7.2, Section 7.2, Problem 46

A specialty-car manufacturer has plants in Auburn, Biloxi and Chattanooga. Three models are produced, with daily production given in the following matrix.







Because of a wage increase, February profits are lower than January profits. The profit per car is tabulated by model in the following matrix.







a.) Calculate $AB$.

b.) Assuming that all cars produced were sold, what was the daily profit in January from the Biloxi plant?

c.) What was the total daily profit (from all three plants) in February?



a.) $\displaystyle AB = \left[ \begin{array}{ccc}
12 & 10 & 0 \\
4 & 4 & 20 \\
8 & 9 & 12
\end{array} \right] \left[ \begin{array}{cc}
1000 & 500 \\
2000 & 1200 \\
1500 & 1000
\end{array} \right] =
\left[ \begin{array}{cc}
12(1000) + 10(2000) + 0 (1500) & 12(500) + 10(1200) + 0 (1000) \\
4(1000) + 4 (2000) + 20(1500) & 4(500) + 4(1200) + 20(1000) \\
8(1000) + 9 (2000) + 12(5000) & 8(500) + 9(1200) + 12(1000)
\end{array} \right] =
\left[ \begin{array}{cc}
32000 & 18000 \\
42000 & 26800 \\
44000 & 26800
\end{array} \right]

$

b.) When we take the inner product of a row in $A$ with a column in $B$, we are multiplying the number of units sold together with its unit price per each type of car, then the result are added to produce the total profit from a specific plant. So the profit in January from the Biloxi Plant is

profit = $4(1000) + 4 (2000) + 20(1500) = \$ 42,000$

c.) Then the profit in February from all three plants is


$
\begin{equation}
\begin{aligned}

\text{profit } =& 12(500) + 10 (1200) + 0(1000) + 4(500) + 4(1200) + 20(1000) + 8(500) + 9(1200) + 12(1000)
\\
=& \$ 71,600

\end{aligned}
\end{equation}
$

In Voices of Freedom 175, why did NOW feel that women’s place in society was on the decline in 1966?

Voices of Freedom, a collection of writings from various authors who give their opinions on social issues, showcased a section from NOW, The National Organization for Women. NOW believed that the place of women in society had been declining because women are not properly recognized for the contributions that they make in society, given that they comprised over half of the population in 1966. Compared to the lives of women from the early 1900s, many more women worked outside the home in various jobs by 1966, but they held jobs of low esteem and low rates of pay compared to most men. And although those jobs were valued less in society compared to jobs which were typically held by men in 1966, NOW believes that women had no real way to move up the ladder and break through the barriers of male dominance in the workforce. So, in 1966, there was a disproportionate amount of women (about seventy-five percent of women by most estimates) working jobs (house cleaners, hospital attendants, clerks, administrative assistants, and secretaries, among others) that were considered less valuable than jobs which were held by men (managers, doctors, lawyers, accountants, and many other esteemed occupations).

Additionally, NOW believed that women only made about sixty percent of the income that men earned for full-time work. Essentially, NOW was arguing that society was not placing a high enough value (which affects rate of pay) on most jobs which were typically held by women in 1966. So NOW wanted society to pay women at rates comparable to the rates men were earning for work that it viewed to be just as valuable as the work men were performing. It is salient to note that NOW was not necessarily arguing for changes in the job roles of women, but rather increases in the pay rates as a reflection of the value of their work in society, which is a different argument entirely.

Furthermore, NOW argued in 1966 that the rapid advancement of technology was making the common roles of women obsolete, and effectively displacing them in society, with no dependable skill set to rely upon in the economy. For instance, women no longer needed to wash dishes or hand wash clothes. Machines were able to do it in 1966. Also, women were living longer in 1966 than in 1906, for example, so they began to devote less time to raising children and more time to working jobs, which diminishes women's value in society as well, according to the text.

All of these factors contributed to the decline of women's place in society in 1966, according to NOW.

In this document, Betty Friedan, one of the founders of NOW or the National Organization for Women, writes that women's status in society was in decline in the 1960s because women's longer lifespans meant that a small portion of their lives would be devoted to child rearing. However, women's roles in rearing children still meant that they were largely barred from professional opportunities. In addition, Friedan writes that technology has made many of the tasks women used to perform around the home unnecessary, and technology has also made the need for physical strength unnecessary in the workplace. The current economy calls for what she calls "creative intelligence" and for positions that women can fill as easily as men can. 
Friedan states that 46.4% of American women currently work outside the home but that 75% of them work in traditionally female occupations such as clerical jobs, housekeeping, sales, factory jobs, or similar work. African-American women are largely concentrated in the lowest-paid jobs. As a result, women earn only 60% of what men earn for full-time work, and the discrepancy between men's and women's wages has been increasing over the last 25 years. In addition, women are losing ground in managerial and professional jobs, as they comprise only 4% of lawyers and 7% of doctors. For these reasons, women's place in society and the economy was declining, according to Friedan.

In what ways was William Pitt responsible for British victory in the Seven Years war?

The Seven Years' War, also known as the French and Indian War, involved most of the great powers of Europe and resulted in significant land gains for Britain, effectively setting it up to become the massive world power it became in the nineteenth century. Pitt the Elder was instrumental in securing British victory in this war, for a number of reasons.
Although the Seven Years' War is dated from 1756, Britain had been at war with France prior to this and was indeed suffering heavily at French hands by the time Pitt became Leader of the House of Commons in 1756. This had, in Pitt's mind, largely been due to the leadership of Newcastle, who at that time held sway in the Commons. One of Pitt's first great successes was in forging an acceptable coalition with Newcastle in order to persuade the Commons to accept his leadership and his proposals for the war effort. Pitt curried great favor with the British people and was known as "The Great Commoner."
Pitt's first key steps in turning around the British defeat against the French were to engage with the Hanoverians and persuade them to go back on the agreements made at the Convention of Klosterzeven. This convention would have ensured that Hanover retreated from the war, leaving Prussia, Britain's ally, vulnerable to attack. Pitt successfully convinced the Hanoverians to return to war as a British ally. This increased the security of the British alliance on the continent, and also increased its number of available troops. Pitt also instituted a series of naval raids on France, although these had limited success at first.
Pitt's idea of utilizing Britain's great naval power to defeat the French was, however, a good one; in 1758 he developed this idea into a new strategy which used the British navy to pin down and capture factions of the French army, thus reducing the resources and troops available to the French. Pitt hoped to win victory in Germany and, subsequently, throughout Europe by ensuring the French had very limited resources in this area with which to fight back. This strategy proved successful in defeating the French land attack on Hanover, which had to be abandoned after the British defeated French forces at the Battle of Minden.
A number of French trading settlements at key points in West Africa also fell to naval attacks, inspiring Pitt to launch further attacks upon French islands in the Caribbean. This afforded the British a significant number of new ports in this area from which to attack if necessary. The great French hope at this stage of the war, the proposed naval attack upon Britain, had to be abandoned because Pitt's naval strategy in global waters was so successful, the defeat at Lagos leaving the French army too decimated to launch the planned attack—although, arguably, this benefit occurred more by luck than through Pitt's judgment.
Pitt also recalibrated the attack on Louisbourg which had previously been tried to no success; the British were able to capture this key city and subsequently Fort Duquesne, which gave them full control of the Ohio Country. This gave the British a good position from which to advance on French-held lands in Canada, ultimately capturing Quebec under the leadership of James Wolfe. When Montreal was captured in 1760, the war in North America was effectively won.
One criticism of Pitt was that his absolute refusal to offer the French any part of Newfoundland meant that the war continued for several unnecessary months beyond the capture of Belle Ile in 1761, a significant morale blow to the French and considered by many to be a sign that they would accept terms of surrender. However, Pitt was eventually able to conclude the war in Europe by increasing the number of British troops serving in the area, made possible by the fact that he had brought the war to an acceptable conclusion in North America.
http://faculty.marianopolis.edu/c.belanger/quebechistory/encyclopedia/SevenYearsWar-FrenchandIndianWar-WilliamPitttakesoverinEngland.htm

Why are there lots of earthquakes around the rim of the Pacific Ocean?

To explain the incidence of earthquakes around the Pacific Rim, we begin one of the central concepts of geology: that of plate tectonics. The Earth’s crust of solid rock is a relatively thin layer (5-50 km thick), while below there is the thick, hot layer known as the mantle. The mantle, although very hot, is considered solid, owing to the great pressure on it. Although it is considered solid, it deforms and flows on long time scales. This allows the Earth’s crust to slowly move. Huge sections of the crust, called tectonic plates, stay together but move relative to other plates. Many plates are continent-sized, but some are smaller, and most move about 1-2 cm per year.
Interesting things happen at the boundaries between crustal plates. They move relative to one another, so in some places they are moving apart, in some they are converging, or moving together, and in some they are sliding past one another, going in opposite directions. Where plates are moving apart, new crust forms from the upwelling of mantle rock to fill in the gap. As hot mantle rock approaches Earth’s surface and experiences less pressure, it melts and the resulting lava wells up and forms new crust. This is occurring in Africa’s Great Rift Valley and in the mid-Atlantic ridge, of which Iceland is a part.
The Pacific Ocean sits mostly on top of a single plate, the Pacific Plate. Most of the boundaries of the Pacific Plate are convergent, meaning plates are moving toward one another. Essentially, all of the surrounding continents are encroaching on the Pacific Plate. Something has to happen to the crust at a convergent boundary! When oceanic crust meets continental crust, it subducts beneath it. That means the crust of the ocean floor bends downward, and as the plates continue to push together, it moves down and down into the mantle and becomes part of the mantle rock. Some areas around the Pacific feature plates moving sideways with respect to one another. The San Andreas fault system in California and Mexico is this kind of boundary.
At all types of plate boundaries, we have rock pushing past other rock that is moving in the opposite direction. Most of the time, friction keeps the solid rocks from moving easily past one another. The rocks remain connected but bend, or deform, as rock to which they are attached continues moving. Strain builds up as the rocks are deformed more and more. When the energy associated with the strain is greater than would be needed to break the rocks outright, the rocks break. Significant motion occurs and a lot of energy is released as rocks “relax” to their undeformed state. This is an earthquake.
In short, the reason there are frequent earthquakes all around the Pacific Rim is that the boundaries of the Pacific Plate underlie this region, and plate boundaries are where earthquakes typically occur, because of the buildup of strain as rocks move in different directions.

Name the theme of "Araby." What textual evidence backs this up? How do you compare/contrast “Araby” to “I Want To Know Why”? How do you compare/contrast “Araby” to The House On Mango Street?

The major themes in "Araby" are longing/desire and disillusion/loss of innocence. Interestingly, both The House on Mango Street and "I Want To Know Why" share the same themes as "Araby."
In "Araby," the unnamed narrator is infatuated with Mangan's sister. He tries to get as many glimpses of her as he can. The narrator believes that his friend's sister is the epitome of elegance, beauty, and goodness. He daydreams about her and imagines going to the bazaar to bring back a gift for her. In the end, however, his hopes are disappointed when he arrives at the bazaar too late to purchase anything of significance or value. The narrator begins to understand that love is more complicated than he imagines. 
In "I Want To Know Why," the unnamed narrator is fascinated by horses. He especially adores Sunstreak, a stallion, and is so enchanted with the horse that his emotions become overwhelmed when he thinks about the animal. In time, the narrator also comes to admire Jerry Tillford, Sunstreak's trainer. When he thinks of Jerry, he experiences feelings akin to worship. The narrator believes that Jerry loves horses as much as he does. He is disillusioned however, when he discovers that Jerry has interests outside of horses. The narrator is particularly disgusted when he discovers Jerry's outside interests entail cavorting with prostitutes. The themes of longing and disillusion are apparent in this coming-of-age story.
In The House on Mango Street, Esperanza dreams of leaving her dilapidated house and her poverty-stricken neighborhood. She yearns for freedom, excitement, and love, all factors that are missing from her current life. Esperanza believes that her neighborhood has little to offer her, but as puberty arrives, she discovers that she is beginning to harbor new thoughts and to feel strange new longings. Like "Araby" and "I Want To Know Why," The House on Mango Street is a bildungsroman. The narrators in all three stories long for things that are just beyond their reach, whether it be horses or a member of the opposite sex.
Unlike "Araby" and "I Want to Know Why," however, the narrator in The House on Mango Street acquires a pragmatic optimism. Esperanza's resolve to leave Mango Street is reinforced by her traumatic sexual assault. However, she soon realizes that much has to happen before she can leave. So, she turns to her writing as a form of catharsis, as a therapeutic exercise, if you will. Even though Esperanza's innocence is lost, she begins to understand the value of waiting and preparing. Her longing is still intact, however; her traumatic experiences and disappointments do not enervate her in the way it does her peers in "Araby" and "I Want To Know Why." Unlike these two stories, The House on Mango Street ends on a hopeful note.

How does Ophelia change over the course of Shakespeare's Hamlet?

Ophelia is very much an emblematic character, very similar to Lavinia in Titus Andronicus. Here Ophelia represents the "flower" in the garden of Denmark. She is directly subject to the stewards of the land that control her. These are in order of importance, Polonius, Laertes, Hamlet and Claudius. Her rational mind is supplied by these men in the play. First Laertes instructs her how to think about Hamlet. In her only real display of authority she likewise instructs her brother in return. But notice that she is simply parroting back to Laertes what he told her. Then note her parting words to her brother: "Tis in my memory lock'd/ And you yourself shall keep the key of it." Laertes controls her rational mind. We'll come back to this at the end.
Next, Polonius steps in on the 'Hamlet' issue and reinforces what Laertes said. He asks her if she believes "his tenders." Her answer is telling. "I do not know... what I should think." Add to this Hamlet's instability which affects Ophelia as well.
Now fast forward to Act 4 Scene 5. Polonius is dead and with his death a sizable portion of her rationality is gone. Claudius summarizes the condition of the garden (and Ophelia):

O, this is the poison of deep grief; it springsAll from her father's death. O Gertrude, Gertrude,When sorrows come, they come not single spiesBut in battalions. First, her father slain;Next, your son gone; and he most violent authorOf his own just remove; the people muddied,Thick and unwholesome in their thoughts and whispers,For good Polonius' death; and we have done but greenly,In hugger-mugger to inter him...

Claudius then concludes, "...poor Ophelia/ Divided from herself and her fair judgment." What rationality she has left is tied to her brother who has just "in secret come from France."
Now turning to Act 4 Scene 7. Two things are happening at the same time. One, mimetic; we see Claudius in the process of corrupting the noble youth Laertes, i.e., taking control of his rational mind. The other diegetic or narrative, occurs off stage and will be conveyed to us by Gertrude after Claudius has seduced Laertes into his evil plan. Ophelia dies, completely free of any awareness of her own distress. What kills her? bad stewardship? Laertes tells us. "Too much of water hast thou, poor Ophelia."   

Ophelia is essentially a pure and virtuous character who is driven insane by the conflicting demands of her father and brother on one hand and her former boyfriend, Hamlet, on the other. She changes from a state of innocence to one of disillusionment and despair as the play goes on. 
At the beginning of the play, Laertes, her brother, tells Ophelia that Hamlet is not serious about her. He says, "For Hamlet and the trifling of his favor, / Hold it a fashion and a toy in blood, / A violet in the youth of primy nature" (I.3.5-7). In other words, Laertes informs Ophelia that Hamlet's attentions are fleeting, and that they will pass because he is changeable young man. Later, her father, Polonius, tells her, "You do not understand yourself so clearly / As it behooves my daughter and your honor" (I.3.97-98). He accuses her of not acting with the modesty she should, but Ophelia is ultimately an honest and honorable person. While the people around her accuse her, she acts with rectitude and obedience.
In Act III, Scene 1, she obeys Claudius, Hamlet's uncle, and her father when they ask her to spy on Hamlet. Polonius even tells her, "Read on this book / That show of such an exercise may color / Your loneliness.—" (I.3.46-49). He asks his daughter to read from a prayer book when she is trying to deceive Hamlet, an act of hypocrisy, so that she seems innocent when Hamlet comes by. She obediently responds. During the conversation that follows, Hamlet tells her, "Get thee to a nunnery. / Why wouldst thou be a breeder of sinners?" (I.3.23-24). He says that she should become a nun so that she won't give birth to more sinners like herself. Ophelia responds to Hamlet's hurtful words only by asking God to help him (line 135).
Throughout all of these manipulations by her father, brother, and former boyfriend, Ophelia doesn't change. She only says, "O, how miserable I am to see Hamlet now and know what he was before!" (I.3.161-162). Her essential good nature is intact.
However, by Act IV she is carried away by grief over how the men around her treat her and becomes mad. In some senses, she also seems to be more aware of the way men mistreat her. She is less innocent and more knowing, even as she is insane. She sings in verse (which, as it isn't in iambic pentameter, marks her as insane): "He is dead and gone, lady, /He is dead and gone. / At his head is a patch of green grass, / And at his feet there is a tomb stone." (IV.5.26-29). This verse signifies that she has become obsessed with death and is depressed and deranged after her father's death. When Claudius asks her how she is doing, she answers, "Well, God'ield you," which means may you get what you deserve. She then sings a song about a young man tricking a young woman into sleeping with him and then not marrying her (lines 40-50).
She has changed because she is now more aware of the way in which men mistreat women. Later, she drowns, and she seems to have done nothing to save herself. As Gertrude says, Ophelia is "As one incapable of her own distress" (IV.7.175). In other words, Ophelia shows no sign of saving herself, as she is resigned to the evil in the world but has decided she wants to pass on to another world so she doesn't have to deal with it. 

What did Gatsby do as a child to help himself become a success?

Gatsby kept a regular schedule for himself, even as a child, to ensure that he would better himself consistently, develop a strong work ethic, and waste no time. He would "Rise from bed" each day at 6:00 a.m.; no sleeping in and wasting the day for him. He would then work out for fifteen minutes, study for an hour, and then work for eight. After work, more exercise via playing some sport for thirty minutes, and then he would "Practice elocution, poise and how to attain it" for one hour. Finally, he would "Study needed inventions" for two hours before bed.
Gatsby also created a list of general "resolves" for himself, in addition to this rigid and well-rounded schedule. He wrote that he would not "waste time" at various locations (perhaps pool halls or bars), he would not use tobacco products, he would take a bath every other day, he would engage in the regular reading of improving materials, save money regularly, and be "better to parents."
Between his schedule and his list of resolves, Gatsby seems to really hit all the bases: he wanted to make the best use of his time, to engage in some physical activity, to be creative, to work hard, to not spend precious time and money on activities that would decrease his ability to do everything else (drinking, smoking, etc.), to be clean and well-rounded, and to be kind. Surely, it seems that a person who has all of these qualities ought to be a success. However, the fact that Gatsby eventually must engage in illegal activities in order to become that "success" seems to indicate that there is something broken in the American system, that, perhaps, the American Dream is only a beautiful fiction.

Gatsby's determination to better himself is made evident in the daily schedule he devised for himself, along with a list of the "general resolves." He wrote them on the last, blank page of a copy of Hopalong Cassidy as a boy, and Mr. Gatz shows this to Nick in chapter nine.The concept is likely inspired by Benjamin Franklin's pursuit of "moral perfection" as outlined in his autobiography; it, too, has a daily schedule and list of desired behaviors and qualities he called "virtues."
According to young Jimmy Gatz's daily schedule, he would rise at 6 a.m. to exercise for thirty minutes. He would study for an hour, work for eight hours, exercise for another thirty minutes, spend an hour working on "elocution" and "poise" and then study "needed inventions" for two hours before bed.
The "general resolves" include not wasting time, avoiding tobacco, bathing, reading, saving money, and being "better to parents."
In short, Gatsby developed goals and the discipline it takes to see them through.
Fitzgerald, F. Scott. The Great Gatsby. Charles Scribner's Sons, 1925.

Single Variable Calculus, Chapter 8, 8.1, Section 8.1, Problem 40

Evaluate $\displaystyle \int x^{\frac{3}{2}}$. Illustrate and check whether your answer is reasonable by graphing both the function and its antiderivative suppose that $c = 0$.

By using integration by parts, if we let $u = \ln x$ and $dv = x^{\frac{3}{2}} dx$, then
$\displaystyle du = \frac{1}{x} dx \qquad v = \frac{2}{5} x^{\frac{5}{2}}$

So,

$
\begin{equation}
\begin{aligned}
\int x^{\frac{3}{2}} \ln x dx = uv - \in v du &= \frac{2}{5} x^{\frac{5}{2}} \ln x - \int \frac{2}{5} x^{\frac{5}{2}} \left( \frac{1}{x} \right)\\
\\
&= \frac{2}{5} x^{\frac{5}{2}} \ln x - \frac{2}{5} \int x^{\frac{5}{2}-1} dx\\
\\
&= \frac{2}{5} x^{\frac{5}{2}} \ln x - \frac{2}{5} \int x^{\frac{3}{2}} dx\\
\\
&= \frac{2}{5} x^{\frac{5}{2}} \ln x - \frac{2}{5} \left[ \frac{x^{\frac{5}{2}}}{\frac{5}{2}} \right] + c\\
\\
&= \frac{2}{5} x^{\frac{5}{2}} \left[ \ln x - \frac{2}{5} \right] + c
\end{aligned}
\end{equation}
$





We can see from the graph that our answer is reasonable, because the graph of the anti-derivative $f$ is increasing when $f'$ is positive. On the other hand, the graph of $f$ is decreasing when $f'$ is negative.

Calculus of a Single Variable, Chapter 3, 3.1, Section 3.1, Problem 21

Given: f(x)=x^3-(3/2)x^2,[-1,2]
First find the critical x value(s) of the function. To find the critical x value(s), set the derivative equal to zero and solve for the x value(s).
f'(x)=3x^2-3x=0
3x^2-3x=0
3x(x-1)=0
x=0,x=1
Plug the critical x value(s) and the endpoints of the closed interval into the original f(x) function.
f(x)=x^3-(3/2)x^2
f(-1)=(-1)^3-(3/2)(-1)^2=-5/2
f(0)=(0)^3-(3/2)(0)^2=0
f(1)=(1)^3-(3/2)(1)^2=-1/2
f(2)=(2)^3-(3/2)(2)^2=2
Examine the f(x) values.
The absolute maximum is at the point (2, 2).
The absolute minimum is at the point (-1,-5/2).

Why does the image of silence play an important role at this point in Of Mice and Men?

In Of Mice and Men, the image of silence plays a vital role in communicating the difficulty with emotional commitment during the time period.
The characters in Of Mice and Men struggle with poverty. The financial conditions that characters like George, Lennie, or Candy experience are trying. However, Steinbeck shows that poverty can also be emotional.  This emotional poverty prevents characters from supporting one another. Steinbeck shows emotional poverty is just as crippling as financial challenges.
Steinbeck illuminates this when he discusses "the silence" in chapter three. When Carlson proposes shooting Candy's dog, Steinbeck writes that Candy "searched the faces" of the men in the bunkhouse for support and was unable to find any. The emotional poverty of the men in the bunkhouse is reflected in how no one speaks out against the killing of Candy's companion.  Even Candy is afflicted with a type of emotional poverty in how he does not bid the dog farewell. He is unable to voice any emotion about someone so close leaving him.  
When Steinbeck writes of "the silence," it reflects the emotionally impoverished condition of the men in the bunkhouse.  The silence shows a reality where people fail to stand up for one another.  "The silence" is the sum total of their emotional commitment.  While the men do not like the silence that has permeated the bunkhouse, they do not say or do anything to show solidarity to Candy or his dog because of their emotional poverty.  Steinbeck uses the silence to communicate this condition.

What is the importance of religious tolerance?

This is an important question, but I really don't like the use of the term "tolerance" in this context.  We use this word to indicate that there is something we do not like, but we are putting up with it, as I might say a teacher tolerated students' misbehavior.  What I do think we want to promote is understanding and respect for other religions.  And this is crucial to getting along in the world today if only because there are different religions, deeply held personal and societal beliefs that people should be permitted to hold in peace.  These beliefs may be similar to or different from our own, but those different can offer us new perspectives, and those similar can help us find common ground with others.  In order to live peacefully in society and to expand one's horizons, other religions should be respected.  This does not mean that we have to agree with another religion's point of view, but it does mean that we should learn about them and at the very least, agree to allow people to hold their beliefs without interference.
What happens when we do not have religious tolerance, much less respect? We have the Crusades.  We have the Islamic State.  We have someone knifing an imam and the beheading of Christians. We have the Holocaust.  Sadly, while these examples may seem extreme, they are the logical consequence of religious intolerance.  If we call America a Christian nation, we are lacking respect for all the Jews, Muslims, Hindus, Sikhs, and others who form our country, which sets citizen against citizen and which relegates other religions to a lesser status.  When the French ban burkinis, the message they are sending is one of intolerance for religious beliefs, sadly, in response to the intolerance of a group of terrorists for the religious beliefs of others. 
Religious beliefs are not meant to be rational.  They are simply beliefs, lacking in evidence and coming from our hearts. We do not want our own religious beliefs to be attacked.  We want to be able to observe our own religions in peace.  To deny someone else the ability to worship without criticism or attack when we find it so distasteful for ourselves to be thus denied seems completely unreasonable.  To do so causes dissension. To do so causes strife. To do so causes wars and genocides.  If we seek to worship in our own ways, it is not rational to prevent others from doing so.  And that surely is the point of religious tolerance, tolerance being the least we should strive for. Even better is to learn, to understand, and to appreciate the differences, all the fascinating spiritual paths that people follow.

College Algebra, Chapter 8, 8.4, Section 8.4, Problem 26

Complete the square to determine whether the equation represents an ellipse, a parabola, a hyperbola, or a degenerate conic. If the graph is an ellipse, find the center, foci, vertices and lengths of the major and minor axes. If it is a parabola, find the vertex, focus and directrix. If it is a hyperbola, find the center, foci, vertices and asymptotes. Sketch the graph of the equation. If the equation has no graph, explain why.


$
\begin{equation}
\begin{aligned}

x^2 + 6x + 12y + 9 =& 0
&& \text{Subtract $9$ and $12y$}
\\
\\
x^2 + 6x =& -12y - 9
&& \text{Complete the square: add } \left( \frac{6}{2} \right)^2 = 9
\\
\\
x^2 + 6x + 9 =& -12y-9+9
&& \text{Perfect square}
\\
\\
(x + 3)^2 =& -12y
&&

\end{aligned}
\end{equation}
$


The equation has the form $(x - h)^2 = -4py$, it is a parabola that has vertex on $(-3, 0)$ and opens downward. It is obtain from the parabola $x^2 = -12y$ by shifting it $3$ units to the left. Since $4p = 12$, we have $p = 3$. So the focus is $3$ units below and the vertex and the directrix is $3$ units above the vertex.

Therefore, the focus is at

$(-3, 0) \to (-3, 0 - 3 ) = (-3, -3)$

and the directrix is the line $y = 0 + 3 = 3$

College Algebra, Chapter 8, 8.4, Section 8.4, Problem 16

Find the center, foci, vertices and asymptotes of the hyperbola $\displaystyle \frac{(y - 1)^2}{25} - (x + 3)^2 = 1$. Sketch its graph.

The shifted hyperbola has center at $(-3, 1)$ and a vertical transverse axis. It is derived from the hyperbola $\displaystyle \frac{y^2}{25} - x^2 = 1$ with center at the origin. Since $a^2 = 25$ and $b^2 = 1$, we have $a = 5, b = 1$ and $c = \sqrt{25 + 1} = \sqrt{26}$. Thus, the foci lie $\sqrt{26}$ units above and below the center. Consequently, the vertices of the hyperbola lies $5$ units above and below the center. By applying transformations, we get

Foci

$\displaystyle (-3, 1) \to (-3, 1 + \sqrt{26})$

$\displaystyle (-3, 1) \to (-3, 1 - \sqrt{26})$

Vertices

$\displaystyle (-3, 1) \to (-3, 1 + 5) = (-3, 6)$

$\displaystyle (-3, 1) \to (-3, 1 - 5) = (-3, -4)$

The asymptotes of the unshifted hyperbola are $\displaystyle y = \pm \frac{a}{b}x = \pm 5x$, so the asymptotes of the shifted hyperbola are


$
\begin{equation}
\begin{aligned}

y - 1 =& \pm (5x + 3)
\\
\\
y - 1 =& \pm 5x \pm 15
\\
\\
y =& 5x + 16 \text{ and } y = -5x - 14



\end{aligned}
\end{equation}
$



Therefore, the graph is

What happens as Scout and Jem are walking to the school for the pageant?

It is a dark, warm, overcast night as Jem and Scout head to the school for the Halloween pageant. Jem says it might rain later. The moon is not out. The children can hardly see, but Scout notes that they are over being afraid of supernatural creatures haunting the night.
Jem carries Scout's ham costume, for which she is grateful. She trips over a tree root. In the schoolyard, Cecil sees them. He has come by car and thinks they have come with Atticus. When he realizes they are alone and don't know he's there, he takes advantage of the opportunity to leap out at them, shine a light on them, and try to scare them. It works. They are startled, if only for moment. Scout admits that Cecil:

had given us a fright, and he could tell it all over the schoolhouse, that was his privilege.

All of this sets the scene for what is to follow when Jem and Scout meet real danger in the form of Mr. Ewell after the pageant.

Scout and Jem are on their way to the Halloween pageant at the high school auditorium. As they approach the Radley residence, Cecil Jacobs suddenly jumps out at them, giving Scout and Jem a bit of a fright. This particular scene is an example of foreshadowing, as it gives us a taste of what's about to happen.
On their way back from the Halloween pageant, Scout and Jem are attacked. This time, it isn't Cecil Jacobs playing a silly prank; this is much more serious. Scout doesn't know it at the time, but they've been attacked by Bob Ewell, still sore at Atticus for publicly humiliating him on the witness stand. In the midst of the ensuing melee, Scout is aware of someone pulling the attacker off her. She assumes it's Jem, but she finds out later that it was Boo Radley. Scout also sees the figure of a strange man carrying Jem to their front door. Once again, she doesn't know who the man is. But as before, it turns out to be none other than Boo Radley.

What are the trifles in Glaspell’s Trifles?

The trifles are the small things the investigators don't notice but the women do. They are Mrs. Wright's quilt, the cage, and the dead canary.
The quilt showcases Mrs. Wright's mental state; it shows that she was unhappy and on edge. The stitches are sloppy and out of place. Mrs. Hale says, "All the rest of it has been so nice and even. And look at this! It's all over the place." Then they hide the quilt from the men and fix the parts that are messed up.
Next, they find the broken cage with the broken door and the busted hinge. This shows them that something violent took place.
Finally, they find the dead canary wrapped in silk. This discovery—along with the cage—helps them understand why Mrs. Wright killed her husband. He killed the bird that brought her comfort. The women hide this from the investigators as well.
All of the trifles are dismissed by the investigators as women's matters that are beneath their notice. However, they are actually the clues that would have let them solve the case.

In Glaspell's play, the "trifles" are the quilt with erratic stitching, the bird cage, and the dead canary in a pretty little box.
Ironically, the "trifles" found in the kitchen are key items to providing the motive for which the men spend their time searching upstairs. They ignore the kitchen since the County attorney has asked the sheriff as they stand in its doorway,

"You're convinced that there was nothing important here--nothing that would point to any motive?"

and the sheriff has replied, "Nothing here but kitchen things."
So, the men go upstairs and leave Mrs. Hale and Mrs. Peters to attend to the broken jars of preserves since "women are used to worrying over trifles." However, the broken jars of preserves are not the only "trifles" that they discover. For, as they straighten the kitchen. Mrs. Peter finds a quilt that Mrs. Wright has worked on; then, Mrs. Hale notices that the sewing is erratic at one point whereas it is neat everywhere else that has been stitched. "Why, it looks as if she didn't know what she was about!" Mrs. Hale exclaims. Then, because bad sewing always makes her "fidgety," she fixes it.
While Mrs. Hales sews, Mrs. Peters gathers the clothing that Mrs. Wright, who is in jail, has requested. Needing a string or something to wrap these items, Mrs. Peters looks in a cupboard and finds a bird cage. This cage has a broken door because a hinge has been pulled apart.
Later, Mrs. Hale suggests that Mrs. Peters take the quilt to Mrs. Wright to finish. Agreeing, Mrs. Peters looks for Mrs. Wright's quilt patches in the sewing basket, but finds none. Then, she sees a pretty red box and, thinking the scissors may be in it, she discovers instead a dead canary wrapped in silk. Its neck has been wrung. Just as they look upon the poor bird in horror, the men descend the stairs.
Facetiously, the county attorney alludes to the wives' remarks about whether Mrs. Wright was going to "quilt or knot" the quilt she was sewing,

"Well, ladies, have you decided whether she was going to quilt it or knot it?"

Mrs. Peters replies with dramatic irony, "We think she was going to--knot it." Dismissively, the attorney responds,

"Well, that's interesting, I'm sure. (Seeing the bird-cage)  Has the bird flown?"

Mrs. Hale tells him that they think the cat got it. She adds that Mrs. Wright liked the bird and was going to bury it in the pretty box.
When the men start back up the stairs, Mrs. Hale and Mrs. Peters confer with one another about the cruelty of Mr. Wright and her terrible isolation and loneliness without children or friends. Their sympathy for this poor woman waxes as they talk; finally, they make their decision to hide the "trifles" of the bird and the box from the sheriff and county attorney.

Describe what happens from the time Frampton Nuttel enters the Sappleton home with particular attention to why things happen the way they do in "The Open Window"?

In "The Open Window," Framton Nuttel brings his frayed nerves and letters of introduction to Mrs. Stappleton's home, but flees in terror the same day.
Having arrived at the Stappleton home, Framton Nuttel finds himself sitting across from Mrs. Stappleton's niece, endeavoring to say something that is proper and appropriate.
Secretly, he wonders if this visit and any others will provide him the purported nerve cure he is supposed to be seeking in the countryside.
Holding his letter of introduction, Framton wonders if Mrs. Stappleton is nice.
After a considerable silence, the niece asks, "Do you know many of the people round here?"
Framton explains that he is stranger, but his sister stayed at the rectory for four years and has provided him with letters of introduction.
Then the girl asks, "Then you know practically nothing about my aunt?" and Framton answers, "Only her name and address."
So, Vera dives right in on her tall tale: "Her great tragedy happened just three years ago...that would be since your sister's time." (The niece, Vera, begins, secure in her surety that Framton will suspect nothing since he know no one.)
She begins her tale of how Mr. Stappleton and Mrs. Stappleton's two brothers went out the open window for a "day's shooting." But, tragically, they were "engulfed in a treacherous piece of bog" and never seen again.
Because their bodies were never recovered, Vera adds, "Poor aunt always thinks that they will come back, and walk in the window as they always did." This is why the window is open now.
Vera continues and tells how Mrs. Stappleton's brother Ronnie would return as he sings, "Bertie, why do you bound?" She adds that even she has an eerie feeling as though they might really return.
Framton is completely taken in and unnerved by this tale. So when Mrs. Stappleton enters, he is relieved, thinking all this talk of hunting will end.
When she is seated, Mrs. Stappleton says, "I hope you don't mind the open window...my husband and brothers will be home directly from shooting." She explains that when they return, she always has them enter through the window rather than traipsing over the carpets.
Framton is horrified as Mrs. Stappleton rambles on about the scarcity of birds and the prospects of ducks. He tries to divert Mrs. Stappleton away from such talk, but she keeps looking out the window.
He grows nervous, wishing he had not visited on this tragic anniversary. He tells Mrs. Stappleton that his doctors have prescribed rest and absence of mental excitement, and then he elaborates upon his ailments to which he gets no audience.
Mrs. Stappleton manages a few sounds, but watches intently out the window for her family. Framton looks in sympathy at the niece, but she is staring in feigned open-mouthed horror out the window.
The figures of the men and the dog become visible  in the twilight. As they near the house, one of the boys sings, "I said, Bertie, why do you bound?" This is just as Vera has described him.
Hearing this song that a dead person is supposed to have sung sends Framton racing to grab his things in the hallway as he flees the Stappleton home. He hurries out and down the lane, believing he has seen the dead.
As he approaches, Mr. Stappleton greets his wife outside the window, "Here we are, my dear." He asks who that was he saw that "bolted out" as they arrived. Mrs. Stappleton tells him, "A most extraordinary man." She says he talked incessantly about his ailments, and without even saying good-bye. "One would think he had seen a ghost." She knows nothing of her niece's fabricated tale, and wonders what is wrong.
Nonchalantly, the girl who has caused all this confusion, says, "I expect it was the spaniel....he told me he had a horror of dogs." Then she launches into a tall tale about a pack of dogs that supposedly attacked Nuttel, and he had to spend the night in a newly dug grave. "Romance at short notice was her specialty."

Should Sam and Eric be considered guilty or innocent for their actions on the island in Lord of the Flies?

I would argue that Samneric should generally be regarded as innocent. They're among the weaker members of the group, timid little creatures precluded by size and age from influencing the course of events. They're bit players in a much bigger drama in which they're hopelessly out of their depth; they are pawns in a deadly power struggle between Ralph and Jack.
It's notable that Samneric are described as "dim shadows." This highlights their subordinate status on the island as well as foreshadows their betrayal of Ralph. Although Ralph implores the twins to keep his hiding place a secret, they confess his whereabouts to the savages, putting his life in imminent danger. Yet it's difficult to see what else they could've done under the circumstances. They were being brutally tortured by the sadistic Roger, so they didn't have much choice in the matter. Besides, having seen what had happened to Piggy, the boys were justifiably worried that they'd be next.

How does the narrator's interpretation of events reflect his or her own interests and desires?

The narrator portrays "Little Mrs. Sommers" in an incredibly sympathetic way. Her fifteen dollars seems like a great sum "to her" as it "stuffed and bulged" her worn-out purse, making her feel important in a way that she has not for quite a long time. She is so careful, so thoughtful about how best to spend it, and we are told that her neighbors often talked of what had been, for Mrs. Sommers, "'better days'" when she did not, apparently, have to be quite so careful with money as she does now. Times are hard for Mrs. Sommers. The following description, especially, seems designed to elicit our sympathies as well:

Mrs. Sommers was one who knew the value of bargains; who could stand for hours making her way inch by inch toward the desired object that was selling below cost. She could elbow her way if need be; she had learned to clutch a piece of goods and hold it and stick to it with persistence and determination till her turn came to be served, no matter when it came.

The narrator invites us to imagine Mrs. Sommers waiting for interminable lengths of time in order to save a scrap of money, like a little bird just waiting its turn for the feeder and fending off larger birds that swoop in to snatch her meager little seeds. It is telling, too, that Mrs. Sommers doesn't even consider purchasing something for herself—she thinks only of her children—until she happens upon the silk stockings. In fact, she'd been so preoccupied with taking care of her children that she'd even forgotten to eat that day: "An all-gone limp feeling had come over her [...]." In this state of exhaustion, with this feeling of being completely spent, Mrs. Sommers gives in to temptation. Who can blame her? Who, in such a depleted state, having denied herself anything pleasurable or beautiful for such a long time, wouldn't be tempted as Mrs. Sommers is? The narrator's refusal to condemn her or to depict her as selfish seems to indicate a great deal of empathy. The narrator, thus, clearly wants to evoke our sympathy for this character.

Intermediate Algebra, Chapter 5, 5.1, Section 5.1, Problem 51

Write the expression $8^{-1}-3^{-1}$ with only positive exponents. Then, simplify the expression.
Remove the negative exponent by rewriting $8^{-1}$ as $\dfrac{1}{8}$. A negative exponent follows the rule of $a^{-n} = \dfrac{1}{a^n}$
$\dfrac{1}{8}-3^{-1}$
Remove the negative exponent by rewriting $3^{-1}$ as $\dfrac{1}{3}$. A negative exponent follows the rule of $a^{-n} = \dfrac{1}{a^n}$
$\dfrac{1}{8}-\dfrac{1}{3}$

To subtract fractions, the denominators must be equal. The denominators can be made equal by finding the least common denominator (LCD). In this case, the LCD is $24$. Next, multiply each fraction by a factor of $1$ that will create the LCD in each of the fractions.
$\dfrac{1}{8}\cdot\dfrac{3}{3}-\dfrac{1}{3}\cdot\dfrac{8}{8}$
Complete the multiplication to produce a denominator of $24$ in each expression.
$\dfrac{3}{24}-\dfrac{8}{24}$
Combine the numerators of all fractions that have common denominators.
$\dfrac{1}{24}(3-8)$
Subtract $3$ to $8$ to get $-5$
$\dfrac{-5}{24}$

Describe the measures an organization could take to minimize adverse impacts on plant and animal communities (biodiversity).

Plant and animal biodiversity are severely threatened in many areas of the world by habitat loss, invasive species, pollution, diseases, climate change, resource over-exploitation, etc. An organization can take some of the following steps to minimize their impact on plant and animal communities:

Reduce, reuse, recycle. The waste stream of any organization needs to be controlled and minimized through the 3R strategy: reduce, reuse, and recycle. These strategies will ensure that less waste is generated and less waste needs to be disposed of. This also saves energy in waste processing and disposal, and less land needs to be converted to landfills.

Compost. Making compost out of biodegradable waste not only reduces the waste but also decreases a company's dependence on fertilizers.

Use environment-friendly raw materials. An organization can switch to using environment-friendly raw materials for their operations. This reduces the synthetic and/or harmful products being released into the environment. The use of environment-friendly cleaning products is one example.

Reduce energy requirements. Energy generation is still mostly fossil-fuel dependent. This causes a degradation of our environment through waste generation (gases, fly ash, etc.). A reduction in energy use will reduce the adverse impact on our environment. An organization can buy energy-efficient appliances, such as computers, fans, air conditioners, etc.

Use renewable energy. Using energy derived from renewable sources, such as the sun (solar energy), wind (wind energy), waves, etc., is a much better option than using fossil fuels.

Use green buildings. An organization can replace the conventional buildings with green buildings, preferably certified by LEED (or other similar agencies). Green buildings have a lower lifetime impact on the environment, use less energy and water, and ensure a smaller impact on the native biodiversity.

Carpool and use public transport. An organization can support carpooling and public transport use by its employees to reduce the amount of vehicular pollution.

Donate to conservation efforts. An organization can donate resources to environmental conservation efforts to minimize the adverse impacts on plant and animal communities.

What is a concrete social, political, and cultural change in Europe after New World colonization?

Europe experienced rapid and profound social, cultural, and political change in the aftermath of the colonization of the New World, but demonstrating the causal relationship between these changes and colonization is complex and difficult. One social change resulting from colonization was also an economic change. Many historians have argued that the influx of wealth–particularly silver–from the New World via the Spanish Empire contributed to the rise of capitalism in Europe. Essentially, it precipitated a permanent shift to a money economy that featured such complex financial instruments as joint-stock companies and powerful credit houses. Cultural changes included the intellectual problems posed by encountering a "new world." There were people there who seemed alien and foreign to Europeans, and intellectuals and religious leaders struggled to make sense of people who did not fit into the so-called "great chain of being" as they understood it. The trope of a "noble savage" emerged in European literature and political theory, and many European writers from Montaigne to Thomas More used American peoples as an idealized counterpoint to European society. The new sense of cultural relativism contributed to the intellectual climate of first the Renaissance and later the Enlightenment. Politically, one of the major changes was the series of wars that broke out between the major powers, especially in the eighteenth century, that were fought at least in part over control of colonial possession in the Americas.

Single Variable Calculus, Chapter 5, Review Exercises, Section Review Exercises, Problem 30

Find the indefinite integral $\displaystyle \int \frac{x^3}{\sqrt{x^2 + 1}} dx$. Illustrate by graphing both the function and its antiderivative (take $C =0$).
If we let $u = x^2 +1$, then $du = 2x dx$, so $\displaystyle x dx = \frac{du}{2}$. Also $x^2 = u - 1$. Thus,

$
\begin{equation}
\begin{aligned}
\int \frac{x^3}{\sqrt{x^2 + 1}} dx &= \int \frac{x^2}{\sqrt{x^2 + 1}} x dx\\
\\
\int \frac{x^3}{\sqrt{x^2 + 1}} dx &= \int \frac{u- 1}{\sqrt{u}} \frac{du}{2}\\
\\
\int \frac{x^3}{\sqrt{x^2 + 1}} dx &= \frac{1}{2} \int \frac{u - 1}{\sqrt{u}} du\\
\\
\int \frac{x^3}{\sqrt{x^2 + 1}} dx &= \frac{1}{2} \int \frac{u}{u^{\frac{1}{2}}} - \frac{1}{u^{\frac{1}{2}}} du \\
\\
\int \frac{x^3}{\sqrt{x^2 + 1}} dx &= \frac{1}{2} \left( \frac{u^{\frac{1}{2}+1}}{\frac{1}{2}+1} - \frac{u^{\frac{-1}{2}+1}}{\frac{-1}{2}+1} \right) + C\\
\\
\int \frac{x^3}{\sqrt{x^2 + 1}} dx &= \frac{1}{2} \left( \frac{u^{\frac{3}{2}}}{\frac{3}{2}} - \frac{u^{\frac{1}{2}}}{\frac{1}{2}} \right) + C\\
\\
\int \frac{x^3}{\sqrt{x^2 + 1}} dx &= \frac{1}{2} \left( \frac{2u^{\frac{3}{2}}}{3} - 2u^{\frac{1}{2}} \right) + C\\
\\
\int \frac{x^3}{\sqrt{x^2 + 1}} dx &= \frac{u^{\frac{3}{2}}}{3} - u^{\frac{1}{2}} + C\\
\\
\text{but } c = 0 \text{ ,so we have}\\
\\
\int \frac{x^3}{\sqrt{x^2 + 1}} dx &= \frac{u^{\frac{3}{2}}}{3} - u^{\frac{1}{2}} + C\\
\\
\int \frac{x^3}{\sqrt{x^2 + 1}} dx &= \frac{\left( x^2 + 1 \right)^{\frac{3}{2}}}{3} - \sqrt{x^2 + 1}
\end{aligned}
\end{equation}
$


Graph the function $\displaystyle f(x) = \frac{\left( x^2 + 1 \right)^{\frac{3}{2}}}{3} - \sqrt{x^2 + 1}$



Graph of antiderivative $\displaystyle f'(x) = \frac{x^3}{\sqrt{x^2 + 1}}$

Where is the summary of Chapter 4 of Blink by Malcolm Gladwell?

In chapter 4, Gladwell continues his purpose to extol the value of "thin-slicing," or those insightful first impressions, and begins discussing how we can control those impressions to our benefit. Here he begins with the story of the Millennium Challenge, a war game conducted in 2000 by the U.S. Joint Forces Command. His point in this story is that Paul van Riper, a retired Marine Corps general who acted as the rogue commander, used the power of first impressions within a set of guidelines to win the challenge against his data-driven opponent. He won by allowing his field personnel the freedom to act on gut instincts during the heat of "battle."
Gladwell takes this concept into the civilian world when he examines the improvisational acting group Mother. Spontaneity is the key to good improv. Only when acting on their split-second instincts can actors create side-splitting comedy. Yet the acting troupe provided a general rule for their thin-slicing: Say yes to everything. This shows how we can control and use our thin-slicing ability to our benefit.
Gladwell then goes on to discuss the "perils of introspection" and warn against overthinking problems and relying too heavily on too much data. The example of doctors in the emergency room trying to diagnose heart attacks shows that by developing an algorithm that uses only the most applicable data, doctors can then use their instincts to give patients better care.
Chapter 4 is key to Gladwell's premise in the Introduction that "we can . . . teach ourselves to make better snap judgments." Here he introduces the reader to "doctors and generals . . . [who] owe their success, at least in part, to the steps they have taken to shape and manage and educate their unconscious reactions."

If you follow the link below, you’ll find a brief summary for each chapter of Blink.
Chapter Four is titled “Paul Van Riper’s Big Victory: Creating Structure for Spontaneity.” Here Gladwell uses examples from the U.S. military, fire fighters, emergency room personnel, and even a comedy improvisation troupe to analyze how people in stressful situations make successful spur-of-the-moment or spontaneous decisions. Each one of these groups straddles a line between needing as much information as possible, and acting as quickly as feasible. The studies that Gladwell presents show that having more information at one’s fingertips can actually mean less success. Yes, a high degree of past practice is involved, and yes, using instincts that draw on that experience are key factors. But people have no time to scrutinize every piece of information on the spot. This is particularly noticeable in the examples of the military war game in the Middle East and the Cook County Hospital emergency room in Chicago. They have to go with brief details based on the whole picture. Gladwell summarizes it this way:

There are, I think, two important lessons here. The first is that truly successful decision making relies on a balance between deliberate and instinctive thinking. … The second lesson is that in good decision making, frugality matters.

In other words, less can be more.