What is Dave's conflict in "The Split Cherry Tree"?

Dave's conflict is with his father. After Professor Herbert punishes the boys who have split the cherry tree in Eif Crabtree's orchard, Dave is worried about how he will explain what has happened to his Pa.
When Professor Herbert has the boys pay for the tree that has been damaged, Dave does not have the money, so he asks his teacher to just whip him with a switch and let him go home early so he can do his chores on the farm. But, Professor Herbert tells Dave that he is too big to whip. As explanation, Dave replies that his father "makes us mind until we are twenty-one years old" and this includes whippings. As he sweeps the school room floor, Dave worries about what his father will do to him when he comes home. He tries to think of what lie he can tell.Then, after Dave arrives home after seven o'clock, his father asks, "What in the world has kept you so?" Dave tells the truth, but Pa wonders; therefore, he declares that he will visit Professor Herbert.
When Pa visits the school, his preconceptions of what Professor Herbert and the methods of teaching are like are soon dispelled as Herbert takes Luster Sexton around the school, demonstrating various things to him. But, Professor Herbert also learns from Mr. Sexton, and a mutual respect between the two men is established. Finally, Pa helps Dave sweep; as he does so, he tells Dave that Professor Herbert is "a good man" and he adds,

"...School has changed from my day and time. I'm a dead leaf, Dave. I'm behind....I'll get a broom and we'll both sweep an hour. That pays your debt."

Dave's conflict is resolved as his father comes to understand Professor Herbert and his reason for having Dave stay after school. Pa helps Dave sweep and restores Dave's and his relationship as father and son.  

Calculus of a Single Variable, Chapter 9, 9.2, Section 9.2, Problem 16

To verify if the given infinite series: sum_(n=1)^oo 2(-1/2)^n converges, recall that infinite series converge to a single finite value S if the limit of the partial sum S_n as n approaches oo converges to S . We follow it in a formula:
lim_(n-gtoo) S_n=sum_(n=1)^oo a_n = S .
To evaluate the sum_(n=1)^oo 2(-1/2)^n , we apply the Law of exponent : x^(n+m) = x^n*x^m .
Then, (-1/2)^n =(-1/2)^(n -1+1)
=(-1/2)^(n -1)*(-1/2)^1
= (-1/2)^(n -1)*(-1/2)
Plug-in (-1/2)^n =(-1/2)^(n -1)*(-1/2) , we get:
sum_(n=1)^oo 2(-1/2)^n =sum_(n=1)^oo 2*(-1/2)^(n -1)*(-1/2)
=sum_(n=1)^oo -1*(-1/2)^(n -1)
By comparing given infinite series sum_(n=1)^oo -1*(-1/2)^(n -1) with the geometric series form sum_(n=1)^oo a*r^(n-1) , we determine the corresponding values as:
a=-1 and r= -1/2 .
The convergence test for the geometric series follows the conditions:
a) If |r|lt1 or -1 ltrlt 1 then the geometric series converges to sum_(n=0)^oo a*r^n =sum_(n=1)^oo a*r^(n-1)= a/(1-r).
b) If |r|gt=1 then the geometric series diverges.
The r=-1/2 falls within the condition |r|lt1 since |-1/2|lt1 or |-0.5| lt1 .
Therefore, the series converges.

By applying the formula: sum_(n=1)^oo a*r^(n-1)= a/(1-r) , we determine that the given geometric series will converge to a value:

sum_(n=1)^oo2(-1/2)^n=sum_(n=1)^oo -1*(-1/2)^(n -1)
=(-1)/(1-(-1/2))
=(-1)/(1+1/2)
=(-1)/(2/2+1/2)
=(-1)/(3/2)
=(-1)*(2/3)
= -2/3 or -0.67 (approximated value)

Calculus of a Single Variable, Chapter 7, 7.4, Section 7.4, Problem 39

Area of the surface obtained by revolving the curve y=f(x) about x-axis between a leq x leq b is given by
S_x=2pi int_a^b y sqrt(1+y'^2)dx
Let us therefore, first find y'.
y'=x^2/2-1/(2x^2)=(x^4-1)/(2x^2)
y'^2=(x^8-2x^4+1)/(4x^4)
We can now calculate the surface area.
S_x=2pi int_1^2 (x^3/6+1/(2x))sqrt(1+(x^8-2x^4+1)/(4x^4))dx=
2pi int_1^2(x^3/6+1/(2x))sqrt((x^8+2x^4+1)/(4x^4))=
2pi int_1^2(x^3/6+1/(2x))sqrt(((x^4+1)/(2x^2))^2)dx=
2pi int_1^2(x^3/6+1/(2x))(x^4+1)/(2x^2)dx=
Multiplying the terms under integral yields
2pi int_1^2 (x^5/12+x/12+x/4+1/(4x^3))dx=
2pi int_1^2(x^5/12+x/3+1/(4x^3))dx=
2pi (x^6/72+x^2/6-1/(8x^2))|_1^2=
2pi(64/72+2/3-1/32-1/72-1/6+1/8)=2pi cdot 47/32=(47pi)/16
The area of surface generated by revolving the given curve about x-axis is (47pi)/16.
Graphs of the curve and the surface can be seen in the images below.

Explain how to compare the view of the world in Lord of the Flies and To Kill a Mockingbird.

Lord of the Flies and To Kill a Mockingbird have contrasting worldviews, which are illustrated by the plot, characters, and tone of both novels. Throughout Lord of the Flies, William Golding reveals his negative worldview by depicting how the boys gradually descend into savagery once they land on an uninhabited island. Golding's belief that human beings are inherently evil is portrayed through the actions of Jack and his hunters, as well as Simon's interaction with the Lord of the Flies. Overall, the boys revert to their primitive nature and engage in barbarism without the influence of society to suppress and control their natural instincts. Golding's negative worldview stems from his participation in WWII, where he fought for the Royal Navy. Of his WWII experiences, Golding has said,

I began to see what people were capable of doing. Anyone who moved through those years without understanding that man produces evil as a bee produces honey, must have been blind or wrong in the head.

In contrast, Harper Lee shares a relatively positive worldview through the perception of Scout and the actions of her father. Atticus Finch is a morally upright lawyer, who valiantly defends Tom Robinson in front of a prejudiced jury. Despite the overt prejudice throughout the community, Atticus has hope that all citizens will one day be perceived and treated as equals. He is also a tolerant man who sees the best in every person and gives them the benefit of the doubt. Atticus even believes that Bob Ewell has overcome his grudge after spitting in his face. Even mean individuals are portrayed as having positive character traits. Both Mrs. Dubose and Aunt Alexandra are portrayed as inherently good people with some positive characters traits. Atticus's perception of people and Scout's accepting, tolerant personality reflect Lee's worldview. Overall, Lee's story depicts how morally upright individuals with integrity positively impact people around them and influence them to change for the better.

According to Wollstonecraft, in what way will bettering women’s education benefit men?

Mary Wollstonecraft is often referred to as one of the forebearers of modern feminist theory. Her eighteenth-century work "A Vindication of the Rights of Woman" essentially postulated that the central issue of gender equality was a woman's right to an education. It's essential to note that this treatise was written at a time when patriarchal society largely viewed women as inferior to men in matters of reason, logic, and intellect.
Wollstonecraft felt these notions were ill-conceived because better educated women (like herself) would be in a more superior position to help contribute to society as a whole. Their contributions, therefore, would ultimately benefit men as well as other women who inhabited that society. Disallowing female contributions from the national discourse literally meant eliminating half of society's potential brainpower.
Moreover, she saw women as the primary educators of the young. Through education, women shaped the mindset of future generations for the benefit of mankind—men and women alike. More specifically, they were molding the minds of young boys who would grow into men and become tomorrow's leaders. Therefore, it was important as educators to be educated themselves.
In addition, she saw educated women as critical to a stable marital relationship, which would of course be of benefit to the man because it would lead to a more cohesive family unit and better sexual experiences. In other words, educated wife, happy life. She felt a woman with strong reasoning abilities and a deep well of knowledge could better maintain a marriage with a man who saw her as an equal, which, again, would result in better-educated children.

Wollstonecraft's ideas were considered radical in her time, but to us they can seem tame and even conservative. In her Vindication of the Rights of Women, she advocates for better education for women primarily so that women can become more useful and companionable wives to their husbands and better mothers to their children. 
She argues that instead of teaching women to be manipulative and silly by giving them little access to knowledge and ideas, women should be educated, like men, as "rational" people so that their husbands will want to talk to them and spend time to them, so that they can offer their husbands wise advice and manage the household well, and so that overall they contribute to the betterment of society. Women are as capable of reason as men, she argues, if they are given access to the same education. 
Wollstonecraft envisions separate spheres for men and women, with men out in public and women in the home. Because women are the parent that raises the children, she believes they should be educated to provide wise guidance. This would provide society with both better adult men and better wives for these men in the future.

How has the United States' role in the world changed in the years from 1945 to the present and what actions by the United Stets in the international arena have generated the most controversy?

Since 1945, the United States has taken a more active role in world affairs.  Directly after WWII, the United States rebuilt the economy of Western Europe through the Marshall Plan.  The United States also sought to stop the spread of communism by assisting governments which were friendly to its interests, such as the pro-Western governments of South Vietnam and Iran.  Sometimes propping up governments friendly to American interests backfired, leading to popular unrest that led to the overthrow of the South Vietnamese and Iranian governments by the people who lived there.  
America has also assisted in humanitarian causes throughout the world, such as leading the way to hunt down Nazi war criminals and helping to put down genocide in Bosnia.  Once again, America's humanitarian record has been uneven—America did little to end the genocide in Rwanda and the aid it provided in Somalia has proven to be quite meager.  Also, America's role in remedying the current refugee crisis in the Middle East is quite small when compared with the role of other Western European nations.  America has also ignored the human rights violations in China and Saudi Arabia, leading to charges of hypocrisy.  
America has also assisted oppressed groups as they have fought against invaders and dictators.  America toppled Saddam Hussein's government and it assisted fighters in Afghanistan in resisting the Soviet Union's invasion.  These have had unintended consequences—Iraq has not been stable in well over a decade and America had to invade Afghanistan after the attacks of September 11 in order to persecute Osama bin-Laden and Al-Qaeda.  
American foreign policymakers have taken action to safeguard the nation's economic and security interests; however, sometimes its actions have proven to lack foresight and have not acknowledged the will of the people who live in those regions.  

At the time of the drafting of the Arizona Constitution, the Progressive Party and movement was very influential in American politics. As such, the framers of the Arizona Constitution added specific powers to the people, such as the recall of judges. What are the pros and cons of such democratic principles being embedded in a state constitution?

There are numerous benefits to this sort of legislative freedom and empowerment for the citizens of the state. While it may seem unorthodox to be able to recall judges and remove them from the position, in the context of any other career, it makes sense. If someone puts another individual in a position, they should also have the ability to remove them from that position if they so choose—a manager can fire an employee who isn’t performing adequately.
This legislation gives power to the people in unprecedented ways. It allows them not only power over who represents them, but also ensures that those individuals maintain the standards to which they were elected.
On the other hand, this makes judicial appointments much more political than they previously were. While there will always be consternation from the opposition over the appointment of a judge, particularly one with a political bend they dislike, this law allows opposing parties to remove judges if they gain enough power. This threatens the career and rights of quality judges and introduces more turnover than is ever necessary.

The main advantage of such a measure is that it brings the legal system closer to the people it's supposed to serve. All too often, the law and its administration can be too distant from the needs of the people. This can serve to undermine confidence in the legal system, which is a dangerous development in any country where the rule of law is paramount. The recall of judges can play a vital role in reestablishing that confidence, giving members of the community a direct stake in the legal system, which allows them to shape its future development.
The biggest downside to judicial recall is that it politicizes the rule of law. The demands of law and justice often conflict with the democratic will of the people. The role of judges is to ensure that the law is faithfully interpreted and applied. In this they are guided by their legal training, knowledge, and experience. The question of whether a particular judgment in a particular case will meet with the approval of the voters shouldn't enter into the equation at all. Law is one thing, democracy another; and the recall of judges is a potentially dangerous mixture of the two, meaning that judges are always thinking of the possibility of recall when making decisions instead of exclusively focusing on securing justice.

One advantage of adding the power of recalling state judges is that it gives the people of the state the ability to remove a judge who may be acting improperly or who may be making decisions that don’t properly follow the rule of law. Without the ability to recall a judge, the people would be stuck with that person until the judge's term of office ended. This power forces judges to act properly in office and apply the law fairly to everybody.
A disadvantage of this power is that it may politicize the position. A judge might be influenced in rendering a decision or determining a sentence based on how the judge feels the public might respond. As a result, a person might not get a fair sentence, or a verdict might be influenced by public opinion instead of just the facts of the case. A judge might fear being recalled with an unpopular decision, even if it is the right decision.
Granting powers to citizens such as the recall of state judges may be beneficial, but it also could have unintended consequences.

Shel Silverstein wrote, "If you are a dreamer, come in. If you are a dreamer, a wisher, a liar, A hope-er, a pray-er, a magic bean buyer, If you're a pretender, come, sit by my fire. For we have many a flaxgolden tale to spin." What is the meaning of “For we have some flax-golden tales to spin,” and why did he use this specific wording?

Flax is a plant that has flowers, but it's even more well known for its seeds. They come in brown or golden varieties. Golden flax has bright yellow flowers, which is a color that symbolizes the sun, happiness, and hope.
The plant is used in making textiles, as well, such as linen. Flax fiber is soft and flexible, as well as shiny. It is said to look like blonde hair when arranged in bundles. This is where the term "flaxen-haired" comes from.
Shel Silverstein was a poet and a wordsmith. Many of the words in the passage from Where the Sidewalk Ends are invented by Silverstein in some way. Instead of saying optimist, or one filled with hope, he invents the word hope-er. He does the same with the word pray-er. His entire message here is to people who value imagination and storytelling. His words are an invitation to join him in creating worlds on the canvas of imagination.
He uses the words "flax-golden tales to spin" as a type of play on words, and also a phrase filled with imagery. It can be understood as a metaphor, as well. Stories are also known as "yarns." Storytellers were often said to "spin" these "yarns," which is a metaphorical way of saying they were telling a story. They weaved the characters, plot and setting together much like a weaver creates a tapestry on a loom.
It isn't accidental that Silverstein chose golden flax, which he then creatively inverts to flax-golden. This is the fiber that resembles blonde hair, as noted earlier. Blonde hair also resembles threads of gold. This shows the value he places on imagination and also the beauty he sees in creating tales. It is reminiscent of tales like Rapunzel, the beloved story of a woman who was locked in a tower and had flowing golden hair.

What are the basic features of an elegy?

The term elegy derives from Greek word elegos (Latin: elegus) which means a song of bereavement. It was typically accompanied by the music of a flute (aulos) in antiquity. The adjectival form of the word is "elegiac." The typical meter of the elegy in antiquity was the elegiac couplet consisting of one line of dactylic hexameter followed by a line of dactylic pentameter, and any poem in this form could be called an elegy. Coleridge attempted an English equivalent of the meter in the following couplet:

In the hexameter rises the fountain's silvery column:
In the pentameter aye falling in melody back.

In English, an elegy remains a poem of bereavement, normally mourning the death of a person, although sometimes a more generalized lamentation. The meter of the poem may vary. Among the most famous elegies in English are Tennyson's "In Memoriam" and Gray's "Elegy Written in a Country Churchyard."

An elegy is a sorrowful poem that bemoans the death of a person, a particular life event, or even a way of life that no longer exists. Written in a somber or mournful tone, intended to elicit strong emotion in its readers or listeners, an elegy is usually comprised of three parts: an initial lamentation for its subject, a section that honors or idealizes the dead, and finally, a section that offers comfort or hope. Some examples of elegies include When Lilacs Last in the Dooryard Bloom’d (Walt Whitman), In Memory of W. B. Yeats and Stop All the Clocks (W. H. Auden), Because I Could Not Stop for Death (Emily Dickinson), and Dirge without Music (Edna St. Vincent Millay).
Although both concern themselves with loss, an elegy differs from a eulogy. The former, traditionally written in couplets, has a set rhyme scheme, whereas the latter is usually free verse read either at graveside or at a memorial service honoring the decedent.

How did the Louisiana Purchase affect the situation of the Native Americans in that region?

In 1803, Thomas Jefferson wanted to open up trade routes through New Orleans and sent a delegation to Napoleon in France with an offer to buy the city for ten million dollars. However, Napoleon surprised the American delegation by offering the entire Louisiana territory for a mere fifteen million dollars. The bargain was too good to pass up, and Jefferson jumped at the chance to expand the western border of the United States. The purchase doubled the size of the country and provided room for the growing population to settle in new lands. However, there were already people living in the Louisiana Territory.
Before the Louisiana purchase, the native peoples did well. They were allowed to inhabit their traditional lands and participated in the French fur trade. The Spanish and French governments left them mostly untouched. That would all change when the United States purchased the land with the ideology of westward expansion.
The concept of Manifest Destiny was a later idea, but the roots of it are entrenched in the purchase of the Louisiana territory. The goal of spreading out the United States and settling the land meant that the native inhabitants of it would need to assimilate or move. Jefferson outlined the idea of his “enlightenment plan,” which would have indigenous peoples adopt a “civilized” agrarian lifestyle to help them become less savage. In a letter to the Marquis de Chastellux Jefferson explained his view on why natives should be “civilized”:

I believe the Indian then to be in body and mind equal to the whiteman

Jefferson’s idea that native peoples were intellectually and materially similar to European peoples was novel for his time but led many of the policy changes he tried to enact in regards to the native peoples living in the Louisiana Territory. While some tribes allowed for relocation to cities in the west, others resisted. In the century following the purchase, there would be many bloody wars and numerous atrocities carried out against the Native Americans who inhabited the lands of the Lousiana Territory.
The first threat to Native Americans after the Louisiana purchase was the loss of the fur trade. The trade supported nearly all economic activity of the interior tribes. The combined effect of new settlers from the east and hostility from tribes in the west meant that there was no way to continue the trade effectively. In Liberty, Equality, and Power, the authors explain the effect of shrinking territory and the loss of the fur trade on Native Americans from the interior:

Faced with shrinking territories, the disappearance of wildlife, and diminished opportunities to be traditional hunters and warriors, many Indian societies sank into despair. Epidemics of European diseases attacked peoples who were increasingly sedentary and vulnerable...Murder and clan revenge plagued the tribes, and depression and suicide become more common. The use of alcohol, which had been a scourage on Indian societies for two centuries, increased (Murrin et. al, 2007)

While native leaders like Tecumseh, Geronimo, and Sitting Bull would wage war against the United States over the next century, US policy became increasingly hostile toward Native Americans of the plains. The inland US Policies, like the Indian Removal Act, worked to harm native peoples by taking their lands, crippling their economic abilities and destroying their cultures. The effect of the Louisiana Purchase on indigenous populations was a net negative, and many of the tribes still exist on the reservations they were forced to move to at the time.

At the time of the Louisiana Purchase in 1803, the vast majority of the inhabitants of that vast region were Native Americans. They, however, were not consulted and had no sway over the transfer of the territory from France to the United States.
In the beginning, the transfer had no effect on the Indians living in the region. The US was not able to settle or control the area for many years. In the long term, however, the consequences were dire. Historically, France never placed many settlers in the New World, so the French had had less disruptive impact on Indigenous North Americans. The United States, on the other hand, was a rapidly growing country with a hunger for more territory. The expansion of the United States to the Pacific in the nineteenth century is known as Manifest Destiny. The Native way of life and the freedom of Native peoples were ultimately doomed.

The Louisiana purchase would have a dramatic impact on the indigenous Native American populations in the region. The purchase nearly doubled the size of the American controlled lands and would later incorporate fifteen states into the Republic. Although the land was controlled by French interests and some contact with Native Americans had occurred, given the sheer size of the territory, it would be unlikely anyone exploring the territory would have human contact for weeks or months.
Native Americans were affected in two significant ways. The first is Native Americans had a much different view of property than settlers. In Native American culture, ownership of property was a foreign concept. It is true that to keep the peace between tribes, tribal leaders would designate hunting areas and boundaries, but that is not the same as owning the property. As settlers moved into the territory, the first conflict between settlers and Native Americans occurred over property.
The second way Native Americans were affected was the destruction of their culture. It is interesting to note President Jefferson was willing to negotiate with a foreign power to purchase the property while at the same time not acknowledging Native Americans had the first claimed the land as their generations before settlers landed on the American continent. It can be argued the dismissal of Native American complaints first registered with the government during the settlement of the lands in the Louisiana Purchase set the tone for future relationships and negotiations. Jefferson pursued policies designed to ingratiate Native Americans to the Republic in order to prevent them from making treaties with other foreign countries. He also believed in the European notion of what a civilized society should look like and pursued policies that attempted to get the mostly nomadic tribes to adopt an agrarian lifestyle much like the Europeans when they first settled in America.
The Louisiana Purchase was the foundation for the philosophy of Manifest Destiny. Free land and other enticements encouraged rapid settling of the land encompassed in the deal furthering the encroachment on Native American land and anti-Native American sentiment.

Initially there were few impacts faced by the Native Americans who lived within the bounds of the Louisiana Purchase. Many had already experienced either French traders or Spanish missionaries and had made up their own minds about white culture before Lewis and Clark arrived to explore the territory. Lewis and Clark had differing experiences with the native groups. The Mandan welcomed the Lewis and Clark expedition and allowed them to overwinter with their group. The Sioux, on the other hand, experienced a smallpox outbreak due to contact with traders and rebuffed the diplomatic attempts made by the Lewis and Clark expedition.
In time, the native groups throughout the territory would feel the presence of Americans more often. Mountain men came and forged alliances with some tribes for both companionship and trade rights. The mountain men in time would serve as guides for the wagon trains heading west. These wagon trains would encroach on hunting grounds and holy sites, and this would lead to the friction between the native groups and the United States government that would be prevalent after the Civil War.

Which sentence in this excerpt from Mark Twain's "The £1,000,000 Bank-Note" is an example of hyperbole? I would have picked up the pear now and eaten it before all the world, but it was gone; so I had lost that by this unlucky business, and the thought of it did not soften my feeling toward those men. As soon as I was out of sight of that house I opened my envelope, and saw that it contained money! My opinion of those people changed, I can tell you! I lost not a moment, but shoved note and money into my vest-pocket, and broke for the nearest cheap eating-house. Well, how I did eat! When at last I couldn't hold any more, I took out my money and unfolded it, took one glimpse and nearly fainted. Five millions of dollars! Why, it made my head swim. I must have sat there stunned and blinking at the note as much as a minute before I came rightly to myself again. The first thing I noticed, then, was the landlord. His eye was on the note, and he was petrified. He was worshiping, with all his body and soul, but he looked as if he couldn't stir hand or foot. I took my cue in a moment, and did the only rational thing there was to do. I reached the note towards him, and said, carelessly:

The sentence that is pure hyperbole is part of the narrator's description of the landlord:

He was worshiping, with all his body and soul, but he looked as if he couldn't stir hand or foot.

The landlord is looking at the £1,000,000 bank-note and experiencing a reaction which is common to most people when they behold an exceptionally large sum of money--or when they meet a man who possesses many millions. Mark Twain does not have to be afraid of misrepresenting the landlord's reaction. The reader understands precisely what the man is feeling and discounts the narrator's description proportionately. The landlord is not literally worshipping the bank-note but is stunned at the beauty and the potential of such a wonderful conception and creation.
Part of the quoted sentence is not hyperbolic--the part that says he looked as if he couldn't stir hand or foot. It is the first half of the sentence that contains the hyperbole. The landlord is the first person (after the narrator) who will see this marvelous bank-note. Mark Twain must have felt that he should describe the first man's reaction as one of extreme awe and wonder, because he couldn't keep describing subsequent reactions of other men to the same bill without getting diminishing effects or even incurring disbelief in the premise. The reader will understand that the other men who see the marvelous bank-note will be experiencing feelings comparable to those of the landlord. 
Part of what makes the scene so funny is that the narrator acts as if the bank-note is nothing but petty cash. 

I reached the note towards him, and said, carelessly:
     "Give me the change, please."

Mark Twain continues with more hyperbole.

Then he was restored to his normal condition, and made a thousand apologies for not being able to break the bill, and I couldn't get him to touch it. He wanted to look at it, and keep on looking at it; he couldn't seem to get enough of it to quench the thirst of his eye, but he shrank from touching it as if it had been something too sacred for poor common clay to handle.

The "change" would have amounted to £999,999 plus approximately seventeen shillings, or in American dollars to $4,999,999. The narrator specifies that he had gone to "the nearest cheap eating house."
Mark Twain's story is the prototype of many such stories that have followed since "The £1,000,000 Bank-Note" was published in 1893. Invariably, a couple of fabulously wealthy men make a bet which involves giving some poor passer-by a huge sum of money to dispose of within a short period of time. In Mark Twain's story the protagonist is given the bank-note as a loan for thirty days.

College Algebra, Exercise P, Exercise P.3, Section Exercise P.3, Problem 62

Determine the distance between



a.) $\displaystyle \frac{7}{5} \text{ and } -\frac{1}{21}$
Let $\displaystyle a = \frac{7}{5} \text{ and } b = -\frac{1}{21}$


$
\begin{equation}
\begin{aligned}
d (a, b) &= |b - a|\\
\\
&= \left| \frac{-1}{21}- \frac{7}{15} \right|\\
\\
&= \left| \frac{-1}{3 \cdot 7} - \frac{7}{3 \cdot 5} \right|\\
\\
&= \left| \frac{\frac{-5}{3}-\frac{49}{3}}{35}\right|\\
\\
&= \left| \frac{\frac{-5-49}{3}}{35} \right|\\
\\
&= \left| \frac{\frac{-54}{3}}{35} \right|\\
\\
&= \left| \frac{-18}{35} \right|\\
\\
&= \left( -\frac{18}{35} \right)\\
\\
&= \frac{18}{35}
\end{aligned}
\end{equation}
$

b.) $-38$ and $-57$
Let $a = -38 \text{ and } b = -57$

$
\begin{equation}
\begin{aligned}
d(a,b) &= |b-a|\\
\\
&= |-57 - (-38)|\\
\\
&= |-57 + 38|\\
\\
&= |-19|\\
\\
&= -(-19)\\
\\
&= 19
\end{aligned}
\end{equation}
$


c.) $-2.6$ and $-1.8$
Let $a = -2.6 \text{ and } b = -1.8$

$
\begin{equation}
\begin{aligned}
d(a,b) &= |b-a|\\
\\
&= |-1.8-(-2.6)|\\
\\
&= |-1.8 + 2.6|\\
\\
&= |0.8|\\
\\
&= 0.8
\end{aligned}
\end{equation}
$

In Shakespeare's Macbeth, who is more powerful: Lady Macbeth or Macbeth?

Even though Lady Macbeth prods her husband on, she has no actual power.  Her only power is in pushing him.  This is why she pushes him.  She wants to have the power of being queen.  Malcolm calls her the “fiend-like queen,” but in reality Lady Macbeth has little to do with Macbeth’s kingdom.  She helped with the initial murder of Duncan, and encouraged him to kill Duncan, but after that she was not involved in the other murders.
Lady Macbeth is inspired when she finds out about the witches’ prophecies that Macbeth is going to be king.   She knows that her husband wants this.  However, she worries that her husband is too wishy-washy to act on his ambitions.

Glamis thou art, and Cawdor; and shalt beWhat thou art promised: yet do I fear thy nature;It is too full o' the milk of human kindnessTo catch the nearest way: thou wouldst be great;Art not without ambition, but withoutThe illness should attend it … (Act 1, Scene 5)

Later, Lady Macbeth does plan everything for her husband and chide him when he doesn’t follow the plan to the letter.  She seems to know what she is doing in planning murders.  However, she doesn’t carry out the murder herself.  She needs him.

LADY MACBETH
Alack, I am afraid they have awaked,And 'tis not done. The attempt and not the deedConfounds us. Hark! I laid their daggers ready;He could not miss 'em. Had he not resembledMy father as he slept, I had done't. (Act 2, Scene 2) 

Relying on her husband must have been hard for such a strong woman.  She turns out to be not as bloodthirsty as she seemed.  Lady Macbeth starts to crack.  Macbeth, it could be argued, was cracking long before he killed Duncan.  He was already envisioning floating daggers.  By the time Macbeth has Banquo killed and sees his ghost at the banquet, Lady Macbeth is making excuses for him.  It won’t be long before she loses her tenuous grasp on reality and is trying to wash her hands of blood long after it is no longer there.

Calculus: Early Transcendentals, Chapter 1, 1.6, Section 1.6, Problem 12

Determine whether $g(x) = \cos x$ is one-to-one.
Remember that the graph of $g(x) = \cos x$ is repeating over intervals. So if we use horizontal
line test, the line will intersect the graph at many points. Thus, $g(x) = \cos x$ is not one-to-one.

What are some examples of idealism in Don Quixote?

Don Quixote's self-invention as a knight triggers a series of idealistic episodes that constitute the bulk of Miguel de Cervantes's novel.
One episode where Quixote shows his idealism is in rescuing the chained men whom he and Sancho run across. He reasons that it is wrong for their guards to have chained them together and that he should release them. After Quixote and Sancho accomplish this, however, the ungrateful rescued men—who are thieves—steal from them, which even Quixote finds discouraging.
Another instance concerns what has become the iconic phrase associated with quixotic behavior: jousting at windmills. Riding through the countryside and encountering windmills, Quixote declares them to be giants who are oppressing the countryfolk. Determined to free them from this scourge, he rides at the mills with lance extended. The blade of one mill clips him and unseats him. Momentarily bested, he moves on to a new adventure.

Don Quixote himself is the figure of idealism in Don Quixote. He so prefers the world depicted in the courtly romances he reads that he decides to reject the sordid everyday world he knows. He determines to be the change he wants to see. He subsequently fashions himself into a knight and travels around the Spanish countryside idealistically looking for people to protect from danger and harm.
In one instance, he encounters a man beating one of his servants. He intervenes to save the servant, reasoning with his employer to agree not to continue the beating. However, once Don Quixote is out of sight, the man beats the servant even more savagely. In another more famous instance, Don Quixote goes charging at windmills on his horse thinking they are giants. His heart is in the right place, as he is trying to protect people from what he thinks are monsters, but all he ends up doing is hurting himself.
As the above examples show, Cervantes critiques Don Quixote's misplaced idealism. It either backfires or causes harm to Quixote without solving any problems. Cervantes's genius is to show Don Quixote's desire for a more ideal world as appealing while critiquing the misplaced idealism by which he goes about trying to right the world's wrongs.

Don Quixote's character is permeated by idealism. Though strictly speaking, that idealism is solely related to his persona as an errant knight rather than to the real Alonso Quixano underneath. In that sense, idealism is virtually synonymous with madness. But when Don Quixote throws off the mask of the knight, it is surprising just how much common sense and wisdom he appears to possess.
However, as a knight, Don Quixote is a complete idealist (or madman). Arguably the most famous example of this is when the Don charges at windmills, believing them to be ferocious giants. His knightly veneration of courtly love leads him to regard a couple of prostitutes outside an inn as ladies of quality. A similar episode takes place when he treats a couple of common goatherds like gentlemen, his social equals. In both of these examples, the Don's idealism, however deluded it may appear, leads to his connecting with people to whom he normally wouldn't give the time of day. There's a hint of satire here; Don Quixote's idealism sheds a revealing light on the conventional relations between different classes at that time in Spanish society.

How has religious radicalization in Central Asia and the Middle East affected United States relations with traditional NATO allies during the last decade? How would you describe its impact on US geopolitical policy?

It appears that religious radicalization in Central Asia and the Middle East has led to increased collaboration between the United States and its NATO allies. By extension, religious radicalization has had an enormous impact on US geopolitical policy.
First, let us talk about NATO. The alliance is made up of 29 countries. Additionally, NATO works with a range of international organizations to preserve geopolitical stability. The partner organizations most pertinent to our discussion would be the Mediterranean Dialogue (MD) and the Istanbul Cooperation Initiative (ICI). The Mediterranean Dialogue is a 7-nation alliance. These nations are Jordan, Mauritania, Morocco, Algeria, Israel, Egypt, and Tunisia. Meanwhile, the ICI is a 4-country alliance made up of the Gulf states of United Arab Emirates, Bahrain, Qatar, and Kuwait.
Since the 2001 attacks on the United States, NATO has increasingly turned its attention toward Central Asia and the Middle East. NATO allies have security interests in the region, as do non-NATO allies. Certainly, the conflicting goals of both parties have greatly influenced US geopolitical strategy in the region.
Let us discuss NATO operations in the Middle East and Central Asia. Within the last decade, NATO has deployed more than 9,000 troops to Afghanistan, financed training operations for Iraqi forces, expanded its collaborative efforts with the MD and ICI, and deployed its NRF (NATO Response Force) in Pakistan. Three important developments within the last decade have affected the relationship between the US and its NATO allies and impacted US geopolitical strategy:
1) The rise of Islamic State:
The US and its NATO allies have collaborated to clear IS out of Syria and Iraq. Here, the BBC reports on which NATO countries have participated in hostilities. It is worth noting that Russia is not part of the alliance. Read the NYT article about the fight against IS below:
Thousands of ISIS Fighters Flee in Syria, Many to Fight Another Day
2) Russian interest and involvement in the Middle East:
To date, the tripartite alliance between Russia, Turkey (a NATO ally), and Iran poses a rising threat to the United States. The partnership between Russia and Iran began when the latter purchased 5 Russian S-300 missile batteries in 2007. Read about the Turkey-Russia-Iran alliance below:
Expanding Russia-Iran-Turkey Alliance Puts the US on Back-Foot
Russia Is In The Middle East To Stay
Russia and Iran open their arms as Turkey loses patience with U.S.
3) The rise of an Arab NATO and its implications for Israel-Palestinian peace efforts:
To date, the Gulf States has two alliances that are committed to combating extremism. They are the Middle East Strategic Alliance (dubbed the Arab NATO and, incidentally, modeled after NATO) and the Islamic Military Alliance. The United States will need the cooperation of these Muslim groups to realize its initiatives and goals in the Middle East. At the same time, it is also committed to its alliance with Israel, a US ally. While it is not clear how Israel would fit into these alliances, there are deep implications in store for Israeli-Palestinian relations. The multitude of concerns here continue to drive US geopolitical strategy in the region.
https://www.brookings.edu/research/natos-growing-role-in-the-greater-middle-east/

Why does Clarisse ask Montag why he is laughing?

Clarisse asks why Montag is laughing after he has laughed three times at her comments. He first laughs when she says she can tell he is a fireman, then laughs when she asks if he reads any of the books he burns, and finally laughs again when she states she has heard firemen used to put out fires, not start them.
Montag laughs because Clarisse says probing and unorthodox things that disturb him. Clarisse asks why he is laughing because she knows that what they are talking about isn't funny. She recognizes that he uses laughter as a defense against thought. She says "You never stop to think what I've asked you."
Clarisse's questioning of Montag's laughter causes him to be thoughtful. He calls her "odd," and she agrees that she thinks and observes too much. Through her, Montag begins to be reawakened to seeing the world around him and to realize he is dissatisfied with his life.

During Montag and Clarisse's first conversation, she tells him that she had heard that long ago firemen used to put out fires instead of starting them. Montag's initial reaction is to laugh at Clarisse's comment, and she asks him why he is laughing. Clarisse tells Montag,

You laugh when I haven't been funny and you answer right off. You never stop to think what I've asked you (Bradbury, 3).

Clarisse's response is significant because it reveals Montag's nature. Similar to the rest of the citizens in Bradbury's dystopian society, Montag fails to closely analyze the world around him and fails to think critically about questions he is presented. Clarisse notices that Montag's automatic response is to laugh instead of thinking about an acceptable response. In contrast, Clarisse is an insightful, curious teenager, who observes and critiques society. Clarisse's introspective nature affects Montag; he begins to examine his life for the first time. Later on, Clarisse asks Montag if he is happy, and he discovers that he is not. Her minor observations, such as Montag's forced, automatic laugh, make Montag question his life. 

Single Variable Calculus, Chapter 3, 3.7, Section 3.7, Problem 28

The equation $c(x) = 339 + 25x - 0.09x^2 + 0.0004 x^3$ represents the cost function for production of a commodity.
a.) Find and interpret $c'(100)$
b.) Compare $c'(100)$ with the cost of producing the 101st item.


$
\begin{equation}
\begin{aligned}
\text{a.) } c'(x) &= 25 - 0.18 x + 0.0012 x^2\\
\\
c'(100) &= 25 - 0.18(100) + 0.0012(100)^2\\
\\
c'(100) &= 19
\end{aligned}
\end{equation}
$

$c'(100)$ means that the cost per 100 units of production is changing at a rate of 19 $\displaystyle \frac{\text{unit cost}}{\text{unit production}}$

$
\begin{equation}
\begin{aligned}
\text{b.) } c(x) &= 339 + 25x - 0.09x^2 + 0.0004x^3\\
\\
c'(101) &= c(101) - c(100)\\
\\
&= 339 + 25(101) - 0.09 (101)^2 + 0.0004(101)^2 - \left[ 339 + 25 (100) - 0.09 (100)^2 + 0.0004 (100)^2\right]\\
\\
c'(101) & = 19.0304
\end{aligned}
\end{equation}
$

It means that the cost increases by 0.0304 as the number of unit production increases by 1 from 100.

What is a summary of the beginning?

At the beginning of the book, Peter, who is in fourth grade and is nine years old, wins a turtle named Dribble at Jimmy Fargo's birthday party and takes it home to his house on West 68th Street in New York City. His mother does not really want him to keep the turtle, and she thinks the turtle smells. Peter's mother is constantly telling him to scrub his hands, while his father, who works in advertising, spends a lot of time watching commercials on TV, including the commercial he wrote for Juicy-O.
Peter's biggest problem is his brother, Farley Drexel Hatcher, nicknamed Fudge, who is two-and-a-half years old. Fudge does things like throw tantrums and eat his mother's flowers. When Mr. Yarby, who is the head of Juicy-O, comes to dinner with his wife, Fudge torments them by doing things like appearing at the table with Dribble, the turtle, and showing up wearing a gorilla mask. Perhaps partly as a result of this, Peter's father loses the Juicy-O account. 

How does Bernard feel about soma?

As the previous Educator has noted, Bernard has a negative attitude toward soma. We see this clearly in chapter 4 when Benito offers him some: when Benito takes out his soma bottle, Bernard “suddenly turned and rushed away.” In other words, Bernard is not only disinterested in taking soma but physically turns away from it. He feels a need to distance himself from soma, suggesting a strong dislike of its qualities.
Perhaps the strongest evidence of his negative attitude towards soma comes in chapter 6, when he and Lenin are together and have met some of her friends in an ice-cream soma bar. Bernard is in a particularly bad mood and declares,

"I'd rather be myself," he said. "Myself and nasty. Not somebody else, however jolly."

For Bernard, then, the problem with soma, and his motivation for avoiding it, is that it can affect a person’s identity. He wants to feel the full range of human emotions, both positive and negative, instead of having them dulled by taking soma. He does not care that this attitude makes him appear an outsider in his society. He would rather be miserable and socially awkward than never experience real feelings.

Bernard is a kind of throwback to the pre-dystopic world. His somewhat unattractive physical appearance is considered an anomaly, leading to speculation that something went wrong during the in vitro process in his case. His personality also doesn't conform to the "perfect world" that the society is intended to be. He tends to have a self-effacing guiltiness, as if he's uncomfortable with the hedonistic values that are promoted in his society—although he embraces them at the same time, as everyone else does.
Soma represents (in medicinal form) the values of the society and its goals of artificial happiness for all. Given Bernard's against-the-grain personality, it's natural that the use of soma would be something that he's uncomfortable with and that he regards with suspicion—just as the whole society leaves him with a feeling of guilt and dissatisfaction.
A glib analysis would conclude that Bernard has an "inferiority complex" and therefore feels undeserving of the instant benefit that soma provides. He also shows signs of OCD (Obsessive-Compulsive Disorder) in little incidents like his worrying about the tap being left on in his flat. Huxley uses this for comic effect, but it indicates that, ironically, Bernard is someone who might actually need soma more than other people do.
By contrast, a person such as Lenina, who isn't inclined to inward meditation and speculation as Bernard is, has no feelings of guilt about taking soma or doing anything else, so she comes across as a kind of "model citizen" of the dystopia.

Bernard dislikes the use of soma because the drug induces a false sense of self. Soma is a drug produced and provided to the residents by the government. The drug is provided with the aim of suppressing people’s feelings and distorting their realities. It allows the people to escape from situations that may lead to stress.
Although Bernard takes soma once in a while, he refuses to take the drug when Lenina offers it to him. He reasons that he would rather be himself instead of allowing the drug to alter his personality.

rather be himself. [Him]self and nasty. Not somebody else, however jolly.

Bernard is rebellious because he is seemingly aware of what goes on around him—for instance, the Solidarity Service, which, as implied, is expected to bring the people together, leaves him feeling empty and alone.
His rebellion extends to most perceptions promoted by the people and the government including practices such as the taking of soma. While most of those who take soma seem to like taking the drug, Bernard seems to be taking it out of obligation to avoid attracting attention.

In But, Not Buddy by Christopher Paul Curtis, what is the difference between Deza's family and Bud's family?

This is a fairly straightforward question and answer.  The key difference between Deza Malone's family and Bud Caldwell's family is that Deza's parents are both still alive.  
In addition to Deza having living parents, she still lives with her parents, too.  They might all be in a shantytown together, but at least the family is still in tact.  Contrast that with Bud's family.  Bud has never known his father.  The main plot of the book is Bud attempting to find his father.  He never does, but he does find his grandfather.  Bud's mother is no longer alive.  She died several years before the book begins.  Bud doesn't know why she died, but he does tell readers that she was sick for about six days before dying.

I said, "I was six years old when it happened, sir. "I don't know why, she was too sick to go to work for six days in a row, then one morning I went into her room and she was dead. But she didn't suffer or nothing, it happened real quick, she didn't even have time to close her eyes, she didn't look like it hurt or nothing."

Bud has been living in orphanages and foster homes ever since his mother died.  

College Algebra, Chapter 7, Review Exercises, Section Review Exercises, Problem 38

Solve the matrix equation $\displaystyle \frac{1}{2} (X - 2B) = A$ for the unknown matrix, $X$ or show that no solution exists, where

$\displaystyle A = \left[ \begin{array}{cc}
2 & 1 \\
3 & 2
\end{array} \right] \qquad B = \left[ \begin{array}{cc}
1 & -2 \\
-2 & 4
\end{array} \right] \qquad C = \left[ \begin{array}{ccc}
0 & 1 & 3 \\
-2 & 4 & 0
\end{array} \right]$


$
\begin{equation}
\begin{aligned}

\frac{1}{2} (X - 2B) =& A
&& \text{Given equation}
\\
\\
X- 2B =& 2A
&& \text{Multiply both sides by scalar } 2
\\
\\
X =& 2A + 2B
&& \text{Add matrix } 2B
\\
\\
X =& 2 \left[ \begin{array}{cc}
2 & 1 \\
3 & 2
\end{array} \right] + 2 \left[ \begin{array}{cc}
1 & -2 \\
-2 & 4
\end{array} \right]
&&
\\
\\
X =& \left[ \begin{array}{cc}
4 & 2 \\
6 & 4
\end{array} \right] + \left[ \begin{array}{cc}
2 & -4 \\
-4 & 8
\end{array} \right]
&&
\\
\\
X =& \left[ \begin{array}{cc}
6 & -2 \\
2 & 12
\end{array} \right]
&&

\end{aligned}
\end{equation}
$

sum_(n=0)^oo 5^n/(2^n+1) Use the Root Test to determine the convergence or divergence of the series.

To apply Root test on a series sum a_n , we determine the limit as:
lim_(n-gtoo) root(n)(|a_n|)= L
or                         
lim_(n-gtoo) |a_n|^(1/n)= L
Then, we follow the conditions:
a) Llt1 then the series is absolutely convergent.
b) Lgt1 then the series is divergent.
c) L=1 or does not exist  then the test is inconclusive. The series may be divergent, conditionally convergent, or absolutely convergent.
In order to apply Root Test in determining the convergence or divergence of the series sum_(n=0)^oo 5^n/(2^n+1) , we let:
a_n =5^n/(2^n+1)
We set-up the limit as: 
lim_(n-gtoo) |5^n/(2^n+1)|^(1/n)=lim_(n-gtoo) (5^n/(2^n+1))^(1/n)
Apply Law of Exponent: (x/y)^n = x^n/y^n and (x^n)^m = x^(n*m) .
lim_(n-gtoo) (5^n/(2^n+1))^(1/n)=lim_(n-gtoo) (5^n)^(1/n)/(2^n+1)^(1/n)
             =lim_(n-gtoo) 5^(n/n)/(2^n+1)^(1/n)
             =lim_(n-gtoo) 5^1/(2^n+1)^(1/n)
             =lim_(n-gtoo) 5/(2^n+1)^(1/n)
Apply the limit property: lim_(x-gta)[(f(x))/(g(x))] =(lim_(x-gta) f(x))/(lim_(x-gta) g(x)) .
lim_(n-gtoo) 5/(2^n+1)^(1/n) =(lim_(n-gtoo) 5)/(lim_(n-gtoo) (2^n+1)^(1/n))
                            = 5 / 2
Note: Applying a^x =e^(xln(a)) , we may let: (2^n+1)^(1/n) = e^(1/nln(2^n+1))
lim_(n-gtoo)1/nln(2^n+1) =oo/oo
Apply L'Hospital's rule:
lim_(n-gtoo)1/nln(2^n+1)=lim_(n-gtoo) ((2^nln(2))/(2^n+1))/1
                                     =lim_(n-gtoo) (2^nln(2))/(2^n+1)
                                     =oo/oo
 Apply again the L'Hospital's rule:
lim_(n-gtoo) (2^nln(2))/(2^n+1)=lim_(n-gtoo) (2^nln^2(2))/(2^nln(2))
                         =lim_(n-gtoo) (ln(2))
                          = ln(2)
Applying lim_(n-gtoo)1/nln(2^n+1)= ln(2) on e^(1/nln(2^n+1)) , we get:
lim_(n-gtoo) e^(1/nln(2^n+1)) = e^(ln(2)) = 2
 
 The limit value L = 5/2 or 2.5 satisfies the condition: Lgt1 since 2.5gt1 .
Conclusion: The series sum_(n=0)^oo 5^n/(2^n+1) is divergent.

Which was the main commodity produced by the Spanish in the Caribbean? gold sugar silver cotton

The main commodity produced by Spain (or any European country for that matter) would be sugar.  Sugar was a very valuable commodity in the colonial era--it was rare enough to be valuable in Europe.  Spices were still a luxury though sugar plantations would make sweets available to more people.  Sugar was also important in making rum, a staple on the world's sailing vessels.  Rum was often included as part of sailors' pay.  it allowed sugar to be preserved on long voyages.  Sugar was also important because its growth was part of the Triangle Trade which provided trade goods from Europe and slaves from Africa.  Per your other choices, gold and silver would be important to the Spanish, but only from North and South America.  The Spanish hoped to find gold in the Caribbean, but it was not there.  Cotton would be too labor intensive and would overly tax the Caribbean soil.  

Please submit an analysis of "The End of the Party" by Graham Greene.

Graham Greene's "The End of the Party" is a psychological horror story. It has many elements of the Gothic: the genre of literature that explores the darker, hidden, and frightening sides of life and the human psyche. Typical of the Gothic, it features a pair of twins, with Peter as the "whole" twin and Francis representing and mirroring the fears in himself that Peter would like to repress and ignore. The story also has elements of the Gothic in the setting, which prominently includes night, darkness, and the imagery of bats. Death hovers over the story like a bat; the story opens with Francis dreaming of dying and ends with his actual death. The corpse is a key feature of the Gothic and also a key example of a doppelgänger—the twin to the human—for the corpse is both human and completely nonhuman, that which is part of ourselves (as we all will die) and that which we fear.
Although Francis and Peter are two distinct individuals and each has his own thoughts—the point of view switches back and forth from Peter to Francis throughout the story—they are also, symbolically, a representation of the other. For example, Francis thinks:

To address Peter was to speak to his own image in a mirror, an image a little altered by a flaw in the glass, so as to throw back less a likeness of what he was than of what he wished to be, what he would be without his unreasoning fear of darkness, footsteps of strangers, the flight of bats in dusk-filled gardens.

However, Peter understands Francis well enough that he also has, if far more repressed, his own fears of the same things. Peter thinks of Francis as "a mirror":

He was, if not Francis himself, at least a mirror to him.

As the day progresses and the time for the party grows nearer, the imagery is filled with foreboding:

Darkness came down like the wings of a bat.

The wind is "cold" as they approach the house where the party will be held, and the nurse's "electric torch," what we would call a flashlight, cuts only a "short trail" through the darkness. At the party, the suppressed cruelty inherent in the games becomes apparent as Francis and Peter try to get Francis out of playing hide and go seek in the darkness:

Six children began to sing, "Cowardy cowardy custard," turning torturing faces with the vacancy of wide sunflowers towards Francis Morton.

The reality of social violence—the establishing of who is "strong" and who is "weak" through a game the children are forced to play—is perhaps more frightening than Francis's fears.
It is significant that when Francis dies, Peter wonders why:

The pulse of his brother's fear went on and on, when Francis was now where he had always been told there was no more terror and no more—darkness.

Is the fear an aspect of Peter as well as Francis? Has Peter externalized and projected the parts of himself that he did not want to face onto his twin, his doppelgänger? The story strongly suggests that Francis is a part of Peter and that, with Francis's death, Peter will have to face himself in a way he has not before.

What seems to have been original purpose of the lottery, and what do people believe about it in Shirley Jackson's "The Lottery"?

The exact purpose of the lottery is nebulous, but apparently it was started as some sort of superstition-based ceremony to ensure crops would grow and produce a sizable yield. Now, it has simply become a ritual the townspeople blindly follow, and those who have an innate proclivity for violence take delight. 
There is truly a sense of blind adherence to tradition in the members of the community. They gather together and "their jokes were quiet and they smiled rather than laughed." When a late Mrs. Hutchinson makes her way through the crowd toward her husband, "[T]he people separated good-humoredly to let her through." Mrs. Hutchinson excuses herself by saying to the man in charge of the lottery, "Wouldn't have me leave m'dishes in the sink, now, would you, Joe?"
When it is time to start the lottery, Mr. Summers says soberly, "guess we better get started, get this over with, so's we can go back to work." As Mr. Summers calls names out, Mr. Adams remarks to Old Man Warner, "They do say. . . that over in the north village they're talking of giving up the lottery." Mr. Warner snorts in disgust and says,

Pack of crazy fools. . . Listening to the young folks, nothing's good enough for them. Next thing you know, they'll be wanting to go back to living in caves, nobody work any more, live that way for a while. Used to be a saying, 'Lottery in June, corn be heavy soon.' First thing you know, we'd all be eating stewed chickweed and acorns. There's always been a lottery.

Then, there are those who simply delight in the violence of the lottery. Before Mr. Summers arrives, Bobby Martin, Dixie Delacroix, and the Jones boys stockpile stones so they have enough ammunition to throw when it is time. Even Mrs. Delacroix, who has spoken in a friendly manner to the victim, Tessie Hutchinson, tells her to "be a good sport" after she is selected. Shortly after saying this, Mrs. Delacroix "selected a stone so large she had to pick it up with both hands." She tells Mrs. Dunbar, "Come on. . . Hurry up!"

people belive what they belive
 

Single Variable Calculus, Chapter 3, Review Exercises, Section Review Exercises, Problem 70

Find $h'$ in terms of $f'$ and $g'$ in the equation $\displaystyle h(x) = \sqrt{\frac{f(x)}{g(x)}}$.

Taking the derivative of $h(x)$ using Chain Rule as well as Quotient Rule



$
\begin{equation}
\begin{aligned}


h'(x) =& \frac{1}{2} \left[ \frac{f9x)}{g(x)} \right] ^{\frac{-1}{2}} \cdot \left( \frac{g(x) f'(x) - f(x) g'(x)}{[g(x)]^2} \right]
\\
\\
h'(x) =& \frac{g(x) f'(x) - f(x) g'(x)}{\displaystyle 2 \sqrt{\frac{f(x)}{g(x)}} [g(x)]^2 }
\\
\\
h' =& \frac{gf' - fg'}{2 \sqrt{fg^3}}

\end{aligned}
\end{equation}
$

Calculus of a Single Variable, Chapter 7, 7.2, Section 7.2, Problem 1

For the region bounded by y=-x+1 revolve about the x-axis, we can also apply the Shell Method using a horizontal rectangular strip parallel to the axis of revolution (x-axis).We may follow the formula for Shell Method as:
V = int_a^b 2pi * radius*height*thickness
where:
radius (r)= distance of the rectangular strip to the axis of revolution
height (h) = length of the rectangular strip
thickness = width of the rectangular strip as dx or dy .
As shown on the attached file, the rectangular strip has:
r=y
h =f(y) or h = x_2-x_1
h = (1-y) -0 = 1-y
Note: y =-x+1 can be rearrange into x=1-y .
Thickness = dy
Boundary values of y: a=0 to b =1 .
Plug-in the values on to the formula V = int_a^b 2pi * radius*height*thickness, we get:
V = int_0^1 2pi* y*(1-y)*dy
Apply basic integration property: intc*f(x) dx = c int f(x) dx .
V = 2pi int_0^1 y*(1-y)*dy
Simplify: V = 2pi int_0^1 (y-y^2)dy

Apply basic integration property:int (u-v)dy = int (u)dy-int (v)dy to be able to integrate them separately using Power rule for integration: int y^n dy = y^(n+1)/(n+1) .
V = 2pi *[ int_0^1 (y) dy -int_0^1 (y^2)dy]
V = 2pi *[y^2/2 -y^3/3]|_0^1
Apply definite integration formula: int_a^b f(y) dy= F(b)-F(a) .
V = 2pi *[(1)^2/2 -(1)^3/3] -2pi *[(0)^2/2 -(0)^3/3]
V = 2pi *[1/2 -1/3] -2pi *[0-0]
V = 2pi *[1/6] -2pi *[0]
V = (2pi )/6 -0
V = (2pi )/6 or pi/3
We will get the same result whether we use Disk Method or Shell Method for the given bounded region revolve about the x-axis on this problem.

What is discovered in Miss Emily's house after her death? Does the non-chronological reordering of the events shape your attitude towards Emily in any way? Why do you think Faulkner chose "we" rather than "I" as the voice for the story? How might this narrative strategy be related to the description of Emily as "a tradition, a duty, and care; a sort of hereditary obligation upon the town"?

1. After Miss Emily's death, the decayed body of Homer Barron is found lying in her bed. Next to his pillow is another one, with an indentation as though someone has lain their head on it, and containing strands of Miss Emily's very identifiable hair.
2. The reordering of events prevents us from immediately connecting the dots, from understanding—definitively—that Emily was afraid of being abandoned (again), especially after Homer Barron loudly proclaimed that he wasn't the marrying type, that Emily purchased the rat poison to kill him and keep him with her, that the smell coming from her home was actually his actively decaying body. This reordering, then, allows us to develop some sympathy for Miss Emily as well as heightening our tension and the intrigue created by the story. If we can jump to the conclusion that she killed him right away, there is little mystery. We are kept in the dark as much as the people in the town were, and this is, frankly, much more interesting for the reader.
3. Faulkner's use of the first-person plural underscores the entire town's relationship with Miss Emily. She is symbolic of so much—the etiquette and social mores and traditions of the post-Civil War South—and the town thinks of her in this way. She is less like a person to them, and more like a symbol, and because they uniformly conceive of her in this way, it makes sense that they would be referred to in the plural.

The conflict between the Catholic Church and the French state dominated eighteenth and nineteenth-century French history and produced virulent anticlerical sentiment among many in France, contributing to the revolutions of 1789, 1830, and 1848 and the Commune of 1871. What were sources of French anticlericalism, and how did it come to shape political events and initiatives in the nineteenth century?

Anticlericalism grew into a powerful force in France in the years preceding the French Revolution. Traditionally, the divine right of kings meant that monarchs were set in place by the power of God, as expressed by the Church; this idea was endorsed particularly powerfully by the French monarchy because of its descent from the Holy Roman emperors, of which Charlemagne was the most famous. As such, one key source of anticlerical feeling was the fact that the clergy was so fundamentally connected to the monarchy. In "endorsing" it, the clergy was seen as contributing to the hierarchical system it imposed upon the French people.
Additionally, the eighteenth century in France, as was the case elsewhere in Europe, was marked by a growing sense that the clergy and others who believed literally in the Bible were limiting the progress of science. The Enlightenment, which characterized liberal European philosophy in the eighteenth century, led many thinkers to oppose the church's anti-scientific stance. Anticlericalism was associated with intellectualism and the pursuit of greater scientific understanding.
Anticlericalism in France exhibited itself in ways that were not dissimilar to those observed in other European nations that had opposed the Catholic church. Its confiscation of Roman Catholic property during the Revolution was similar to what had occurred in England several centuries before, although these objections had begun under Henry VIII for entirely different political reasons. But the beliefs of Martin Luther and others were echoed in the revolutionaries' claims that the church's greed was a leech on the nation and that its property needed to be redistributed among the people. For the majority of the nineteenth century, the church in France was able to survive on the understanding that it no longer controlled the French state: it obeyed with its privileges greatly diminished and its power limited. This went some way toward satisfying the anticlerical concerns about the church's abuse of power over the people.
When the Third Republic was created in 1871 after the Franco-Prussian War, tensions rose again, and it became clear that this subservient state of the church could no longer be sustained. On the contrary, anticlerical sentiment rose to greater heights, resulting in the suppression of the religious freedoms of groups such as the Jesuits and defining customs such as marriage as wholly secular. This was a powerful statement, as it recategorized marriage as something permitted and offered by the state, rather than having any connection to God; the privileges of marriage became entirely secular privileges. Marriages in church alone were no longer legal, which stripped a great deal of the church's remaining power away. Church and state were formally split in France in 1905.
This only marked the culmination of a force which had been set loose with the French Revolution. As soon as the idea of divine control had been stripped away, the door was opened for the interrogation of what powers the church could claim over the people and where each man's moral guidance could come from. However, the initial provisions made by Napoleon in the Concordat of 1801 would never be sufficient to satisfy the desires of Enlightenment thinkers for revolution: while it did diminish the power of the church, it did not limit its control over education, and it maintained Catholicism's status as the primary religion in France. As such, anticlerical feeling and frustration continued to ferment. Both anticlerical Christians, who opposed the church's continuing privileges, and a growing faction of atheists, fueled by the development of socialism in Europe, continued to protest against the church and campaign for further reduction of its powers. Only with the separation of church and state in 1905 was the force of anticlericalism diminished in French politics, having finally achieved what the Revolution had led it to hope for a century earlier.
https://onlyjoking.hypotheses.org/65

https://www.britannica.com/topic/anticlericalism

Precalculus, Chapter 7, 7.4, Section 7.4, Problem 50

(2x^4+8x^3+7x^2-7x-12)/(x^3+4x^2+4x)
Since the above expression is an improper rational expression , the first step is to divide and express it as a sum of simpler fractions such that the degree of polynomial in the numerator is less than the degree of polynomial in the denominator.
Dividing the above expression using long division method yields,
(2x^4+8x^3+7x^2-7x-12)/(x^3+4x^2+4x)=2x+(-x^2-7x-12)/(x^3+4x^2+4x)
Since the polynomials do not completely divide , we have to continue with the partial fractions of the remainder expression.
Now let's factorize the denominator of the remainder expression,
x^3+4x^2+4x=x(x^2+4x+4)
=x(x+2)^2
Let, (-x^2-7x-12)/(x^3+4x^2+4x)=A/x+B/(x+2)+C/(x+2)^2
=(A(x+2)^2+B(x)(x+2)+Cx)/(x(x+2)^2)
=(A(x^2+4x+4)+B(x^2+2x)+Cx)/(x(x+2)^2)
=(x^2(A+B)+x(4A+2B+C)+4A)/(x(x+2)^2)
:.(-x^2-7x-12)=x^2(A+B)+x(4A+2B+C)+4A
equating the coefficients of the like terms,
A+B=-1 ------- equation 1
4A+2B+C=-7 ------- equation 2
4A=-12
A=-12/4
A=-3
Plug the value of A in equation 1,
-3+B=-1
B=-1+3
B=2
Plug the value of A and B in equation 2 ,
4(-3)+2(2)+C=-7
-12+4+C=-7
C=-7+12-4
C=1
(-x^2-7x-12)/(x^3+4x^2+4x)=(-3)/x+2/(x+2)+1/(x+2)^2
:.(2x^4+8x^3+7x^2-7x-12)/(x^3+4x^2+4x)=2x-3/x+2/(x+2)+1/(x+2)^2

Who was Robert Frost?

Robert Frost was an American poet born in San Francisco, California at the end of the 19th century. He wrote a number of his most famous poems, including "Stopping by Woods on a Snowy Evening," "The Road Not Taken," and "After Apple Picking" fairly early on in his career. Frost is often referred to as an American nature poet; however, the general appeal of his poetry is not found merely in its nature imagery, but in its metaphorical musing on the nature of life, death, work and happiness, and these themes are illuminated by the detailed images he creates.
Frost came from a fairly wealthy family, but he was expected to make his own way and work for a living. He attended Harvard briefly and also tried to earn a living as a farmer. However, his early years did not see him established in a steady vocation. Frost lived in a number of places, including England, and around the New England states. His travels exposed him to many people and sights that inspired his work. His poetry seemed to flourish best when he settled in Vermont, but prior to that Frost was obliged to take on occasional teaching jobs to support his family. Eventually he was able to make his living as a poet.
Frost won the Pulitzer Prize for poetry four times; this is one of the highest accolades available to poets. Also, Frost's work has been anthologized more often than perhaps any other American poet's. Having one's poetry included in an anthology usually indicates that the poet's work is considered important enough to be part of the literary canon.
Frost's work is well loved for its universal appeal and simple language that reveals deep truths about the human condition; he could be called the most famous American poet.

Single Variable Calculus, Chapter 2, 2.1, Section 2.1, Problem 4

Given the curve $y= \sqrt{x-2}$ and the point $J(3, 1)$ that lies on the curve.


a. Use your calculator to find the slope of the secant line $JK$ (correct to six decimal places) for the following values of $x$ if $K$ is the point $(x,\sqrt{x-2})$.


$
\begin{equation}
\begin{aligned}

&\text{ (i) } 2.5 && \text{ (v) } 3.5 \\
&\text{ (ii) } 2.9 && \text{(vi) } 3.5 \\
&\text{ (iii) }2.99 && \text{(vii) } 3.01\\
&\text{ (iv) } 2.999 && \text{(viii) } 3.001
\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}

\begin{array}{|c|c|c|c|c|c|}
\hline\\
& K_x(x) & K_y(\sqrt{x - 2}) & J_x & J_y & \text{Slope of secant line} JK = \left(\frac{J_y - K_y}{J_x - K_x}\right) \\
\hline\\
(i) & 2.5 & \frac{\sqrt{2}}{2} & 3 & 1 & 0.585786 \\
\hline\\
(ii) & 2.9 & \frac{3 \sqrt{10}}{10} & 3 & 1 & 0.513167 \\
\hline\\
(iii) & 2.99 & \frac{3\sqrt{11}}{10} & 3 & 1 & 0.501256 \\
\hline\\
(iv) & 2.999 & 0.99 & 3 & 1 & 0.500125 \\
\hline\\
(v) & 3.5 & \frac{\sqrt{6}}{2} & 3 & 1 & 0.449489 \\
\hline\\
(vi) & 3.1 & \frac{\sqrt{110}}{10} & 3 & 1 & 0.488088 \\
\hline\\
(vii) & 3.01 & \frac{\sqrt{101}}{10} & 3 & 1 & 0.498756 \\
\hline\\
(viii) & 3.001 & 1.0005 & 3 & 1 & 0.499875\\
\hline
\end{array}

\end{aligned}
\end{equation}
$


For example,
@ x = 2.5,

$
\begin{equation}
\begin{aligned}
J_y \sqrt{x-2} & = \sqrt{2.5-2}\\
& = \frac{\sqrt{2}}{2}
\end{aligned}
\end{equation}
$

@ x = 2.9,

$
\begin{equation}
\begin{aligned}
J_y \sqrt{x-2} & = \sqrt{2.9-2}\\
& = \frac{3\sqrt{10}}{10}
\end{aligned}
\end{equation}
$



b. Guess the value of the slope of the tangent line to the curve at $J(3,1)$ using the results in part (a).

Based from the values we obtain from the table, the slope of the tangent line seems to have a value of $\displaystyle \frac{1}{2}$

c. Find an equation of the tangent line to the curve at $J(3,1)$ using the slope in part (b).

Using point slope form:


$
\begin{equation}
\begin{aligned}

y - y_1 =& m(x - x_1)\\
y - 1 =& \frac{1}{2} (x-3)\\
2(y- 1) =& x - 3\\
2y - 2 =& x -3\\
2y =& x - 3 + 2\\
y =& \frac{x - 1}{2}


\end{aligned}
\end{equation}
$


d. Sketch the curve, two of the secant lines, and the tangent line.

What happened to the milk that disappeared and to the apples from the orchard?

The milk and apples go the pigs. The pigs commandeer all the milk for themselves, even though the hens mentioned that Farmer Jones used to mix some of the milk in their mash. Of course, the animals don't know for certain at first that the milk has gone to the pigs. The scene unfolds as follows:

"What is going to happen to all that milk?" said someone.
. . .
"Never mind the milk, comrades!" cried Napoleon, placing himself in front of the buckets. "That will be attended to. The harvest is more important. Comrade Snowball will lead the way. I shall follow in a few minutes. Forward, comrades! The hay is waiting."
So the animals trooped down to the hayfield to begin the harvest, and when they came back in the evening it was noticed that the milk had disappeared.

The pigs are unanimous in saying they need all the windfall apples for themselves. They explain to the other animals that they need the apples for their brainwork. They say they are eating the apples for the sake of the other animals, though its hard to imagine that that is the real reason. Note, too, how in the quote below, the pigs admit to drinking the milk:

The whole management and organisation of this farm depend on us. Day and night we are watching over your welfare. It is for YOUR sake that we drink that milk and eat those apples.

This shows how, from early on, the pigs are setting themselves apart from the other animals and treating themselves as a privileged class. The other animals at first expect the milk and apples to be divided up evenly, according to the principles of animalism, and are too quick to believe the lame explanations the pigs come up with for taking the extra food.

Is the relationship between Brutus and Cassius genuine?

The relationship between Brutus and Cassius is primarily a political, rather than a personal one. Although they are friends and related by marriage their alliance is based upon their status as political actors within the Roman state. They come to share a common vision—a Rome without Caesar—but they differ in their motivations. Cassius resents Caesar for depriving him of the role in public life to which he believes himself entitled on account of his noble blood. Brutus, however, is more idealistic, seeing Caesar's dictatorship as a fundamental threat to the republican system he so much venerates and cherishes.
Whatever ties exist between the two men in terms of blood, class, and political ideology, there's no doubt that this is never really a relationship of equals. Initially, it's Cassius who's top dog. He cynically manipulates Brutus to get him to join the conspiracy against Caesar. He also plays on Brutus's famed nobility and his honorable intentions to persuade him to get involved.
After the assassination Brutus becomes the dominant partner in the relationship. Cassius stroked his vanity to get him on board for Caesar's murder, but Brutus's ego has given him an exalted sense of his own destiny. He disregards Cassius's sage advice at Philippi, with disastrous consequences. And though they are subsequently reconciled, their relationship only becomes one of equals when they both choose to die in the same way.

Analyze the methods used by Fitzgerald to introduce his main characters in chapter one of The Great Gatsby.

Fitzgerald is careful to set the tone from the start in introducing the main characters. Nick is presented as a listener, an observer, a steady, modest Midwesterner who has been taught not to flaunt his privileges. The initial implication is that we can rely on him as a storyteller and narrator of events.
Nick, however, presents each character through the lens of his own prejudice. He is careful from the start to speak of Gatsby as larger than life, as a "gorgeous" dreamer who transcends the "foul dust" of the people around him. From the outset, Gatsby is cast in a mythic glow. Fitzgerald's technique is to have Gatsby hover as a disembodied presence in chapter one, more concept than person. He is not introduced in the flesh until later in the novel. In chapter one, he is a mystery, mentioned but not concretized.
In contrast, Nick paints Tom Buchanan in a solid and slightly contemptuous way from the start. Tom might be vastly wealthy, owning a string of polo ponies, but his glory days were as a college football player and are already behind him. He is depicted as a man of limited intellect who spreads misery: in chapter one, we learn he is having an affair. Nick shows him to us immediately in all his physicality, from his pose with legs apart, overlooking his domain as its master, to his racist dialogue about "Nordics."
Nick also introduces us to Daisy and Jordan in the flesh, characterizing from the beginning Jordan's cool pose of detachment in the lift of her chin, and Daisy's charm. Yet the women also have an ethereal, otherworldly quality, seemingly blown about the room in their white dresses as if they are on a journey, with the billowing of the white curtains like the billowing of sails and the wine carpet like the "wine-dark sea" in The Odyssey. Similarly to Gatsby, though shown in the flesh, they are both a little mysterious. Daisy, especially, troubles Nick. He returns from his evening feeling she has put on an act and "played" him somehow.
With these four characters, our perceptions will build from our first impressions. We are primed from the start to like Gatsby, dislike Tom, and find the women enigmatic.

What would be a good thesis statement for this book?

There are two ways that I recommend going with a thesis for this book. I would either have a thesis that focuses on a character analysis of Helga, or I would have a thesis that does an examination of one or two of the major themes present in the book. Make sure that the thesis statement is making some kind of argument that the paper is required to prove to readers. The following might work well: Although Helga is motivated to find her place in the world, her spirit is eventually beat down by the quicksand of the racism and sexism that exists in the world around her.
This thesis is specific in its intent; however, it is broad enough to give your paper the freedom to analyze two themes, as well as provide a character analysis of Helga. If those themes don't resonate well with you, then use the same thesis template and swap in whatever theme(s) you feel strongly about.

How are haiku's and limericks different?

Haikus and limericks are both poems. However, they differ in terms of length, rhyme scheme, and the presence of humor.A limerick poem consists of five lines. It follows the rhyme scheme of AABBA. This means that the first, second, and fifth lines rhyme, and the third and fourth lines rhyme. A limerick is usually comical. Some of the most famous limericks are nursery rhymes.

Ding, Dong, Bell is one example of a limerick nursery rhyme:
 
Ding, dong, bell; Kitty’s in the well.Who put her in?  Little Tommy Green.Who pulled her out?  Little Tommy Trout.What a naughty boy was that,To drown poor Pussy Cat.
 
A haiku, on the other hand, consists of five lines. While it does not rhyme, its lines do follow a specific syllable pattern. The first line always has five syllables, the second line has seven syllables, and the third line has five syllables. Haikus tend to be more serious than limericks. They are often about nature, and they are known for being direct and to the point.
 

The following haiku is written by a famous poet named Basho Matsuo:
 
An old silent pond...A frog jumps into the pond,splash! Silence again.
http://www.literarydevices.com/limerick/

https://poets.org/poems?field_form_tid=414

In I Know Why the Caged Bird Sings, what insight into the future does Maya Angelou seem to gain after recounting the past?

After recounting the past, Maya Angelou realizes she has the ability to thrive despite the insidious influence of racism and the dysfunction of her childhood.
Maya comes to see her past experiences strengthened her resolve to live victoriously and confidently. In the introduction to the book, we are told Maya wrote her story because of her grief at Martin Luther King, Jr.'s death. In recounting her past, Maya is able to make peace with the imperfections in her life and accept that her place in the future need not be defined by the mistakes or the trials of the past. Essentially, she can be as successful as she chooses to be; in this, she remembers her mother's advice:

On my way out of the house one morning she said, “Life is going to give you what you put in it. Put your whole heart in everything you do, and pray, then you can wait.” Another time, she reminded me that “God helps those who help themselves.”

In recounting her past, she realizes those who love her will always support and encourage her in her time of need, and she draws strength from this knowledge. In the book, she recalls how she was raped by Mr. Freeman, her mother's live-in boyfriend.
She was only eight at the time, and the experience was painful, humiliating, and dehumanizing. She recalls that Bailey managed to wrest from her the identity of her rapist. Maya relates how her brother wept at the side of her hospital bed when he discovered who raped his sister. She maintains it was fully fifteen years before Bailey cried like that again. During her recovery, her uncles guarded her, and Bailey read to her for hours.
Maya eventually manages to overcome her trauma, and she goes on to become the first black streetcar conductor in San Francisco at the age of fifteen. The book ends with Maya learning she has what it takes to be a good mother.

Mother whispered, “See, you don’t have to think about doing the right thing. If you’re for the right thing, then you do it without thinking."

So, in recounting her past, Maya realizes strength is gained from adversity, and each acquired victory is a testament to the power of the human spirit. This knowledge allows her to look forward to the future with confidence and courage.

How do elements in "The Most Dangerous Game" make it a commercial fiction story?

Originally published in Collier's in 1924, Richard Connell's short story "The Most Dangerous Game" achieved both commercial and literary success. It spawned a number of radio and motion picture adaptations as well as being widely anthologized in high school and college literature textbooks. Although now it is certainly considered a great literary achievement, it also has several elements that originally made it highly commercial. Popular author and writing instructor William Bernhardt has qualified those factors which make a story a commercial success.
First, it must have "readability," and "The Most Dangerous Game" is certainly a page turner. Connell grips his reader from the opening reference to the mysterious "Ship-Trap Island" through the nerve wracking hunt between Zaroff and Rainsford. Second, there must be "strangeness" to the story. This element is revealed early on in when Rainsford happens upon the strange chateau in the middle of a deserted island. The appearance of the deaf and mute Ivan at the door of the chateau adds to this "strangeness." Third, the story should provide controversy. In Connell's work the controversy surrounds the ethicality of big game hunting. The character Whitney introduces the controversy early in the story by suggesting that animals experience fear and pain.
Fourth is what Bernhardt calls "big actions with big consequences." By calling Zaroff a cold blooded killer and refusing to hunt with him, Rainsford's actions lay the ground work for the coming hunt and suspenseful action which dominates the second half of the story. Fifth, the story must have, what Bernhardt labels a "nuanced uniqueness." By this, he means the story must be well within a particular genre of stories, yet it should be slightly different. "The Most Dangerous Game" qualifies because, while it is an adventure story set in an exotic locale like so many other adventure stories, the element of man hunting man makes it different from other stories in the same category.
Sixth, the story must have "extreme situations." What could be more extreme than a man hiding in a jungle attempting to save himself from a maniacal sociopath? Rainsford himself creates these extreme situations when he lays various traps for Zaroff such as the "Malay man-catcher" and the "Burmese tiger pit." Finally, the author must give the reader a reason to care about the story. While this is certainly a subjective category it seems likely that most readers are reasonably interested in the well being of Rainsford, especially after his harrowing swim after falling from the yacht. Because of the black and white nature of the hunt, the reader is most certainly rooting for Rainsford to escape the diabolical General Zaroff.
 
https://www.writersdigest.com/editor-blogs/there-are-no-rules/the-7-essential-elements-of-a-bestselling-novel

Compare and contrast life in the court with life in the country in As You Like It. What are one's "enemies" in each locale? What can be accomplished in one setting that cannot be accomplished in the other?

The contrast between court and country in As You Like It is a stark one. The country, in the shape of the Forest of Arden, is a place of banishment for good people. They are typically victims of enemies at court who have conspired to have them expelled to this political wasteland. Yet, exile can also be a blessing in disguise and a means of escape from the artificialities of court life. As Duke Senior explains,

Now, my co-mates and brothers in exile,
Hath not old custom made this life more sweet
Than that of painted pomp? Are not these woods
More free from peril than the envious court? (act 2, scene 1).

The exiles may have been deprived of the pomp and circumstance of court life, but their new life is a more natural existence—more in keeping with humankind's existence before the Fall. The icy wind may blow and cause us to shiver, but at least there is a certain honesty about it. You know where you stand with the elements, which is more than can be said for the two-faced lackey at court who flatters you to your face but spreads false rumors about you behind your back. Honest enemies are so much better than dishonest ones.
The honesty of the elements is reflected in the earthy, no-nonsense love between Touchstone and Audrey. Their relationship is entirely free of the trappings of courtly love encapsulated by Orlando's lushly romantic wooing of Rosalind. Touchstone's understanding of love may be a tad crude and bawdy, but, like the icy wind that often howls through the forest, at least there is a certain rugged honesty about it.
The forest exerts an almost magical effect on the characters of As You Like It, acting as a kind of purgative, cleansing the souls of those who enter it. Duke Senior, as we have already seen, seems almost relieved of the burdens of his worldly existence. Distinctions of class and gender often dissolve amidst the natural environment of the forest's lush green shade. A number of characters in the play look to the forest as a haven from the social rigidities of the court and as an opportunity to shed the artificial identities placed upon them by a hierarchical society. They adopt alternative personas, transgressing boundaries of gender and class in a way that would be unthinkable in the outside world.
Celia, for example, casts off her nobility to disguise herself as a poor woman. This gives her a freedom she has never previously enjoyed. In her new identity, she no longer has to worry about being robbed. She can also finally be loved and accepted for who she really is. It is instructive that Celia can only find true love with Oliver in the woodland environment and not at court. By falling in love with a woman he believes to be poor and humble, Oliver is radically transformed. In the world outside, it is fair to say that Oliver was hardly the most selfless or giving of characters.

What are two adjectives that describe Mercutio?

Mercutio is one of the main characters in William Shakespeare's tragedy Romeo and Juliet. Critics have often considered Mercutio one of the playwright's finest characters. He is the best friend of Romeo and so is allied with the Montague family. Mercutio's name may have been derived from the Roman messenger god Mercury. Someone who is considered mercurial has the attributes of unpredictability, and that certainly suits Mercutio. From the first time he enters, in act 1, scene 4, he is a whirling dervish, so to speak, trading barbs with Romeo about his friend's unrequited love for Rosaline and then launching into the long speech about Queen Mab which he seems to weave out of thin air. The beginning of the Mab speech is lighthearted: "She is the fairies’ midwife, and she comes / In shape no bigger than an agate stone . . . Sometime she gallops o’er a courtier’s nose . . . Tickling a parson’s nose as he lies asleep." But it descends into a dark tirade:

This is the hag, when maids lie on their backs,That presses them and learns them first to bear,Making them women of good carriage.This is she


The speech exemplifies Mercutio's unpredictable nature as he personifies a range of emotions from a gregarious affinity for his friends to a dark side riddled with rage and violence. He again demonstrates this unpredictability during act 3, scene 1 when he berates Benvolio, accusing the harmless Benvolio of always being ready to fight:


Thou—why, thou wilt quarrel with a man thathath a hair more or a hair less in his beard thanthou hast. Thou wilt quarrel with a man for crackingnuts, having no other reason but because thouhast hazel eyes.



This biting, yet benign, cynicism stays under control until Romeo refuses to fight Tybalt. Mercutio changes his attitude quickly, erupting into violence which will ultimately lead to his death.

Another adjective for Mercutio is provided by his friend Benvolio, who labels Mercutio "brave" when it's discovered that Mercutio's wound has been fatal:


O Romeo, Romeo, brave Mercutio is dead.That gallant spirit hath aspired the clouds,Which too untimely here did scorn the earth.




Mercutio is indeed brave for standing up for his friend when Tybalt calls Romeo a "villain." He is both tragic and heroic in his bravery as he feels he cannot let the hated Tybalt get away with slandering Romeo. He further shows his bravery (and unpredictability) during his dying scene when he seems to poke fun at his own wound:


No, ’tis not so deep as a well, nor so wide asa church door, but ’tis enough. ’Twill serve. Ask forme tomorrow, and you shall find me a grave man.




It's often been suggested by critics that it seems Shakespeare kills off Mercutio too early in the play, noting that he may have done so because Mercutio is such an arresting figure who was stealing the show away from the title characters.

How does Fortunato become locked in the chains so easily?

Edgar Allan Poe, the creator of the story, has made it easy for Montresor to chain Fortunato to the granite wall and easy to build a stone wall to conceal him. Here is how Montresor describes the crypt and the chains.

Within the wall thus exposed by the displacing of the bones, we perceived a still interior crypt or recess, in depth about four feet, in width three, in height six or seven...A moment more and I had fettered him to the granite. In its surface were two iron staples, distant from each other about two feet, horizontally. From one of these depended a short chain, from the other a padlock. 

Fortunato is in a "crypt or recess" only four feet deep and three feet wide. Its height is only about the same height as a man. Montresor only has to build a small wall of stones in order to conceal his victim. This enables Poe to finish the story quickly. It also explains how Montresor is able to build a stone wall when he cannot have had much experience. The stone wall only has to be three feet wide and six or seven feet high.
The chains must have been there for more than a century. The iron staples holding the chains to the rock wall behind Fortunato are only about two feet apart, and one chain is described as short. The padlock may be attached to a much shorter chain. It is an old-fashioned padlock that has to be locked with a key and not snapped shut like our modern padlocks. Fortunato would be pinned against the rock wall behind him. It should only take a matter of seconds to wrap the short chain around his waist and lock the padlock at the tightest link so that the victim would have hardly any freedom of movement.
Poe has specified that the crypt or recess is about four feet deep. This depth is necessary to prevent Fortunato from reaching out and pushing against the stone wall, either while Montresor is building it or after Montresor leaves and the mortar is still wet. Fortunato's arms would only be three feet long at most. He might try to touch the masonry but find it frustratingly just out of reach.
Poe has made Montresor's work as easy as possible. Since Fortunato is drunk, it is understandable that Montresor could wrap one short chain around his waist with one hand and insert the padlock with the other before his victim realized what was happening.
The reader understands that Montresor wants to kill Fortunato but does not understand how Montresor intends to do it until he has chained his victim to the rock wall and has shut the padlock. At this point Poe achieves the "single effect" he intended. After this effect of horror is achieved, Poe would want to finish his story as quickly as possible. No doubt this explains why the crypt or recess is so small--only about three feet wide and six or seven feet high. Montresor can finish the wall-building quickly and describe the whole process in only a few sentences. 

I hastened to make an end of my labour. I forced the last stone into its position; I plastered it up. Against the new masonry I re-erected the old rampart of bones. For the half of a century no mortal has disturbed them. In pace requiescat!

One of the biggest reason has to do with the fact that Fortunato is very, very drunk. The narrator makes sure to have him drink as much wine as possible as they progress along the passageways. Of course Fortunato had been drinking all day given that it was during the "supreme madness of the carnival season." The narrator has also directed the attention of Fortunato to the Amontillado, something so rare and wonderful that Fortunato can think of nothing else. He cannot possibly suspect that there is a chance of anything untoward happening as they progress into the vaults.
Because Fortunato is so focused on finding the wine, it even takes him a moment to become alarmed after he has been chained to the wall. As the narrator describes, he was "bewildered" to find himself at the end of the tunnel and it only took a moment to chain him to the granite wall.

Analyze: What does the Mayflower Compact explicitly say? What does it suggest through its careful diction, or word choice, and use of imagery?

The Mayflower Compact established the rules by which the Pilgrims would abide in their new colony. Written in 1620, it established allegiance to the king of England. The document also stated that the members of the colony would create a "civil body politic," or a self-government, by which they would make the laws and regulations that were best for the ruling of the colony. The signatories also promised allegiance to the colony and promised to serve its needs.
The document is carefully worded, and its diction is quite clever. The document commits the colonists to both the king and to the colony. The way in which the document is phrased makes no distinction between being loyal to God, to the king of England, or to the colony. Instead, the document suggests that it is possible for the colonists to be loyal to king, country, and colony, and the document is careful to avoid a distinction between loyalty to these different elements.
The imagery conveyed by the document is solemn, or serious. The document presents a picture of the colonists signing the compact "solemnly" and in the company of each other. The image is one of seriousness, mutual respect, and obedience. It's also one in which the colonists believe they are in the presence of God, and they take that commitment very seriously.

The Mayflower Compact acknowledges that the signatories will remain loyal to their sovereign, King James, and to their mission, establishing a religious colony for "the advancement of the Christian faith." They recognize King James as both their king and religious authority.
Furthermore, the men who signed the compact agree that they are forming a self-governing body to organize the colony and preserve the mission. They are empowering themselves to establish laws, acts, constitutions, ordinances and elect or appoint officers to act in the best interest of the colony. They pledge their "obedience" to carrying out these intentions and sign their names to the compact that they are all agreeing to.
The word "covenant" has both a religious connotation as well as the denotation that the men who have signed are all in agreement.

In the Mayflower Compact, the pilgrims start by expressing their unswerving loyalty to King James I:

In ye name of God Amen· We whose names are vnderwriten, the loyall subjects of our dread soueraigne Lord King James by ye grace of God, of great Britaine, franc, & Ireland king, defender of ye faith, &c."

The pilgrims had unintentionally arrived at Cape Cod, miles from their destination in Virginia due to storms and inclement weather. They now found themselves outside the boundaries of the Virginia Company patent which had been granted by the king. This led to a number of pilgrims on board The Mayflower insisting that they were no longer answerable to the terms of the original patent. The Compact was a response to the incipient rebellion, an attempt to impose some semblance of order upon an increasingly mutinous ship's company. That being the case, it was necessary for the pilgrims to begin their document with an open expression of loyalty to the king who had granted the Virginia Company their Royal Charter.

Haueing vndertaken, for ye glorie of God, and aduancemente of ye christian ^faith and honour of our king & countrie, a voyage to plant ye first colonie in ye Northerne parts of Virginia· doe by these presents solemnly & mutualy in ye presence of God, and one of another, couenant, & combine our selues togeather into a ciuill body politick; for ye our better ordering, & preseruation & fur=therance of ye ends aforesaid; and by vertue hearof, to enacte, constitute, and frame shuch just & equall lawes, ordinances, Acts, constitutions, & offices, from time to time, as shall be thought most meete & conuenient for ye generall good of ye colonie:  vnto which we promise all due submission and obedience.  In witnes wherof we haue herevnder subscribed our names at Cap=Codd ye ·11· of Nouember, in ye year of ye raigne of our soueraigne Lord king James of England, france, & Ireland ye eighteenth and of Scotland ye fiftie fourth. Ano: Dom ·1620·

In the remainder of the document, the pilgrims formalize their establishment of a government, a "civil body politick" to which they agree to subject themselves upon landing. The message is clear: the pilgrims may be outside the boundaries of the original legal agreement but they are not outside the law. They have established a temporary government, and it will be a government of laws. The king did not authorize the unleashing of anarchy upon the colonies, and he can be sure that the pilgrims will behave as decent, upstanding British subjects should. The pilgrims solemnly swear before God that they will establish a lawful government in full obedience to King James. Swearing to God gives the pilgrims' words an added force as no one could truly doubt their Christian faith. These words are chosen carefully to provide reassurance to the king that the pilgrims are genuine in their stated aim to set up a civil government on American soil under his sovereignty.
https://www.history.com/topics/colonial-america/mayflower-compact

Calculus of a Single Variable, Chapter 5, 5.1, Section 5.1, Problem 81

We are asked to locate any relative extrema or inflection points for the graph of y=xlnx :
The domain of the function is x>0.
Extrema can only occur at critical points; that is when the first derivative is zero or fails to exist.
y'=lnx+x*1/x ==> y'=lnx + 1
This function is continuous and differentiable for all x in the domain, so setting y'=0 we get:
lnx+1=0 ==> lnx=-1 ==> x=1/e~~0.368
For 01/e it is positive, so the only extrema is a minimum at x=1/e.
Inflection points can only occur when the second derivative is zero:
y''=1/x>0 forall x so there are no inflection points.
The graph: