How do you think the "feminism" in Trifles differs from the "feminism" in Machinal?

Both Susan Glaspell’s Trifles and Sophie Treadwell’s Machinal are dramas that explore gender roles and feminism in their stories of murder.
Glaspell’s Mrs. Wright murders her husband because he was an abusive partner. Knowing this, Mrs. Peters and Mrs. Hale conceal the damning evidence that would prove Mrs. Wright’s guilt. The two women do this right under the noses of their husbands, who believe their wives are incapable of such a conspiracy. Feminism in this story means women helping other women whom they feel deserve said help. The women in the play effectively save Mrs. Wright from a fate they don’t think is justified.
Conversely, Treadwell’s Helen never wants the marriage or child she has with George in the first place. George never mistreats her, but Helen despises him. When she conspires to murder George, Helen receives no sympathy from any other women, unlike Glaspell’s Mrs. Wright. In fact, Helen is doomed to the electric chair for her crimes. Feminism in this play indicates that a patriarchal society completely stifles a woman’s potential, forcing her into a life she doesn’t want. If a woman dares to escape this life, society will punish her gravely. Helen is a less sympathetic character because she doesn’t fit the victim role that society expects of women who wield violence in order to get what they want. Treadwell, I think, emphasizes that women are not delicate creatures who need to be protected.

How do Pip's great expectations come true?

Pip's "expectations" come true only in the most ironic of ways (and even then, only briefly). Pip becomes obsessed with becoming a gentleman after meeting the beautiful but cruel Estella while playing at the house of her wealthy guardian, Miss Havisham. When Mr. Jaggers, Miss Havisham's lawyer, visits Pip several years later and informs him that he is due to inherit a fortune, Pip assumes that Miss Havisham is his benefactor. This in turn leads him to a second conclusion: that Miss Havisham intends him to marry Estella. With this in mind, Pip leaves his blacksmithing apprenticeship and goes to London, where he receives a gentleman's education and lives on an allowance as he waits to come into full possession of his property.
Shortly after he turns twenty-three, however, Pip returns home to find Magwitch—the convict he helped escape years earlier—in his apartment. Magwitch explains that he has been Pip's mysterious benefactor for all these years; Miss Havisham had simply led Pip on as part of her greater scheme to avenge herself on men. Pip is horrified to learn that his future is not at all what he had expected it to be:

Miss Havisham’s intentions towards me, all a mere dream; Estella not designed for me; I only suffered in Satis House as a convenience, a sting for the greedy relations, a model with a mechanical heart to practice on when no other practice was at hand; those were the first smarts I had (chapter 39).

He further feels that he cannot accept Magwitch's fortune, knowing that it came from a convict, but this in and of itself poses a problem because he is by this point deeply in debt. Ultimately, Pip does warm to Magwitch and helps him in his (unsuccessful) escape attempt. In the end, however, he has little to show for his career as a gentleman beyond self-knowledge: Estella marries Bentley Drummle, and Pip is saved from debtor's prison only thanks to Joe's kindness. Dickens even subverts another common literary trope when Biddy, Pip's faithful childhood friend, declines his marriage proposal in favor of Joe. With nothing left for him in England, Pip joins Herbert in Egypt and begins working as a clerk, ultimately achieving modest success in this position. As for Estella, the novel is ambiguous; Dickens wrote two endings, one of which holds out the hope that Pip and Estella may ultimately end up together, in partial fulfillment of Pip's early "expectations." The original ending, however, makes it clear that the two go their separate ways.

Were power struggles and segregation a problem amongst black South Africans during the postapartheid period?

There were indeed divisions and power struggles among black South Africans during the apartheid era. The main struggle was between the African National Congress, the principal political and military movement struggling against the system of forced segregation imposed on the country’s blacks by the minority white government, and the nationalist movement of the Zulu tribe called the Inkatha Freedom Party led by Chief Gatsha (Mangosuthu) Buthelezi. Buthelezi had been aligned with the ANC but eventually broke from it due to the tactics required to remove apartheid and calculations of what was in the best interest of the Zulu Nation, the largest tribe in South Africa. Buthelezi enjoyed a great deal of legitimacy among the Zulu, and his opposition during the 1980s to the Western-backed anti-apartheid economic sanctions and boycott movement was a major source of irritation between him and the leadership of the ANC.
Buthelezi believed that the level of economic development that the KwaZulu territories enjoyed was a symbol of the advancements blacks could make even under apartheid and that sanctions against South Africa by Europe and North America would prove damaging to all South Africans, not just the small minority of whites in power. His positions on the anti-apartheid movement and his decision to champion the causes of the KwaZulu Nation above all others remained a point of contention with the ANC throughout the 1980s and made him highly unpopular among anti-apartheid activists in the United States.

Calculus: Early Transcendentals, Chapter 7, 7.1, Section 7.1, Problem 34

int_0^1r^3/sqrt(4+r^2)dr
Let's first evaluate the indefinite integral using the method of substitution,
Substitute x=4+r^2, =>r^2=x-4
=>dx=2rdr
intr^3/sqrt(4+r^2)dr=int(x-4)/(2sqrt(x))dx
=1/2int(x/sqrt(x)-4/sqrt(x))dx
=1/2int(sqrt(x)-4/sqrt(x))dx
=1/2((x^(1/2+1)/(1/2+1))-4(x^(-1/2+1)/(-1/2+1)))
=1/2((x^(3/2)/(3/2))-4(x^(1/2)/(1/2)))
=x^(3/2)/3-4x^(1/2)
substitute back x=r^2+4 and add constant C to the solution,
=(r^2+4)^(3/2)/3-4(r^2+4)^(1/2)+C
Now let's evaluate the definite integral,
int_0^1r^3/sqrt(4+r^2)dr=[(r^2+4)^(3/2)/3-4(r^2+4)^(1/2)]_0^1
=[(1^2+4)^(3/2)/3-4(1^2+4)^(1/2)]-[(0^2+4)^(3/2)/3-4(0^2+4)^(1/2)]
=[(5)^(3/2)/3-4(5)^(1/2)]-[4^(3/2)/3-4(4^(1/2)]
=[(5^(3/2)-12(5)^(1/2))/3]-[(2^2)^(3/2)/3-4*2]
=[5^(1/2)((5-12)/3)]-[2^3/3-8]
=[-7/3sqrt(5)]-[8/3-8]
=(-7/3sqrt(5))-((8-24)/3)
=-7/3sqrt(5)-(-16/3)
=-7/3sqrt(5)+16/3
=1/3(16-7sqrt(5))

How did Ben Franklin contribute to the founding of America before the Revolution?

Benjamin Franklin began his professional life as a printer.  He was the owner of a newspaper, the Pennsylvania Gazette, and he also published Poor Richard's Almanac.  His work on the almanac brought Americans popular wisdom as well as useful planting and astronomy tables.  While in Philadelphia, Franklin helped to establish a fire department and a library.  He was also influential in establishing the University of Pennsylvania.  Franklin's experiments in electricity brought him worldwide fame before the Revolution.  Franklin invented the lightning rod.  He also created a musical instrument called the armonica, but sadly it never gained widespread popularity.  
Politically, Franklin helped to create the Albany Plan in 1754 as a way for the colonists to organize in order to better fight the French and Indian War.  The British opposed the plan, as they feared organized colonial resistance.  The Albany Plan was the forerunner to the Articles of Confederation.  
https://www.history.com/topics/american-revolution/benjamin-franklin

What is Johnson's style and vision in his Idler's essays?

Johnson wrote 91 of the Idler's 103 essays. He's a melancholic moralist as well as a satirist in these essays. Johnson wants to help us live better and wiser lives; he wants to be useful to his audience. As he says, with gentle satire, poking fun at his audience in the third Idler essay, his essays are for those:

who awake in the morning, vacant of thought, with minds gaping for the intellectual food, which some kind essayist has been accustomed to supply.

He lives in hope, or more precisely, in wishing, perhaps in vain, for the triumph of hope over experience, as he said of second marriage. One of his hopes, expressed in the third essay, is that people will learn to think for themselves and trust their own opinions.
Johnson's style is epigrammatic and exemplifies the balance prized in eighteenth century writing. We can see an example of this in Idler number 14, called "Robbery of Time." In the line below we can note the balancing of "kindness" in the first clause with "follies" in the second. The sentence also acts as a pithy saying, or, in other words, is epigrammatic. It is a wise saying we might want to remember:

If we will have the kindness of others, we must endure their follies.

The essay continues in the same measured, balanced style, summing different types of time wasters in a few short, pithy phrases.

He who cannot persuade himself to withdraw from society, must be content to pay a tribute of his time to a multitude of tyrants; to the loiterer, who makes appointments which he never keeps; to the consulter, who asks advice which he never takes; to the boaster, who blusters only to be praised; to the complainer, who whines only to be pitied; to the projector, whose happiness is to entertain his friends with expectations which all but himself know to be vain...

What do you believe was the single greatest problem facing African nations during the era of decolonization around 1960? Sovereignty and Security, National Unity, or Basic Human Services?

While all three were important challenges facing newly decolonized African nations in 1960, sovereignty and security was the biggest problem in a world dominating by a Cold War between western capitalist democracies and Soviet socialism. African nations needed to establish security and sovereignty before they could address the other two challenges, and were hard put to do so in the international climate of that era. 
The African nations granted autonomy in the 1950s-1960 in general faced challenges establishing sovereignty and security independent of their former colonial masters because of the legacy of colonialism. These new nations did not have good infrastructure in place when they achieved freedom: they lacked the kind of roads, power grids and communication networks common in countries with a long history of independence. Further, the colonial administrators installed by the foreign powers tended to have the most expertise in running these countries, and they left after independence, leaving less experienced administrators in charge. Finally, the political systems put in place by the colonial powers had been structured largely to benefit the people at top, not the citizens of the country as a whole. In particular, the first two issues (lack of infrastructure and expertise) often forced the African nations to rely on their former colonial masters, and the lack of a cohesive system of government that benefitted all citizens made it easy for outside governments to foment dissent. 
While many African nations hoped to sidestep the politics of the Cold War powers, security concerns in both the East and the West meant that countries like the U.S. were prone to interfere in issues of African national sovereignty when they believed their own interests were at stake. For example, in 1960, Patrice Lumumba, the Congo's first prime minister, gave a speech interpreted by the U.S. and its western allies as dangerous, so the U.S., Belgium and others worked to have Lumamba assassinated and a more pro-Western government imposed, regardless of whether or not this benefitted the Congo or its people. 
Thus, international political concerns of world powers during the Cold War and lack of a developed infrastructure, lack of an experienced native political class and lack of inclusive government left African sovereignty and security shaky and at risk in 1960.  Problems of sovereignty and security needed to be solved before the African nations could address  other issues such as basic human services and building national unity in territories with arbitrary borders established by colonial powers. 

In F. Scott Fitzgerald's The Great Gatsby, how have Jay Gatsby and George Wilson been affected by other characters' selfishness and greed?

Both Jay Gatsby and George Wilson were chasing the American Dream, and both were somewhat out of touch with reality in their inability to realize that the American Dream is really a fiction.  Gatsby felt certain that he could repeat the past, if only he could acquire the money to keep Daisy in the life to which she's accustomed.  He doesn't realize that being a bootlegger will tarnish both him and his fortune in her eyes, and that a criminal could never please her or achieve the American Dream.  Wilson, likewise, thinks that if he can just get a hold of Tom Buchanan's car, he can turn it for profit, enough to improve his situation and, eventually, to pave the way for him and his wife, Myrtle, to leave the valley of ashes.  Hard and honest work does not help him to achieve the American Dream, either.  The only way to get rich, then, is to engage in illegal activity (which shuts one out from the dream), and if one engages in actual, legitimate hard work, one can never earn enough to achieve the dream.  There is, simply, no path to it.  Gatsby doesn't understand that he can't reach the dream, and neither does Wilson, but they both continue to believe they can for the majority of the novel.  It is not until they are affected in a significant way by others' selfishness that they become disillusioned, and even Gatsby never really does.  After Daisy kills Myrtle and allows Gatsby to take the blame for it, when Wilson realizes that his wife's been cheating on him with Tom, Wilson finally realizes the hopelessness of his endeavors and takes his own life.  If Gatsby realizes anything, it's that Daisy is not going to call, that she has slipped from his fingers again.

What is the book about and what does the story mean?

Animal Farm is a cautionary tale about how easily people can be duped by a dictator if they are not careful, especially if they are not careful about how language is used. It is an allegory, or retelling, of how the Russian Revolution, which began with the great hope of establishing a state run for the benefit of working people, turned into the nightmare of Stalinist totalitarianism.
Orwell transforms the story of the Russian Revolution into a revolt by animals who take over their mismanaged farm and decide to run it themselves. They start out with high hopes that they can create a society based on the idea of all animals as equal. At first, they all work hard together for the common goal of survival. They decide on Seven Commandments to rule the animals. These commandments not only declare that all animals are equal, but also outline a way of life that rejects human standards. They sing a song, "Beasts of England," that uses rich imagery to envision a future state in which all animals live prosperously.
Almost from the start, however, the pigs, who are the most intelligent animals, begin to set themselves apart and take more privileges. At first, they make this sound reasonable. After Napoleon, a pig based on Stalin, takes over, however, the other animals lose more and more privileges, and their language is simplified and dumbed down. By the end of the story, all the animals but the pigs are in the same—or worse—state of poverty they were in when Farmer Jones ran the farm. The pigs are behaving just like humans—in fact, they have become human. They gradually twist the Seven Commandments into one: all animals are equal, but some are more equal than others.
Orwell wants people to be careful so that those with evil intent don't twist language to seize control of a country and oppress everyone else.

Single Variable Calculus, Chapter 3, 3.1, Section 3.1, Problem 11

a.) The graph of the distance as a function of time of a particle is shown below suppose that it starts moving to the
right along a horizontal line. When is the particle moving to the right? Moving to the left? Standing still?








$
\begin{array}{|c|c|c|}
\hline\\
\text{Right} & \text{Left} & \text{Standing Still}\\
\hline\\
0 < t < 1 & 2 < t < 3 & 1 < t < 2\\
\text{and} & & \text{and}\\
4 < t < 6 & & 3 < t < 4\\
& & \\
\hline
\end{array}
$


b.) Draw the graph of the velocity function.



The graph is obtained by evaluating the slopes of the curve in the intervals given in part(a) using point slope form.
For example @ $0 < t < 1$
$\displaystyle \text{Velocity } = m = \frac{3-0}{1-0} = 3$

Intermediate Algebra, Chapter 3, 3.3, Section 3.3, Problem 58

Determine an equation of the line passing through the points $(-2,5)$ and $(-8,1)$.

(a) Write the equation in standard form.

Using the Slope Formula,

$\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - 5}{-8-(-2)} = \frac{-4}{-6} = \frac{2}{3}$

Using Point Slope Form, where $m = \displaystyle \frac{2}{3}$ and $(x_1,y_1) = (-2,5)$



$
\begin{equation}
\begin{aligned}

y - y_1 =& m(x - x_1)
&& \text{Point Slope Form}
\\
\\
y - 5 =& \frac{2}{3} [x - (-2)]
&& \text{Substitute } x = -2, y = 5 \text{ and } m = \frac{2}{3}
\\
\\
y - 5 =& \frac{2}{3}x + \frac{4}{3}
&& \text{Distributive Property}
\\
\\
3y - 15 =& 2x + 4
&& \text{Multiply each side by $3$}
\\
\\
-2x + 3y =& 4 + 15
&& \text{Subtract each side by $(2x - 15)$}
\\
\\
-2x + 3y =& 19
&& \text{Standard Form}

\end{aligned}
\end{equation}
$



(b) Write the equation in slope-intercept form.


$
\begin{equation}
\begin{aligned}

-2x + 3y =& 19
&& \text{Standard Form}
\\
\\
3y =& 2x + 19
&& \text{Add each side by $2x$}
\\
\\
y =& \frac{2}{3}x + \frac{19}{3}
&& \text{Slope Intercept Form}

\end{aligned}
\end{equation}
$

What is the purpose of the dream at the end of the story "Battle Royal" by Ralph Ellison?

Ralph Ellison’s “Battle Royal” is the first chapter of The Invisible Man. It tells the story of an African American teenager who is pitted against other young men in a blind “battle royal” for the amusement of white men, who then presented him with a scholarship to a black college. The narrator then gives the valedictorians speech to the group and repeats the phrase “social responsibility,” which the men love to hear.
The dream at the end of the story is a commentary on Booker T. Washington’s idea that social responsibility, rather than social equality, should be the goal of African Americans in the United States. The narrator, though he is chasing the American dream, understands that pushing social responsibility will ultimately be a fool's errand. He will never be accepted, and he will always be asked to fight for what he has—as he does in the “battle royal” for the white men that act as benevolent benefactors. Ellison is making a point at the end of the story, explaining that social equality is the only thing that will bring real progress to African Americans in the United States.
The Dream is poignant; it epitomizes the reality of what social responsibility means for African Americans in the United States. When the narrator opens the envelope, he receives in the dream the note inside says,

"To Whom It May Concern," I intoned. "Keep This Nigger-Boy Running."

The message of the note that he will have to chase the dream for his entire life relates to the idea of choosing social responsibility over social equality. If he continues to play by the rules set by white society, he will be chasing the dream forever. Until he and all African Americans choose to embrace the fight for equality, they will never be equal, and they will never have to stop chasing the dream that White America puts before them.

The narrator has the dream after returning home, overjoyed after having won "a scholarship to the state college for Negroes." In the dream, he is drooling blood, and he realizes that the "gold coins" for which he and the other young black men in the ring were scrambling are nothing but tokens advertising a brand of automobile. He looks at a picture of his grandfather, whose eyes seem to follow him. All of this indicates that his hard work, as well as his willingness to suffer brutality in exchange for respect, is futile. To further highlight the absurdity of the narrator's situation, Ellison situates his dream in a circus.
The briefcase in the dream is a simulacrum of the briefcase that the narrator wins after the Battle Royal. But in the dream, instead of finding the coveted scholarship notice, he finds a mise-en-abîme of envelopes. The detail that each envelope is "official" and stamped with a state seal could symbolize either the narrator's sense of his own importance and impending success or systemic complicity in the narrator's oppression. It could also indicate both of those things.
The narrator's grandfather informs him that those empty envelopes are "years." Only one envelope contains a message which justifies the existence of all the other envelopes: "To Whom It May Concern, Keep This Nigger-Boy Running." The message means that the narrator will always pursue success, for this is what society teaches him to do, but he will never achieve his full ambitions, because he is black and discriminated against. His grandfather's laughter, which rings in his ears when he awakes, is a mockery of the narrator's foolishness and inability to understand what he has read. The narrator continues to have this dream, which is a warning of his social condition, for many years before he understands what it means.

It seems clear that the grandfather's deathbed warning combined with the narrator's grueling battle experience has unsettled the narrator; his dream contains information about life's beginnings and endings, and the knowledge he now carries about his life as a black man. 
The grandfather's refusal to laugh at the dream circus clowns seems to symbolize the seriousness of the narrator's situation. Graduation from high school is a milestone, usually a time for optimism; for the narrator, instead, it is a mirthless time. Graduating from childhood to adulthood means accepting the full weight of society's treatment of black men.
The envelopes the narrator dreams himself opening are symbolic of the endless endurance tests he has been put through, and will be put through as he ages. Like the "battle royal" of the previous evening, the narrator must perform a number of arbitrary tasks for permission to do what he wants to do, to achieve anything greater for himself. (This unending rabbit hole of envelope-opening seems to reference Booker T. Washington's "politics of respectability" argument.)
We can only guess Ellison's purpose in using a dream sequence to comment on these themes. Perhaps he means to highlight that a black man's agency can be taken away from him even in the subconscious, so punitive is society's judgment. 

Dystopian characteristics?

The book The Twenty-One Balloons is a story about a utopian society. It's an ideal place of respect for everybody's individuality. A dystopia is the opposite. The Merriam-Websterdictionary defines "dystopia" as follows.

An imaginary place where people lead dehumanized and often fearful lives.

If you compare that simple definition to the society that is present in the story, it should be clear that the people are not living in a dystopia. The dictionary definition provided is fairly limited, and dystopian novels have continued to be popular among readers. While each individual story may be different, there are some consistent characteristics present in various dystopian societies.
There is some kind of leader or concept that is supposed to be worshiped by the people in the story.
Information, freedom, and independent thought are restricted or illegal. This characteristic especially stands out against The Twenty-One Balloons because that is a story about a society that values cooperation, creativity, and individuality.
Propaganda is used to control people.
Surveillance is used constantly to monitor and control the population.
Citizens are taught to fear the outside world.
Uniformity is an important part of societal control. Individuality is not promoted.
Society members are dehumanized.
http://www.readwritethink.org/files/resources/lesson_images/lesson926/DefinitionCharacteristics.pdf

Why are three main sections of the novel Hard Times by Charles Dickens entitled "Sowing," "Reaping," and "Garnering"?

Sowing means planting crops (seeds), reaping is harvesting the full-grown crops, and garnering is picking up the pieces that are left over after the harvest. Sowing and reaping are intimately related to the Bible, closely associated with the Biblical adage that one reaps what one sows.
In part 1, Gradgrind "sows his seeds" by educating his two children, Louisa and Tom, into his materialist, utilitarian philosophy. They are taught to disparage love, sentiment, the arts, and most of all the magic and whimsy of the circus as represented by Sissy Jupe. Gradgrind misguidedly raises his two children to be hard-head, money-oriented, and practical. He plants a bad crop, speaking metaphorically.
In part 2, as the title suggests, Gradgrind and his children reap what they have sown, which is misery. Louisa marries Bounderby, a man thirty years her senior, for money rather than love and, as a result, is easily seduced by a younger man who exploits her vulnerability and does not have her interests at heart. Tom robs from the bank where he works as an intern. Both of these actions grieve Gradgrind, leading him to repent of how he has raised his children.
In garnering, the Gradgrinds pick up the broken pieces of their "harvest" or lives. Sissy Jupe tries to help them. Nevertheless, the coldness of both Tom and Louisa's characters has already been planted, and little can be done to help these two miseducated figures find happiness.

Charles Dickens's novel Hard Times, which is a social criticism, is divided into three sections. These sections act as thematic titles.
Sowing
In this section, Dickens introduces his main characters, among whom is Mr. Gradgrind, whose utilitarian fact-philosophy does not allow emotion or imagination to partake in learning or experience. In fact, Gradgrind holds this conviction: 

Facts alone are wanted in life.... Facts: nothing else will ever be of any service.... This is the principle on which I bring up my own children, and this is the principle on which I bring up these children. Stick to Facts....! (Ch.1)

Likewise, just as the factories grind out a product, the educational preparation of Mr. M'Choakumchild is also churning out a product since the children are taught in the same utilitarian manner:

He had worked his stony way...and had taken the bloom off the higher branches of mathematics and physical science, French, German, Latin, and Greek. (I, Ch. 1)

Imagination is discouraged. Even marriage is a practical arrangement. For instance, when Mr. Gradgrind talks with his daughter about marriage with Mr. Bounderby, there is a silence between them as the "deadly statistical clock" sounds hollow. "Father," said Louisa, "do you think I love Mr. Bounderby?" Hearing this, Gradgrind is "discomfited" by such a question about emotion: 

"Well, my child," he returned, "I - really - cannot take upon myself to say." (I, Ch.15)

Through his elimination of imagination and insistence upon cold facts, Mr. Gradgrind calculates everything, even the marriage of his daughter. So, when Louisa remarks, "What does it matter?" it becomes apparent that the seeds of utilitarianism have been sown. 
Reaping
In the second part of Hard Times, the factories that govern the dreary lives of the workers are the objective correlative of their dehumanization. Lives are a mere drudgery; children's innate play is sacrificed to machinery. In this industrialized environment, there is only the reaping of facts and things without any consideration for feelings. Louisa is in a loveless marriage with an owner of a factory, the much older Bounderby, and her brother Tom is amoral. Their impersonal father, so intent upon teaching his children only "facts," has reaped the product of his philosophy: offspring who have parts of them destroyed.Further in this second part, Stephen Blackpool, a power-loom operator at Bounderby's factory, informs the other workers of his awareness of their dehumanization as they work for Bounderby: 

Look how we live, ...and look how the mills is awlus a-goin’, and how they never works us no nigher to onny distant object-‘ceptin awlus Death. (II,Ch. 5)

In this factory town, people have been converted into lifeless, loveless mechanical beings. It is a miserable Louisa who later returns to her father and collapses, telling him he has damaged her heart with his lack of warmth, denial of emotion, and insistence upon only facts:

“[W]hat have you done with the garden that should have bloomed once, in this great wilderness here?”(II, 12)

Garnering
The accumulation of dehumanizing experiences leads to the act of Tom Gradgrind in which he robs a bank and causes Stephen Blackpool to be implicated because Tom has had this poor, uneducated man loiter before Bounderby's bank for a few nights and appear suspicious.The seeds planted in the first section of the novel, the strict utilitarian Gradgrind's insistence upon facts, and the denial of emotion have led to the amoral behavior of Tom and the despairing collapse of Louisa in the second section. In the third section, then, the characters attempt to "garner," or find, what they have missed in their lives so that they may better their existence, using new emotional resources to stabilize themselves. What has been missed in the "reaping" are the feelings and imagination that Sissy, who has lived with her circus-performer father, finally brings to the Gradgrinds as she moves in with them.

Describe the types of styles of European art and architecture during the Middle Ages.

The style of architecture mostly closely associated with the Middle Ages is the Gothic. Gothic architecture was developed in France in the twelfth century and spread across most of Europe. It is characterized by pointed arches, flying buttresses, and ribbed vaulting. Ribbed vaulting was an innovation that allowed a building to support windows higher up. Windows in the upper or clerestory level of a building are particularly associated with Gothic cathedrals. Flying buttresses support a building from its outside, so they can be seen extending out from the walls of a cathedral or other large building. Gothic architecture is also characterized by decorative features such as gargoyles.
A form of medieval architecture that predates the Gothic is the Romanesque. If pointed arches are the chief distinguishing feature of the Gothic, rounded arches characterize the Romanesque. Romanesque architecture has thick walls, solid rounded towers, and other rounded surfaces. It evolved between the sixth and eleventh centuries from the architecture of the Roman Empire. 
Art in the Middle Ages was primarily devoted to Christian subjects and evolved over the course of time from stiff, flat, and static to more realistic. It also developed a greater sense of perspective or depth.

College Algebra, Chapter 2, 2.2, Section 2.2, Problem 34

Make a table of values and sketch the graph of the equation $y = x^3 - 1$. Find the $x$ and $y$ intercepts.

$
\begin{array}{|c|c|}
\hline\\
\text{Let } x & y = x^3 - 1 \\
\hline\\
-3 & -28 \\
\hline\\
-2 & -9 \\
\hline\\
-1 & -2 \\
\hline\\
1 & 0 \\
\hline\\
2 & 7 \\
\hline\\
3 & 26\\
\hline
\end{array}

$

To solve for $y$ intercept, we set $x = 0$


$
\begin{equation}
\begin{aligned}

y =& 0^3 - 1
\\
\\
y =& -1

\end{aligned}
\end{equation}
$


Thus, the $y$ intercept is at $(0,-1)$

To solve for the $x$ intercept, we set $y = 0$


$
\begin{equation}
\begin{aligned}

0 =& x^3 - 1
\\
\\
x^3 =& 1
\\
\\
x =& \sqrt[3]{1}
\\
\\
x =& 1

\end{aligned}
\end{equation}
$


The $x$ intercept is at $(1, 0)$

As President-elect Donald Trump makes his staff and cabinet suggestions, we need to think about what direction we think the adminstration will move in. Will he be open to advice? Will he be able to accomplish all that he promised during the campaign? And finally what are his strengths and weaknesses? Whatever your political affiliation, please consider facts more than opinions.

Though Trump has not appointed his Secretary of State and other positions yet, it is fair to say so far that Trump is moving in a very conservative direction. His nominee for Secretary of Education, Betsy DeVos, is a fan of charter schools and vouchers, and his nominee for Health and Human Services, Tom Price, is opposed to the healthcare plan referred to as "Obamacare." Betsy DeVos has been particularly controversial, as she believes that the free market should play a role in public education; her stance is decidedly on the right. Experts believe Trump is assembling the most conservative administration to date, though some of his appointees such as Nikki Haley, currently the Republican Governor of South Carolina, for U.N. Ambassador, are more moderate in nature. 
Some of Trump's picks have indicated that he won't be a mainstream conservative but will follow his own independent thinking. Some people consider this independent thought a strength. For example, His current frontrunner for Secretary of State is Rex Tillerson, the CEO of Exxon Mobil. Tillerson has no previous government experience; however, most of the recent Secretaries of State have had some public service experience before serving as Secretary of state. 
It is not clear whether Trump will be open to advice, but, so far, he has largely followed his own lead. For example, he receives very few intelligence briefings and called the President of Taiwan, Tsai Ing-wen, which is not the protocol for incoming Presidents because of the ongoing tensions between Taiwan and China. Trump seems to be escalating U.S. tensions with China. While diplomats criticized this move and wish that Trump were more open to advice, others said Trump's independent moves are wise and could mark a more belligerent stance towards China's trade and economic policies. 
Trump will not clearly be able to deliver on all his campaign promises. For example, he is not going to jail Hillary Clinton. He is poised to dismantle Obamacare, but it's not clear how he would do so while maintaining the protection for people who are already sick when they sign up for insurance. If there is no mandate for people to sign up for health insurance, there may not be enough money in insurance pools to cover sick patients, and his plan may be financially unfeasible. It's not clear whether he could build a wall along the border with Mexico, though he may be able to do so without Congressional approval. Again, it may come down to funding. 
Many people consider Trump's unwillingness to follow precedent and protocol a strength, while others consider it brash, arrogant, and dangerous. This quality is considered a strength and a weakness in different camps. His strength is that he rallies his supporters' enthusiasm, but if he is unable to form a popular mandate (as, after all, he lost the popular vote), it will be a decided weakness. He needs to build bridges with other sectors of the American population.

Calculus: Early Transcendentals, Chapter 4, 4.9, Section 4.9, Problem 16

The most general antiderivative R(theta) of the function r(theta) can be found using the following relation:
int r(theta)d theta = R(theta) + c
int (sec theta*tan theta - 2 e^theta)d theta = int (sec theta*tan theta)d theta - int (2 e^theta)d theta
You need to use the following formulas:
sec theta = 1/(cos theta)
tan theta = (sin theta)/(cos theta)
sec theta*tan theta = (sin theta)/(cos^2 theta)
int (sec theta*tan theta)d theta = int(sin theta)/(cos^2 theta) d theta
You need to solve the indefinite integral int(sin theta)/(cos^2 theta) d theta by substitution cos theta = t => -sin theta d theta = dt . Replacing the variable yields:
int(sin theta)/(cos^2 theta) d theta= int (-dt)/(t^2) = 1/t + c = 1/(cos theta) + c
int (2 e^theta)d theta = 2e^theta + c
Gathering all the results yields:
int (sec theta*tan theta - 2 e^theta)d theta = 1/(cos theta) -2e^theta + c
Hence, evaluating the most general antiderivative of the function yields R(theta) = 1/(cos theta) -2e^theta + c.

From what point of view is this story told?

Jack London's adventure story set in the Yukon is told from a third-person omniscient point of view. That means that the narrator knows the thoughts, actions, and feelings of all the characters; in the case of "To Build a Fire," the narrator's subjects are the unnamed man and the dog who accompanies him.
We know that the narrator knows the thoughts of the dog because the narrator says, "it knew this was no time for traveling."
Likewise, the narrator knows what is in the mind of the protagonist because even when the man does not speak, the narrator says, for example, "he was glad he was without a sled."
The omniscient narrator also knows things that the dog and the man do not know and communicates them to the reader, such as, "It was 75 below zero." London chooses this point of view of narration to develop characterization and plot in the only way possible since the dog cannot speak and the man dies at the end of the story (in the 1908 version).

What issues has instability in Latin America posed to the United States?

Throughout recent history, Latin America has had a significant impact on the United States due to its proximity and close trade relations. There are many economic and political ties between the two regions. Cuban instability has perhaps had the greatest impact on the United States in comparison to instability in other Latin American countries.
Economic Issues Related to Instability
Latin America is the single largest foreign supplier of oil to the United States of America. Any instability in the Latin American supply chain has a corresponding impact on oil prices and availability in the United States. Any instability in regions that supply oil leads to a spike in prices on the American market, which in turn raises the cost of food and other goods that require transportation.
Political Instability
President Kennedy cited Latin America as being "the most critical area in the world." While the United States takes an active role in the development of many different countries around the world, close proximity makes political instability in Latin America of particular concern. The Cold War is a good example of this complex political relationship at work. Between 1947 and 1989, Latin America became a battlefield between capitalism and communism. In an effort to minimize the instability created by these competing ideals, the United States put pressure on nearby Latin American nations to declare their opposition to the Soviet Union. The Rio Pact in 1947 is a primary example of this.
American military intervention has often been the result of instability in Latin America. 1959 marked a period of unrest in Cuba after Fidel Castro's defeat of Batista. Castro's regime nationalized American companies and cut ties between Havana and Washington. In response, the Kennedy administration placed a trade embargo on the island of Cuba, which has had lasting economic effects on both nations to this day. Both the Eisenhower and Kennedy administrations used military intervention to further destabilize the Cuban Revolution and isolate the island from other Latin American countries. These tensions reached a peak at the Bay of Pigs in 1961, and since that time, Cuba and the United States have had strained relations. American government officials feared that communism would spread from Cuba throughout Latin America and potentially to the United States if left unchecked.
In summary, instability in Latin America has historically impacted the United States economically and politically.
http://resources.primarysource.org/c.php?g=767969&p=5508129

https://www.cfr.org/report/us-latin-america-relations

What is the link between operations management and strategic planning?

Let's start by defining some terms. Operations management is essentially about keeping things organized in the operations or production arm of your business. It involves procuring the raw materials required to do the job, managing workers and ensuring that machinery remains in mint condition.
Strategic planning is the process of figuring out where you want your business to go; what areas you want to grow and what your plans for the future are.
So, how do they work together? If strategic planning is the heart and backbone of your business, then operations management is the arms and legs. Strategic planning is where the high level decisions and plans are made, and operations managers are the people who do the work and make these goals realities.
For example, let's consider a factory that makes shoes. Strategic planning, which is carried out by upper management, would determine that output needs to be produced by 20 per cent in the next financial year. Operations managers would then step in and make sure that the factory had enough machines to make the extra shoes. They would also order the extra raw materials required and make sure they had enough staff to keep the factory running for enough hours to meet the new target.
https://www.topmba.com/mba-programs/what-operations-management

Operations management can be summarized as planning, organizing, controlling, and performing all activities necessary to turn inputs into outputs. Its main function is to ensure the business processes are performed efficiently by utilizing minimal resources and effectively to produce the output that the customer needs and expects.
Strategic planning is responsible for setting the priorities and focusing all resources available towards achieving the business’ goals and objectives. Its main function is to ensure the best decisions are made with regards to the customer, resources, and business activities.
Operations management is related to strategic planning because planning is a key function of operations. Strategic planning is necessary for ensuring business processes are focused on the intended goals and objectives. It will also eliminate waste of resources and improve the effectiveness of business processes, which is key to operations management.
https://strategymanage.com/resources/strategic-planning-basics/

https://www.investopedia.com/terms/o/operations-management.asp

Sherlock Holmes was very observant. Give two examples

Sherlock Holmes's particular faculty for observation is one of his defining characteristics. It is through his capacity to observe and interpret from the tiniest details that he is able to make his deductions, and consequently Watson, the narrator of the stories, is at pains to demonstrate this faculty to the reader. In the short story "A Scandal in Bohemia," for example, Watson is driven to visit Holmes by a desire to see how he is now "employing his extraordinary powers." Holmes immediately observes that Watson has "put on seven and a half pounds" since the last time they saw each other, from which he infers that Watson is well-suited to married life. Holmes also observes that Watson has "a most clumsy and careless servant girl." When Watson suggests that Holmes's deductive faculty is akin to witchcraft, Holmes is at pains to show him how logical, in fact, his deductions are. He identifies cuts on the inside of Watson's left shoe as indicative of the shoes having been scraped by a careless person in an attempt to remove mud that had been encrusted on to the shoes. Holmes is able to deduce from this that not only the careless servant girl, but also the fact that Watson has been recently out in particularly vile London weather.

What side of Dally do we see in chapter 6?

In chapter 6 of S.E. Hinton's novel The Outsiders, we see a different side of Dallas Winston, who is nicknamed Dally.
Prior to this chapter, we see Dally as the toughest member of the gang. He has a police record and is streetwise. He knows exactly what to do when Johnny and Ponyboy come to him scared after Bob's murder. Dally also shows his arrogance at the drive-in when he interacts with Cherry Valance.
In chapter 6, we see a more tender side of Dally. He shows his care and concern for his friends, particularly Johnny. When Johnny announces that he's planning to turn himself in, Dally respects the decision instead of just shutting him down or telling him it's a stupid idea. He says "You sure you want to go back? Us greasers get it worse than anyone else."
He also gets angry at Johnny, but out of protective concern for his friend. Johnny wants to know if his parents have asked about him. Throughout the book, we've seen the neglect and abuse Johnny's parents have shown him, so Dally's anger is because Johnny still cares about his parents. Dally thinks he should just write his parents off and realize that the gang is his family now. Dally further explains his reason for getting angry in the quote below:

"Johnny," Dally said in a a pleading, high voice, using a tone I had never heard from him before, "Johnny, I ain't mad at you. I just don't want you to get hurt. You don't know what a few months in jail can do to you. Oh, blast it, Johnny"—he pushed his white-blond hair back out of his eyes—"you get hardened in jail. I don't want that to happen to you. Like it happened to me . . ."

This is the first time readers see Johnny pleading with anyone, for any reason. He is showing his love for Johnny, too, because he wants to explain that he isn't mad at him. Also, much like a father figure, he doesn't want Johnny to go to jail because he wants something better for his friend than the life he's experienced.

What is a theme of Helen Keller's The Story of My Life?

One theme of Helen Keller's The Story of My Life is perseverance. Despite being disadvantaged by her blindness and deafness and frustrated by the limitations of her sign language, Keller maintains her memories of speech and works to regain her ability to communicate effectively. Even after learning how to communicate with her teacher, Miss Sullivan, and read Braille, Keller is determined to regain her ability to speak and works toward it until she accomplishes her goal. As an adult, Keller decides to attend Radcliffe College, which was not specifically for blind or deaf students. She perseveres through the difficulties of attending a college unequipped to accommodate her. Keller ultimately graduates with honors. Throughout the book, Keller perseveres through the limitations of being blind and deaf and manages to accomplish her goals of communicating, regaining speech, and attending college through hard work and dedication.

Is methanol good for nature?

Arguments can likely be made for saying that methanol is both good and bad for the environment. Like other fuels, methanol burns. As a result, it contributes to carbon emissions and pollution. However, when compared to other fuels, methanol is "cleaner" in a variety of ways. One definite benefit to methanol is that it biodegrades quite nicely. It can readily degrade in water, air, and soil. It also rapidly dilutes to low concentrations. The degradation rates of methanol can be measured with a "half life." This is how long it will take for half of the "bad" part of the material to degrade. Most of the time, methanol's half life is less than a week. What this means is that cleanup is quicker and easier in the event of a catastrophic spill because nature is doing a lot of the cleanup as well at a quick rate. That is a good thing for nature.
http://energyskeptic.com/2015/methanol/

Single Variable Calculus, Chapter 7, 7.7, Section 7.7, Problem 4

Determine the numerical value of a.) $\cos h 3$ and b.) $\cos h (\ln 3)$

a.) $\cos h 3$

Using Hyperbolic Function


$
\begin{equation}
\begin{aligned}

\cos h x =& \frac{e^x + e^{-x}}{2}
\\
\\
\cos h 3 =& \frac{e^3 + e^{-3}}{2}
\\
\\
\cos h 3 =& \frac{\displaystyle e^3 + \frac{1}{e^3}}{2}
\\
\\
\cos h 3 =& \frac{e^6 + 1}{2e^3}
\\
\\
\cos h 3 =& 10.067662


\end{aligned}
\end{equation}
$


b.) $\cos h (\ln 3)$

Using Hyperbolic Function


$
\begin{equation}
\begin{aligned}

\cos h x =& \frac{e^x + e^{-x}}{2}
\\
\\
\cos h(\ln 3) =& \frac{e^{\ln 3} + e^{- \ln 3}}{2}
\\
\\
\cos h(\ln 3) =& \frac{\displaystyle e^{\ln 3} + \frac{1}{e^{\ln 3}}}{2}
\\
\\
\cos h(\ln 3) =& \frac{\displaystyle 3 + \frac{1}{3}}{2}
\\
\\
\cos h(\ln 3) =& \frac{\displaystyle \frac{9 + 1}{3}}{2}
\\
\\
\cos h(\ln 3) =& \frac{10}{2(3)}
\\
\\
\cos h(\ln 3) =& \frac{10}{6}
\\
\\
\cos h(\ln 3) =& \frac{5}{3}

\end{aligned}
\end{equation}
$

College Algebra, Chapter 5, 5.5, Section 5.5, Problem 20

A sample of radon-222 has decayed to $58 \%$ of its original amount after 3 days.

(a) Find the half-life of radon-222.

(b) How long will it take the sample to decay to $20 \%$ of its original amount?




Recall the formula for radioactive decay

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

where

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

$m_0$ = initial mass

$r$ = rate of decay

$t$ = time

$h$ = half-life

a.) To solve for the half-life, we must find $r$, so


$
\begin{equation}
\begin{aligned}

0.58 m_0 =& m_0 e^{-r(3)}
&& \text{Divide each side by } m_0
\\
\\
0.58 =& e^{-3r}
&& \text{Take $\ln$ of each side}
\\
\\
\ln (0.58) =& -3r
&& \text{Recall } \ln e = 1
\\
\\
r =& \frac{- \ln (0.58)}{3}
&& \text{Divide each side by } -3
\\
\\
r =& 0.1816
&&

\end{aligned}
\end{equation}
$



Now the half-lfe is..



$
\begin{equation}
\begin{aligned}

r =& \frac{\ln 2}{h}
\\
\\
h =& \frac{\ln 2}{r}
\\
\\
=& \frac{\ln 2}{0.1816}
\\
\\
=& 3.82 \text{ days}

\end{aligned}
\end{equation}
$


b.) Then, if $m(t) = 0.20 m_0$, then



$
\begin{equation}
\begin{aligned}

0.20 m_0 =& m_0 e^{-0.1816 t}
&& \text{Divide each side by } m_0
\\
\\
0.20 =& e^{-0.1816 t}
&& \text{Take $\ln$ of each side}
\\
\\
\ln (0.20) =& -0.1816 t
&& \text{Recall } \ln e = 1
\\
\\
t =& \frac{\ln(0.20)}{-0.1816}
&& \text{Solve for } t
\\
\\
t =& 8.86 \text{ days}
&&

\end{aligned}
\end{equation}
$

What are individuals' responsibilities to the community?

One story illustrates that responsibility to the community lies in being honest and direct, not permitting yourself to hide in subterfuge, and in having the perceptiveness to get involved with events beyond your own four walls, outside your windows, when needed, as when a woman's life may depend upon it.
The final segment of "Getting By" describes a party Gary Soto and his wife Carolyn throw to celebrate the release of his first poetry collection. With their cottage filled with friends and relatives not seen "in nine months--or years!" Soto's sister Debra drags him to a bedroom window where she points at a woman on top of a "tin shed in the back yard" yelling obscenities in self-defense at a man waving a steak knife at her. Soto pulls down the shade. He contemplates calling the police.

Pulling down the shade, I felt inclined to telephone the police. I hesitated, however, and went over to tell Carolyn about what was happening outside. She rushed ... and peeked through the shade. They were gone.

A moment later Debra tugs on Soto's sleeve saying the woman is at the front door. When he opens to her, she pretends to have a broken-down car and asks to use the phone, refusing to meet his stare. He watches her and wonders if he should directly tell her that he knows it was trouble with a man and a steak knife, not trouble with a broken-down car, that brought her to his door.
Not wanting to embarrass someone so clearly in need of comfort, not wanting to get involved, he waits, walks her to the door, and wishes her luck with her car. She thanks him.

But I said nothing, for fear of getting involved, and when the young woman was off the telephone I walked her to the door and--very stupidly--wished her luck in getting her car started. On the steps she half-turned to me and ... said, "Thanks."

Although Soto does not draw morals and lessons at the conclusions of his stories, there is a clear implication that he would have done well to have acted on his inclination to intervene in trying to rescue her from violence and that he did poorly in engaging in subterfuge with her. For the young woman, there would have been a natural inclination to hide the truth as people tend to shy away from strangers who are in danger: homes and families are instinctively protected from invasion by dangerous elements.
But for Soto, there was that half-turned-toward inclination to intervene on her behalf. He would have done well to respond to it if for no other reason than that she may have seen a new pattern of being. Two of an individual's responsibilities to the community are (1) to follow beneficial inclinations that have the potential to lead to good and (2) to reject the inclination to hide in subterfuge.
Gary Soto Biography
https://www.scholastic.com/teachers/authors/gary-soto/

What do you think is meant by the last line of the story? How does it relate to one of the themes in “Games at Twilight”?

The final sentence of "Games at Twilight" is the following line.  

He lay down full length on the damp grass, crushing his face into it, no longer crying, silenced by a terrible sense of his insignificance.

Ravi has just attempted to claim victory in the game, and all of the other children merely cast him aside. They do not believe that he has earned victory, because they have all moved on to different games. In fact, all of the other children completely forgot about Ravi and the fact that he was still playing the game.
A theme of "Games at Twilight" is the interplay between fantasy and reality. When the reader first meets Ravi, it is fairly clear that he is not happy about his location in the hierarchy of children. He's cowering in fear by himself with his finger in his nose and swallowing snot balls. That is not the image of a strong leader type. Once Ravi has found a good hiding place, though, his thoughts wander into the realm of fantasy. He begins to envision what it will be like to win the game. He imagines that all of the other kids will praise his efforts, and he will be crowned a champion of sorts.

What fun if they were all found and caught—he alone left unconquered! He had never known that sensation. . . He hugged his knees together and smiled to himself almost shyly at the thought of so much victory, such laurels. 

Ravi convinces himself that his fantasy will become his reality when he reaches the "den." Unfortunately, the reality of the situation is the complete opposite of his fantasy. Ravi is not praised at all. Instead, Ravi is ridiculed by the other children.

"Stop it, stop it, Ravi. Don’t be a baby. Have you hurt yourself?''

The reality of the situation is that Ravi is just as insignificant to the other children as he always was, and that is what the final line of the story is pointing out to readers.

Why does Bill ask Sam to reduce the ransom amount?

Bill asks Sam to reduce the ransom amount because he believes that it would be cruel to expect a father to pay so much for his ill-behaved child's return. It is also likely (based on his interactions with Johnny) that Bill has little faith Johnny's father will pay the two thousand dollars they are requesting.
To placate Bill, Sam asks for a ransom of fifteen hundred dollars in his letter to Ebenezer Dorset. However, Bill's fears are realized when he and Sam receive correspondence from Johnny's father. In his letter, Ebenezer Dorset tells the men that their ransom demand is much too high. Instead, he makes a counteroffer, requesting that the men pay him 250 dollars cash in order to take Johnny back.
Ebenezer finishes up his letter with a warning: the men had better bring Johnny back at night, so that the neighbors do not see the boy returning. Ebenezer hints that the neighbors will not be too pleased to see Johnny home and might take out their anger on Bill and Sam. This humorous story ends with Bill running as fast as he can towards the Canadian border after paying 250 dollars to Ebenezer Dorset to take Johnny back. 

What do you think is the reason for Cory's death?

Ultimately, we can't know why Richard Cory decided to kill himself. The poem is from the view of the people who live near him; they don't know his innermost thoughts or the problems he might have in his life. They know him as someone to pass on the streets; they don't know him as a real person.
When Richard Cory shoots himself, the people in the town are surprised. They had no idea that he was unhappy about anything. They see him as living a blessed, successful life and see themselves as less in comparison.
There's no mention of Cory having a family or friends. They don't say whether he's in good health—though they have no indication to the contrary. There is no real indication of why he ultimately shot himself. He was deeply unhappy about something and decided to commit suicide because of it.

We don't know for sure why Richard Cory puts a bullet through his head one calm summer night. All we can do is speculate. On the face of it, Richard seems to have everything going for him. He's handsome, rich, and well respected by everyone in the town. But as we know, appearances can often be deceptive. And the townsfolk judge Richard on the basis of his appearance—on the side that he presents to the world. But they don't really know him all that well; they don't know what's going on inside his brain.
There are all kinds of reasons why people commit suicide. Perhaps Richard was experiencing depression or some other mental health issue. Maybe he was suffering from some physical ailment that was causing him pain but which he was able to hide from everyone. We simply don't know. However, one thing seems certain: Richard Cory, for all the wonderful things he had in his life, was deeply unhappy about something. What that something was will remain a mystery.
https://www.poetryfoundation.org/poems/44982/richard-cory

sum_(n=1)^oo (1/n^2-1/n^3) Determine the convergence or divergence of the series.

sum_(n=1)^oo(1/n^2-1/n^3)
Apply the series sum/difference rule:
=sum_(n=1)^oo1/n^2-sum_(n=1)^oo1/n^3
Observe that both the series are p-series of the formsum_(n=1)^oo1/n^p
Recall that the p-series test is applicable for the series of the form sum_(n=1)^oo1/n^p ,where p>0  
If p>1 , then the p-series converges
If 0Now, both the series have p>1
As per the p-series test , both the series converge and so their sum/difference will also converge.
Hence the series sum_(n=1)^oo(1/n^2-1/n^3) converges.

How had the technology of warfare changed between the American Civil War and World War I? What effects did these changes have on tactics and strategy?

Technology changed significantly between the Civil War and World War I. In the Civil War, metal-plated shapes were an anomaly and used in river warfare only; by World War I, these ships became the norm and the massive battleships were considered the pride of the major powers' navies. All the major powers of World War I used submarines to sink merchant shipping, and this altered the rules of war, as a submarine had to hide under the sea before attack. During the Civil War, it was standard procedure to give crews time to leave the ship before it was attacked. German unrestricted submarine warfare was one of the reasons that the United States joined World War I.
The airplane brought a new dimension to warfare that was not present during the Civil War. While the Union used observation balloons during the Peninsula Campaign, these were not the norm, and both armies used cavalry to scout enemy lines. The airplane, first developed in 1903, became a useful war weapon for reconnaissance and even early bombing, though the first planes could not carry massive bomb loads. Civilians became targets with the German zeppelin raids as well. By 1917, planes were becoming more adept at attacking ground targets and enemy planes—all of this would be a precursor for the next world war, which would prove even more destructive. The airplane and the submarine meant that the average worker now joined the front-line infantryman as a target in warfare; this change in strategy made major cities important targets just as much as objectives on the field of battle.
By the end of the Civil War, both armies were mainly using rifles. The breechloader gave the infantryman more firepower than ever before. By the time of World War I, the machine gun crew gave the defender a distinct advantage, and both sides began to dig elaborate trench systems protected by yards of barbed wire, another American invention. This led to a stalemate on the western front, which lasted from the end of 1914 until the fall of 1918. Most infantry carried bolt-action rifles, which were more accurate and afforded a greater rate of fire than the rifles of the Civil War, though these rifles did not use the .58 caliber bullet like many of the Civil War weapons. The new bullet offered more power and both sides experimented with hollow point rounds that left large exit wounds. Both the Central and Allied powers were desperate to break through the trenches and resorted to poison gas, a byproduct of industrial processes. Chlorine and mustard gas became a terror in the trenches, and both sides developed gas masks. The British developed the tank, but tactics did not catch up with technology. In many cases, the tank did not have infantry support behind it in order to follow up on the gains it made. Both sides developed massive artillery to blast through trenches and barbed wire systems—new developments in explosives meant that the artillery had a greater range than ever before.
The technology of World War I outpaced the tactics. Soldiers were lost by the thousands in frontal attacks on trench systems. Sanitation still had not changed much from the Civil War; soldiers died of influenza and infection because conditions in the trenches were horrible. The trenches were a breeding ground for both disease and vermin, and ultimately this killed more soldiers than the bullets.

Illustrate the characteristics of supply chain.

There are several important characteristics of a supply chain. One characteristic is to use data to help the company determine inefficiencies and to develop solutions to problems. A second characteristic is to have a proper inventory of materials. Having too much or too little of an item can hinder the supply chain. A third characteristic is to be able to be flexible to meet rapidly changing market conditions. It also important to fulfill orders quickly and accurately.
There are a few other characteristics of a supply chain. One is to be able to customize supply chain processes that meet individual needs of consumers. Another is to be able to develop alternatives to current resources that have a limited supply such as fossil fuels. Finally, a supply chain must comply with the rules and the regulations that are established at the local, state, and national levels.

What are Jeremiah's laments in chapter 15?

In the second section of Jeremiah 15, Jeremiah expresses fear for his life, terrified of his angry countrymen. God reminds Jeremiah to listen to God's words rather than let Jeremiah's countrymen influence him.
First (verses 10–14), the prophet laments that, because of the words he is preaching, his fellow countrymen hate him. God answers that He will protect Jeremiah, and then He reveals His plans to exile Israel.
In the next segment (15–21), Jeremiah points out that he has been a faithful prophet, and he questions whether God will save him. "Your help seems as uncertain as a seasonal brook," Jeremiah says, indicating that he never knows exactly when God will come to his rescue.
To Jeremiah, God's help seems like a brook: it comes and it goes. Its presence can't be relied on. Or perhaps, God has abandoned Jeremiah completely, "like a spring that has gone dry."
God reassures Jeremiah that He will protect His spokesman. Jeremiah needs to return to God and to listen to God rather than to people. "You must influence them," God says. "Do not let them influence you!"

Single Variable Calculus, Chapter 2, 2.2, Section 2.2, Problem 36

(a) Illustrate the function $\displaystyle y = \frac{\tan 4x}{x}$ by graphing and zooming in toward the point where the graph crosses the $y$-axis, estimate the value of $\lim \limits_{x \to 0} f(x)$.



When the viewing rectangle is a small number, the limit of the function is identifiable at 4 as shown on the graph on the left side.
However, if the viewing rectangle approaches a large number, the limit of the function will not be clearly identifiable.

(b) Evaluate $f(x)$ for values of $x$ that approach 0. Check if the results match your answer in part($x$).




$
\begin{array}{|c|c|}
\hline
x & f(x)\displaystyle \frac{\tan 4x}{x}\\
\hline
0.01 & 4.0021347\\
0.001 & 4.0000213\\
0.0001 & 4.0000002\\
-0.01 & 4.0021347\\
-0.001 & 4.0000213\\
-0.0001 & 4.0000002\\
\hline
\end{array}
$



$
\begin{equation}
\begin{aligned}
\lim\limits_{x \to 0} \displaystyle \frac{\tan 4x}{x} & = \frac{\tan [4(0.0001)]}{0.0001 } = 4.0000002\\
\lim\limits_{x \to 0} \displaystyle \frac{\tan 4x}{x} & = 4.0000002
\end{aligned}
\end{equation}
$

What do the gifts that Clarisse gives Montag represent?

Montag meets 17 year-old Clarisse on the way home after work one night. Among other things, she asks him if he, as a fireman, reads the books before he burns them and if he is happy. Both questions startle him because reading books is illegal and being happy seems never to have crossed his mind. Like these two questions, Montag notices this young neighbor girl doing things that people in their society don't normally do or even think about doing. For example, Montag curiously notices when Clarisse shakes walnuts out of a tree and knits a sweater. This isn't behavior suited for "normal" people in Montag and Clarisse's society and that forces him to pay attention to something outside of the social and cultural norms that he is used to. The following is the passage that details the gifts that Clarisse gives to Montag:

. . . three or four times he found a bouquet of late flowers on his porch, or a handful of chestnuts in a little sack, or some autumn leaves neatly pinned to a sheet of white paper and thumbtacked to his door (28).

First of all, the fact that someone is giving gifts without expecting anything in return is symbolic, because Clarisse does something others in society don't do: she thinks of others. These random acts of kindness seem radical in nature and represent another time lost to those living in Montag's world, but they represent an age old ritual called "making friends." As a result, the gifts represent friendship and a connected emotional feeling that Clarisse wants to express to Montag. In fact, she tells him that she likes him and doesn't expect anything from him when he asks why he feels as though he's known her for years. Notice, too, that the flowers, the nuts, and the leaves all come from nature and the natural world around them. In Montag's society, people are usually distracted by digital, loud, and manmade things such as seashells, TVs, and fast cars. By giving Montag gifts from nature, Clarisse not only demonstrates her childlike curiosity and friendship, but she also uses those gifts to represent the forgotten natural world around them that many in their society miss out on enjoying.

What motivates Ivan and General Zaroff?

Ivan is General Zaroff's Cossack bodyguard and servant, who attends to the general, protects him, punishes unruly prisoners, and helps him hunt humans. Ivan is portrayed as an unintelligent person, who takes pleasure in torturing the prisoners that refuse to participate in the general's game.
Similar to Ivan, who has an affinity for torturing prisoners and is a rather violent man, General Zaroff also takes pleasure in hurting people. General Zaroff is a fanatical hunter, who attempts to satisfy his desires by hunting humans on Ship-Trap Island. The general admits to Rainsford that he is driven to hunt humans because he enjoys the challenge of hunting rational, intelligent beings.
While the general insists that he is a civil person, he is depicted as a ruthless, bloodthirsty murderer. Overall, what motivates both Ivan and General Zaroff is their affinity for harming individuals and imposing their will on defenseless people.

In the novel The Absolutely True Diary of a Part-Time Indian by Sherman Alexie, are there any obvious hyperboles that are related to the identity of Junior?

Hyperbole is a type of figurative language that involves using exaggerated terms, rather than literal descriptors, to convey the great emotion or importance of a topic or feature. In the novel The Absolutely True Diary of A Part-Time Indian, the narrator, Junior, often employs hyperbole when talking about his identity and his experiences. To start off, the title of the book itself presents a form of hyperbole. The phrase "absolutely true" is hyperbolic and in itself suggests that the book may contain some exaggerations.
On page 11, Junior writes, "I can’t blame my parents for our poverty because my mother and father are the twin suns around which I orbit and my world would EXPLODE without them." Here, we have an example of figurative language and hyperbole. Junior's parents are not literally twin suns, and his world would not literally "EXPLODE" without them, but the exaggerated, descriptive language serves to stress the deep importance of Junior's parents to his identity and his world.
https://dictionary.cambridge.org/us/dictionary/english/hyperbole

Junior uses many hyperboles to describe himself and his identity. He says that he was so skinny as a small child that "I'd turn sideways and disappear." He also describes his feet as so big that, given his big feet and skinny body, "I looked like a capital L walking down the road." He states that his head is so big that other kids' heads orbited around it, much as planets orbit around the sun. He describes himself as "the biggest retard in the world" because he has a stutter and a lisp at age 14. Though these descriptions may in part be based in reality, Junior describes himself in an exaggerated way, using hyperboles. The reader is supposed to understand that Junior's self-descriptions are exaggerations and are not strictly true. 

What are three ways in which humans depend on interaction with one another?

A popular saying is that "No man is an island." This is true on many levels. People depend on interaction with each other in terms of commerce and trade. It is hard for one person to be able to satisfy their own wants and needs on their own. People need to be able to either trade for what they want or to be able to spend money to obtain the goods and services that would make them the most comfortable.
People also need some sort of governance; this usually entails having both rights and responsibilities to the government and one's fellow citizens. Without law and order, power would go to whoever was best armed or strongest, and people would live like animals.
Finally, people need warmth and socialization in order to be healthy. Studies have shown that older people live longer and better lives when they are able to maintain their social circles—be it through family, work, or hobbies. Children learn language and social norms by interacting with each other. Without these interactions, people would not know how to interact since interacting in polite society is not innate behavior, but learned behavior. People need social interaction for cognitive development as well as to develop interpersonal skills.  

What is the main lesson of "The Interlopers"?

One lesson that the narrative of "The Interlopers" presents is that people should not become mired in issues that are not essential to the quality of their lives.
The plot of Saki's story revolves around an ancient grudge that two young men have allowed to become foremost in their lives as they have inflamed the hatred between their two families, who once disputed a small tract of land:

The feud might, perhaps, have died down or been compromised if the personal ill-will of the two men had not stood in the way; as boys they had thirsted for one another's blood, as men each prayed that misfortune might fall on the other.

Of course, the old maxim "Be careful what you wish for" is also applicable to the narrative of "The Interlopers," as well as the senselessness of their feud, since misfortune does, indeed, befall the two enemies. Unfortunately, it has taken a disaster to effect a change of heart in the two men, and as fate would have it, this realization comes all too late. For it is only after the two men are pinioned under the fallen branches of a huge beech tree, lying hurt and helpless, that Ulrich von Gradwitz arrives at the understanding of the real insignificance of his feud with Georg Znaeym in light of their life and death situation. Unfortunately, when the two old enemies finally put away their feud, it is too late because they are confronted with death in the shape of fierce wolves who hear their cries for help.

Why was Thomas Jefferson worried about the Louisiana Purchase?

Jefferson's whole political philosophy was based on a radical distrust of central government power and a correspondingly narrow interpretation of that power under the terms of the Constitution. The Louisiana Purchase seemed to go against Jefferson's long-standing republican principles. For one thing, the Constitution did not authorize the federal government to buy property from foreign governments, yet that's precisely what the Purchase involved. Jefferson's Federalist opponents immediately seized on what appeared to be the president's hypocrisy and made an issue out of it.
Jefferson didn't want to be seen as playing fast and loose with the Constitution, but at the same time, he didn't want to lose this once-in-a-lifetime opportunity to expand American territory at what was a fairly reasonable cost. He sent the Louisiana Purchase to the Senate—without amendments—for ratification. Republican control of the Senate ensured that the measure passed comfortably after only a two-day debate—Jefferson's enormous constitutional gamble had paid off.

The purchase to which you are referring is the Louisiana Purchase; this was one of the largest land acquisitions in American history in which Jefferson bought the Louisiana Territory from France. Jefferson had reasons to be concerned, but the deal was too good to let escape. Jefferson's diplomats were only allowed to negotiate for the use of the port of New Orleans—they were not authorized to buy this land. Congress was informed after the fact—all of this is a little ironic since Jefferson is known as a strict constructionist of the Constitution. Also, no one knew the exact parameters of the purchase and some were worried that there would be future land conflicts with Spain and Britain. No one knew what was in the new land either—much of the Louisiana Territory had not seen any white explorers. This intrigued more than worried Jefferson as he sent the Lewis and Clark expedition as a military venture told to also make scientific observations.

Write out the examples of simile and metaphor in the short story 'a worn path'

A metaphor in Willa Cather's 1941 short story "A Worn Path" is found in the first paragraph as the narrator describes the manner in which Phoenix Jackson walks: "with the balanced heaviness and lightness of a pendulum in a grandfather clock." Through this metaphor the reader understands that Phoenix is measured and consistent in her gait, just as a pendulum is measured and consistent as it marks time.
In the same opening paragraph, Cather employs a simile to deepen her characterization of Phoenix as she undertakes her journey. She carries a cane made from an umbrella, and the narrator observes that it made a serious and steady sound in the quiet woods "like the chirping of a solitary little bird." This particular simile also introduces the idea that the main character is small and birdlike in her movements; this comparison deepens the bird motif already introduced in the character's name: Phoenix Jackson.
Using both a machine (a pendulum) and an animal (a bird) as comparisons, Cather begins her characterization of a woman with strength, determination, and the ability to endure despite her slight stature and advanced age.

How does Fitzgerald present Daisy's marriage to Tom as dysfunctional?

On Nick Carraway's first visit to Tom and Daisy's estate, Jordan Baker explains that it is public knowledge that Tom has a "woman," who he sees on a regular basis and is even bold enough to call from his home. In chapter 2, Fitzgerald depicts Tom's affair when Nick attends a party at Tom's New York City apartment, where he carries out his affair with Myrtle. Daisy is well aware of her husband's infidelity, and Jordan even tells Nick that Daisy initially did not want to marry Tom. She also tells Nick that Tom cheated on Daisy during their honeymoon, which initially surprised her. Daisy is also unhappy with her marriage and begins having an affair with Jay Gatsby. When Daisy and Tom attend Gatsby's party, Daisy even goes out of her way to offer Tom her golden pen to take down a random woman's number. Despite the fact that both Tom and his wife are miserable in their marriage and cheat on each other, they remain together. Daisy remains with Tom because he is secure in his wealth, and Tom recognizes that his social status and affluence are enough to keep Daisy around.

In the story "Once Upon a Time," why does Nadine Gordimer choose the words "happily ever after" and "once upon a time?"

At the beginning of the story, Nadine Gordimer gives the frame story. She tells the reader that she has been asked to write a children's story for an anthology. Initially, she does not accept the offer, replying that she does not write children's stories. She doesn't like the idea that she "ought" to write something. However, her creaking house and worries about crime in the area prevent her from going back to sleep. So, she begins to tell herself a bedtime story. This is to be the so-called children's story that she mentioned earlier. This is her children's story within the frame story. 
Sticking with the traditional fairy tale form, she uses phrases like "once upon a time" and "happily ever after." She describes a family in a crime-ridden town, similar to her own. In order for them to "live happily ever after," they continue to improve the security of their home. Eventually, a once simplistic home becomes more like a prison designed to keep criminals out. In the end, the little boy, inspired by a fairy tale from a book his grandmother (referred to as a "wise old witch") had given him, tries to get through the security coil. He is killed and the story ends. Gordimer uses those phrases ("happily ever after" and "once upon a time") because she'd been challenged to write a children's story. The phrase "happily ever after" turns out to be quite ironic (situational irony) because the story ends in tragedy. 
Gordimer's story alludes to the transition in South Africa from the apartheid to an unknown future. The family in the story claims not to be racist but they do worry about people "of another color." Gordimer uses the frame story and the story within the story to allude to South African culture (1989 at the time it was published) and how it is not a fairy tale situation. Therefore, the "happily ever after" phrases are meant to be ironic.

Precalculus, Chapter 7, 7.3, Section 7.3, Problem 44

You should notice that the system is indeterminate, since the number of variables is larger than the number of equations.
2*(2x + 3y + 3z) = 14 => 4x + 6y + 6z = 14 => 4x = 14 - 6y - 6z
Replace 14 - 6y - 6z for 4x in the second equation, such that:
4x = 44 - 18y - 15z => 14 - 6y - 6z = 44 - 18y - 15z
12y + 9z = 30 => 4y + 3z = 10 => 4y = 10 - 3z => y = 5/2 - (3/4)z
Replace back 5/2 - (3/4)z for y in equation 4x = 14 - 6y - 6z , such that:
4x = 14 - 6( 5/2 - (3/4)z ) - 6z
4x = 14 - 15 + (9/2)z - 6z
4x = -1 - (3/2)z => x = -1/4 - (3/8)z
Hence, evaluating the solutions to the system, yields x = -1/4 - (3/8)z, y = 5/2 - (3/4)z, z = z.

What is the reason Squeaky does not do chores in "Raymond's Run"?

Squeaky has a very important job in “Raymond’s Run” by Toni Cade Bambara, and it is not doing housework. Each member of the family has his or her own responsibilities. Her mother takes charge of the housework while Squeaky attends to her developmentally disabled brother, Raymond. This allows her mother to complete her daily chores, and allows Squeaky to continue with her running practice routine.

All I have to do in life is mind my brother Raymond, which is enough.

Caring for Raymond takes time, dedication, and loyalty. In order for Squeaky’s mother to care for the household, she requires her daughter to care for Raymond, who needs constant attention. In the past, George, Squeaky’s other brother, had the task of caring for Raymond but he was not as fierce at defending him as Squeaky is. Although Raymond is chronologically older than Squeaky, he is not as developmentally advanced. Squeaky takes her job seriously to the point of fighting with anyone who questions Raymond’s appearance or abilities. Sometimes she has to run interference for him when he upsets the people relaxing in the park. In order to keep him safe, she instructs him to walk closest to the buildings on Broadway so he does not run into the busy street or play in the puddles next to the street while pretending the curb is a tightrope.

And sometimes after a rain he likes to step down off his tightrope right into the gutter and slosh around getting his shoes and cuffs wet. Then I get hit when I get home. Or sometimes if you don’t watch him he’ll dash across traffic to the island in the middle of Broadway and give the pigeons a fit. Then I have to go behind him apologizing to all the old people sitting around trying to get some sun and getting all upset with the pigeons fluttering around them, scattering their newspapers and upsetting the waxpaper lunches in their laps. So I keep Raymond on the inside of me, and he plays like he’s driving a stage coach which is OK by me so long as he doesn’t run me over or interrupt my breathing exercises, which I have to do on account of I’m serious about my running, and I don’t care who knows it.

Caring for, and defending Raymond is difficult job which Squeaky performs with heartfelt diligence. This allows her mother to accomplish the household chores. Although taking care of Raymond is a constant job, Squeaky manages to practice her ever important breathing exercises.

What is Scout's attitude towards ghosts?

To Kill a Mockingbird is, in large part, a coming-of-age tale, the story of a girl named Scout and how she lost her innocence. Her father, Atticus Finch, is her stronghold, full of love, wisdom, and guidance. He helps his daughter process the happenings around her and put her experiences in perspective. In one of Scout’s conversations with Atticus, he tells her “there are other ways of making people into ghosts,” and she comes to understand, through her observations and experiences, that he is referring to people who are alive, but feel invisible to the rest of world. Scout learns that Tom Robinson has been ostracized from society, and she recognizes that the person he truly is has been suppressed by the people who condemned him. She also knows that Boo Radley shut himself off from world around him, and in doing so, he became invisible; he existed only in the shadows.

Scout's attitude towards ghosts is summed up at the end of the novel, when she selects a ghost story to read with Atticus.
At the end of To Kill a Mockingbird, in Chapter 31, Scout goes to bed after a terrifying evening. Bob Ewell has stalked her and her brother, Jem, attempting to attack her with a knife. During the struggle with Bob Ewell, Jem's arm has been broken. Boo Radley has brought Scout and Jem home to Atticus.
Though all is well, by the end of the night, when Scout requests a book from Atticus, he feels that the story she has selected, titled "The Gray Ghost," might not be the best choice after such a scary evening. Scout points out to her father, ironically, books are the only thing she feels is scary, and as he reads to her, she falls asleep.

What would you have done if you were faced with a problem like the one in "The Cold Equations" short story?

In Tom Godwin's science fiction story "The Cold Equations," we see a familiar moral conveyed in a new way: sometimes, rules are there for a reason. The captain of the ship, Barton, knows that the reason for the "no stowaways" rule is not simply bureaucracy, but that an additional person would endanger the rest of the crew, possibly causing their deaths. As such, he decides that Marilyn must be ejected from the vehicle, sacrificing one life to save many. In this instance, however, his job is made easier by the fact that Marilyn agrees with his logic and sacrifices herself without a struggle.
In responding to the question of what you would do in a similar situation, you would need to consider the context. It is difficult to argue against sacrificing one life instead of dooming ten people to die, but might it not depend on the life that needed to be sacrificed? A great moral question explored in much science fiction is that of whether some lives are more valuable than others. Would you jettison, say, a brain surgeon to save ten manual laborers? Why, or why not? Would you find it more difficult to make the choice Barton made if the person disagreed with you and put up a fight, or expressed distress?

Calculus of a Single Variable, Chapter 5, 5.6, Section 5.6, Problem 70

This function is defined on [-1, 1] and is differentiable on (-1, 1). Its derivative is f'(x) = 1/sqrt(1-x^2) - 2.
The derivative doesn't exist at x = +-1. It is zero where 1-x^2 = 1/4, so at x = +-sqrt(3)/2. It is an even function and it is obviously increases for positive x and decreases for negative x. Hence it is positive on (-1, -sqrt(3)/2) uu (sqrt(3)/2, 1) and negative on (-sqrt(3)/2, sqrt(3)/2), and the function f increases and decreases respectively.
This way we can determine the maximum and minimum of f: -1 is a local (one-sided) minimum, 1 is a local one-sided maximum, -sqrt(3)/2 is the local maximum and sqrt(3)/2 is a local minimum.

In Golding's Lord of the Flies, what does Ralph want the boys to do after exploring the Castle Rock?

After Samneric report having seen the Beast, Ralph's control over the group continues to erode, furthering the downward spiral that began when the hunters allowed the fire to go out. Ralph insists that they need to relight the fire, and reminds them that their primary concern should be rescue, no matter the danger. However, they also need to deal with the Beast. They decide to scout the only part of the island that Jack hasn't been to - Castle Rock - and see if the Beast is there. If not, it must be on the mountain, and they need to go there anyway to relight the fire.
The hike to Castle Rock is stressful, but once Ralph and Jack scout it and determine there is no Beast, the remaining boys begin to distract and entertain themselves by pushing a large rock off the cliff into the water, foreshadowing the future use of that strategy to "defend" themselves. Ralph attempts to direct everyone to the mountain, but is met with whining; it's midday and sunny, and the boys have forgotten their fears. They would rather stay at Castle Rock, play games, roll more rocks, and otherwise put off the responsibilities that Ralph is demanding of them. His leadership struggles continue through Chapter 7, and though he manages to get everyone to the mountain, his common sense gets the better of him when they try to scale it at dusk; ironically, Jack later brands him a coward for his refusal. 

Please explain how the U.S. Supreme Court's interpretation of the Fourth Amendment and the creation of the Exclusionary Rule have effected the manner in which law enforcement officers conduct themselves? Has the Fourth Amendment made the job of enforcing the law more difficult? Do you think the protections under the Fourth Amendment go too far towards limiting law enforcement agencies' use of certain investigative techniques previously available to the police?

It is entirely appropriate that the Bill of Rights has a provision addressing the individual citizen's right to privacy from government authorities. The authors of the Constitution knew how vitally important it was to protect citizens from violations of their privacy, especially with respect to invasions of their homes by agents of the government. It was in this context that the Fourth Amendment to the Constitution was drafted, debated, and ratified. That amendment reads as follows:
"The right of the people to be secure in their persons, houses, papers, and effects, against unreasonable searches and seizures, shall not be violated, and no warrants shall issue, but upon probable cause, supported by oath or affirmation, and particularly describing the place to be searched, and the persons or things to be seized."
The difficulties of policing a modern society and prosecuting criminal cases through the judicial system might suggest that the most speedy means of assembling a strong case against a defendant is best. Investigating officers who, in the course of doing their job, might view illegal items (ex: unregistered guns, drugs, etc) would naturally want to seize those items. The problem, however, is that these seizures may very well violate the wording and the spirit of the Fourth Amendment.
There have been quite a number of major court cases decided by the U.S. Supreme Court regarding the ability of law enforcement officers (and others, like school principals--Safford v. Redding, 2009) to seize evidence. Of particular interest happens to be one of the earliest of these decisions, Weeks v. United States. In this 1914 decision, the Supreme Court formally outlined what became known as "the exclusionary rule." The exclusionary rule is meant to discourage law enforcement from conducting illegal searches by stating that any evidence found in an illegal search cannot be used against the defendant in court. This decision represented one of the most important applications of the Fourth Amendment in the nation's history. In this particular case, police had searched and gathered evidence from Fremont Weeks' home without a warrant (court issued permission to search someone's property). The Supreme Court ultimately ruled that, because the evidence used to prosecute Weeks had been obtained without a proper warrant, it was inadmissible in court.
The question, then, is about impact on law enforcement's ability to execute their mission despite a series of Supreme Court decisions that have limited their ability to intrude on the privacy of others. Though the use of the "exclusionary rule" has resulted in the overturning of convictions and consequent release of "criminals," there is little to suggest that public safety has been threatened by the Courts' rulings. Of course, you can argue that the Fourth Amendment and of the Exclusionary Rule have, in some cases, undermined criminal investigations and potential prosecutions. The requirement for a properly obtained warrant, however, is a bedrock of American justice. (Additionally, history has clearly demonstrated that successful prosecutions can be built through the use of court-sanctioned warrants.)
There is little or no evidence that the Fourth Amendment and the Exclusionary Rule have impaired public safety. Though police might enjoy a legal system that allowed for warrantless searches, we can all recognize that the Bill of Rights, while subject to interpretation, is, or should be, absolute. 
 

How does George Orwell see the real nature of imperialism?

In many of his writings, Orwell views imperialism as a mechanism for economic power, for enabling the Western nations to have a higher standard of living by exploiting underdeveloped countries. However, in "Shooting an Elephant" he goes further and develops the theme of imperialism as a means by which the industrialized countries control their own populations.
In the narrative Orwell makes it clear that the British are hated by the Burmese, but also that Orwell, a British policeman, has no love either for the "native" population, including the seemingly benign Buddhist priests. It is impossible even for a policeman or a soldier having the best of intentions, and the most liberal mindset, to feel favorable to people who are constantly jeering him and taunting him on the street. The elephant incident brings these emotions of mutual dislike to a head.
Though the "natives" obviously resent the British presence, they also seem to have adopted the attitude that since the white man has put himself in charge, he is the one who can and must take care of all problems. When the elephant goes "must," running wild and causing havoc (including killing a laborer by stamping him into the ground), Orwell has no choice but to take action. He repeats over and over that "I did not want to kill the elephant," for he realizes that the attack of "must" is already passing. The elephant will soon become harmless again, and can be recaptured by its owner, with no further death or damage. Yet a crowd has gathered, urging him to neutralize the elephant, as it were. Because he's the white man, he is expected to act, despite his not wanting to, and despite the fact that the crowd of Burmese are not capable of forcing him to. It is to save face that Orwell must pull the trigger and kill the elephant.
It is at this point, as he holds the rifle, that Orwell has an epiphany about why imperialist countries act as they do. He has been put in a position—that of being forced to do something unnecessary and against his own moral code—where he lacks freedom, though as the white man he's supposed to be the one in charge. "When the white man turns tyrant, it is his own freedom he destroys....He becomes a hollow, posing dummy, the conventionalized figure of a sahib." In other words, both conquered and conqueror have become enchained as a result of the imperialist government's power-lust. The difficulty of killing the elephant, when Orwell has to pour shot after shot into him, is symbolic of the dysfunctionality and cruelty of the whole situation. When the elephant is felled, a shout of triumph goes up from the crowd, probably partly because they have at least unconsciously realized that this is a victory over not just the elephant, but over the British invaders as well.

Explain how the market system provides a strong incentive for technological advancement and creative destruction. Within your answer, provide 3 virtues of the market system. How does the circular flow model fit into this discussion?

There is a trite but true old adage, "Build a better mousetrap, and the world will beat a path to your door." While this may be true in any economic system, it is particularly so in a market economy.
A market economy is characterized by private control of the means of production, such as factories, raw materials, and capital. There is also private control of pricing, and private (individual and business) control of buying decisions (consumption). All of these decisions are, in theory, based on enlightened economic self-interest: sellers will try to maximize their profits, while consumers will try to satisfy their needs and wants at the lowest cost.
Another important characteristic of a market system is that it rewards scarcity. A classic model in microeconomics is the monopoly, where supply is restricted to drive up the price, rewarding the seller with a monopoly profit over and above what is needed to produce the goods and remain in business.
A person or firm that develops unique or superior technology and that can effectively protect that technology from being acquired by competitors (through patents, etc. and/or internal security), can effectively act as a monopolist as long as their technology remains both exclusive and superior. This has been the goal of countless inventors and "start-ups" for generations.
The circular flow model is useful in considering the economy's response to a successful new technology. Banks and the like provide financing for both buyers and sellers. Consider, for example, how the success of a new technology is likely to influence lenders in evaluating another new technology in a related field: the more money is coming from consumers of the new product, the more profit the producer is making and the more certain it becomes that loans made to fund the start-up will be repaid.

The market system (more commonly known as capitalism) is a system in which companies are owned by private individuals or organizations with the express purpose of making a profit.
The motivation for technological advancement in a capitalist economy is obvious: the more advanced a company is, the more quickly and efficiently it can operate and the higher its turnover and profits will be.
Creative destruction—doing away with long-established practices to pave the way for innovation—is highly sought after in market systems due to their competitive nature. In order to keep up with one's competitors, a company must constantly evolve.
Three virtues of the market system would be: firstly, there is greater innovation due to the incentive of profit; secondly, there is increased productivity in workers based on the incentive to gain and sustain employment in order to earn capital; and thirdly, businesses are streamlined and more efficient than they would be in a command economy.
This discussion involves circular flow of income because this model exemplifies the classic capitalist lifestyle of earning to spend and then needing to earn more.
https://www.investopedia.com/ask/answers/033015/what-are-some-advantages-market-economy-over-other-types-economies.asp

https://www.investopedia.com/terms/c/creativedestruction.asp

https://www.investopedia.com/terms/circular-flow-of-income.asp

The market system, also simply called capitalism, is a system wherein resources are privately owned and economic activity is generated and directed by fluctuations in the market, including changes in price. There are several virtues of this system which help incentivize technological advance and creative destruction—a process of "industrial mutation" which continuously seeks to improve the existing economic structure by destroying what does not work and freeing up resources to be better implemented (Joseph Schumpeter, 1942). These virtues might include:
1. In a capitalist system, people are working in their own self-interest and in pursuit of their own economic goals. Therefore, it is in their best interest to ensure the system is working as well, economically, as it can, because their ultimate goal is to make more money, which might be best achieved by destroying ineffective mechanisms and generating more efficient technology to achieve ends.
2. In the market system, the existence of the market itself incentivizes suppliers, inventors, merchants, and consumers to work with and compete against each other. Because of this competition, in pursuit of a higher market share, firms are incentivized to try out new things and be continually "better," technologically, than those they are competing against.
3. In a privately-owned market, although there is usually some intervention from the government in capitalist countries, decisions are effectively taken by the consumers and producers, rather than by the government. This spreads the economic risk and drives entrepreneurs to swing the market in their own direction through the production of new ideas and products.
"Circular flow" describes the interplay in the capitalist market which keeps it going and drives innovation: this is the flow of resources and revenue between purchasers and businesses, and between businesses and their suppliers. Economic resources and revenue flow between businesses and households, encouraging consumers to buy, and therefore incentivizing suppliers and entrepreneurs to continually innovate in pursuit of consumer money and purchasing power.
http://highered.mheducation.com/sites/dl/free/0070969523/837456/MicroeconomicsSampleChap02.pdf

Which inference can be best made about why the king is described as “semi-barbaric” rather than wholly barbaric?

The king is regarded as "semi-barbaric" in the sense that he has been influenced by his distant Latin neighbors. His ideas are described in the tale as "polished" and "sharpened" by Latin influence, which implies that he's steeped in the culture and learning of antiquity. However, despite this, he still retains vestiges of his indigenous heritage, whose barbaric nature manifests itself in the cruel "lady or tiger" punishment the king imposes upon those who displease him.
Yet there seem to be significant similarities between the "barbarism" of the king's own culture and the "civilized" life of the Romans. The king has a large arena in which brutal gladiatorial contests take place and in which the religiously unorthodox regularly meet a savage end at the claws and teeth of starving wild animals. This is precisely what used to happen in ancient Rome.
Had the king restricted himself to this form of punishment then perhaps he would've been regarded as fully civilized rather than in the least bit barbaric. The suspicion remains that his "lady or tiger" method of punishment is considered barbaric, not because it involves violence and bloodshed involved (after all, Roman punishments were often far worse), but because it is an expression of indigenous culture, which is not something imported from Rome and therefore deemed to be "uncivilized."