What elements in our current society is this story warning us about? How are we heading for this version of dystopian society?

Le Guin is warning us about elements that already exist in our society. The story was first published over thirty years ago, but the conditions it describes feel as relevant now as they did then. The elements of society that the story is representing are those in which someone is suffering for the benefit of someone else. One example is smart phones. These devices are made in China by people who are paid very little and work long hours. The work itself is repetitive and straining on hands and eyes, and the workers barely make enough to survive and live in poorly-maintained company-owned dorms as shown in this article.
America and other wealthy countries use up a disproportionately large portion of the worlds resources. According to the Worldwatch Institute, "the 12 percent of the world’s population that lives in North America and Western Europe accounts for 60 percent of private consumption spending, while the one-third living in South Asia and sub-Saharan Africa accounts for only 3.2 percent." For someone to have the good life, someone else must go without.
The story isn't warning us about the way things may become as much as it is acknowledging the disparity that already exists.

Le Guin published "The Ones Who Walk Away from Omelas" in 1973, and it holds up quite well as a cautionary tale today.  Le Guin has exaggerated for effect, of course, but in some ways it does feel as though we could be on our way to a dystopian society, at least in the United States, Western Europe, and perhaps a few other places in the world.  This is a personal perspective, and other people will no doubt have different views.  There are two elements to Le Guin's tale to consider, first, the hiding of unpleasantness and second, the neglect or mistreatment of those we do not want to see.  Let's look at some examples of this "first world" problem. 
Consider the treatment of the homeless in society.  People do not want to see the homeless in their communities.  Merchants complain that consumers will not shop in areas where there are homeless people on the streets.  The police complain that they make more work for them.  Middle-class people cringe when they see them.  The solution -  to hide them, of course!  Shelters are one way, and simply driving them away so they can go somewhere else is another.  There are remarkably few programs designed to attack the problems that make people homeless in the first place.  But if we can't see them, as we cannot see that child hidden away, we can be perfectly happy. The homeless are just one sacrifice to our happiness.
Today, in the United States, in addition to being racially segregated, communities are more socioeconomically segregated than ever before.  This is our way of keeping the child hidden from our view.  Who wants to see unpleasant poor people all the time, people who look tired and hungry, people who don't wear the latest styles, people who do not speak as we speak?  In my own city, public housing was originally built as far away as possible from nice neighborhoods.  If we can surround ourselves with people like us, we don't have to look at all those people and be reminded that they exist. We sacrifice the poor on the altar of prosperity.  
Prisons in the United States are overwhelming filled with African-American and Latino poor people. This is another good way to hide these people we don't want to see. It is not a coincidence that the consequences of using a cheaper form of cocaine has led to severe sentences, while the use of the more expensive version has not.  It is not a coincidence that many of the people incarcerated are mentally ill.  These are the child in the story.  These are the people we don't want to see. If we hide them away in cages, our lives will be all sunshine and blue skies.  If we can just sacrifice enough of these people, all will be well. 
Immigrants are another group people feel somehow ruin their nice lives. And in fact, one presidential candidate has risen to his present heights on the platform of deporting them and keeping others from coming in.  We need not just put them in the basement; we can get rid of them altogether.  If we do that, America will somehow be great again, great because we won't have to deal with these needy people who want to pursue the American dream, too. 
The only light on the horizon I have seen has been the mainstreaming of the disabled, in schools and in employment.  When I was in elementary school, the learning disabled were confined to one classroom in the basement of the school, tucked away just like the child in Omelas.   Learning disabled students are to a large degree part of regular classrooms, and I often see disabled people working in my own neighborhood.  And yet, I hear grumbling about this, too, from people who do not want to see this.  It somehow ruins people's pretty pictures of the world. 
I would say that the story has a great deal of resonance in today's world, or at least in many parts of it.  We do not want to even see imperfections, much less ameliorate them.  Our happiness, we believe, depends upon hiding these imperfections away, our own form of sacrifice to the gods.   

What are some reasons why Odysseus should not be immortalized?

Odysseus is an important literary figure and thus it makes sense that students should continue to read the Homeric epics and learn about him. However, there is a difference between studying someone and idolizing or emulating that person.
Odysseus is a trickster figure such as Loki in Norse mythology or Coyote in the Native American tradition. What this means is that he is clever, but often unscrupulous. Two of his major exploits, the Trojan Horse and his defeat of the Cyclops, revolve around deception. A particularly morally questionable act is the deception he uses to try to obtain the bow of Philoctetes, as seen in Sophocles's play.
In Homer, Nestor combines wisdom with a strong moral compass as opposed to Odysseus who is clever but often seems more self-serving. While Odysseus's cleverness is essential to the defeat of Troy, and often tactically superior to more straightforward stratagems, the fact that he lies without remorse and is willing to use shady means to achieve his ends makes him a less than an ideal character to emulate.

What are some examples of hypocrisy in The Man That Corrupted Hadleyburg?

Mark Twain's novella, for all its humor, is a melancholy discourse on human frailty. The title is ironic, because Hadleyburg has actually not been corrupted by the mysterious stranger. It was, in fact, corrupt to begin with.
The central hypocrisy of the town lies in its complacent perception of itself. When the Richardses are trying to figure out who did the good deed of giving the stranger the twenty dollars, they conclude it must have been Barclay Goodson, because no one else in the town would have done it—in other words, everyone else was too ungenerous. And Goodson was the most hated man in Hadleyburg, except for the Reverend Burgess. The minister is hated for having committed some indiscretion; Mr. Richards is the only one who knew Burgess to be innocent, but he kept this knowledge to himself out of cowardice. As Richards confesses on his death bed,

You know the thing that was charged against Burgess years ago. My testimony, and mine alone, could have cleared him, and I was a coward, and left him to suffer disgrace—

Yet Richards is outwardly presented in Mark Twain's narrative as if he is still a kind of exemplar of virtue, at least in comparison with the rest of the town. It's significant that the most hypocritical thing about Richards is his having destroyed the relationship between Goodson and his fiancee, Nancy Hewitt, by revealing that Nancy has partial African American ancestry. The information is given to us almost in passing, but it is typical of Mark Twain's understated criticisms of America's hypocrisy about race. Richards seems to look back at this, without irony, as a "good deed" for which Goodson has been grateful to him.
Perhaps the saddest thing in the entire story is that the elderly Richardses really are, in spite of their own faults, more deserving than anyone else in the town of the "reward" represented by the sack of gold-painted lead coins. The bogus nature of this fortune is emblematic of Hadleyburg's hypocrisy and of the meaninglessness of the material wealth this most "honest and upright town in all the region" has obsessed over.

The sanctimonious tone with which the incorruptible reputation of Hadleyburg is established at the beginning of the story makes it clear that its people cannot be or cannot remain as honest as they appear. When Mary and Edward Richards are discussing who could have given the stranger $20, they both agree that the only person charitable enough to do so was Barclay Goodson, who was hated in Hadleyburg because he was honest about the community's faults. Edward then reveals that the only other man hated as much as Goodson, the Reverend Burgess, was wrongly accused in a matter when Edward knew he was innocent, but was too cowardly to declare it. Hypocrisy was obviously present in Hadleyburg long before the bag of gold arrived there.
The hypocrisy of eighteen of the claimants to the gold is made public in part III of the story, when the Reverend Burgess reveals the false basis of their claims. The actual message in the bag is rather ingenious, since no loyal citizen of Hadleyburg would wish to be caught comparing the town unfavorably with Hell. Therefore, even if anyone had been able to produce the entire remark, s/he would have been marked out as hypocritical for describing the town in this way while pretending to be proud of its honesty. Mary and Edward are hypocritical in exactly the same way as Edward was when he failed to clear the name of the Reverend Burgess, through silence. Later, however, they renounce their hypocrisy, which has been making them anxious and unwell, confessing their guilt and failing to cash the checks the stranger gives them as a result of their deception.

A good portion of The Man That Corrupted Hadleyburg, by Mark Twain, is centered around exposing hypocrisy. The people of Hadleyburg pride themselves on being upright citizens, unable to be corrupted. There are nineteen couples/families who are considered the "principal citizens" of the town, and they all think themselves to be the most morally upstanding people you could find.
However, in pursuit of the stranger's gold, each and every single member of those nineteen couples becomes a hypocrite. They all claim to be incorruptible and to never give in to temptation. But when the stranger gives each of them the opportunity to lie in order to achieve great wealth, not a single one of them turns down the chance—this makes them hypocrites. Each couple is exposed for their hypocrisy, except for the Richards, who essentially die of extreme anxiety and guilt, thinking that their fellow townspeople know about their dishonesty.
Edward Richards was also a hypocrite at a point before the story starts—Burgess was accused of something he did not do (we never learn the specifics of the accusation), and Edward knew he was innocent. Despite his claims of being an entirely honest man, Edward did not defend Burgess, fearing disapproval from others.

What is the meaning of the quote "Lottery in June, corn be heavy soon"?

Old Man Warner, the oldest man in town, repeats this old saying in Shirley Jackson's "The Lottery" as a way to express his disdain for other communities that have decided to give up the lottery as a community tradition.
The saying, "Lottery in June, corn be heavy soon" is meant to sound like an aphorism, or an old saying that goes back so far in time, it can't be argued, altered, or ignored. The inclusion of the lottery in an aphorism makes the existence of the lottery as normal and commonplace and inevitable as a June rainstorm or a July harvest of corn.
The fact that Old Man Warner is the speaker of the saying indicates that the tradition of the lottery goes back generations and generations; if he, the oldest man in town, repeats a saying of this old style, the tradition behind it must go back even further than the reader might have expected at the start of the story.

What details suggest Jim and Della are capable of sacrifice in "The Gift of the Magi" by O. Henry?

What do you predict jim's gift will be? Explain. 
In the gift of the magi

Della and Jim Dillingham are willing to sacrifice their most prized possessions to buy each other a Christmas present.
In the exposition of "The Gift of the Magi," Della counts over the little money she has saved, recalling with some shame how she saved money by "bulldozing the grocer and vegetable man and the butcher." Della bartered with them to try to save some money for Jim's Christmas gift. Della's loving intentions are apparent from the beginning. When she sells her luxurious hair of which she is so proud, Della's willingness to sacrifice whatever she can to give a nice present to her husband is even clearer.
Similarly, in order to purchase a gift for his beloved wife, Jim Dillingham is willing to relinquish his gold watch, his only prized possession, which is an heirloom passed from his grandfather to his father and now to him. Moreover, his unselfish love for Della is certainly evinced when he sees Della sold her hair; he does not become angry or resentful that he sold his watch unnecessarily, as Della can no longer use the hair combs Jim purchased with the money he received for the watch.
When they each receive their gifts, neither makes any begrudging remark. Instead, Della hugs the combs and says positively, "My hair grows so fast, Jim!" Jim, too, reacts positively, saying, "Della... let's put away our Christmas presents and keep 'em awhile." Their love for each other is worth any sacrifice.

Single Variable Calculus, Chapter 5, Review Exercises, Section Review Exercises, Problem 36

Determine the derivative of the function $\displaystyle f(x) = \int^{\sin x}_1 \frac{1-t^2}{1+t^4} dt$ using the properties of integral.
$\displaystyle \frac{d}{dx} \int^{\sin x}_1 \frac{1-t^2}{1+t^4} dt = \frac{d}{dx} \left( \int^u_1 \frac{1-t^2}{1+t^4} dt\right)$

$
\begin{equation}
\begin{aligned}
g'(x) &= \frac{d}{du} \left( \int^u_1 \frac{1-t^2}{1+t4} dt \right)\\
\\
g'(x) &= \frac{d}{du} \left( \int^u_1 \frac{1-t^2}{1+t^4} dt \right) \frac{du}{dx}\\
\\
g'(x) &= \frac{1 - u^2}{1+u^4} \frac{du}{dx}\\
\\
g'(x) &= \frac{1(\sin x)^2}{1+(\sin x)^4} \cdot \cos x\\
\\
g'(x) &= \frac{\left( 1 - \sin^2 x\right)(\cos x)}{1 + \sin^4 x} && \Longleftarrow \text{ (Apply Pythagorean Identity } \sin^2 \theta + \cos^2 \theta = 1)\\
\\
g'(x) &= \frac{\left( \cos^2 x \right)(\cos x)}{1 + \sin^4 x}\\
\\
g'(x) &= \frac{\cos^3 x}{1 + \sin^4 x}
\end{aligned}
\end{equation}
$

How is Mel's discussion of love ironic?

Mel, a cardiologist, is talking as if he is an expert on love, on matters of the heart. As Nick, the narrator, says with ill-concealed irony,

My friend Mel McGinnis was talking. Mel McGinnis is a cardiologist, and sometimes that gives him the right.

And yet, despite his alleged expertise in the matter, Mel experienced an acrimonious divorce from his first wife, Marjorie. Mel thinks he can illustrate the meaning of true love by an anecdote about an old man and his wife he treated in the hospital after they had been in a near-fatal car accident. However, his recounting of the story is punctuated by persistent bickering with his current wife, Terri. We sense that all is not well in the marriage, making Mel's claim to know the true meaning of love all the more ironic.
Furthermore, Mel heaps scorn on the idea that Terri's ex-husband Ed was motivated by love for her when he committed suicide. At the same time, however, he is so lacking in self-awareness that he fails to see the parallel between his own anger at Terri and the physical violence that Ed often displayed toward her. As Mel believes that love is purely spiritual, he is unable to acknowledge that it can also be displayed through actions and words.

Why is Portia upset?

Although Portia is a young woman, she has already grown “aweary of this great world” (act 1, scene 2). In her conversation with Nerissa, her maid, she admits the disadvantages of having a “hot temper,” and that her situation is better than most people’s, as she stands to inherit a fortune. We assume that her father had died a while ago because she is no longer in mourning. Portia is bound to the terms of his will, and the concept she is stuck on is “choose.” She keeps hoping for sympathy from Nerissa regarding the apparently airtight terms of her father’s will: “Is it not hard, / Nerissa, that I cannot choose one nor refuse none?” Nerissa defends the dead man’s “virtue” and “good inspirations.”
Portia has already embarked on the quest for her future husband according to the will’s terms: it is a lottery system, by which the man who chooses correctly among three caskets will be the one she marries. Her father was totally confident in the system he devised, which includes hidden meanings assigned to each casket. As Nerissa puts it, these messages ensure that Portia will “never be chosen by any / rightly but one who shall rightly love.” From the suitors she has met so far, Portia remains unconvinced. One only talks about his horse, another does nothing but frown, another is frivolous, and so forth. As the German lord drinks nonstop, Portia laments: “I will do any / thing, Nerissa, ere I'll be married to a sponge.” In sum, she is worried that no one will prove suitable:

If I live to be as old as Sibylla, I will die as
chaste as Diana, unless I be obtained by the manner
of my father's will.
http://www.opensourceshakespeare.org/views/plays/play_view.php?WorkID=merchantvenice&Act=1&Scene=2&Scope=scene

When the audience is first introduced to Portia in act 1, scene 2, she is in a melancholy mood and laments to Nerissa about her difficult situation. Portia expresses her displeasure regarding her inability to choose the person she wants to marry. Portia has agreed to honor her deceased father's wishes that she will marry the suitor who chooses the correct casket. In order to win Portia's hand in marriage, her suitor must read several riddles and choose from three caskets made out of three different materials. In one of the three caskets is a portrait of Portia, which indicates that the suitor has chosen the correct casket. Not only is Portia upset that she cannot choose the man she wants to marry, but she is also depressed about her current suitors. As Nerissa proceeds to describe Portia's suitors, Portia highlights their various undesirable character traits and is disturbed that one of them might become her future husband. Overall, Portia is upset because she is powerless to marry who she wants and does not have positive feelings about any of her current suitors.

Calculus of a Single Variable, Chapter 5, 5.5, Section 5.5, Problem 33

To solve a logarithmic equation, we may simplify or rewrite it using the properties of logarithm.
For the given problem log_(3)(x^2)=4.5 , we may apply the property:
a^((log_(a)(x))) = x
The "log" cancels out which we need to accomplish on the left side of the equation.
Raising both sides by the base of 3:
3^((log_3(x^2))) = 3^(4.5)
x^2= 3^(4.5)
Taking the square root on both sides:
sqrt(x^2) =+-sqrt(3^(4.5))
x= +-11.84466612
Rounded off to three decimal places:
x=+-11.845 .
Plug-in the x-values to check if they are the real solution:

log_3(11.845^2)=4.5 so x = 11.845 is a real solution.

Now let x=-11.845
log_3((-11.845)^2)
log_3(140.304025)=4.5 so x = -11.845 is a real solution.

So, x= 11.845, x = -11.845 are both solutions.

Which of the boxplots in the enclosed image is skewed with an outlier?

In the attached image, the boxplot for Region C is both skewed and has an outlier. 
 
In statistics, a  boxplot is a way to show numerical data in their quartiles. A boxplot consists of a rectangle with two "whiskers" extending in each direction. The rectangle at the center of the boxplot represents the interquartile range (the first quartile to the third quartile). The line inside of the rectangle represents the median. The whiskers on either side of the rectangle can represent different things, but commonly represent the minimum and maximum.
 
A boxplot is skewed if the data set is not symmetric. A simpler way to understand the concept of a skewed boxplot is to think of slicing the box down the middle. Are the two halves roughly mirror images of each other? If they are, the boxplot is symmetric. If the two halves are not mirror images of each other, the boxplot is skewed.
 

Outliers in statistics are simply points of data that are distant from other observations. In a boxplot, outliers are shown by floating points that are linearly plotted alongside the box and whiskers.
 
Knowing the definitions above, we can refer back to the attached image, and define the following properties for the data in boxplot C:

It is skewed because the box portion of the graph is asymmetrical.
It has an outlier because there is a point floating outside the box and whiskers on the right side.  
http://www.physics.csbsju.edu/stats/box2.html

Please write a summary of the article "Exploring the impact of police officer education level on allegations of police misconduct" by Jennifer Manis, Carol Archbold, and Kimberley D. Hassell.

In their scholarly article “Exploring the Impact of Police Officer Education Level on Allegations of Police Misconduct,” (International Journal of Police Science and Management, December 1, 2008), authors Jennifer Manis, Carol Archbold, and Kimberley D. Hassell set out to determine whether a positive correlation exists between the level and type of education police officers received and the propensity for complaints against them for police misconduct.
The relationship between levels of education among police officers and performance of duties by those officers has been the subject of considerable study over the past several decades. Many police departments have in fact imposed more stringent academic requirements on potential police officer candidates over the past 30 years, with a college degree becoming the minimal level of education required as opposed to a mere high school diploma (or GED equivalency). Understanding the laws that they are sworn to enforce and how to interact with a socially, culturally, and ethnically diverse public, it was determined, required a higher level of education. Additionally, those with college degrees almost by definition are older and more emotionally mature than those who apply to law enforcement academies with a high school diploma.
Manis, Archbold, and Hassell did not merely seek to understand the correlation, if it exists, between level of education and likelihood of being accused of misconduct. They also sought to determine whether the type of degree or field of study emphasized bore any relationship to the likelihood of such accusations. In other words, they sought to determine whether a degree in Criminal Justice would better prepare police officer candidates for the arduous task of enforcing laws than degrees largely unrelated to law enforcement (e.g., Political Science, Humanities, etc.). The authors’ findings indicated that no such correlation exists between the type of degree and the propensity for a police officer to face charges of police misconduct. That, then, is the conclusion of Manis, Archbold, and Hassell’s study: The type of college degree earned bore no relationship to probabilities of misconduct. Police officers with backgrounds in Criminal Justice were neither less likely to be accused of police misconduct than those with degrees in other fields of study nor more likely to be accused.

Precalculus, Chapter 9, 9.5, Section 9.5, Problem 33

You need to use the binomial formula, such that:
(x+y)^n = sum_(k=0)^n ((n),(k)) x^(n-k) y^k
You need to replace x^2 for x, y^2 for y and 4 for n, such that:
(x^2+y^2)^4 = 4C0 (x^2)^4 + 4C1 (x^2)^3*(y^2)^1 + 4C2 (x^2)^2*(y^2)^2 +4C3 (x^2)*(y^2)^3 +4C4 (y^2)^4
By definition, nC0 = nCn = 1, hence 4C0 = 4C4 = 1 .
By definition nC1 = nC(n-1) = n, hence 4C1 = 4C3 = 4.
By definition nC2 = nC(n-2) = (n(n-1))/2 , hence 4C2 = (4(4-1))/2 = 6
(x^2+y^2)^4 = x^8 + 4(x^6)*(y^2) +6 (x^4)*(y^4) +4 (x^2)*(y^6)+ (y^8)
Hence, expanding the complex number using binomial theorem yields the simplified result (x^2+y^2)^4 = x^8 + 4(x^6)*(y^2) +6 (x^4)*(y^4) +4 (x^2)*(y^6)+ (y^8).

What does Austen mean by "sense" and "sensibility"?

The terms “sense” and “sensibility” are used to describe the personalities of Elinor and Marianne Dashwood, the two sisters who serve as protagonists in the novel. “Sense” refers to common sense. Elinor is the level-headed one of the two, keeping her emotions in check. She maintains this control throughout the course of the novel, as she watches the man she loves, Edward Ferrars, stay true to Lucy, the woman he is secretly engaged to. Though he has fallen in love with Elinor, he is a man who keeps his promise, putting aside his own feelings, which makes him an ideal companion for Elinor.
“Sensibility,” which describes Marianne, is closer to our current usage of the word “sensitivity.” Marianne’s emotions are worn proudly on her sleeve. She falls in love easily but unwisely with the dashing Willoughby. He breaks her heart, choosing instead to marry a wealthier woman.
Both Elinor and Marianne must take on some of the characteristic of the other in order to resolve their relationships. In the end, Elinor marries Edward (after Lucy marries his brother), while Marianne marries the more stable Colonel Brandon.

Calculus: Early Transcendentals, Chapter 6, 6.1, Section 6.1, Problem 33

The red curve refers to the graph of the first function: y =xsin(x^2) while the the the blue curve refers to the graph of the second function: y=x^4 .



As shown in the xy-plane, the two graphs intersect , approximately, at the following points: (0,0) and (0.9,0.65).
Based on these intersection points, the limits of integration with respect to x will be from x= 0 to x=0.9.
The formula for the " Area between Two Curves" is:
A= int_a^b[f(x)-g(x)]dx
such that f(x)gt=g(x) on the interval of [a,b].
This is the same as A = int_a^b[y_(above) - y_(below)]dx
where the bounded area is in between y_(above) = f(x) and y_(below)= g(x) .

Applying the formula on the given problem, the integration will be:
A = int_0^(0.9)[x*sin(x^2) - x^4]dx
= [-(cos(x^2)/2) -x^5/5] |_0^(0.9)
= [-(cos((0.9)^2)/2) -(0.9)^5/5]-[-(cos((0)^2)/2) -0^5/5]
=-0.4628472164 - (-0.5)
= -0.4628472164 + 0.5
= 0.03715278360
~~ 0.0372 as the Area of the region bounded by the curves shown above.

Single Variable Calculus, Chapter 7, 7.2-2, Section 7.2-2, Problem 46

Find an equation of the tangent line to the curve $y = \ln (x^3 - 7)$ at the point $(2, 0)$.


$
\begin{equation}
\begin{aligned}

\text{if } y =& \ln (x^3 - 7), \text{ then}
\\
\\
y' =& \frac{\displaystyle \frac{d}{dx} (x^3 - 7)}{x^3 - 7}
\\
\\
y' =& \frac{3x^2}{x^3 - 7}

\end{aligned}
\end{equation}
$


Recall that the first derivative is equal to the slope of the tangent line at some point.

Thus, at point $(2, 0)$,


$
\begin{equation}
\begin{aligned}

y' =& \frac{3(2)^2}{2^3 - 7}
\\
\\
y' =& 12

\end{aligned}
\end{equation}
$


Therefore, the equation of the tangent line to the curve can be determined by using the point slope form.


$
\begin{equation}
\begin{aligned}

y - y_1 =& m (x - x_1)
\\
\\
y - 0 =& 12 (x - 2)
\\
\\
y =& 12 x - 24

\end{aligned}
\end{equation}
$

What is the main theme in "Birches"?

Frost's main theme in "Birches" is that life is beautiful and good, more desirable than heaven. He was 40 when he published the poem, and it reveals the feelings of a man in middle age looking both ahead toward death and backward to childhood.

Frost shows the beauty of nature in his imagery surrounding the birch tree. In the passage below, it has been bowed down by winter's ice, but now the weather is warm enough that the ice begins to melt and shatter:

Soon the sun's warmth makes them shed crystal shells
Shattering and avalanching on the snow-crust—
Such heaps of broken glass to sweep away
You'd think the inner dome of heaven had fallen.

The ice is so beautiful that Frost likens it to the dome of heaven falling.

This tension between earth and heaven, childhood and adulthood, runs through the poem. The permanently bowed rich trees might make us think of aged people, but Frost associates this bowed look with youth, such as of girls on their hands and knees, throwing their damp hair over their faces to dry in the sun.

In the end, the poem's main theme is a longing for the earth and a deep aching appreciation of what life has to offer. Even when living brings sadness, Frost doesn't want to die or go to heaven. Instead, he writes:

I'd like to get away from earth awhile


And then come back to it and begin over.

He also writes that he'd like to go "toward" heaven by climbing up a birch tree, but be set down again on earth:


Earth's the right place for love:
I don't know where it's likely to go better.
I'd like to go by climbing a birch tree,
And climb black branches up a snow-white trunk

Toward heaven, till the tree could bear no more,
But dipped its top and set me down again.

In "Birches," Robert Frost uses a natural phenomenon, the bending of birch trees when they become covered with ice, as a vehicle for expressing a deep and reverent love for living. In his imagination, he thinks of the birch branches being bent by a boy swinging on them and leaving his permanent mark as he conquers them one by one.
The poem takes a turn from admiring the beauty of the natural world, the sight of gracefully bent birch branches, to an examination of where the speaker is in his life:

So was I once myself a swinger of birches
And so I dream of going back to be.

He dreams of his carefree boyhood, gently lamenting that in adult life, life can feel "like a pathless wood" that delivers setbacks and painful, even if minor, injuries. The speaker wishes for the opportunity to live his life again and dreads the time when he will be taken away from Earth, "the right place for love," never to return.

y=(x^2+11x+18)/(2x+1) Graph the function.

We are asked to graph the function y=(x^2+11x+18)/(2x+1) :
Factoring the numerator yields:
y=((x+9)(x+2))/(2x+1)
There is a vertical asymptote at x=-1/2. The x-intercepts are at -2,-9.
There is no horizontal asymptote as the degree of the numerator is greater than the degree of the denominator. The slant asymptote, found by division, is y=1/2x+21/4.
The graph:

 
 

What are the 3 basic memory processes? How does each work to permit memory?

This is a very basic look at the three processes of memory. There is a massive amount of highly technical information about this topic, and there are also many things we don't yet have a full understanding of. This just scratches the surface.
Encoding: The brain encodes when it receives sensory information. Short-term memories are not retained. Long-term memories are strengthened by the power of the perceived event and by repetition. Encoding can happen in four ways:
Visual encoding—what we see.
Auditory encoding—what we hear.
Tactile encoding—what we touch.
Semantic encoding—information we encode based on particular meanings or contexts.
Storage: Once encoding is complete, we have a memory stored in our brain. It is thought that a memory is not necessarily stored in just one place, but in multiple places in the brain, possibly to make it easier to avoid losing memories. The memory is stored in the form of neurons that behave in a way that recreates the original event—making us “remember” it.
Recall: Also sometimes called “retrieval,” this is the process of accessing the information that has been stored in our brains in the form of long-term memories. There are two ways to access memories: recognition (as when you see a familiar object or person, then remember what or who it is), and recall (as when you remember a fact or information you do not currently have before you). When we forget something or lose a memory, it is thought by many scientists that the recall process has failed, rather than the storage process.
https://human-memory.net/memory-recall-retrieval/

https://science.howstuffworks.com/life/inside-the-mind/human-brain/human-memory.htm

Single Variable Calculus, Chapter 1, 1.3, Section 1.3, Problem 60

Assume that you invest $x$ dollars at 4% interest compounded annually, then the amount $A(x)$ of the investment after one year is $A(x) = 1.04x$. Find $A \circ A$, $A \circ A \circ A$, and $A \circ A \circ A \circ A$. What do these compositions represent? Write a formula for the composition of $n$ copies of $A$.



$
\begin{equation}
\begin{aligned}


A \circ A =& 1.04 (1.04x) &&= 1.0816x , \quad \text{ total investment after 2 years.}\\

A \circ A \circ A =& 1.04 (1.04)(1.04x) &&= 1.249x, \quad \text{ total investment after 3 years.}\\

A \circ A \circ A \circ A =& 1.04(1.04)(1.04)(1.04x) &&= 1.699x , \quad \text{ total investment after 4 years.}\\

\end{aligned}
\end{equation}
$



These compositions represent the growth of interest after $"n"$ years. Therefore, the total investment after $"n"$ years can be written as $ \cdots$


$A(x) = 1.04^n (x)$

What questions remained after the Civil War was over?

The status of the freed people in the southern (and border) states was the principal issue left unresolved in 1865 at the close of the war. There was, in fact, the closure established by the complete Union victory and the Constitutional amendments outlawing slavery and making all people of any race citizens of the United States. After a brief period during Reconstruction when the federal government under Grant's administration did what it could for African Americans federal troops were withdrawn, and the southern states implemented Jim Crow laws to enforce segregation and oppression. This situation lasted for another 90 years.
Though not directly related to the war, two other issues in US life remained unresolved as of 1865. Unfair conditions of free labor continued to exist at least until unionization began late in the nineteenth century. And there was no closure or fairness in the treatment of Native Americans. The US army continued to fight an ongoing war with the indigenous people, and given that the Civil War was over, full attention was devoted to the completion of the transcontinental railway, accomplished in 1869. White settlement in the far west was accelerated, and within just over 20 years the last resistance of the indigenous population to the takeover of their land was defeated. With the situation of non-white peoples overall, the country had not fulfilled its promise of freedom and equality.

The end of the Civil War brought about an end to the attempts of southern secessionists, however, it also left open many questions on how to move forward as a nation. The country struggled with a number of questions that were not easily solved.
First of all, what was to be done with the leaders of the Confederacy and the soldiers who fought for them? Confederate President Jefferson Davis had led a rebellion against the United States. His soldiers had waged war against the federal army and killed its soldiers. A debate ensued over how they should be punished. Some wanted Confederate leaders hung as traitors. Others pushed for clemency in the name of peace and reconciliation. In the end, clemency was granted when President Andrew Johnson granted a pardon to anyone who took part in the Confederate rebellion.
There was also the question of all the newly liberated slaves. Four million African Americans were liberated as a result of emancipation. How they were to adjust to a life of freedom was a big concern. The Federal Freedman's Bureau was set up to aid in their transition. It provided education, food, clothing, and job training for hundreds of thousands of newly freed former slaves.
The military occupation of the former secessionist states was another question after the end of the Civil War. After the war and during Reconstruction the Federal Army occupied the former Confederate States. It was unclear how long they would need to be there in order to safeguard African American rights and stamp out any lingering secessionist tendencies. It was decided that the occupation would continue until the occupied states ratified the post-war constitutional amendments.

What is an example of irony in the story "The Necklace" by Guy de Maupassant?

"The Necklace" by Guy de Maupassant is an ironic story in the sense that Mathilde Loisel was ultimately brought down by what she wanted most in life — expensive things. Mathilde was a pretty girl who was raised in a modest family, but she always wanted to be rich. Even when she married a clerk, she still desired riches out of her reach. One day, Mathilde's husband brought her an invitation to a lavish party, but Mathilde did not want to go because she did not think she owned anything enough to wear to the party. Her husband encouraged her to wear her best ball gown, but she did not think it was good enough. She went to Madame Forrestier and borrowed one of her best necklaces for the party. Mathilde loved the necklace and the attention it brought her at the party; she finally had the fame she always coveted. It was not until after the party that Mathilde realized she lost the necklace. In a panic, Mathilde and her husband went to a jeweler to attempt to replace the necklace. An exact replica would cost 36000 francs, far more than the humble clerk's salary. The couple borrowed money at usurious rates. Mathilde worked as a maid to help pay off the loans. The couple did this for ten years. After ten years, Mathilde ran into Madame Forrestier again. Madame Forrestier commented that Mathilde looked terrible, and Mathilde explained she lost Madame Forrestier's necklace and bought her another one to replace it. At that point, Madame Forrestier told Mathilde the necklace was a piece of costume jewelry made of paste that cost less than 400 francs. This is the irony of the situation. Mathilde coveted fame and riches her entire life, but was miserable when she got it. The jewelry she borrowed thinking it was worth so much was something she could have easily bought in a novelty shop.  
https://americanliterature.com/author/guy-de-maupassant/short-story/the-necklace

Why is Banquo the only person Macbeth fears?

In Act III, Scene 1, Macbeth expresses his fear of Banquo and his desire to have him murdered.

There is none but heWhose being I do fear; and under himMy genius is rebuked, as it is saidMark Antony's was by Caesar. He chid the sisters,When first they put the name of King upon me,And bade them speak to him; then prophet-likeThey hail'd him father to a line of kings:

Macbeth appears to fear Banquo mainly because the three witches promised Banquo that his offspring would be a whole line of Scottish kings. This obviously gives Banquo a good motive for wanting Macbeth dead. Macbeth can't tell what Banquo is thinking, though. He may be plotting to assassinate Macbeth, or he may be content to wait for Macbeth to die. Banquo makes Macbeth feel inferior, as Octavius Caesar made Mark Antony feel inferior when they shared the rulership of the Roman Empire. Shakespeare records Antony's feelings about Octavius in his play Antony and Cleopatra. Macbeth has become king, but he never really feels like a king. He might feel more self-confident if he had an heir to succeed him on the throne, but he and his wife are childless. Banquo appears to be full of confidence, and he has a son named Fleance who could conceivably become king of Scotland if Macbeth died or was assassinated. Banquo really looks like a king. Macbeth says of him in the same soliloquy quoted above:

Our fears in BanquoStick deep, and in his royalty of natureReigns that which would be fear'd. 

Macbeth hopes to relieve himself of his multiple fears by having both Banquo and Fleance assassinated. In this same scene, he has a meeting with the two murderers he has recruited to kill Banquo and Fleance. It seems significant that Macbeth does not consider killing Banquo himself. This may be at least partly because he is afraid of him.

int 1 / ((x-1)sqrt(x^2-2x)) dx Find or evaluate the integral by completing the square

We have to evaluate the integral: \int \frac{1}{(x-1)\sqrt{x^2-2x}}dx
We can write the integral as:
\int \frac{1}{(x-1)\sqrt{x^2-2x}}dx=\int \frac{1}{(x-1)\sqrt{(x-1)^2-1}}dx
  Let x-1=t
So , dx=dt
hence we can write,
\int \frac{1}{(x-1)\sqrt{(x-1)^2-1}}dx=\int \frac{1}{t\sqrt{t^2-1}}dt
 Let u=t^2
So, du=2tdt
implies, dt=\frac{1}{2t}du
Therefore we have,
\int\frac{1}{t\sqrt{t^2-1}}dt=\int \frac{1}{t\sqrt{u-1}}.\frac{du}{2t}
                  =\int \frac{1}{2u\sqrt{u-1}}du
Now let v=\sqrt{u-1}
So, dv=\frac{1}{2\sqrt{u-1}}du=\frac{1}{2v}du
Hence we have,
\int \frac{1}{2u\sqrt{u-1}}du=\int \frac{2vdv}{2(v^2+1)v}
                   =\int \frac{dv}{v^2+1}
                    =tan^{-1}(v)+C  where C is a constant.
                     =tan^{-1}(\sqrt{u-1})+C
                      =tan^{-1}(\sqrt{t^2-1})+C
                      =tan^{-1}(\sqrt{(x-1)^2-1})+C
                       =tan^{-1}(\sqrt{x^2-2x})+C
 

Why is Christian education a necessity in the modern age?

A Christian would likely choose Christian education because it helps strengthen the faith "triangle." The three parts of that triangle are church, home, and school. A family can effectively teach a child from a Christian perspective at home. That teaching might include Bible stories, basic tenets of faith, and behavior from a Christian perspective. Going to church will further deepen and bolster a child's faith education. He or she will be a part of the larger Christian community by attending church.  
Attending a Christian school will even further integrate faith into that child's life. Church is maybe 90 minutes per week, which, if that is the only time a person spends on his or her faith every week, is not a lot of focus on faith and religion. Family time can increase that, but for at least 35-40 hours per week a child is in school, not in church or spending time with his or her Christian family. Attending a Christian school allows a child to learn the standard curriculum mandated by the state while at the same time having it taught from a Christian perspective. The faith base and standard education are woven together instead of being held separately, which public schools require.  
Christian families also might choose Christian education because private, Christian education often hold students to higher standards than public schools. Consequently, test scores and college admittance rates are frequently higher for students in private, Christian schools.  
Christian families also may choose Christian education because their child is more likely to be surrounded by friends and families who share the child's basic understanding of morals and behavior. This reinforces what the family teaches at home and what the church teaches on Sundays. 
Churches often encourage Christian education because students educated in Christian schools are more likely to make church attendance a part of their life for their entire life. A study was done on this very concept a few years ago. It is called the Cardus Education Survey. I've attached the findings for you in the 'Sources' section below.  
As for Christian education being a necessity in the modern age, I can't confidently claim it is an absolute necessity. I teach in a Christian school, and believe in all of the advantages that I wrote above. I also believe a child can receive a good education from a public school and grow up to be a strong Christian as well. If a family's goal is to teach a child that the Christian faith is all encompassing, and that faith is integral to all aspects of life and subjects, then only having the child learn about faith and God at home and in church presents the child with a lopsided Christian worldview. In that light, Christian education is necessary to educate a child about God and religion in as many aspects of his or her life as possible. 
http://www.tpcs.org/about-us/Cardus-Cardus_Education_Survey_Phase_I_Report.pdf

What was Thomas Jefferson's view on the economy?

Thomas Jefferson had several views regarding the economy. He believed the federal government should play a very limited role in the lives of the American people. This included having a limited government role in the economy. Thomas Jefferson got rid of unpopular taxes, such as the tax on whiskey. He reduced the size of the army and prevented the navy from expanding while he was president. He was opposed to Alexander Hamilton’s financial plan creating a national banking system, because he believed it was against the Constitution and because it increased the role of the federal government in the lives of the American people.
Thomas Jefferson was willing to take actions to protect Americans even if those actions hurt the American economy. The passage of the Embargo Act in 1807 was designed to protect American merchants whose ships were being attacked by France and by Great Britain when these countries were at war with each other. This law prevented Americans from trading with other countries. However, it eventually had to be replaced because the economic effects adversely impacted the American economy and the American people.
Thomas Jefferson favored policies that helped American farmers. He saw the United States primarily as an agricultural country and wanted farmers to be successful. He generally opposed protective tariffs, as he believed they negatively impacted farmers.

On which date was India partitioned?

India was partitioned on August 15, 1947. The decision was taken to divide the country into two nations, India and Pakistan, in order to resolve religious conflicts that had been ongoing for centuries because of rivalry and fighting between the majority Muslim and majority Hindu populations. At the time of the partition, India had also just succeeded in winning its independence from the British Empire, and on the same day as this independence was formalized, the two nations of Pakistan (formed of majority Muslim people) and India (majority Hindu population) became officially recognized. As such, Pakistan was technically never a part of the British Empire. However, because the land that is now Pakistan was then India, Pakistan is recognized as part of the Commonwealth in its own right, with its citizens having special status with regard to the UK.

In Letter 7 of The Screwtape Letters by C.S. Lewis, what is the cruel dilemma about whether the demons should conceal their existence?

In Letter 7, Screwtape writes that the demon race is faced with a "cruel dilemma." Here is the dilemma: "When the humans disbelieve in our existence we lose all the pleasing results of direct terrorism and we make no magicians. On the other hand, when they believe in us, we cannot make them materialists and skeptics."
In this letter, Screwtape talks about what he calls "Materialist Magicians," a reference to those who believe in a vague spirituality but who disavow the existence of demons. While Screwtape relishes the idea of deceiving mankind about the existence of demons, he is irritated that doing so costs the demon race the inability to capitalize on and to take credit for acts of "direct terrorism."
Furthermore, when humans disbelieve in demons, the demon race cannot make more "magicians." These "magicians" are human beings who believe in spiritual forces but who refuse to accept the existence of either God or the Devil. In other words, "magicians" reject both traditional religion and secularism. Screwtape prefers people to believe in a vague, magical "Life Force" (a third alternative) so as to be unaware of the danger they're in: "I have great hopes that we shall learn in due time how to emotionalize and mythologize their science to such an extent that what is, in effect, a belief in us, (though not under that name) will creep in while the human mind remains closed to belief in the Enemy."
On the other hand, when humans believe in the existence of demons, they cannot be made "materialists and skeptics." This means that those who believe in the existence of demons are not so readily trapped in a materialist mindset and are more aware of the machinations of the demons.
To Screwtape, the solution to this dilemma is to get to a point where the people are divided into opposing factions. He relates this to the war effort: Screwtape doesn't care who becomes pacifists or patriots, as long as people forget all about God. He encourages Wormwood to work to create extremes, either from a right-wing or left-wing perspective. The only thing they must guard against is people practicing "extreme devotion to the Enemy" (God).

Let him begin by treating the Patriotism or the Pacifism as a part of his religion. Then let him, under the influence of partisan spirit, come to regard it as the most important part. Then quietly and gradually nurse him on to the stage at which the religion becomes merely part of the “cause,” in which Christianity is valued chiefly because of the excellent arguments it can produce in favor of the British war-effort or of Pacifism.

This is a difficult passage, but I hope that what I've written is helpful.

Beginning Algebra With Applications, Chapter 3, 3.1, Section 3.1, Problem 74

Solve the equation $\displaystyle -\frac{1}{4} = c - \frac{2}{3}$ and check
if your answer is correct.

$
\begin{equation}
\begin{aligned}
-\frac{1}{4} + \frac{2}{3} &= c - \frac{2}{3} + \frac{2}{3} && \text{Add $\displaystyle \frac{2}{3}$ from each side} \\
\\
\frac{(-1)(3) + 2(4) }{12} &= c && \text{Get LCD}\\
\\
\frac{-3 + 8}{12} &= c\\
\\
\frac{5}{12} &= c
\end{aligned}
\end{equation}
$

By checking,

$
\begin{equation}
\begin{aligned}
-\frac{1}{4} &= \frac{5}{12} - \frac{2}{3} && \text{Replace the variable by the given number, } \frac{5}{12}\\
\\
\frac{-1}{4} &= \frac{5- 2(4)}{12} && \text{Evaluate the numerical expressions, then get the LCD}\\
\\
\frac{-1}{4} &= \frac{5-8}{12}\\
\\
\frac{-1}{4} &= \frac{-3}{12} && \text{Divide the right side of the equation by } 3\\
\\
-\frac{1}{4} &= - \frac{1}{4} && \text{Compare the results}
\end{aligned}
\end{equation}
$


The results are same; Therefore, $\displaystyle \frac{5}{12}$ is a solution of the equation $\displaystyle -\frac{1}{4} = c - \frac{2}{3}$

Flannery O’Connor's story “A Good Man is Hard to Find” uses The Misfit as an agent of change. How does The Misfit as an agent of change in the story for the other characters, and why is he qualified to make that change?

The Misfit acts an agent of change because he shocks the grandmother out of her complacency. He murders her entire family, and it is clear that he is about to murder her. All of a sudden, everything she has relied on to keep her safe has no value. She has been proud of being a lady, but when she uses that status to appeal to The Misfit, she realizes it has no value to him. She also relies on her money, but that too fails her, as The Misfit has no interest in a bribe.
As she faces death, the grandmother is stripped down to her essentials. She has nothing to rely on but God, and in this moment, God's grace pours down on her, allowing her to love The Misfit as one of her own children just as he is about to kill her.
The Misfit is not really qualified to make a change in the grandmother. Only God's grace can do that. But The Misfit becomes the catalyst or agent of her change by stripping away her props and forcing her to confront reality.

How many moons does the sun have?

The sun has zero moons. A moon is a natural satellite of a planet, a dwarf planet, or even an asteroid. The sun is not one of those items. The sun is a star, and stars do not have moons; however, stars do have natural satellites. The natural satellites of a star are called planets, dwarf planets, asteroids, and/or comets. Our sun has eight planets that revolve around it. They are Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, and Neptune. Most of those planets have at least one moon in orbit; however, Mercury and Venus do not have any moons. In addition to those 8 planets, our solar system currently has 5 dwarf planets. While Jupiter and Saturn do have many more moons than the other planets, the size of the planet doesn't directly relate to the number of moons that a planet has. Earth is larger than Mars, yet Mars has twice as many moons as Earth. Pluto, as a dwarf planet, currently has five moons.
https://solarsystem.nasa.gov/moons/overview/

https://www.universetoday.com/60072/what-is-a-moon/

Calculus of a Single Variable, Chapter 3, 3.4, Section 3.4, Problem 17

Given: f(x)=(1/2)x^4+2x^3
Find the critical values for x by setting the second derivative of the function equal to zero and solving for the x value(s).
f'(x)=2x^3+6x^2
f''(x)=6x^2+12x=0
6x(x+2)=0
x=0,x=-2
The critical value for the second derivative is x=0 and x=-2.
If f''(x)>0, the curve is concave up in the interval.
If f''(x)<0, the curve is concave down in the interval.
Choose a value for x that is less than -2.
f''(-3)=18 Since f''(-3)>0 the graph is concave up in the interval (-oo,-2 ).
Choose a value for x that is between -2 and 0.
f''(-1)=-6 Since f''(-1)<0 the graph is concave down in the interval (-2, 0).
Choose a value for x that is greater than 0.
f''(1)=18 Since f''(1)>0 the graph is concave up in the interval (0, oo).
Because the direction of concavity changes twice and because f''(-2)=0 and
f"(0)=0 there will be an inflection point at x=-2 and x=0.
The inflection points are (-2, -8) and (0, 0).

Based on the clues given in the story, does the princess send the young man to the lady or to the tiger in "The Lady or the Tiger?"

Based on the clues, it is likely that the princess sent her lover to his death.
Stockton tells us that this story is a sort of personality test.  However, it seems that there is plenty of evidence that the princess has her lover killed. Stockton spends a lot of time telling us about her nature. He tells us that the semi-barbaric king has a semi-barbaric daughter.

This semi-barbaric king had a daughter as blooming as his most florid fancies, and with a soul as fervent and imperious as his own. As is usual in such cases, she was the apple of his eye, and was loved by him above all humanity.

The description “semi-barbaric” means that both of them are very passionate and a little bit savage. When the king finds out that the princess has a lover, he is very angry. His reaction is to throw the lover upon his system of justice, the arena. In the arena, the princess knows that he will choose one of two doors. One door will produce a tiger, and the other will produce a lady. Which does she choose?

The more we reflect upon this question, the harder it is to answer. It involves a study of the human heart which leads us through devious mazes of passion, out of which it is difficult to find our way.

If she chooses the tiger, it is because she cannot stand for him to have the lady. We are told that she knows who the lady is and is jealous of her. That seems like a good enough reason to believe that she chooses the tiger. She is jealous, she is not deeply in love with this boy, and she is a passionate but not particularly sentimental girl. She most likely chooses the tiger, and the boy goes to his death.

int 8^(-x) dx Find the indefinite integral

By definition, if the function  F(x) is the antiderivative of f(x) then we follow
the indefinite integral as int f(x) dx = F(x)+C
 where: f(x) as the integrand
           F(x) as the anti-derivative function 
           C  as the arbitrary constant known as constant of integration
 For the problem int 8^(-x) dx, we may apply u-substitution then basic formula for exponential function.
 
Using u-substitution, we let u = -x  then du = -1 dx .
By dividing both sides by -1 in du = -1 dx , we get -1 du = dx .
Applying u-substitution using -x =u and dx=-1 du in  int 8^(-x) dx
, we get:  int 8^(u) * (-1) du =  -1 int 8^u du
 
Applying the basic integration formula for exponential function: 
int a^u du = a^u/(ln(a)) +C where a is a constant.
  Then (-1) int 8^u du = 8^u/(ln(8)) +C
To express  it in terms of x, we plug-in u=-x to get:
-8^(-x)/(ln(8)) +C
Recall 8 = 2^3 . It can be also be written as:
-(2^3)^(-x)/(ln(2^3))+C
Recall the logarithm property: ln(x^n) = n ln(x) then ln(2^3) = 3 ln(2)
It becomes 
 The final answer can be -8^(-x)/(ln(8))+c or  -2^(-3x)/(3ln(2))+C .
 

Discuss the perspective and message of the speakers in the following poems: "Let America Be America Again," "Open Letter to the South," "Theme for English B," and "Harlem." Also, explain the related themes throughout each poem.

Langston Hughes examines several common themes throughout the four assigned poems. One of the predominant themes addressed in each of the poems is the oppression of the speaker. In each poem, the speaker appeals to the disenfranchised members of society and associates with their struggles. The speaker examines the perspective of exploited lower-class members of society such as immigrants, laborers, and African Americans. Hughes also addresses the differences between the marginalized members of society and the privileged members throughout the poems. The speaker juxtaposes the advantages of privileged Americans with the plight of the oppressed citizens.Another common theme that Hughes examines throughout the selected poems is a call for social change. In each poem, Hughes encourages the marginalized members of society to fight for social change. Whether the speaker is encouraging his teacher to view race relations with a new perspective or calling disenfranchised members to challenge the current social structure, Hughes inspires the reader to enact social change.The themes of unity and equality are also examined throughout the four assigned poems. The speaker illuminates and discusses the similar circumstances between African Americans, disenfranchised members of society, and white citizens. Hughes argues for equality and encourages all members of society to work together to achieve the American dream. The speaker appeals to common goals between citizens with different ethnic backgrounds and races in hopes of attaining equality, justice, and harmony. The speaker's desire to integrate into American society is also evident throughout each of the poems.

What person is The Narrow Road to the Deep North written in? Is it an autobiography?

Matsuo Basho's The Narrow Road to the Deep North is written from the first-person point of view. He was born in Japan, and the text of the story I found presented both the Japanese and English versions together. The text tells of his and Kawai Sora's travels through Edo, Japan (modern-day Tokyo) to Ogaki (also in Japan). The text follows Basho along in the form of what he calls a "travel diary." The intent behind the journey was to witness and visit the places prior poets (ones Basho admired) had seen.
The text is readily identified as a first-person narrative based upon Basho's use of pronouns. He uses the pronouns "I" and "we" to describe his and his traveling partner's (Sora) journeys.
His journey takes place in 1689. The journey, which took 156 days, details the scenes and people Basho and Sora came across. Basho begins many of the entries with the date (the number of the day he is on for his journey). The text, spattered with poetry (many in haiku), details the mountains, rivers, and villages his travels allowed him to experience. Therefore, readers are not only entertained using prose descriptions of the scenery, they are entertained with his poetic voice as well.
Technically, one could identify the text as autobiographical. By definition, an autobiography is a first-person text written to tell of that person's life (from his or her perspective). Therefore, while Basho defines his text as a "travel diary," a more common term would be that of an autobiography.

Intermediate Algebra, Chapter 4, 4.2, Section 4.2, Problem 46

Solve each system $
\begin{equation}
\begin{aligned}

x - 3y + 7z + w =& 11 \\
2x + 4y + 6z - 3w =& -3 \\
3x + 2y + z + 2w =& 19 \\
4x + y - 3z + w =& 22

\end{aligned}
\end{equation}
$ by expressing the solution in the form $(x,y,z,w)$.


$
\begin{equation}
\begin{aligned}

3x - 9y + 21z + 3w =& 33
&& 3 \times \text{ Equation 1}
\\
2x + 4y + 6z - 3w =& -3
&& \text{Equation 2}
\\
\hline

\end{aligned}
\end{equation}
$




$
\begin{equation}
\begin{aligned}

5x - 5y + 27z \phantom{-3w} =& 30
&& \text{Add; New equation 2}

\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}

-2x + 6y - 14z - 2w =& -22
&& -2 \times \text{ Equation 1}
\\
3x + 2y + z + 2w =& 19
&& \text{Equation 3}
\\
\hline

\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}

x + 8y - 13z \phantom{+2w} =& -3
&& \text{Add; New equation 3}

\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}

-x + 3y - 7z - w =& -11
&& -1 \times \text{ Equation 1}
\\
4x + y - 3z + w =& 22
&& \text{Equation 4}
\\
\hline

\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}

3x + 4y - 10z \phantom{+w} =& 11
&& \text{Add; New Equation 4}

\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}

65x - 65y + 351z =& 390
&& 13 \times \text{ New Equation 2}
\\
27x + 216y - 315z =& -81
&& 27 \times \text{ New Equation 3}
\\
\hline

\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}

92x + 151y \phantom{-351z} =& 309
&& \text{Add; New Equation 3}

\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}

50x - 50y + 270z =& 300
&& 10 \times \text{ New Equation 2}
\\
81x + 108y - 270z =& 297
&& 27 \times \text{ New Equation 4}
\\
\hline

\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}

131x + 58y \phantom{-270z} =& 597
&& \text{Add; New Equation 4}

\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}

92x + 151y =& 309
&& \text{Equation 3}
\\
131x + 58y =& 597
&& \text{Equation 4}

\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}

-5336x - 8758y =& -17922
&& -58 \times \text{ Equation 3}
\\
19781x + 8758y =& 90147
&& 151 \times \text{ Equation 4}
\\
\hline

\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}

14445x \phantom{+8758y} =& 72225
&& \text{Add}
\\
x =& 5
&& \text{Divide each side by $14445$}

\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}

92(5) + 151y =& 309
&& \text{Substitute } x = 5 \text{ in New Equation 3}
\\
460 + 151y =& 309
&& \text{Multiply}
\\
151y =& -151
&& \text{Subtract each side by $460$}
\\
y =& -1
&& \text{Divide each side by $151$}

\end{aligned}
\end{equation}
$




$
\begin{equation}
\begin{aligned}

5 + 8(-1) - 13z =& -3
&& \text{Substitute } x = 5 \text{ and } y = -1 \text{ in Equation 1}
\\
5 - 8 - 13z =& -3
&& \text{Multiply}
\\
-3 - 13z =& 0
&& \text{Combine like terms}
\\
-13z =& 2
&& \text{Add each side by $3$}
\\
z =& 0
&& \text{Divide each side by $-13$}

\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}

5 - 3(-1) + 7(0) + w =& 11
&& \text{Substitute } x = 5, y = -1 \text{ and } z = 0 \text{ in Equation 1}
\\
5 + 3 + 0 + w =& 11
&& \text{Multiply}
\\
8 + w =& 11
&& \text{Combine like terms}
\\
w =& 3
&& \text{Subtract each side by $8$}

\end{aligned}
\end{equation}
$


The solution set is $\displaystyle \left \{ (5,-1,0,3) \right \}$.

How can a multidisciplinary approach to history be used in studying European History?

I think that one example of a multidisciplinary approach to teaching European History would involve integrating literature as a part of instruction.
Embracing literature and history is a natural, effective, and interdisciplinary approach to make content come alive.  When we use literature as an embedded part of the instructional process, greater understanding of history emerges.  For example, teaching about European History during World War I gains greater significance when pulling from the literature of the time period.  The historical conditions of the battlefield and trench warfare are so viscerally understood when reading works such as Remarque's All Quiet on the Western Front.  In this instance, literature allows the pain and alienation of World War I to resonate in the student's mind. Another example of how literature can better enhance the understanding of European History can be seen in teaching Machiavelli's The Prince. Machiavelli's work illuminates the intellectual currents of the Renaissance that played such a large part in the formation of European identity.  It can also bring out how leaders approached the task of governance.  Students gain more insight about European history when they read the literature that influenced it. Teaching literature alongside history allows them to better understand what it was like to live and experience a particular time period.  

From To Kill a Mockingbird, how would I write a short script based on "Scout Walks Boo Home," but she never saw him again due to his shyness and childlike behavior?

If one were to write a short script about Scout walking Boo home on the night that he saves her life, it would certainly be one-sided because he doesn't speak. Scout, therefore, would have all of the lines, and she would have to verbally interpret Boo's body language for the audience to understand. Within the script, then, stage directions might be useful to indicate Boo's part. For example, some ways to describe Boo's movements could be as follows:

"When Boo Radley shuffled to his feet, . . . every move he made was uncertain, as if he were not sure his hands and feet could make proper contact with the things he touched. He coughed his dreadful raling cough, and was so shaken he had to sit down again. His hand searched for his hip pocket, and he pulled out a handkerchief. He coughed into it, then he wiped his forehead . . . His hand tightened on mine and he indicated that he wanted to leave" (277-278).

From the passage above, examine Boo's mannerisms and body language, then apply those into the script. Scout even says that the way Boo communicates is through "his body English," which she could mention in the script as well. 
As far as what Scout might say on the way to Boo's house, she might say a few things in the script that she wished to say from the novel. For example, Scout feels as though she and her family haven't been as neighborly as they could have been as expressed in the following excerpt:

"Neighbors bring food with death and flowers with sickness and little things in between. Boo was our neighbor. He gave us two soap dolls, a broken watch and chain, a pair of good-luck pennies, and our lives. But neighbors give in return. We never put back into the tree what we took out of it: we had given him nothing, and it made me sad" (278).

Maybe at the end of the script Scout could mention that she will suggest to Atticus to send Boo Radley a gift for helping them out that night. Or maybe Scout promises to tell Jem everything when he's awake in the morning, too. Whatever Scout says, she does know that she most likely will never see Boo again. However, she would rather respect his wishes than annoy him by trying to get him to communicate if he doesn't want to. 

What was the bet in Anton Chekhov's "The Bet"?

The story opens with the banker recalling a party fifteen years ago. The banker, the lawyer, and others are discussing capital punishment and which is more humane: the death penalty or life in prison. The banker claims that capital punishment (the death penalty) is more humane because it kills the man at once whereas life in prison "drags the life out of you" over many years. The lawyer disagrees. He says the death penalty and life in prison are both immoral but life in prison is preferable because some life is better than none.
The banker hypothetically bets the lawyer two million dollars/rubles that he could not stay in solitary confinement for five years. The lawyer inexplicably raises it to fifteen years for the same amount of money. They set the terms of the bet. The lawyer must remain in his prison for fifteen years. It is to be a lodge in the banker's garden. He is to have no contact with other people. He can not even hear a human voice, receive letters, or newspapers. He is allowed a musical instrument, any books he wants, and he can smoke and drink wine. His only contact with the outside world is through a small window through which he would receive food, books, and so forth. If any of these conditions are broken or if he leaves the lodge, the banker wins and keeps his two million.
The lawyer fluctuates between idleness, loneliness, and intense study. On the night before the final day, the banker considers killing the lawyer because giving up the two million will essentially bankrupt him. His wealth had decreased considerably over those fifteen years. The banker enters the lawyer's cell and finds a statement written by the lawyer who claims he will leave early, thus breaking the bet. The lawyer has become nihilistic. He now finds life to be meaningless and therefore the money is useless to him. He leaves early, breaking the bet.
Chekov once had a third section but eventually omitted it. In this section, the banker made it a habit of giving praise to the lawyer as a way of assuaging his guilt. The lawyer reappears one day and demands a large sum of money or he will commit suicide. The banker agrees and says that the lawyer wins the bet. Since Chekov omitted this part, readers have supposed that he was unsure how this story should end or what the story should mean. Chekov seems to be making a study of the psychology of the two men rather than suggesting some main point or moral to the story.

The bet is between the lawyer and the banker. The subject matter of their bet is over the morality of the death penalty. The banker believes the death penalty is more humane than life in prison, but the lawyer disagrees. The lawyer believes life in prison is a more humane option because he believes that some life is better than no life. He then says, 

The death sentence and the life sentence are equally immoral, but if I had to choose between the death penalty and imprisonment for life, I would certainly choose the second. To live anyhow is better than not at all.

The banker then bets the lawyer 2 million rubles that the lawyer couldn't stay in solitary confinement for 5 years. The lawyer agrees to the bet, but oddly increases his confinement time to 15 years for no increase in possible winnings. The bet begins at noon the following day.

Summarize the article "Rethinking Proportionality Under The Cruel and Unusual Punishments Clause" at http://scholarship.law.ufl.edu/cgi/viewcontent.cgi?article=1274&context=facultypub

The article proposes that proportionality reviews are crucial in efforts to correctly interpret the Cruel and Unusual Punishments Clause. Additionally, proportionality highlights a retributive rather than a restorative concept of justice. Thus, to quantify excessiveness, one would need to consult prevailing moral standards rather than popular, shifting definitions of cruelty.
This article proposes that new approaches to proportionality would allow the Supreme Court to nullify death penalty verdicts for non-homicidal cases and to restrict life-without-parole sentences for juvenile offenders. The article states that a proportionality review is critical because the Supreme Court has failed to furnish a rational definition of proportionality and to employ concrete solutions that ensure proportionality.
In the past, the Supreme Court often rejected death penalties or life sentences even when there was no clear societal consensus against them. In these instances, the Court relied on a fictionalized consensus to justify its own arbitrary verdicts. At other times, the Court relied on its own independent judgment to define cruel and unusual punishment. In short, the Court lacked a definitive standard for measuring excessiveness.
As history shows, the original Framers interpreted the Eighth amendment in light of prior practice. Later, nineteenth-century law experts supported the notion that the Punishment Clauses rejected both excessive and barbaric retribution. However, they based this support on entrenched definitions of excessiveness. Basically, the Court needs a clear standard for defining "cruel and unusual punishment," a standard that must not be influenced by shifting public opinion, the Court's independent judgment, or the machinations of legislators.

What are some examples of the impact of the internment camp on the family in the book Farewell to Manzanar?

Jeanne Wakatsuki's Farewell to Manzanar paints a disturbing picture of a dark chapter of American History, specifically the internment of Japanese citizens into camps, in this case Manzanar. The ordeal had a terrible physical and psychological impact on the Wakatsuki family. Manzanar was constructed quickly and with very little regard to sanitation and basic decency. The family was also separated, the patriarchal Mr. Wakatski being forced to a different camp after being arrested. Those living in the camp were forced to share a small supply of badly prepared food and live in horribly cramped living quarters that afforded little privacy. There were not enough warm clothes to go around, and drafts and dust came through holes in the living area. In particular, Jeanne's mother is bothered horribly by the toilets that have no walls around them. These indignities severely wound the pride of the family, and soon they stop having meals together.

The internment camp was hurriedly put up, and minimal efforts were directed towards health and sanitation. People suffered from diarrhea and other sanitation related diseases. Jeanne suffered from exposure to the filthy conditions and the situation affected the family.
Group living in the internment camp forced the people, including the Wakatsuki family, to share all the available amenities. In addition, the rooms were small, and the situation affected individual privacy. For instance, the young couples in the Wakatsuki family were forced to share the small space with their parents.
The internment camp also affected the family psychologically. Years after the camps were closed, the Japanese people carried the shame associated with living in the camps, and Jeanne was among those affected by the experience.
The Wakatsuki family was also split by the relocation. Mr. Wakatsuki was arrested and separated from his family. His son was forced to take charge of the family when they settled in Manzanar.

Single Variable Calculus, Chapter 1, 1.3, Section 1.3, Problem 54

Assume that a spherical balloon is being inflated and the radius of the balloon is increasing at a rate of 2 cm/s.

(a) We need to express the radius $r$ of the balloon as a function of the time $t$ (in seconds).


$
\begin{equation}
\begin{aligned}
r(t) =& 2t\\
\end{aligned}
\end{equation}
$


(b) find $V \circ r$ and explain, if $V$ is the volume of the balloon as a function of the radius.


$
\begin{equation}
\begin{aligned}

Volume =& \displaystyle \frac{4}{3} \pi r^3; \text{ but } r=2t\\

Volume =& \displaystyle \frac{4}{3} \pi (2t)^3\\

Volume =& \displaystyle \frac{32 \pi}{3} t^3, \text{ volume of the sphere as a function of time.}
\end{aligned}
\end{equation}
$

Without a doubt, one of the most significant events in postwar America was the black civil rights movement of the 1950s and 60s. In an essay, discuss the origins or key events in the 1940s and early 50s that help explain the emergence of the civil rights movement. What specific agencies, groups, ideas, and events help explain the success of the mainstream freedom movement (not Black Power) from the early 1950s to the mid-1960s? In addition, how did the ideology, style, and tactics of the Black Power movement, including the Black Panthers, differ from the mainstream movement of Martin Luther King? Be sure to provide specific examples and details to support your argument.

There are several questions posed here. This response will look at the first—the origins of the civil rights movement in the 1940s and early 1950s. We tend to think of the civil rights movement as an event of the late 1950s and 1960s, beginning with Brown v. Board of Education in 1954. But in reality, Brown v. Board was the culmination of a series of legal battles, mostly waged by the NAACP, that were part of the origins of the movement. Beginning in the 1930s, the NAACP began to challenge segregation in institutions as varied as public transportation, labor unions, and universities. This was part of a strategy that eventually brought the practice of segregation in public schools into the contest. The NAACP also helped bring the issue of lynching before the public, raising awareness of the violence that undergirded Jim Crow society.
The civil rights movement also took root in World War II. This happened for several reasons. For one thing, it was not lost on many people that the struggle against Nazi Germany was a fight against a regime that was based on racism. Some politicians and soldiers recognized the contradiction of fighting against a racist regime overseas while tolerating racism at home. This was given voice by a Pittsburgh newspaper that described the war as viewed by African Americans as a "Double-V" campaign. They had to fight for freedom overseas as well as at home, and many recognized the war as an opportunity to achieve both. It was also the case that many black soldiers who participated in the war overseas were in no mood to face discrimination at home.
Finally, some civil rights organizations formed in the 1940s and early 50s. The most important was CORE, or the Congress of Racial Equality. CORE would eventually become famous for its sponsorship of the Freedom Rides in the early 1960s, but CORE was born in Chicago out of groups who protested discrimination in that city. Their tactics included the "sit-ins" that would become famous nationwide after the "Greensboro Four" used the tactic in the downtown Woolworths store in Greensboro, North Carolina. While the civil rights movement really began to gain momentum in the late 1950s, its roots stretched back much further, and it should be remembered that resistance to Jim Crow segregation began as soon as it was established. The freedom struggles of the 1950s and 60s drew on a long tradition of black activism at the grassroots level.
http://nationalhumanitiescenter.org/tserve/freedom/1917beyond/essays/crm.htm

https://kinginstitute.stanford.edu/encyclopedia/sit-ins

https://www.history.com/topics/black-history/congress-of-racial-equality

The CORE (Congress of Racial Equality) sent their first April Freedom Fighters into the South in 1947; these were activists who rode interstate buses to test the 1946 Supreme Court ban of segregated interstate bus routes. CORE sponsored the majority of the subsequent Freedom Rides in the early 60s, and we cannot forget Rosa Parks's refusal to give up her seat in the colored section of a bus in Montgomery, Alabama, to a white passenger. She was arrested for civil disobedience, and her defiance became an influential symbol of the civil rights movement.
After participation of African Americans in the Second World War, June A. Philip Randolph formed the League for Nonviolent Disobedience Against Military Segregation in 1948, paving the way for Truman's executive order ending segregation in the US military later that year. In 1947, Jackie Robinson emerged as a popular leader in the pre–civil rights movement, becoming the first African American to play professional sports.
Between the 1940s and 1960s, black urban culture developed during the Harlem Renaissance, contributing to an expansion of arts and literature. Novels such as Ralph Ellison's Invisible Man (1952) and James Baldwin's Go Tell It on the Mountain (1953) increased black representation in literature, inspiring the artistic movement of the civil rights era. Additionally, Gwendolyn Brooks became the first African American to win the Pulitzer Prize, for her poetry book Annie Allen (1949).

The events in the 1940s and 1950s that gave rise to the modern Civil Rights movement include the "Double Victory" campaign for African American veterans of World War II. This campaign involved the recognition that veterans who had fought in the war deserved, and should push for, civil rights for all African Americans. In addition, the landmark 1954 Supreme Court case Brown v. Board of Education, which made segregation in public schools illegal, forced the issue of desegregation in southern schools and in other public places.
One of the first events of the modern Civil Rights campaign was the Montgomery Bus Boycott of 1955-1956, during which Martin Luther King, Jr., a Baptist preacher (originally from Georgia) in Atlanta, led a non-violent movement to desegregate the city buses. Later, his Southern Christian Leadership Conference (SCLC) and the student offshoot of the group, the Student Nonviolent Coordinating Committee (SNCC), used non-violent protests, including tactics such as sit-ins, demonstrations, speeches, and boycotts, to desegregate public places and transportation. The movement also pushed for voting rights and was successful in part because of its ability to mobilize massive grassroots support and its appeal to northern whites and African Americans across the nation. Later, the Black Power movement moved away from non-violence and favored a more confrontational approach, as well as an interest in fostering Black Pride rather than promoting desegregation. 

What is the real tragedy in Loman's family in Death of a Salesman?

The real tragedy with the Loman family in Death of a Salesman is a combination of lack of action, aptitude and attitude to attain the superbly high goals that the men of the family set for themselves.
Most people argue that the Lomans' true problem was their obscene ambition with attaining an American Dream that Willy built for them. The argument is also that such an American Dream was phony because it is based on shallow parameters, such as being "well-liked," attaining financial success with little work, and becoming popular. Although those are indeed the tenets of Willy's dream, calling the Lomans "ambitious" would be a problem.
First, ambitious people know what they want, stick with a plan, and fight until the end to get their goal. Additionally, truly ambitious people are not scared of defeat because they are willing to get up and try again by all means necessary. Third, people who really want a lot often already have a lot. Think of the quintessential "rich getting richer" paradigm, which presupposes that the ultimate ambitious person is that who has achieved a lot and still wants to achieve more.
Now, look at the Lomans. Here is Willy, dreaming of being like Dave Singleton, the salesman who could sell anything out of his hotel room. Biff wants to be "something" but he does not know what. Happy wants women, looks, popularity, and the position of his boss at his job. All three men are justifiably ambitious, but none of them has a single plan in place to carry on. They simply dream, hope, make limited attempts, and then find blame in one another, or something else, to diffuse their lack of action.
This being said, the true tragedy in the life of the Lomans can be summarized in one word: "indolence." Lack of movement, planning, changing, and moving toward a goal is their true problem. It is something that they have learned to live with, and they believe it to be the norm. It is also the reason why the three men are stunted compared to their peers, and why the Lomans may never really amount to anything as great as what they think.

y = 3-x , y=0, y=2, x=0 Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the line x = 5

For the region bounded by y=3-x , y=0 , y=2 , and x=0 revolved  about the line x=5 , we may apply Washer method for the integral application for the volume of a solid.
 The formula for the Washer Method  is:
V = pi int_a^b [(f(x))^2-(g(x))^2]dx
or
V = pi int_a^b [(f(y))^2-(g(y))^2]dy
where f as function of the outer radius 
         g as a function of the inner radius
To determine which form we use, we consider the horizontal rectangular strip representation that is perpendicular to the axis of rotation as shown on the attached image. The given strip  has a thickness of "dy " which is our clue to use the formula:
V = pi int_a^b [(f(y))^2-(g(y))^2]dy
For each radius, we follow the x_2-x_1 . We have x_2=5 since it a distance between the axis of rotation and each boundary graph.
For the inner radius, we have: g(y) = 5-(3-y) simplified to g(y)=2+y
Note: y_(below) for the inner radius is based from y =3-x rearrange into x= 3-y
For the outer radius, we have: f(y) = 5-0  simplified to f(y)=5 .
Then the boundary values of y  is a=0 and b =2 .
Then the integral will be: 
V = pi int_0^2 [(5)^2-(2+y)^2]dy
Expand using the FOIL method on:
(2+y)^2 = (2+y)(2+y)= 4+4y+y^2 and 5^2=25 .
The integral becomes: 
V = pi int_0^2 [25 -(4+4y+y^2 )]dy
Simplify:
V = pi int_0^2 [25 -4-4y-y^2 ]dy
V = pi int_0^2 [21-4y-y^2 ]dy
Apply basic integration property:
int (u-v-w)dy = int (u)dy-int (v)dy-int (w)dy
V = pi [ int_0^2 21dy - int_0^2 4ydy -int_0^2 y^2dy]
For the integration of  int 21 dy , we apply basic integration property: int c dx = cx .
 For the integration of int_0^2 4ydy and int_0^2 y^2dy , we apply the Power rule for integration:  int y^n dx = y^(n+1)/(n+1) .
V = pi [ 21y - 4*y^2/2 -y^3/3]|_0^2
V = pi [ 21y - 2y^2 -y^3/3]|_0^2
Apply the definite integral formula: int _a^b f(x) dx = F(b) - F(a) .
V = pi [ 21(2) - 2(2)^2 -(2)^3/3]-pi [ 21(0) - 2(0)^2 -(0)^3/3]
V = pi [ 42 - 8 -8/3]-pi [ 0-0-0]
V = pi [ 94/3]-pi[0]
V =(94pi)/3 or 98.44 (approximated value)

In "Chee's Daughter" by Juanita Platero, why is Chee at a hard point in his life?

Chee is at a hard point in his life because his wife has just succumbed to the coughing sickness; her death, though not unexpected, has left him comfortless. To add to his grief, his wife's family has claimed Chee's little daughter for their own.
Chee's mother tells her son that there is nothing he can do about it, as the custom is that a little girl belongs to her mother's people. Undeterred, Chee goes to reason with his father-in-law, Old Man Fat, but he is unsuccessful in claiming his daughter back. So, not only is Chee bereft of his wife, but he has also lost custody of his little daughter.
In the end, Chee decides to earn his daughter back. He works the land and plants a variety of vegetables, believing what he has always been taught: "that a man took care of his land and it in turn took care of him." At the end of the season, after collecting a full harvest, Chee again approaches his in-laws. This time, however, the tables have been turned. His in-laws are no longer confident in their ability to earn an easy living. The trading post has been closed, and tourists have become scarce. This means that Old Man Fat can no longer collect rent from the trader who rented his strip of land, and he can no longer make money off of tourists.
When his in-laws see the wonderful harvest Chee has brought to them, they grudgingly consent to let Chee take his daughter back with him. So, with the harvest from his work in the fields, Chee is finally able to banish his grief by reclaiming the one who is most precious to him. 

Intermediate Algebra, Chapter 4, 4.1, Section 4.1, Problem 14

Decide whether the ordered pair $(5,2)$ is a solution of the system $
\begin{equation}
\begin{aligned}

2x - y =& 8 \\
3x + 2y =& 20

\end{aligned}
\end{equation}
$.

We substitute the ordered pair to the equations

Equation 1


$
\begin{equation}
\begin{aligned}

2x - y =& 8
&& \text{Given equation}
\\
2(5) - 2 =& 8
&& \text{Substitute $x = 5$ and $y = 2$}
\\
8 =& 8
&&

\end{aligned}
\end{equation}
$


Equation 2


$
\begin{equation}
\begin{aligned}

3x + 2y =& 20
&& \text{Given equation}
\\
3(5) + 2(2) =& 20
&& \text{Substitute $x = 5$ and $y = 2$}
\\
15 + 4 =& 20
&&
\\
19 =& 20
&&

\end{aligned}
\end{equation}
$


The ordered pair $(5,2)$ is not the solution of the system.

explain the purpose of the stevensons

Early in the story, Mike and Frances are talking about how they will spend their Sunday. They consider going back to bed together, and Frances mentions that the Stevensons have asked them to come over around 1 p.m. They will all leave New York for the afternoon for a drive in the country. Mike playfully dismisses the idea, indicating that he'd prefer to spend the day with Frances.
As the day progresses, Frances confronts Mike about his wandering eye, which he initially tries to defend as harmless. However, the conversation about his tendency to check out other women eventually turns serious when he admits to Frances that "I love you, but I also want them."
Frances becomes pleading and tearful, and Mike admits that it is conceivable that one day he will act on his desire for another woman. Frances absorbs this confession coolly and suggests that they go for the drive with the Stevensons after all. It seems that the Stevensons become at least a temporary buffer for the profound tension Mike's admissions have created. It seems that Frances at this point has had enough of being alone with Mike and wants a diversion from the intensity of their conversation.

Create an organization chart for the company that you currently work for, or for a company that you have worked for in the past. Alternatively, create an organization chart for a company that a friend or family member currently works for or a company they have worked for in the past.

An organizational chart shows the relationships between people who work at a company, as well as the relationships between the departments or functions of the company. It is usually completed in a hierarchical fashion, with the head of the organization at the top, followed by the people who are close to the top in the hierarchy and working its way down to the people who have lower levels in the organization.
For example, a manufacturing company's organizational chart might show the Board of Directors at the top, at the same level as the chairperson or president of the company. Beneath that person might be branches to different functions or departments of the company. The vice-presidents in charge of sales, manufacturing, human resources, and accounting might all be at the same level. Within each of those departments, there might be further divisions, such as into different regional sales departments (East Coast, Midwest, West Coast, South, etc.), and into the different positions in each department. For example, the human resources department might include a vice-president, human resource generalists below that person, and a person who conducts training below that person or people. Generally, people who share the same position are at the same level. To figure out the organizational chart for the company you choose, you might have to interview someone who works there or someone who works in the human resources department to fill you in about the different positions in the company and how they are ranked and organized.  

Why was Martin Luther King’s “I Have A Dream” speech so pivotal in American history? Did it redefine the nature of America and of the American Dream?

Martin Luther King, Jr. delivered his famous "I Have a Dream" speech on August 28, 1963, during the March on Washington for Jobs and Freedom. His speech was pivotal because it brought civil rights and the call for African-American rights and freedom to the forefront of Americans' consciousness.
It is estimated that over 250,000 people attended the march, which also received a great deal of national and international media attention. The speech helped make Civil rights an issue that attracted by African American and white people in a national coalition. In the speech, Dr. King promoted his idea of non-violent resistance as a means of achieving equality and stated, "We must not allow our creative protest to degenerate into physical violence." His words helped gain passage of the Civil Rights of 1964, which provided for equal rights for African-American people. In addition, the speech was one of the most eloquently written and most movingly delivered speeches in American history. It is still studied today as an example of fine rhetoric.
Dr. King gave his speech in front of the Lincoln Memorial, which was symbolic because Lincoln had signed the Emancipation Proclamation in 1863, exactly one hundred years before, freeing the slaves in the Confederacy. Dr. King mentioned this symbolism in his speech, stating, "Five score years ago, a great American, in whose symbolic shadow we stand today, signed the Emancipation Proclamation." He went on to say, however, that "the Negro is still languished in the corners of American society and finds himself in exile in his own land." By speaking in front of the Lincoln Memorial, Dr. King contrasted the majesty of the memorial with the reality of the condition of African Americans in the country, who were still disenfranchised and treated like second-class citizens at best.
In his speech, Dr. King called for equality and redefined the American Dream not as one of prosperity alone but as one of freedom and equality. In a series of passages that began with the words "I have a dream," King stated his vision of equality and brotherhood in all parts of the United States. For example, he stated:

"I have a dream that one day on the red hills of Georgia, the sons of former slaves and the sons of former slave owners will be able to sit down together at the table of brotherhood."

Dr. King redefined America not as a place in which only white people were entitled to the promises of liberty and freedom but as a place in which everyone had the right to these promises and to the potential for acceptance and equality. He redefined the American Dream not merely as the right of whites to access life, liberty, and the pursuit of happiness but as the right of all people to do so and to live with the full acceptance of others. He believed that Americans could not be free until everyone was free, and so he redefined the American Dream as not only an individual promise but as a communal promise as well. 
https://kinginstitute.stanford.edu/king-papers/documents/i-have-dream-address-delivered-march-washington-jobs-and-freedom

How are poems "Wild Swans at Coole" as well as "Leda and the Swan" by Yeats related?

Both poems are about swans, as their titles indicate, and both poems are about change and loss.
In "Leda and the Swan," Leda changes by losing her innocence as she is brutally raped by Zeus disguised as a swan. The narrator wonders if Leda received "knowledge" from Zeus in exchange for being "mastered" by his "brute blood" and "indifference." Was there any redemption for her in this experience?
In "Wild Swans at Coole," the narrator watches 59 swans on the lake at Coole and regrets the changes that have come to him since he first viewed the swans on this lake 19 years ago. He writes:

And now my heart is sore.All's changed since I, hearing at twilight,The first time on this shore

The narrator doesn't spell out exactly what the changes are he has experienced, but change always involves loss, and these changes have bruised or left "sore" the narrator's heart. He contrasts his changes to the unchanging beauty of the swans. Unlike him:

Their hearts have not grown old

Both poems also rely heavily on imagery—showing what we can experience through sight, sound, touch, taste and smell—to convey the very different actions of the swans in each poem.

Is the phrase "one foot in heaven" spoken by Elizabeth to John Proctor in act IV of The Crucible a play on the idiom "one foot in the grave"?

In act four, Salem's authority figures allow Elizabeth Proctor to visit her husband in prison with the hope that she will convince John to confess to witchcraft, which would save his life and prevent the community from rebelling against the court. When John asks his wife if anyone has confessed, she responds by saying that many have offered confessions in order to avoid death. John then asks if Rebecca Nurse has confessed, and Elizabeth responds by saying,

Not Rebecca. She is one foot in Heaven now; naught may hurt her more (Miller, 134).

It could be argued that Elizabeth's comment is a play on the idiom "one foot in the grave," which typically has a negative connotation and means that a person is close to dying. Given the fact that Rebecca Nurse is such a righteous, morally upright woman, her death will be viewed as a reward. Elizabeth's comment also has a positive connotation because it implies that Rebecca will spend eternity in heaven. Elizabeth's play on the idiom "one foot in the grave" also reveals her respect and admiration for Rebecca Nurse. At the end of the play, Rebecca becomes a martyr for refusing to confess: she dies at the gallows with her faith, integrity, and honor intact.

In Act IV, Scene 9, Elizabeth tells John Proctor that Rebecca Nurse "is one foot in heaven now. Naught may hurt her more." Proctor is trying to get the people who are accused of witchcraft to confess so that they will be pardoned. However, Rebecca, as Proctor realizes, will not confess to be a witch as he is contemplating doing himself. Instead, as Proctor says, Rebecca will "go like a saint." Rebecca is a devout and respected member of the Salem community. When Elizabeth says that Rebecca "is one foot in heaven," it does not exactly mean that she has "one foot in the grave." True, she will be executed soon, so in that sense, she has one foot in the grave. However, there is an additional meaning to the phrase "one foot in heaven," which is that Rebecca is so virtuous and devout that she is on her way to becoming a saint in heaven. 

What passage or passages from the novel A Passage to India are good illustrations of how the author handles narration, point of view, and perspective to contribute to the overall meaning of the novel?

The incident in the mosque in chapter 2 provides a very good illustration of how Forster handles narration, point of view, and perspective. While staying in a third-person omniscient narration, the author provides Dr. Aziz's perspective first as he sits alone in the mosque after having been treated shabbily by the Englishwomen who took his carriage and after having been brushed off by Mr. Callendar. Sitting alone in the mosque, far from English people, Dr. Aziz thinks:

But the mosque—that alone signified, and he returned to it from the complex appeal of the night, and decked it with meanings the builder had never intended. Some day he too would build a mosque, smaller than this but in perfect taste, so that all who passed by should experience the happiness he felt now.

Dr. Aziz finds the mosque to be a refuge away from English people. It is a place where he can feel safe and not feel like a second-class citizen. Forster conveys Dr. Aziz's perspective and feelings. 
Later, when Dr. Aziz sees Mrs. Moore, an Englishwoman, in the mosque, he feels that she is violating the sacred space of the mosque. However, he grows to like her, as Forster conveys in the following passage:

He was excited partly by his wrongs, but much more by the knowledge that someone sympathized with them. It was this that led him to repeat, exaggerate, contradict. She had proved her sympathy by criticizing her fellow country woman to him, but even earlier he had known. The flame that not even beauty can nourish was springing up, and though his words were querulous his heart began to glow secretly.

The author conveys Dr. Aziz's warmth toward Mrs. Moore as she criticizes the Callendars. He has an unexpected connection with Mrs. Moore because she is willing to criticize a fellow English person in the company of an Indian person.
In the next chapter, Forster, while staying in the third person, is able to capture Mrs. Moore's perspective on the incident in the mosque after she speaks about it with her son: 

The note of anxiety in his voice made her feel that he was still a little boy, who must have what he liked, so she promised to do as he wished, and they kissed good night. He had not forbidden her to think about Aziz, however, and she did this when she retired to her room. In the light of her son's comment she reconsidered the scene at the mosque, to see whose impression was correct. Yes, it could be worked into quite an unpleasant scene.

After speaking with her son, Mrs. Moore feels uncomfortable about sharing confidences with Dr. Aziz. The author is able to capture both Dr. Aziz's and Mrs. Moore's perspective on the incident in the mosque.