g(x)=5/(2x-3), c=-3 Find a power series for the function, centered at c and determine the interval of convergence.

If x is a variable, then an infinite series of the form sum_(n=0)^ooa_n(x-c)^n=a_0+a_1(x-c)+a_2(x-c)^2+......+a_n(x-c)^n+..... is a power series centered at x=c, where c is a constant.
Given g(x)=5/(2x-3) , c=-3
Let's write g(x) in the form a/(1-r)
g(x)=5/(2x-3)
=(5/2)/(x-3/2)
=(5/2)/(x+3-3/2-3)
=(5/2)/(x+3-9/2)
=(5/2)/(-9/2(1-2/9(x+3)))
=((5/2)(-2/9))/(1-2/9(x+3))
=(-5/9)/(1-2/9(x+3))
So a=-5/9 and r=2/9(x+3)
So, the power series for g(x) is sum_(n=0)^ooar^n
=sum_(n=0)^oo(-5/9)(2/9(x+3))^n
=-5sum_(n=0)^oo(2^n(x+3)^n)/9^(n+1)
This power series is a geometric series and it converges if |r|<1
|2/9(x+3)|<1
-1<2/9(x+3)<1
-9<(2x+6)<9
-9-6<2x<9-6
-15<2x<3
-15/2Interval of convergence is (-15/2,3/2)
 

Explain why the "front-buttoned" jackets were a sign of independence for Sevens.

In chapter six, Jonas reminds his sister, Lily, how excited she was when she received her front-buttoned jacket as a Seven. In Jonas's community, children the ages of four, five, and six are all required to wear jackets that fasten down the back so that other children will have to help them get dressed. The reasoning behind requiring children to wear jackets that fasten down the back is to nurture interdependence. The Committee of Elders values interdependence and attempts to foster cooperation among the youth by requiring them to wear unique jackets that fasten down the back. Children are then forced to rely on their peers for help, which fosters camaraderie among them. Once the children turn seven years old, they are given jackets with buttons in the front, which are a sign of independence. At the age of seven, children are no longer forced to rely on their peers for help getting dressed, which is why they are a sign of independence.

In Lois Lowry's The Giver, before a child becomes a seven, the buttons on their jackets are at the back. These children cannot button their jackets themselves. They must depend on parents and peers to help them get dressed. This develops a sense of interdependence in the children. They learn to rely on others to care for them and to care for others in need. They also indicate the child's age and maturity level to other people in the community.
Seven is the age when children take the first steps toward becoming independent and caring for themselves. For the first time, these children have to take responsibility for their own appearance, rather than relying on others. It is a visible indicator that they are growing up and will soon need to take on other responsibilities.

sum_(n=1)^oo 2(-1/2)^n Verify that the infinite series converges

To verify if the given infinite series: sum_(n=1)^oo 2(-1/2)^n converges, recall that infinite series converge to a single finite value S  if the limit of the partial sum S_n as n approaches oo converges to S . We follow it in a formula:
lim_(n-gtoo) S_n=sum_(n=1)^oo a_n = S .
To evaluate the  sum_(n=1)^oo 2(-1/2)^n , we apply the Law of exponent : x^(n+m) = x^n*x^m .
Then, (-1/2)^n =(-1/2)^(n -1+1)
                        =(-1/2)^(n -1)*(-1/2)^1
                        = (-1/2)^(n -1)*(-1/2)
Plug-in (-1/2)^n =(-1/2)^(n -1)*(-1/2) , we get:
sum_(n=1)^oo 2(-1/2)^n =sum_(n=1)^oo 2*(-1/2)^(n -1)*(-1/2)
                          =sum_(n=1)^oo -1*(-1/2)^(n -1)
By comparing given infinite series  sum_(n=1)^oo -1*(-1/2)^(n -1) with the geometric series form sum_(n=1)^oo a*r^(n-1) , we determine the corresponding values as: 
a=-1 and r= -1/2 .
The convergence test for the geometric series follows the conditions:
a) If |r|lt1  or -1 ltrlt 1 then the geometric series converges to sum_(n=0)^oo a*r^n =sum_(n=1)^oo a*r^(n-1)= a/(1-r).
b) If |r|gt=1 then the geometric series diverges.
The r=-1/2 falls within the condition |r|lt1 since |-1/2|lt1 or |-0.5| lt1 .
Therefore, the series converges.
 
By applying the formula: sum_(n=1)^oo a*r^(n-1)= a/(1-r) , we determine that the given geometric series will converge to a value:
 
sum_(n=1)^oo2(-1/2)^n=sum_(n=1)^oo -1*(-1/2)^(n -1)
                            =(-1)/(1-(-1/2))
                             =(-1)/(1+1/2)
                            =(-1)/(2/2+1/2)
                             =(-1)/(3/2)
                             =(-1)*(2/3)
                             = -2/3 or -0.67 (approximated value)

For how long was Brian missing?

Thirteen year old Brian Robeson boards a plane to visit his father, who is working in Canadian oil fields. He is traveling from the New York City area to the Canadian wilderness, and he isn't excited about the trip. He is upset with his father for divorcing his mother and upset about his father's secret, that he calls "the secret," that led to their eventual divorce. Brian is the sole passenger on this plane, accompanied by only a pilot. While in the air, the pilot begins to feel bursts of pain:

And now a jolt took him like a hammer blow, so forcefully that he seemed to crush back into the seat, and Brian reached for him, could not understand at first what it was, could not know. And then knew. Brian knew. The pilot's mouth went rigid, he swore and jerked a short series of slams into the seat, holding his shoulder now . . . 'Chest! Oh God, my chest is coming apart!' . . . The pilot was having a heart attack.

Before Brian or the pilot are able to communicate with anyone over the radio, the plane crashes; the pilot dies and the plane sinks to the bottom of a lake. Brian is left stranded in the Canadian wilderness with little but a hatchet to help him survive. 
In the epilogue, readers find out that Brian was alone in the woods for 54 days before he was rescued by another pilot. 

When the pilot rescued Brian he had been alone on the L-shaped Lake for fifty-four days. During that time he had lost seventeen percent of his body weight. He later gained back six percent, but had virtually no body fat—his body had consumed all extra weight and he would remain lean and wiry for several years.

The epilogue shares how many of the effects from living in the woods, such as his lower body weight and his deep thoughtfulness, would stay with him as he grew older. He learned, for instance, to value food deeply. The book explains that he would stand in the grocery store, spellbound by the abundance of food that people can access with ease. He remembers how difficult it was to search for berries and to hunt while abandoned, without any companion, for the two approximate months that he was lost. Through his great trials, Brian learns to appreciate the conveniences of the modern world that many people overlook. 

Please explain the policy of Appeasement.

Appeasement in international relations means giving in to another nation's foreign policy desire in return for a concession. It is a form of diplomacy meant to avert war by arriving at an amicable solution to a conflict between states.
Appeasement has been discredited since World War II. It is most associated with Neville Chamberlain, prime minister of Great Britain in the late 1930s. Chamberlain is notorious for having tried to appease Hitler by giving him the Czech Sudetenland, which essentially meant ceding him all of Czechoslovakia. It was a backstab to the Czechs, but Chamberlain was sure it would avert another war. The "deal" was that Hitler would stop his aggressions if he got Czechoslovakia.
Chamberlain and many in the British upper classes were not opposed to a strong Germany as a bulwark against the Soviet Union.
Chamberlain was wrong that the Nazis would stop once they attained Czechoslovakia. Hitler was unappeasable and kept on going until he ignited World War II.
It is important to assess the personalities a nation is dealing with in foreign policy and not to allow wishful thinking to overcome reason.

Appeasement is a policy of giving in to demands now in return for a future promise. This policy can best be seen in the events leading to the start of World War II dealing with Adolf Hitler’s desire to control the Sudetenland, which was a part of Czechoslovakia. Hitler had been annexing land in Europe. He had moved his troops into the Rhineland, which was supposed to be demilitarized, and he had taken over Austria. He then wanted to take over the Sudetenland in Czechoslovakia because many Germans lived there. The leaders of Great Britain and France, Neville Chamberlain and Edouard Daladier, met with Hitler and Benito Mussolini to discuss this demand. An agreement was reached in 1938 known as the Munich Pact. In this agreement, the Allies allowed Hitler to take the Sudetenland in return for Hitler's promise to take no more land in the future. The leaders of Great Britain and France were hoping to avoid war by giving in to Hitler’s demands. This policy failed when Hitler took the rest of Czechoslovakia in 1939.
https://www.history.com/this-day-in-history/munich-pact-signed

https://www.thoughtco.com/world-war-ii-munich-agreement-2361475

int sqrt(25x^2+4)/x^4 dx Find the indefinite integral

To solve the indefinite integral, we follow int f(x) dx = F(x) +C
where:
f(x) as the integrand function
F(x) as the antiderivative of f(x)
C as the constant of integration.
For the given integral problem: int sqrt(25x^2+4)/x^4dx , we may apply integration by parts: int u *dv = uv - int v *du .
Let:
u =sqrt(25x^2+4)
Apply Law of Exponent: sqrt(x) = x^(1/2) , we get:  u =(25x^2+4)^(1/2)
To find the derivative of u , we may apply Power rule for derivative: d/(dx) u^n= n* u^(n-1) * d/(dx)(u)
u' = 1/2 *(25x^2+4)^(1/2-1) * d/(dx) (25x^2+4)
u' = 1/2*(25x^2+4)^(-1/2)* (50xdx)
u' = 25x(25x^2+4)^(-1/2)dx
Apply Law of exponent: 1/x^n =x^(-n) .
u' = (25x)/(25x^2+4)^(1/2)dx or(25x)/sqrt(25x^2+4)dx
 Let: v' = 1/x^4 dx
To find the integral of v' , we apply  Law of exponent: 1/x^n =x^(-n) and Power rule for integration:int x^n dx = x^(n+1)/(n+1) +C .
v = int v'
  = int 1/x^4 dx
  = int x^(-4) dx
  = x^(-4+1)/(-4+1)
  = x^(-3)/(-3)
  = - 1/(3x^3)
Apply the formula for integration by parts using the following values: u =sqrt(25x^2+4) , u' =(25x)/sqrt(25x^2+4) dx , v'= 1/x^4 dx and v=- 1/(3x^3) .
int sqrt(25x^2+4)/x^4dx =sqrt(25x^2+4)*-( 1/(3x^3)) - int(25x)/sqrt(25x^2+4)*(- 1/(3x^3))dx
                              =-sqrt(25x^2+4)/(3x^3) - int -25/(3x^2sqrt(25x^2+4))dx
To evaluate the integral part, we may apply the basic integration property: int c*f(x) dx = c int f(x) dx .
int -(25x)/(3x^3sqrt(25x^2+4))dx =-25/3int 1/(x^2sqrt(25x^2+4))dx
The integral resembles one of the formulas from the integration table for rational function with roots. We follow:
int (du)/(u^2sqrt(u^2+a^2)) = -sqrt(u^2+a^2)/(a^2x) +C
For easier comparison, we may apply u-substitution by letting: u^2 = 25x^2 or (5x)^2 then u=5x and du = 5dx or (du)/5 = dx . When we let u^2 =25x^2 , it can be rearrange as x^2=u^2/25 . Applying the values, the integral becomes:
-25/3int 1/(x^2sqrt(25x^2+4))dx =-25/3int 1/((u^2/25)sqrt(u^2+4))*(du)/5
                                         =-25/3int 25/(5u^2sqrt(u^2+4))du
                                        = -125/3int 1/(u^2sqrt(u^2+4))dx
By comparing "u^2sqrt(u^2+a^2) " with "u^2sqrt(u^2+4) ", we determine the corresponding value: a^2=4 . Applying the aforementioned integration formula for rational function with roots, we get:
-125/3int 1/(u^2sqrt(u^2+4))dx =-125/3* [-sqrt(u^2+4)/(4u)] +C
                                      =(125sqrt(u^2+4))/(12u) +C
Plug-in u^2= 25x^2 and u =5x on  (125sqrt(u^2+4))/(12u) +C , we get the indefinite integral:
int -25/(3x^2sqrt(25x^2+4))dx=(125sqrt(25x^2+4))/(12*5x) +C
                                       =(25sqrt(25x^2+4))/(12x) +C .
For the complete indefinite integral, we get:
int sqrt(25x^2+4)/x^4dx =-sqrt(25x^2+4)/(3x^3) - int -25/(3x^2sqrt(25x^2+4))dx
                             =-sqrt(25x^2+4)/(3x^3)-(25sqrt(25x^2+4))/(12x) +C

What does it mean to say that there were two American revolutions? How were they related?

The event most commonly referred to as the American Revolution is the War of Independence. From 1775 to 1783, the American Colonies fought a war against the government of King George III of Great Britain. The Second American revolution that comes to mind is the American Civil War, which was fought from 1861-1865 during which the southern States declared their independence from the Federal Government and fought a War of Rebellion in order to establish their own autonomy as the Confederate States of America.
The Revolutionary War and the Civil War were both characterized by armed rebellions against the established centralized government. Both resulted in protracted campaigns that inflicted heavy casualties on the combatants and heavy tolls on the populace. They also both resulted in significant course shifts for the direction of the Nation, and left a lasting imprint on the minds of the people of the United States.

Single Variable Calculus, Chapter 3, 3.5, Section 3.5, Problem 42

Determine the derivative of the function $y = \sqrt{x+\sqrt{x+ \sqrt{x}}}$


$
\begin{equation}
\begin{aligned}
y' &= \frac{d}{dx} \left(\sqrt{x+\sqrt{x+ \sqrt{x}}}\right)\\
\\
y' &= \frac{d}{dx} \left(x+\sqrt{x+ \sqrt{x}}\right)^{\frac{1}{2}}\\
\\
y' &= \frac{1}{2} \left(x+\sqrt{x+ \sqrt{x}}\right)^{\frac{-1}{2}} \frac{d}{dx} \left( x + \sqrt{x+\sqrt{x}}\right)\\
\\
y' &= \frac{1}{2} \left(x+\sqrt{x+ \sqrt{x}}\right)^{\frac{-1}{2}} \left[ \frac{d}{dx} (x) + \frac{d}{dx} (x + \sqrt{x})^{\frac{1}{2}} \right]\\
\\
y' &= \frac{1}{2} \left(x+\sqrt{x+ \sqrt{x}}\right)^{\frac{-1}{2}} \left[ 1 + \frac{1}{2} (x+ \sqrt{x})^{\frac{-1}{2}} \frac{d}{dx} (x+\sqrt{x})\right]\\
\\
y' &= \frac{1}{2} \left(x+\sqrt{x+ \sqrt{x}}\right)^{\frac{-1}{2}} \left[ 1 + \frac{1}{2} (x+\sqrt{x})^{\frac{-1}{2}} \left( \frac{d}{dx} (x) + \frac{d}{dx} (x)^{\frac{1}{2}}\right)\right]\\
\\
y' &= \frac{1}{2} \left(x+\sqrt{x+ \sqrt{x}}\right)^{\frac{-1}{2}} \left[ 1 + \frac{1}{2} (x+\sqrt{x})^{\frac{-1}{2}} \left( 1+ \frac{1}{2}(x)^{\frac{-1}{2}}\right) \right]\\
\\
y' &= \left[ \frac{1}{2 \left( x+ \sqrt{x+\sqrt{x}}\right)^{\frac{1}{2}}}\right] \left[ 1 + \left( \frac{1}{2\sqrt{x+\sqrt{x}}}\right) \left( 1 + \frac{1}{2\sqrt{x}}\right)\right]\\
\\
y' &= \frac{ 1+\frac{1+\frac{1}{2\sqrt{x}}}{2\sqrt{x+\sqrt{x}}}}{2 \sqrt{x\sqrt{x+\sqrt{x}}}}


\end{aligned}
\end{equation}
$

What is the resolution in "The Monkey's Paw"?

The resolution at the end of "The Monkey’s Paw" is left ambiguous. After Mr. White’s first wish accidentally results in the death of his son Herbert, Mrs. White forces him to wish that Herbert was alive again. In the final moments of W. W. Jacobs’s short story, Mr. White uses his final wish, and the knocking at the door goes away. When he opens it, no one is there, and we learn that “The streetlight opposite shone on a quiet and deserted road.” "The Monkey’s Paw" works through themes of fate and causality, and the lack of clear resolution at the end emphasizes these themes.
Mr. White’s first two wishes appear in the story in the form of dialogue, and thus the reader knows precisely what he has asks for. With the first wish in particular, we are able to analyze the chain of cause and effect: we can see how his wish for 200 pounds brings about the death of his son.
With the final wish, this dynamic is reversed: we see the first signs of his wish (its effect), but we do not know what he has asked for. Morris tells the White family that the paw was designed to show the power of fate and teach a lesson to those who try to challenge it. The first wish certainly supports this idea, and the final line of the story reveals an unnerving degree of isolation. We know that their son is not there, and given the cursed origin of the paw, we can assume that another tragedy probably awaits the White family. Did Mr. White wish for his son to go away, or for there to be no one outside his door? What if no one is left alive in the world except Mr. and Mrs. White? The ambiguity at the end draws attention to the risk of trying to control fate.

From the story "A Very Old Man with Enormous Wings" by Gabriel Garcia Marquez, explain the lines: "He awoke with a start, ranting in his hermetic language and with tears in his eyes, and he flapped his wings a couple of times which brought on a . . . cataclysm in response."

The late Colombian author and journalist Gabriel Garcia Marquez was known for his surrealistic style of writing, as well as for his journalistic nonfiction depictions of his native land. His short story "A Very Old Man with Enormous Wings" fits neatly into his surrealistic fictional style. This particular story, however, also fits into something of an unofficial genre involving themes wherein the general populace is in dire need of spiritual rejuvenation or in need of a heroic figure onto which to cling for security or salvation and believes, incorrectly, that it has discovered some such figure. Films like Being There and Down and Out in Beverly Hills, to name just two, successfully depicted these situations, the former illuminating the perceived need for wise leadership, the latter for purity of soul. "A Very Old Man with Enormous Wings" is about the discovery of an old, decrepit man with wings in whom the local population invest their hopes for some sign of divine presence. There is nothing save his wings to suggest anything magical or mystical about him--the popular perception is that, because of his wings, he is an angel--but he quickly becomes a symbol of hope and the elixir for the myriad ills brought before him.
The old man, it turns out, is apparently lacking in the mystical or spiritual powers that the local population assumes on his behalf. As Marquez's narrator notes, the old man's "only supernatural virtue seemed to be patience." In short, the masses are growing disillusioned, and the old man is growing increasingly irritable and lethargic. The narrator notes concerning the increasingly contentious relationship:

"The only time they succeeded in arousing him was when they burned his side with an iron for branding steers, for he had been motionless for so many hours that they thought he was dead."

It is this passage that is immediately followed by the reference to the old man being awoken "with a start...." What, then, is the meaning behind Marquez's description of the old man's hermetic language and teary eyes and the flapping of his wings? The author is emphasizing the old man's weariness and frustration with being perceived as a form of deity to be exploited and, after the onset of disillusionment among the people, to be ridiculed and harassed.
Stories such as those referenced above and Marquez's invariably display the disillusionment of the populace when the hoped-for deity or hero is revealed to be imperfect. The proverbial idol with feet of clay has proven a resilient theme for many stories over the years, beginning, obviously, with the Bible. Marquez's very old man with enormous wings is just that: an old man with wings, and, apparently, nothing more.

What is the connection between the historical record and the film Revolution (1985) starring Al Pacino? I need help forming my thesis statement for my 800-word history essay. In particular, the assignment should insert the missing African-American voice from the film and expand on the experience of the film’s main character, Tom Dobb, who represents the poor/laboring class among the soldiers. I am required to use at least five primary sources from the Voices Reader in Chapters 2 and 4 or 5 and the movie Revolution. Any help with forming a thesis statement would be greatly appreciated.

The accuracy of the film Revolution has been questioned by some critics, who point out aspects of Dobb’s work that support the fictional story at the expense of historical truth. Primarily, they stress Dobb’s use of melodrama, which characterizes critical scenes, and his choice of which events and facts to highlight and which to omit.
Historical writers, like any writers, exercise creative license when they produce their works of art, and inevitably, the have to choose, from among the vast amounts of material available to them, the material that would best support their story and convey the ideas they want to convey. Therefore, in determining historical accuracy, it is necessary to compare the events portrayed in the film to the same events explained by people who witnessed them. The characters' actions might be realistic within the plot of the film but unrealistic when considering the events that were omitted but add clarity to the picture.
For example, the scene at Valley Forge is thought to distort the facts considerably. The Patriots did not have to evade the British soldiers to smuggle supplies into the camp, for instance, though this is the account that Dobbs gave. Dobbs most likely included this scene not only to support the plot but also to emphasize the Patriots’ fear of the British. The fear of the British was real and pervasive—but the events that unfold in the story to demonstrate that fear are questionably different than those that actually took place.
As far as the error of omission goes, Dobbs omits a lot of battles and details in order to develop his plot and the relationships between the characters. This begs the question of whether he omits these details because they clash with the story. And, if he omits details because they clash with the story, how much does he alter the facts he includes in order to move his plot to conclusion?

In formulating your thesis, you should think about the ways in which the film accurately or inaccurately depicts the experience of the working person (represented by Tom Dobb in the film) during the American Revolution and the way in which the concerns of African-Americans are not represented in the film. Your thesis might address both of these points.
First, try to think about the ways in which the film captures the experience of working-class soldiers in the American Revolution and compare these experiences to your primary source documents. In the film, for example, Tom Dobb receives a note for $70 from the American government for his boat, but, after the war, he only receives $40. He also never receives the land he was promised for fighting in the war. How does Dobb's experience compare with that of the real-life Joseph Plumb Martin, who fought in the Continental Army (this is one of your documents)? Martin feels that soldiers should have received land after the war and writes of the Continental Army's officers, “The truth was, none cared for them; the country was served, and faithfully served, and that was all that was deemed necessary. It was, soldiers, look to yourselves; we want no more of you." Your thesis can compare the experiences of real-life soldiers such as Martin with that of Tom Dobb and his son, Ned, in the movie. 
The experience of African Americans is not included in the movie, and your thesis can comment on this absence. In the body of your paper, you can examine primary sources such as Benjamin Banneker's 1791 letter to Jefferson in which he takes Jefferson to task for denying black people the same rights Jefferson demanded for Americans in the Declaration of Independence. Banneker writes the following:

"In detaining by fraud and violence so numerous a part of my brethren under groaning captivity and cruel oppression, that you should at the same time be found guilty of that most criminal act, which you professedly detested in others, with respect to yourselves."

When composing your thesis, think about whether the film does justice to the actual experiences of African Americans and the poor during the Revolution. Does the film accurately capture the experiences of the working class and African Americans during the Revolution? By answering this question, you will be able to produce a solid thesis that will provide a roadmap for the rest of your paper and that will include the necessary documents. 

Why does Portia lie to Lorenzo and tell him that she is going to a monastery in Act three, Scene 4?

Portia has decided to travel to Venice disguised as a lawyer in order to defend Antonio. This means she has to dress up as a man and also that she has to come up with some explanation for her disappearance that won't reveal where she is really going and what she is really doing. As she is bringing Nerissa as her clerk, also disguised as a man, she has to account for her absence as well.
Therefore, she tells Lorenzo that she and Nerissa are going into a monastery to pray for a few days, and he will have to run the household.
On one level, this is simply a plot device that accounts for any questions the audience might have about how Portia could wholly disappear without people raising alarms about her safety. Beyond that, however, there is humor or irony in Portia saying she going into a monastery—a completely reclusive and modest activity—when in fact she is doing the opposite, asserting herself in the world in a forceful and creative way.

In Act three, Scene 4, Lorenzo praises Portia for being noble and understanding in regards to her husband's friendship with Antonio. Portia responds by saying that she never regrets doing a good thing and proceeds to tell Lorenzo that she will be leaving him in charge of her household until Bassanio returns. Portia lies to Lorenzo by telling him that she has made a secret vow to God to live in prayer and contemplation alone until her husband returns. She also says that she and Nerissa will be staying at a monastery two miles away and nobody is to bother them while they are there. The reason Portia lies to Lorenzo is because she plans on traveling to Venice where she will dress up and impersonate Doctor Balthazar in order to influence Antonio and Shylock's court case. Portia does not want Lorenzo or anybody else knowing that she is leaving Belmont, which is why she tells Lorenzo that she needs to be alone in the monastery.

What do the settings reflect in "The Story of an Hour"?

In "The Story of an Hour," the setting reflects the Victorian Age in which the feme covert laws were in effect. These laws that greatly restricted women and their ownership of property profoundly affected women, and these affects are  exemplified in the character of Louise Mallard. 
A restricted life
The repression under which Mrs. Mallard dwells is evinced in several ways. The doctor perceives her as a woman "with a heart trouble," and she must be treated with delicacy. So, when she must be told that her husband is on the list of those thought dead from the railroad disaster, Mr. Mallard's friend Richard hurries to the Mallard home in order to carefully break the news of the tragedy to his wife. And, when she is told, Mrs. Mallard does not stand stunned, but, instead, cries with "wild abandonment,"as though there were more than loss involved in her life. Then, she insists upon going up the stairs alone. 
Her own room and a sense of freedom
When Mrs. Mallard enters her bedroom, she sinks into a "comfortable, roomy armchair" that faces an open window. Exhausted by the emotion of the fatal news, she looks outside over the tops of trees that are "aquiver with the new spring life." In the air is "the delicious breath or rain," and she hears a song being sung on the street. The sky has "patches" of blue that have collected in the west facing her window.Clearly, Mrs. Mallard has entered a fresh, new, hopeful setting as she sits in her home looking to the western horizon, enjoying her feelings and contemplating the change in her life. Finally, the words spill from her, "free, free, free!" Her pulses beat quickly and she is warmed by the coursing blood in her veins. Under the law, her property, surrendered in marriage, now returns to her and she "drink[s] in the elixir of life through the open window."
The staircase down
Louise Mallard rises and answers the pleas of her anxious sister.

There was a feverish triumph in her eyes, and she carried herself unwittingly like a goddess of Victory.

She puts her arm around her sister Josephine and they descend the stairs together. Unexpectedly, however, the front door opens and Brently Mallard enters with no knowledge of the train wreck; for, he had been far from the scene.Mrs. Mallard is so shocked to realize that life will return her to the role of repressed wife that she dies" of heart disease--of joy that kills." 
https://www.library.hbs.edu/hc/wes/collections/women_law/

President Higgins stresses the importance of individuals increasing their awareness of poverty in Ireland and deciding that it is an important issue to address. He emphasizes that humans are interdependent beings and acknowledges the power that social cohesion can have in eradicating issues like poverty. Based on President Higgins's viewpoint, how does social policy manage human interdependencies?

This is a great question! I will define social policy and provide an explanation of how it manages interdependence.
Irish social policy is based upon the idea that government is responsible for the welfare of the general public. In this instance, the foundational principle of social policy is interdependence, which is defined as the mutual reliance between groups of people. President Michael Higgins argues that this social cohesion is crucial to the fight against poverty. From that standpoint, any social policy that is crafted must focus on the management of human interdependencies. Basically, this type of social policy is vested in preventing social fragmentation. 
Such a social policy manages human interdependence through education, a realigning of national taxation policy, and mutual cooperation between economies. For example, President Michael Higgins maintains that the teaching of philosophy is crucial to changing widely accepted worldviews. 
In terms of mutual cooperation between economies, President Higgins supports the economic interdependence between Ireland and Great Britain, an interdependence that promotes intellectual cooperation and shared innovation. Last but not least, social policy is focused upon eradicating economic disparity through a realigning of tax policy. A welfare-based state focuses on raising taxes to pay for social programs that address the housing, food, employment, and health care needs of the economically disadvantaged. 

What type of novel is Treasure Island by Robert Louis Stevenson?

Treasure Island is a coming-of-age story.
Treasure Island is also an adventure novel. While its genre is technically historical fiction because its setting is the 1700s, Robert Louis Stevenson wrote it with the intention of creating a narrative rich in action and suspense. Despite his suggestions of the ambiguity of morality with the character Long John Silver, Stevenson composed this coming-of-age story for his son.
A boy named Jim Hawkins discovers a sea chest containing maps and a journal. Since his father is dead, he takes the maps to the local physician, Dr. Livesey, who becomes very interested because it is a map for buried treasure on an island. The doctor then talks with the local squire Trelawney, who proposes buying a ship and searching for this treasure. Jim goes along as the cabin boy.
Once on the sea, Jim overhears the crew and learns they are pirates who intend to steal the treasure after the ship lands on the island. This is why Long John Silver, the "cook," has exerted more control over them than the captain of the ship. Once the ship approaches the treasure island, the crew becomes very rowdy, leading Captain Smolett to have half the crew go ashore and the other half remain on the ship. Jim smuggles himself along. He meets Ben Gunn, who was with Captain Flint when he buried the treasure. While this is happening, Dr. Livesay finds Captain Flint's stockade. When he hears the screams of a crew member being murdered by Long John Silver, Livesay decides to move the honest crew off the ship to the fort. A battle then begins.
During a hiatus, Jim sneaks away and borrows Ben Gunn's boat so he can go to the ship and cut the anchor rope, setting the ship adrift. His little boat gets smashed, so he jumps to the bowsprit of the ship and climbs aboard. He is attacked by Israel Hands. A knife hits Jim in the shoulder, but he manages to shoot the pirate. This is Jim's coming-of-age moment, and he makes other moral choices afterwards.
A certain moral ambiguity accompanies the pirates, especially Long John Silver. He kills one of the crew, but this pirate is really evil, and he later saves Jim from the pirates, saying,

You won't fight, as gentlemen o' fortune should; then, by thunder, you'll obey, and you may lay to it! I like that boy now; I never seen a better boy than that. He's more a man than any pair of rats of you in this here house, and what I say is this: let me see him as'll lay a hand on him—that's what I say, and you may lay to it.

Thus, Long John Silver becomes one of the "good-bad" villains compared to the others. In the end, Long John Silver slips away, so moral judgment never falls upon him. In this way, Stevenson avoids damaging an interesting character in literature.

Do you think it is right for some one to take the law into his/her own hands because some one has harmed this person? (This question is in reference to A Tale of Two Cities)

Wars and matters of national interest notwithstanding, it is morally wrong for a person or persons to seek revenge against others, especially when it involves taking human life. 
Madame Defarge knits the names of the enemies of the revolution, but it is because of her personal vendetta that she knits into her handiwork the name Evremonde. The Marquises Evremonde are both dead; they are the guilty ones. Charles Darnay, né Evremonde, has left France and never injured anyone. Furthermore, she has also recorded Dr. Manette in her list because he has pleaded for the life of Charles Evremonde (Darnay), the husband of his beloved daughter. 
When Monsieur DeFarge is troubled that Dr. Manette is on the list, he says to his wife,

"Extermination is a good doctrine, my wife...in general, I say nothing against it. But this Doctor has suffered much; you have seen him to-day; you have observed his face when the paper was read."

Angered and with contempt, Madame Defarge counters,

"Yes, I have observed his face! I have observed his face to be not the face of a true friend of the Republic." (Bk.3, Ch.12)

Madame Defarge would have Dr. Manette exterminated because he has allowed his daughter Lucie to marry Charles Darney, who is actually an Evremonde, the sworn enemies of Madame Defarge because the Evremonde twins raped her older sister and killed her sister, her sister's unborn child, her brother, and her father.

Explain how Saki makes the surprise ending of "The Interlopers" seem logical.

Georg's and Ulrich's family have been fighting over a piece of land for generations. Ulrich's grandfather wins the land in a lawsuit, but Georg's family continued to poach upon it, regardless of the determination of the court. In a sense, both men have continuously attempted to own and tame the land. This land is in the forest. It is wild. These men have attempted to own, cultivate, and rule over this piece of wild land. They have attempted to regulate the land with their civilized laws and notions of "owning land." But this is nature. It seems illogical to impose a law on something that is inherently wild. So, the "civilized" Georg and Ulrich are the interlopers. They are trying to impose their way of life onto nature itself. 
They've spent their lives fighting each other, each thinking that his opponent is the interloper. But nature (the wolves) show that both men have been interloping on their (wolves') land. So, it is morbid but logical that the true interlopers are exposed in the end. This is a classic story of the hunters becoming the hunted. 

Which of these 7 elements (totalitarian government, rigid caste system, society is closely monitored, highly developed technology, violence and pain, environmental disasters, lack of free choice) appear in The Giver? Give reasons explaining your answer.

I would like to argue that "society is closely monitored" in The Giver more than just "somewhat" and that Jonas's society does have "highly developed technology."
The citizens in The Giver are observed and monitored constantly, not just by each other and the Elders, who need to do that in order to eventually assign appropriate jobs, but by some kind of "police" as well. We learn this when Jonas notices something unusual about an apple (he starts to be able to perceive it as red) and tries to take it home to explore the object further. He is then immediately reprimanded by the loudspeaker reminding everyone that fruits and snacks are to be eaten, not to be played with. While the announcement is made in an impersonal way, Jonas knows that it applies to him and that his action has been noticed.
The technology in Jonas's society is highly developed; however, its use is scrupulously controlled, and it is used only for specific purposes: to (presumably) benefit society, never for entertainment. The following are some of the many examples of the results of advanced technology:
a high level of climate control achieved in the region where Jonas lives—there is no inclement weather
feats of genetic engineering—all people in the community, with few exceptions, look the same. "They" are working on eliminating blue eyes, like Jonas's and Gabriel's, and red hair, like Fiona's
babies are produced by artificial insemination
a well-developed surveillance system, as evident in Jonas's experience with the apple; also, the Giver is able to show Jonas the videotape of the "release" performed earlier, and he can communicate from his "dwelling" with the outside world through some kind of video conference system
All of the above point to the remarkable achievements in science and technology, rigidly controlled by those who have power but not available to most of the community.

Totalitarian Government: Yes
A totalitarian government is characterized as a governing body that dictates almost every aspect of society and represses individual freedoms in order to control its citizens. Throughout the novel, Jonas's society is controlled by the Committee of Elders, who have the authority to issue and enforce laws. Every citizen is required to follow the laws and regulations of society, or else they are "released." The citizens have no say with regard to their individual freedoms and must obey the laws set by the Committee of Elders. After a citizen's third transgression, they are "released," which is a euphemism for being killed. As in other totalitarian regimes, the citizens of Jonas's society are exposed to propaganda and taught that the laws enforced are necessary for their safety and well-being. The citizens blindly accept the laws set forth and are content to live without their individual freedoms. The goal of the totalitarian government in the novel is to create a society void of emotional and physical pain. In order to maintain this society, the government strictly regulates every aspect of its citizens' lives.
Rigid Caste System: No
Unlike other fictional societies, there is no rigid caste system found in The Giver. Every individual is treated equally in Jonas's society and given the same opportunities. Other than the Receiver and Giver, who are given special privileges because of their important occupations, the citizens live among each other as equals. One could argue that the Committee of Elders is the upper class, but there is still no evidence of a rigid caste system in Jonas's society.
Society Is Closely Monitored: Somewhat
Throughout the novel, the Committee of Elders is continually observing the citizens, particularly the younger children. During the Ceremony of Twelve, the Chief Elder explains how the Committee carefully observes each child before assigning them to an occupation. The citizens also closely regulate themselves and report misconduct. However, there are no Thought Police or telescreens in the walls of the citizens' homes like in 1984.
Highly Developed Technology: No
Jonas's society is in many ways not much more developed than ours. The most sophisticated technology explicitly mentioned in Jonas's society is when a plane flies over the community. They also issue statements over a loudspeaker, which would not be considered an advanced piece of technology.
Violence and Pain: No
As was mentioned earlier in this response, the goal of the governing body is to prevent violence and pain, which is the reason individual freedoms are repressed. Jonas and the Giver are the only members of society who have experienced pain. When Jonas receives his Assignment, he is unnerved when he is told that he will experience pain for the first time. The Receiver and Giver contain all of the community's pain and knowledge throughout the novel. The general population does not understand pain or violence—though the society does have a darker relationship with death, or "release."
Environmental Disasters: No
Throughout the novel, Jonas's community does not experience an environmental disaster. Environmental disasters impact the natural environment and are caused by human activity. The only disaster that is mentioned involved the Giver's daughter releasing her painful memories into the community. However, the natural environment of the community was never affected throughout the novel.
Lack of Free Choice: Yes
As was mentioned earlier in this response, the Committee of Elders strictly regulates society. The citizens are forbidden from acting upon their impulses and are not given their individual freedoms. In Jonas's society, marriages are arranged, children selected, and occupations assigned. Citizens are expected to play their roles in society and obey the decisions of the Elders. Individuals are not free to think and behave as they please. Failure to comply with society's expectations results in being "released."

Single Variable Calculus, Chapter 8, 8.2, Section 8.2, Problem 32

Determine the integral $\displaystyle \int \tan^6 (ay) dy$

Let $u = ay$, then $du = ady$, so $\displaystyle dy = \frac{du}{a}$. Thus,


$
\begin{equation}
\begin{aligned}

\int \tan^6 (ay) dy =& \int \tan^6 u \cdot \frac{du}{a}
\\
\\
\int \tan^6 (ay) dy =& \frac{1}{a} \int \tan^6 u du
\\
\\
\int \tan^6 (ay) dy =& \frac{1}{a} \int \tan^4 u \tan^2 u du
\qquad \text{Apply Trigonometric Identity } \sec^2 u = \tan^2 u + 1
\\
\\
\int \tan^6 (ay) dy =& \frac{1}{a} \int \tan^4 u (\sec^2 u - 1) du
\\
\\
\int \tan^6 (ay) dy =& \frac{1}{a} \int (\tan^4 u \sec^2 u - \tan^4 u) du
\\
\\
\int \tan^6 (ay) dy =& \frac{1}{a} \int \tan^4 u \sec^2 u du - \frac{1}{a} \int \tan^4u du

\end{aligned}
\end{equation}
$


We integrate the equation term by term

@ 1st term

$\frac{1}{a} \int \tan^4 u \sec^2 u du$

Let $v = \tan u$, then $dv = \sec^2 u du$. Thus


$
\begin{equation}
\begin{aligned}

\frac{1}{a} \int \tan^4 u \sec^2 u du =& \frac{1}{a} \int v^4 dv
\\
\\
\frac{1}{a} \int \tan^4 u \sec^2 u du =& \frac{1}{a} \left( \frac{v^{4 + 1}}{4 + 1} \right) + c
\\
\\
\frac{1}{a} \int \tan^4 u \sec^2 u du =& \frac{v^5}{5a} + c
\\
\\
\frac{1}{a} \int \tan^4 u \sec^2 u du =& \frac{(\tan u)^5}{5a} + c
\\
\\
\frac{1}{a} \int \tan^4 u \sec^2 u du =& \frac{\tan^5 u}{5a} + c


\end{aligned}
\end{equation}
$


@ 2nd term



$
\begin{equation}
\begin{aligned}

\frac{1}{a} \int \tan^4 u du =& \frac{1}{a} \int \tan^2 u \tan^2 u du
\qquad \text{Apply Trigonometric Identity } \sec^2 u = \tan^2 u + 1
\\
\\
\frac{1}{a} \int \tan^4 u du =& \frac{1}{a} \int \tan^2 u (\sec^2 u - 1) du
\\
\\
\frac{1}{a} \int \tan^4 u du =& \frac{1}{a} \int (\tan^2 u \sec^2 u - \tan^2 u) du
\\
\\
\frac{1}{a} \int \tan^4 u du =& \frac{1}{a} \int \tan^2 u \sec^2 u du - \frac{1}{a} \int \tan^2 u du
\qquad \text{Apply Trigonometric Identity } \sec^2 u = \tan^2 u + 1 \text{ for the 2nd term}
\\
\\
\frac{1}{a} \int \tan^4 u du =& \frac{1}{a} \int \tan^2 u \sec^2 u du - \frac{1}{a} \int (\sec^2 u - 1) du

\end{aligned}
\end{equation}
$


For the 1st term, let $v = \tan u$, then $dv = \sec^2 u du$. Thus,


$
\begin{equation}
\begin{aligned}

\frac{1}{a} \int \tan^4 u du =& \frac{1}{a} \int v^2 dv - \frac{1}{a} (\tan u - u) + c
\\
\\
\frac{1}{a} \int \tan^4 u du =& \frac{1}{a} \left( \frac{v^{2 + 1}}{2 + 1}\right) - \frac{1}{a} ( \tan u - u ) + c
\\
\\
\frac{1}{a} \int \tan^4 u du =& \frac{v^3}{3a} - \frac{\tan u}{a} + \frac{u}{a} + c
\qquad \text{Substitute value of } v
\\
\\
\frac{1}{a} \int \tan^4 u du =& \frac{(\tan u)^3}{3a} - \frac{\tan u}{a} + \frac{u}{a} + c
\\
\\
\frac{1}{a} \int \tan^4 u du =& \frac{\tan^3 u}{3a} - \frac{\tan u}{a} + \frac{u}{a} + c

\end{aligned}
\end{equation}
$


Combine the results of the integration term by term


$
\begin{equation}
\begin{aligned}

\int \tan^6 (ay) dy =& \frac{\tan^5 u}{5a} - \left( \frac{\tan^3u}{3a} -\frac{\tan u}{a} - \frac{\tan u}{a} + \frac{u}{a} \right) + c
\\
\\
\int \tan^6 (ay) dy =& \frac{\tan^5 u}{5a} - \frac{\tan^3 u}{3a} + \frac{\tan u}{a} - \frac{u}{a} + c
\qquad \text{Substitute value of } u
\\
\\
\int \tan^6 (ay) dy =& \frac{\tan^5 (ay)}{5a} - \frac{\tan^3 (ay)}{3a} + \frac{\tan (ay)}{a} - \frac{\cancel{a}y}{\cancel{a}} + c
\\
\\
\int \tan^6 (ay) dy =& \frac{\tan^5 (ay)}{5a} - \frac{\tan^3 (ay)}{3a} + \frac{\tan (ay)}{a} - y + c

\end{aligned}
\end{equation}
$

How did Melba spend most lunches at school?

After previous attacks from angry white students, Melba spent most of her lunches at Central High alone. She avoided the cafeteria, preferring to eat in a more secure spot.
Because there were no uniformed officials or National Guardsmen in the cafeteria, the nine African American students were often exposed to harassment from belligerent white students. Melba relates how her friend, Minnijean was attacked in the cafeteria a day before winter vacation began.
Accordingly, five African American students had entered the cafeteria for lunch that day. On her way back from the lunch line, Minnijean was taunted by two white boys. Minnijean had a big bowl of chili on her tray, and the boys would not let her pass. They heckled her, kicked at her, tried to trip her, and called her names.
Meanwhile, Melba watched helplessly from a distance. She knew that if she tried to help Minnijean, other white students would rush in. Since there were only five African American students in the cafeteria, Melba was afraid to intervene; they were outnumbered 200 to 1.
Events soon came to a head after Minnijean lost control of her tray and the heckling boys were splattered with chili. A school official soon showed up to take Minnijean away. Later, a white student cruelly taunted Melba with the information that Minnijean had been suspended. Events such as this prompted Melba to spend most lunches by herself, away from the cafeteria.

Why was John Locke regarded as the father of classical liberalism?

Classical liberalism is the set of ideas most identified (within the United States at least) as "libertarianism." Classical liberalism formed in opposition to hereditary monarchy, particularly monarchy's absolutist variant.
Locke, writing in the late seventeenth century, articulated many of the ideas held dear by classical liberals. One was that every human being had certain rights that could not be taken away by a government without one's consent. This was because the government did not grant people these rights in the first place. They were rather "natural rights," that is, they were inseparable from the human condition. So government by the consent of the governed was a fundamental belief of classical liberalism, and it followed that government should be as unobtrusive as possible into the lives of the people who gave it permission to govern. Taxes should be very low, government interference in the economy should be minimal (so as not to deprive people of their property rights), and government should be, as much as possible, a reflection of the will of the people—or at least those with property. Classical liberals also, like Locke, supported civil liberties like freedom of religion, due process in the courts, free press, and other institutions we would associate with modern liberal democracies. Locke's On Toleration was a touchstone for religious tolerance, and he generally favored the free press. So for these reasons, Locke is considered the founder of classical liberalism.

Single Variable Calculus, Chapter 4, 4.7, Section 4.7, Problem 6

First the dimension of a rectangle with area $1000 m^2$ whose perimeter is as small as possible.
Let $A$ and $P$ be the area and the perimeter of the rectangle respectively.
So, $A = xY$; $xy = 1000$
We have, $\displaystyle x = \frac{1000}{y} \quad \Longleftarrow \text{(Equation 1)}$

Also, $P = 2x + 2y$
Substitute Equation 1

$
\begin{equation}
\begin{aligned}
P &= 2 \left( \frac{1000}{y} \right) +2y\\
\\
P &= \frac{2000}{y} + 2y
\end{aligned}
\end{equation}
$

when $P' = 0$,

$
\begin{equation}
\begin{aligned}
P' &= \frac{-2000}{y^2} +2\\
\\
0 &= \frac{-2000}{y^2} +2\\
\\
y^2 &= \frac{2000}{2}\\
\\
y &= \sqrt{1000}\\
\\
y &= 10\sqrt{10}m
\end{aligned}
\end{equation}
$

So,

$
\begin{equation}
\begin{aligned}
x &= \frac{1000}{y} = \frac{1000}{10\sqrt{10}}\\
\\
x &= 10 \sqrt{10}m
\end{aligned}
\end{equation}
$

Therefore, the rectangle has length $x = 10 \sqrt{10}m$ and width $y = 10 \sqrt{10}m$

Is A Raisin in the Sun a drama or a tragedy?

While A Raisin in the Sun certainly bears elements of a tragedy, including a bleak inciting incident, plainly flawed characters, and an incredibly cynical view on the true nature of humanity, particularly where greed is concerned, the play falls a bit more neatly into the category of a drama. The main distinction that sets it apart from a traditional tragedy is that it lacks a tragic hero, or a particular character that suffers a grim fate due to an insurmountable flaw. Indeed, the action of the play revolves around an entire family, exploring the relationships and dynamics between the characters through conflicts that tend to be more episodic. This are all elements of a drama. Furthermore, though there are many tragic turning points and dark eventualities in the play, it does end on a positive note.

Lorraine Hansberry's play A Raisin in the Sun would fall into the category of domestic drama and would not be considered a tragedy. In a domestic drama, the emphasis is placed on specific members of the same family, and their relationships and struggles are depicted. Domestic dramas typically focus on lower- or middle-class families, whose members struggle with everyday problems concerning financial difficulties, marital issues, illness, or family strife. In contrast, a tragedy is a drama where the main character suffers as a result of his or her tragic flaw and illustrates the terrible events experienced by a heroic individual. Lorraine Hansberry's play A Raisin in the Sun lacks a tragic hero and does not correspond to Aristotle's definition of a tragedy. The reason A Raisin in the Sun is considered a domestic drama is because Hansberry depicts the everyday struggles of the Younger family and portrays how the insurance check alters their lives. The play also ends on a hopeful, positive note as Walter Jr. demonstrates his integrity by refusing to sell Lena's home back to the white community of Clybourne Park.

What was the doctor's observation?

When Johnsy falls ill with pneumonia and fails to show any sign of recovery, the doctor visits and tells Sue the following:

"She has one chance in—let us say, ten," he said, as he shook down the mercury in his clinical thermometer. "And that chance is for her to want to live. This way people have of lining-u on the side of the undertaker makes the entire pharmacopoeia look silly. Your little lady has made up her mind that she's not going to get well. Has she anything on her mind?"

There is another version of the story in circulation, but the doctor's observation is similar. He questions if Johnsy has anything to live for or if anything is weighing on her mind. He says that Johnsy does have a small chance to live, but she must want to live. He cannot do anything to save her until she is ready to live. Johnsy, however, is determined to die, claiming that she will die when the last leaf falls from the tree outside their window.
Once she notices that the "leaf" is not falling, her will to live returns. The doctor then returns as well, and he makes a new observation:

"Even chances," said the doctor, taking Sue's thin, shaking hand in his. "With good nursing you'll win."

The next day he returns again and notes:

"She's out of danger. You won. Nutrition and care now—that's all."

The doctor's observation in the beginning of the story proves to be true. In order to live, Johnsy needed to want to do so.

When the doctor comes to see Johnsy, who is sick with pneumonia in her Greenwich Village apartment, he tells her roommate Sue that:

"She has one chance in—let us say, ten," he said, as he shook down the mercury in his clinical thermometer. "And that chance is for her to want to live."

The doctor goes on to ask if Johnsy has anything to live for. Sue responds that Johnsy has wanted to paint the Bay of Naples some day. The doctor remains dubious, thinking that is not enough. He says to Sue,

whenever my patient begins to count the carriages in her funeral procession I subtract 50 per cent from the curative power of medicines.

Unfortunately, the case does not look good for Johnsy, who does not have a strong will to live. When Sue finds her counting backwards from ten to nine to six, she asks her what is going on. Johnsy explains that she is watching the leaves fall from the gnarled old ivy vine growing on the house twenty feet away. Johnsy tells Sue that when the last leaf falls from the vine, then she will die. This news is alarming to Sue, who tries to pooh-pooh it as nonsense. However, she remembers the doctor's words that half the battle for Johnsy to live is her state of mind. Therefore, Sue is very worried.

Johnsy is very sick with pneumonia, and her roommate and friend Sue is very worried about her and calls the doctor to come to their apartment in Greenwich Village. The doctor observes in Johnsy that her mental and emotional state are both rather shaky, and he admits that he cannot heal any patient who does not want to get better and who does not want to live. The doctor asks Sue to help Johnsy to recover her enthusiasm for life. Without this energy and will to live, the doctor predicts that Johnsy will succumb to the pneumonia, as he has seen it happen before with other patients. The doctor also wonders if Johnsy's sadness and emptiness could be explained by boy problems, which confuses Sue.

Does the author uses the phrase “the autumn towards the close of day” as a symbol of death, war, night, or fall? What does fishing symbolize in this story (peace, family, friendship, or danger)?

This quotation comes from the story "Two Friends" by Guy de Maupassant. This story concerns two friends who used to meet each other regularly on Sundays to fish before the Franco-Prussian war broke out; the core action of the story focuses on their decision to meet up again during the war. They decide to return once more to their old fishing spot, and there they are accused of espionage by Prussian soldiers.
The phrase "in the autumn, toward the close of day," is used primarily in a literal sense: it describes the "glorious spectacle" of the sun setting at the end of the day which Monsieur Sauvage would sometimes remark upon when the two men's fishing trips were a regular occurrence. As such, it represents, straightforwardly, both night and fall. On a symbolic level, however, this spectacle, with the river tinged with red and the "leaves . . . already turning at the first touch of winter," could be seen to represent the coming war that will put an end to the fishing trips and jollity. The autumnal scene depicted marks the end of the retrospective section which sets the tone for the interaction between Sauvage and Morissot before war came.
For Morissot and Sauvage, fishing represents the bond of friendship between them. At the end of the story, before the men are shot, the last thing Morissot sees before he bids goodbye to his friend is "the still quivering fish glisten[ing] like silver." Throughout the early part of the story, the two men wonder when they will be able to fish again; the idea of fishing reminds them of peacetime, but the act of fishing represents their connection to each other insofar as they want to fish even while knowing that it is dangerous.

How are Whitney's views on hunting different from Rainsford's?

In the beginning of Richard Connell's short story "The Most Dangerous Game," two big game hunters sit on the deck of a yacht speeding toward South America where they will hunt jaguars. After an initial discussion concerning a nearby island, their conversation turns to the plight of the animals they hunt. Whitney suggests that the animals experience feelings such as fear and pain. When Rainsford claims that the animals have no understanding of what is happening to them, Whitney says,

"Even so, I rather think they understand one thing—fear. The fear of pain and the fear of death."

Rainsford rejects this point of view, asserting the world is "made up of two classes—the hunters and the huntees." For Rainsford, it doesn't matter what the animal feels. It only matters that he is able to indulge in his favorite pastime. Whitney, however, acknowledges implicitly that hunting is cruel to the animals. Rainsford calls this nonsense and accuses Whitney of being soft and unrealistic. Ultimately, this conversation is later revealed to be ironic. In the end, Rainsford understands what it is like to be a "beast at bay" and it is likely that his hunting days are over after his encounter with General Zaroff. During the hunt he experiences the fear and pain which Whitney had expressed aboard the yacht in the beginning of the story.

College Algebra, Chapter 9, 9.6, Section 9.6, Problem 22

Evaluate the expression
$
\left(
\begin{array}{c}
5\\
2
\end{array}
\right)
\left(
\begin{array}{c}
5\\
3
\end{array}
\right)
$

Recall that the binomial coefficient is denoted by $\displaystyle \left( \frac{n}{r} \right)$ and is defined by
Substituting $n = 5$ and $r = 2$ gives

$
\begin{equation}
\begin{aligned}
\begin{array}{c}
5\\
2
\end{array}
=
\frac{5!}{2!(5-2)!}
=
\frac{5!}{2!3!}
&=
\frac{5\cdot 4 \cdot \cancel{3 \cdot 2 \cdot 1}}{(2\cdot1)(\cancel{3 \cdot 2 \cdot 1})}\\
\\
&= \frac{5 \cdot 4}{2 \cdot 1} = \frac{20}{2}\\
\\
&= 10
\end{aligned}
\end{equation}
$


Substituting $n = 5$ and $r = 3$ gives

$
\begin{equation}
\begin{aligned}
\left(
\begin{array}{c}
5\\
3
\end{array}
\right)
=
\frac{5!}{3!(5-3)!}
=
\frac{5!}{3!2!}
&=
\frac{5\cdot 4 \cdot \cancel{3 \cdot 2 \cdot 1}}{\cancel{3 \cdot 2 \cdot 1}(2\cdot 1)}\\
\\
&= \frac{5 \cdot 4}{2 \cdot 1} = \frac{20}{2}\\
\\
&= 10
\end{aligned}
\end{equation}
$

Thus,

$
\left(
\begin{array}{c}
5\\
2
\end{array}
\right)
\left(
\begin{array}{c}
5\\
3
\end{array}
\right)
= (10)(10)
= 100
$

Who is Osvaldo Cruz in the novel Monster?

Osvaldo Cruz is a fourteen-year-old neighborhood gang member who participates in the robbery of a local corner store. Osvaldo testifies during the trial that James King, Richard "Bobo" Evans, and Steve Harmon were all in collaboration and participated in the crime. Osvaldo mentions that the only reason he agreed to participate in the robbery was because he felt threatened by Bobo. Osvaldo's job during the robbery was to stand outside of the store and throw a garbage can in the way of anyone attempting to catch James and Richard. Osvaldo also comments that Steve Harmon's role was the lookout. When Kathy O'Brien cross-examines Osvaldo, she reveals his violent, immoral character and he admits that he had to cut an innocent person's face in order to join the Diablos. Osvaldo Cruz may be telling the truth about the people who participated in the robbery, but the jury views him as an unreliable witness who is simply benefiting from testifying. 

How should I write a bed time speech for children?

I think that bedtime speech means the same thing as bedtime story.  You can prepare your speech in the same way that you would prepare any other speech.  Before beginning, you must consider two main things -- your message and your audience.  As the question mentions, your audience is children.  Next is your message.  It's a story, but what is the story about?  If the child is a girl, perhaps something about a princess.  It doesn't have to be a princess, but I would make the protagonist a female.  If you are speaking to a boy, then make the main character a male.  If the child is young, then the story line is going to have to be short and simple.  They simply do not have the attention span to last for much beyond ten minutes.  Based on my own three children, the story should be exiting, but not scary.  Remember, the child is hearing this before bed.  You don't want your story to cause the child to lay awake in fear for the next hour.  Keep your language simple, and use a lot of color in your narration because it will help with visualization.  Some people feel differently about this last part, but I like to end bed time stories with an actual ending.  Bring the story to a close rather than leaving it with a cliffhanger.  Again, you want the child relaxed and ready for sleep.  You don't want them continuing to think about the story until very late at night.    

What measure did Ashoka take to spread Buddhism?

Emperor Ashoka, also known as Ashoka the Great, was a leader of the Mauryan dynasty and ruled most of what is now modern-day India. Conflict was a way of life for most people of the world at that time, and it was no different in ancient India. Eight years into his reign Ashoka waged war against the kingdom of Kalinga. Eventually, after a long and bitter struggle, Kalinga was conquered, a feat which none of Ashoka's ancestors had managed to achieve. But Ashoka's victory came at a terrible human cost. Even by the standards of the day, the devastation caused by the war was massive, with hundreds of thousands of people perishing in the savage conflict. Legend has it that Ashoka was so shocked by the sheer scale of the carnage that he renounced violence and became a Buddhist.
Whatever the reasons behind Ashoka's conversion, there is little doubt that he was sincere in his newfound religious convictions. He subsequently set about promoting Buddhism, not just in India, but also throughout the wider world. He built numerous shrines and monasteries; he sent missionaries to far-off places such as Greece and Egypt; his son Mahinda became a Buddhist monk and spread the religion to Sri Lanka, where it still remains the dominant religion to this day.
Ashoka remained remarkably respectful and tolerant of other religions. His policy of tolerance greatly strengthened his kingdom, leading to growing political stability and economic prosperity.
https://www.britannica.com/biography/Ashoka

What is Elizabeth's proof that John is a good man?

In Act Two, Elizabeth says, "I do not judge you.  The magistrate sits in your heart that judges you. I never thought you but a good man, John . . . —only somewhat bewildered."
They have just been arguing because John had not originally told Elizabeth that he had been alone with Abigail when Abigail confessed that the appearance of witchcraft was only "sport." He has just revealed that he was, in fact, alone with the girl with whom he'd once had an affair, and Elizabeth becomes upset because he was "not open with [her]" when they spoke before. John loses his temper now, insisting that Elizabeth only judges him rather than looking for the good in him. Her response indicates that she does think he's a good man, and it is actually he who doubts it. We can assume, then, that the years John and Elizabeth spent together have already convinced her of his goodness.
Further, it is, perhaps, his guilty conscience that makes her think of him as good, too. True, he did commit a sin, but his remorse for it could be seen as evidence that he is good, as a wholly sinful person would likely not feel such regret.

Is Pi Patel's story honest in Yann Martel's Life of Pi?

The other posted answer to the student's question—"Is Pi Patel's story honest in Yann Martel's Life of Pi"—addresses this issue quite well. The selected quotes capture the essence of the story well, as does the accompanying analysis. There is often in literature a sense that capturing the essence of a true story is sufficient to convey the author's meaning. A certain amount of fictionalization is necessary for dramatic purposes. Historical novels and films very often use poetic license as a justification for distorting the truth. Dramatization, after all, is the idea, not the plain, dry facts of an actual situation or individual. It is for this reason that I have selected the following passage from the final section of Life of Pi, in which the protagonist is addressing his interrogators' questions about the veracity of his story:

"I know what you want. You want a story that won't surprise you. That will confirm what you already know. That won't make you see higher or further or differently. You want a flat story. An immobile story. You want dry, yeastless factuality."

There can be a legitimate distinction between "honesty" and "factuality." As the other educator's response notes, only Pi knows with absolute certainty what parts, if any, of his narrative are factual and which are embellishments or complete fabrications. The "truth" usually lies somewhere in between. Pi's story involving animals clearly leans heavily toward the unbelievable, but who are we, the readers, to indict his credibility simply because we believe that story to be false? The story with animals, however, rings false precisely because of the circumstances of his life on that boat. The tragedy of the ship's sinking and consequent loss of his family followed by a long period at sea in a tiny boat on a vast ocean under the beating sun would traumatize most of us. Trauma, including post-traumatic stress disorder, can certainly distort perceptions of reality. Pi may have imagined the animals out of a need to keep his mind focused during his long sojourn, and his interest in animals, as with Martel himself, is obviously real. To Pi, the animals may have been real because his mind tricked him into believing the animals were real. Alternatively, he may have consciously fabricated the animals to, as he states, make his story more entertaining. 
Pi's story is honest. It is honest because it accurately captures the essence of the individual. It is almost certainly not, however, the truth. 

There is no way to know if Pi is telling an honest story or not.  In fact, that is the very question that Pi and author Martel leave readers with at the end of the book.  Pi is being interviewed about the sinking of the ship and the following 227 days.  He narrates two stories.  One is with animals and is full of amazing things.  It is practically unbelievable.  The other story contains none of those things, but it is more believable.  Pi boldly asks the interviewer which story he likes better.  Pi points out that the factual details did not change in either story, and the investigators can't prove which version is the true version.  They have to take his word for it. 

"So tell me, since it makes no factual difference to you and you can't prove the question either way, which story do you prefer? Which is the better story, the story with animals or the story without animals?"

Because of that single quote, I do not think that Pi is a completely honest story teller.  I believe that he is honest when it comes to telling the cold hard facts.  

"In both stories the ship sinks, my entire family dies, and I suffer."

Beyond that though, I think much of the story is imaginative embellishment on the part of Pi. 

Who wins the battle between Annie or John in "Tickets, Please" by D.H. Lawrence?

There are two aspects to the conflict between Annie and John. One is the personal conflict between just the two of them. The other is the broader conflict between the women as a group and John as a symbol of all men, not just his own individual person. The reader can evaluate if one of them wins in either or both areas.
As each individual woman was dealing with John separately, they were competing with each other. In doing so, they were endowing him with the power to choose among them. Annie initially feels competitive with the other women, and this feeling is exaggerated when John moves on to his next choice. She then realizes, however, that none of the women is really benefitting in this arrangement; in fact, quite a few women have gotten pregnant and had to leave their jobs. Once she decides to unite the women to oppose him, her position changes. Taking on a leadership role and getting all the women to join in the mission, she wins. John is vanquished; the women behave “as if he had never existed,” D. H. Lawrence says. Because their “solution” is violence, however, Annie could be considered to lose, as the women have second thoughts once they beat up John. They experience a “terrifying, cold triumph.”
Viewed another way, however, even if Annie herself does not exactly win, John definitely loses. What he had valued was his power to manipulate the women into competing over him and to have a series of meaningless, sexual relationships. He will never be able to do that again—at least, not with the tram women.

Neither John nor Annie won the battle. Annie got involved with John for the thrill and excitement even though she was aware of his tendencies with women. However, as their intimate encounters continued, she grew possessive and wanted him for herself. John never had any intention of settling with one lady and used his good looks and charm to conquer as many women as he could. When John rejected Annie and moved on to the next woman, she was left wounded and plotted revenge.
The author tells us that although Annie succeeded in her revenge by ganging up with the rest of John’s victims to physically harm him, none of them felt triumphant. John staggered away defeated and in tatters, no longer appealing to those who once adored him.

Summarize the article "Terrorism as a War Crime" by Sebastien Jodoin.

As its title indicates, "Terrorism as a War Crime" is an article that considers the possibility that considering terrorism in the context of the laws of armed conflict might "contribute to international efforts directed to combating terrorism" (2). Many aspects of international laws concerning warfare explicitly outlaw certain acts during warfare, such as the intentional targeting of civilian populations and so-called "ruses of war," that are part and parcel of terrorist acts. So terrorism in and of itself violates these laws of war. Because terrorists often claim that their acts are justified because they serve a just cause, or because they charge that civilians within a state are culpable for the actions of that state, terrorist acts not only represent a violation of humanitarian laws, but a challenge to the moral basis of these laws. As Jodoin observes, terrorism entails a "different moral conception of war, one which inexorably leads to a concept of total warfare" (16). Terrorism, by holding civilians responsible for the actions of their nation, basically eliminates the distinctions between armed forces and civilians that are the very basis of humanitarian laws of war. The problem is that the fact that terrorists are themselves often non-state actors has presented problems for nation-states, and therefore humanitarian laws have been mostly viewed as a hinderance to fighting terrorism. Jodoin argues that this is unfortunate, because humanitarian law, unlike the essentially criminal approach to dealing with terrorism in international law, treats terrorism in terms of the act itself—"prima facie apolitical"—instead of its intent (23). Humanitarian law bans acts of violence against non-combatants, and those who violate this law are terrorists. While international humanitarian law cannot stop terrorism, as the author observes:




If the primary purpose of the law of armed conflict is the limitation of chaos and human suffering prevalent in armed conflicts, then its potential to address the anarchy and anguish caused by terrorism is significant. (27)

Therefore the humanitarian laws of armed conflict should be applied to the war on terror.
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2942157

Single Variable Calculus, Chapter 5, Review Exercises, Section Review Exercises, Problem 44

Suppose that a particle moves along a line with velocity function $v(t) = t^2 - t$, where $v$ is measured in meters per second.
a.) Find the displacement of the particle during the time period $0 \leq t \leq 5$.

$
\begin{equation}
\begin{aligned}
\int^{t_2}_{t_1} v(t) dt &= s(t_2) - s(t_1)\\
\\
\int^{t_2}_{t_1} v(t) dt &= \int^5_0 \left(t^2 - t \right) dt\\
\\
\int^5_0 \left(t^2 - t \right) dt &= \int^5_0 t^2 dt - \int^5_0 t dt\\
\\
\int^5_0 \left(t^2 - t \right) dt &= \left[ \frac{t^{2+1}}{2+1} - \frac{t^{1+1}}{1+1} \right]^5_0\\
\\
\int^5_0 \left(t^2 - t \right) dt &= \left[ \frac{t^3}{3} - \frac{t^2}{2} \right]^5_0\\
\\
\int^5_0 \left(t^2 - t \right) dt &= \frac{(5)^3}{3} - \frac{(5)^2}{2} - \frac{(0)^3}{3} + \frac{(0)^2}{2}\\
\\
\int^5_0 \left(t^2 - t \right) dt &= \frac{125}{3} - \frac{25}{2}\\
\\
\int^5_0 \left(t^2 - t \right) dt &= \frac{175}{6} m\\
\\
\int^5_0 \left(t^2 - t \right) dt &= 29.17m
\end{aligned}
\end{equation}
$

b.) Find the distance traveled during this time period
Note that $v(t) = t^2 - t = t(t - 1)$, and $t(t-1) = 0$ then $t = 0$ and $t = 1$

$
\begin{equation}
\begin{aligned}
\int^5_0 |v(t)| dt = \int^5_0 \left| t^2 - t \right| dt &= \int^1_0 - \left( t^2 - t \right) dt + \int^5_1 \left( t^2 - t \right) dt\\
\\
\int^5_0 |v(t)| dt = \int^5_0 \left| t^2 - t \right| dt &= \int^1_0 \left( -t^2 + t \right) dt + \int^5_1 \left( t^2 - t \right) dt\\
\\
\int^5_0 |v(t)| dt = \int^5_0 \left| t^2 - t \right| dt &= \left[ \frac{-t^{2+1}}{2+1} + \frac{t^{1+1}}{1+1} \right]^1_0 + \left[ \frac{t^{2+1}}{2+1} - \frac{t^{1+1}}{1+1} \right]^5_1\\
\\
\int^5_0 |v(t)| dt = \int^5_0 \left| t^2 - t \right| dt &= \left[ \frac{-t^3}{3} + \frac{t^2}{2} \right]^1_0 + \left[ \frac{t^3}{3} - \frac{t^2}{2} \right]^5_1\\
\\
\int^5_0 |v(t)| dt = \int^5_0 \left| t^2 - t \right| dt &= \left[ \frac{-(1)^3}{3} + \frac{(1)^2}{2} + \frac{(0)^3}{3} - \frac{(0)^2}{2} \right] + \left[ \frac{(5)^3}{3} - \frac{(5)^2}{2} - \frac{(1)^3}{3} + \frac{(1)^2}{2} \right]\\
\\
\int^5_0 |v(t)| dt = \int^5_0 \left| t^2 - t \right| dt &= -\frac{1}{3} + \frac{1}{2} + \frac{125}{3} - \frac{25}{2} - \frac{1}{3} + \frac{1}{2}\\
\\
\int^5_0 |v(t)| dt = \int^5_0 \left| t^2 - t \right| dt &= \frac{59}{2}m\\
\\
\int^5_0 |v(t)| dt = \int^5_0 \left| t^2 - t \right| dt &= 29.5m
\end{aligned}
\end{equation}
$

Single Variable Calculus, Chapter 3, 3.6, Section 3.6, Problem 41

Determine the equation of the tangent line to the hyperbola $\displaystyle \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ at the point $(x_0, y_0)$

Taking the derivative of the curve implicitly we have...


$
\begin{equation}
\begin{aligned}

\frac{1}{a^2} (2x) - \frac{1}{b^2} \left( 2y \frac{dy}{dx} \right) =& 0
\\
\\
\frac{dy}{dx} =& \frac{xb^2}{ya^2}

\end{aligned}
\end{equation}
$


Using Point Slope Form


$
\begin{equation}
\begin{aligned}

y - y_0 =& m(x - x_0)
\\
\\
y - y_0 =& \frac{xb^2}{ya^2} (x - x_0)

\end{aligned}
\end{equation}
$


Multiplying $\displaystyle \frac{y}{b^2}$ or both sides of the equation we have


$
\begin{equation}
\begin{aligned}

\frac{y}{b^2} (y - y_0) =& \frac{x}{a^2} (x - x_0)
\\
\\
\frac{y^2}{b^2} - \frac{y y_0}{b^2} =& \frac{x^2}{a^2} - \frac{xx_0}{a^2}
\\
\\
\frac{xx_0}{a^2} - \frac{yy_0}{b^2} =& \frac{x^2}{a^2} - \frac{y^2}{b^2}


\end{aligned}
\end{equation}
$


From the given equation, we know that $\displaystyle \left( \frac{x^2}{a^2} - \frac{y^2}{b^2} \right) = 1$ so

$\displaystyle \frac{xx_0}{a^2} - \frac{yy_ 0}{b^2} = 1$

Hence, the equation of the tangent line at point $(x_0, y_0)$

Why did William Blake write "Auguries of Innocence"?

William Blake wrote "The Auguries of Innocence," a poem that was not published until years after his death, to affirm the great importance of small, seemingly insignificant details of life. It is a cry of anger against the petty cruelties of human society. Some have called it a summary of the philosophy he expresses in his Songs of Innocence and Experience.
Blake refused to belong to any church and rejected organized religion—he viewed it as filled with hypocrisy. To him, the church too often overlooked or rationalized suffering and pain, especially the suffering of innocent creatures without power, such as children and animals.
In the poem, Blake describes some of the suffering that many would brush off as unimportant, arguing that this pain does, in fact, matter greatly. For example, he writes that a caged robin enrages heaven, and a starving dog "predicts the ruin of the State."
All of life is interconnected, Blake argues. He states near the end of the poem that unless we see life through the eyes of those who are suffering ("Born in an Night to perish in a Night"), we "Believe a Lie."

Why was the marriage of Bassanio and Portia a cause of double celebration? What marred the joy of this celebration?

In act three, scene 2, Bassanio correctly chooses the lead casket, which holds a picture of Portia inside. Portia is ecstatic that Bassanio has chosen correctly and presents him with a ring before Gratiano congratulates them. Gratiano then says that he wishes he could be married at the same time as Bassanio and Portia. He reveals his love for Nerissa by mentioning that he fell in love with her the first time he saw her. When Gratiano initially expressed his love to Nerissa, she promised that she would marry him if Bassanio chose the correct casket. The fact that Gratiano and Nerissa have also decided to get married at the same time as Bassanio and Portia is cause for celebration. Unfortunately, Salerio interrupts the joyful moment by bringing Bassanio a letter from Antonio explaining how his merchant ships have been lost, which means that Antonio has forfeited on his loan from Shylock and will die.

In That Was Then, This Is Now, what does Mark mean when he says, “That was then, this is now”?

At the end of the novel, Bryon goes to visit Mark, who is in a reformatory. While Bryon is sitting across from Mark in a visiting room, Bryon says Mark looks hard and sinister. Bryon asks Mark how his life is going, and Mark replies by commenting on how terrible it is in the reformatory. Mark then tells Bryon he wanted to see him just to make sure he still hated him. Mark doesn't allow Bryon to explain himself and says he can't get away with things the way he used to, which is why he's constantly in trouble. Bryon becomes desperate to connect with Mark and says, "We were like brothers. . . You were my best friend" (81). Mark responds by laughing at Bryon and says, "Like a friend once told me, 'That was then, this is now'" (82). Mark's comment refers to how his relationship with Bryon has permanently changed. Bryon and Mark used to be best friends, but after Bryon called the authorities on Mark, Mark's attitude towards Bryon changed forever. Mark no longer views Bryon as a friend and the fun times they used to spend together are in the past. 

Find the area of the zone of a sphere formed by revolving the graph of y=sqrt(r^2-x^2) , 0

The function y = sqrt(r^2 - x^2)   describes a circle centred on the origin with radius r .
If we revolve this function in the range 0 <=x <=a , a < r about the y-axis we obtain a surface of revolution that is specifically a zone of a sphere with radius r .
A zone of a sphere is the surface area between two heights on the sphere (surface area of ground between two latitudes when thinking in terms of planet Earth).
For the range of interest 0 <=x<=a , the zone of interest is specifically a spherical cap on the sphere of radius r . The range of interest for y corresponding for that for x is sqrt(r^2-a^2) <= y <= r .
The equivalent on planet Earth of the surface area of such a spherical cap could be, for example, the surface area of a polar region. This of course makes the simplifying assumption that the Earth is perfectly spherical, which is not the case.
To calculate the surface area of this cap of a sphere with radius r , we require the formula for the surface area of revolution of a function x = f(y) (note, I have swapped the roles of x and y for convenience, as the formula is typically written for rotating about the x-axis rather than about the y-axis as we are doing here).
The formula for the surface area of revolution of a function x = f(y) rotated about the y-axis in the range alpha <= y <= beta is given by
A = int_alpha^beta 2pi x sqrt(1+ ((dx)/(dy))^2) \quad dy
Here, we have that alpha = sqrt(r^2 - a^2) and beta = r . Also, we have that
(dx)/(dy) = -y/sqrt(r^2-y^2)
so that the cap of interest has areaA = int_sqrt(r^2-a^2)^r 2pi sqrt(r^2-y^2) sqrt(1+(y^2)/(r^2-y^2)) \quad dy
which can be simplified to
A =2pi int_sqrt(r^2-a^2)^r sqrt((r^2-y^2) + y^2) \quad dy
= 2pi int_sqrt(r^2-a^2)^r r dy   = 2pi r y |_sqrt(r^2-a^2)^r = 2pi r (r -sqrt(r^2-a^2))
So that the zone (specifically cap of a sphere) area of interest A =
= pi (2r^2 - 2rsqrt(r^2-a^2))
This marries up with the formula for the surface area of a spherical cap
A = pi (h^2 + a^2)
where a is the radius at the base of the spherical cap and h is the height of the cap. The value of h is the range covered on the y-axis, so that
h = r -sqrt(r^2 - a^2)   and
h^2 = 2r^2 - 2rsqrt(r^2 - a^2) - a^2   and
h^2 + a^2 = 2r^2 - 2rsqrt(r^2 - a^2)
 
 
http://mathworld.wolfram.com/SphericalCap.html

http://mathworld.wolfram.com/SurfaceofRevolution.html

https://www.scientificamerican.com/article/earth-is-not-round/?redirect=1&error=cookies_not_supported&code=e6764ca4-36e8-4b78-b577-bf04205f7a98

How does Iago plant the idea of Desdemona's infidelity in Othello's mind, and how does he make it grow?

Act 3, Scene 3 is the fateful moment in the play when Iago plants the first seeds of suspicion in Othello's mind. As always, Iago is remarkably subtle, using sly hints and innuendo to carry out his foul deed. At the beginning of the scene, Cassio is in conversation with Desdemona, hoping that she will intercede with her husband on his behalf to get him reinstated as Lieutenant.
Iago and Othello suddenly enter; Cassio hurriedly departs. It all looks rather suspicious, even though there is absolutely nothing going on between Cassio and Desdemona. There is a perfectly valid reason for Cassio's haste: he is still embarrassed about his drunken antics the night before. Nevertheless, Iago immediately spies his opportunity and takes it:

IAGO
Ha! I like not that.
OTHELLO
What dost thou say?
IAGO
Nothing, my lord: or if—I know not what.
OTHELLO
Was not that Cassio parted from my wife?
IAGO
Cassio, my lord! No, sure, I cannot think it,That he would steal away so guilty-like,Seeing you coming.
OTHELLO
I do believe 'twas he.

Notice how Iago explicitly says that he does not think that Cassio would leave "so guilty-like." Yet, at the same time, he is deliberating establishing a link between Cassio and the word "guilty," immediately sowing more than a hint of suspicion in Othello's mind. Iago's evil ploy appears to bear fruit almost at once. Othello starts acting abruptly toward Desdemona when she asks him when he might accede to Cassio's request:

Prithee, no more; let him come when he will, / I will deny thee nothing.

When they are alone together, Iago asks Othello further leading questions about Cassio, designed to fan the flames of jealousy further. Sensing Othello's growing suspicion, Iago takes things up a notch:

Good my lord, pardon me:Though I am bound to every act of duty,I am not bound to that all slaves are free to.Utter my thoughts? Why, say they are vile and false;As where's that palace whereinto foul thingsSometimes intrude not? who has a breast so pure,But some uncleanly apprehensionsKeep leets and law-days and in session sitWith meditations lawful?

Again, Iago is using innuendo to manipulate Othello. He is implying that he has negative thoughts about Cassio, but he dare not let on what they are. He knows that Othello will compel him to reveal what he claims to know about Cassio. Othello pretends to be unconcerned, but Iago knows that is not the truth. In order to seal the deal, Iago needs some hard evidence. There is not any, of course, so he makes it up. His wife, Emilia, picks up Desdemona's dropped handkerchief, a love token from Othello, and gives it to Iago. He then plants it on Cassio to "prove" that Desdemona gave him Othello's precious gift.
By the end of act 3, Othello has completely renounced his love for Desdemona, and Iago has managed to exert complete control over him. Desdemona's days are numbered.

What qualities do we see in Tom Canty which are appropriate for a king?

Tom Canty displayed a thirst for knowledge by reading widely and consulting those in the position to help him in his quest. In leadership, some level of knowledge and wisdom is required in order to effectively lead the people, and Tom yearned for knowledge.
Tom was ambitious and yearned for a better life. He hoped to improve his condition despite the negativity and ridicule he encountered from his family and friends. When the opportunity presented itself, Tom organized a royal court and established an elaborate mimic kingdom.
Through his character and mannerisms, Tom became influential among his friends and the community at large. Tom earned the respect of the older people from his community because he offered them solutions when they  consulted him concerning the issues they faced.
When he found himself in the real royal court, Tom learned fast and tried to adjust to his new condition. Despite the different mishaps that led the people in the court to believe that he was mad, Tom succeeded in carrying himself with royal dignity.
https://www.owleyes.org/text/prince-pauper/read/dedication

According to Rosencrantz and Guildenstern, how has Hamlet received their inquiries ?

The king, Claudius, feels some disbelief that Hamlet's old friends from school are unable to figure out the cause of the prince's odd and crazy behavior. Guildenstern assures the king that Hamlet is not exactly happy to be questioned about his feelings, saying,

Nor do we find him forward to be sounded.But with a crafty madness keeps aloofWhen we would bring him on to some confessionOf his true state. (3.1.7-10)

In other words, Hamlet avoids their questions and refuses to give them straight answers when they try to encourage his confidence. Gertrude, Hamlet's mother, wants to know if he has treated them well, and Rosecrantz says that Hamlet has behaved like a gentleman toward them, but Guildenstern's story differs somewhat. He tells Gertrude that Hamlet has acted "with much forcing of his disposition," meaning that Hamlet seemed to have to force himself to be nice to them (3.1.13). Rosencrantz claims, also, that Hamlet didn't really ask them any questions about themselves, so he didn't seem particularly eager to make conversation with the pair.

After Rosencrantz and Guildenstern meet with Hamlet, Claudius and Gertrude question them about what they have discovered.
Claudius asks if they have found out why Hamlet is acting like a lunatic. 
Rosencrantz says Hamlet confessed he feels distracted but that he did not explain why. When Gertrude asks if Hamlet received them well, Guildenstern says he behaved like a gentleman.
When Gertrude asks them if they found out about any activity that Hamlet might enjoy, Rosencrantz responds by saying that Hamlet has been interested in a group of actors that arrived at the court. Rosencrantz said he thought Hamlet had arranged for the actors (players) to stage a play:

Madam, it so fell out that certain players We o'erraught on the way. Of these we told him, And there did seem in him a kind of joy To hear of it. They are here about the court, And, as I think, they have already order This night to play before him.

Claudius says he is pleased ("it doth much content me") to hear of Hamlet experiencing "joy" because of these players. He tells Rosencrantz and Guildenstern to encourage Hamlet in this interest. Claudius does not realize, though the audience does, the irony in what he says: Hamlet is interested in putting on a play so that he can prove whether or not Claudius is guilty of murdering Hamlet's father. 

What are Henry David Thoreau's views on correspondence and daily news?

The answer to this question can be found in Henry David Thoreau's Walden. More specifically, a reader should check the chapter titled "Where I Lived, and What I Lived For." The specific set of quotes comes fairly early in the section:

For my part, I could easily do without the post-office. I think that there are very few important communications made through it. To speak critically, I never received more than one or two letters in my life—I wrote this some years ago—that were worth the postage . . . And I am sure that I never read any memorable news in a newspaper.

Thoreau doesn't come out and expressly say that reading news and letters is a "waste of time," but it is clear that he believes this to be mostly true. He just says it much more eloquently:

To a philosopher all news, as it is called, is gossip, and they who edit and read it are old women over their tea.

The reason that Thoreau feels this way is that he believes that most news isn't new news at all. He says that once he has read a story about a particular topic, he doesn't need to read a similar story about the same kind of thing happening elsewhere.

we never need read of another. One is enough. If you are acquainted with the principle, what do you care for a myriad instances and applications?

Thoreau goes on to explain how international news is no better. He explains how news from England and Spain isn't news at all. He claims that it is just the same information repackaged with different names.
Thoreau feels this way because he believes that people's obsession with the news gossip gets in the way of living deliberately in a person's own immediate reality. He prefers to live his own experiences rather than read about other people's experiences.

Let us spend one day as deliberately as Nature, and not be thrown off the track by every nutshell and mosquito's wing that falls on the rails . . . Be it life or death, we crave only reality. If we are really dying, let us hear the rattle in our throats and feel cold in the extremities; if we are alive, let us go about our business.

How would you "translate" a scene from Death of a Salesman into visual/aural expressions on the stage? Who would you cast for the characters and why? What kind of sets, costumes, lighting, sound, and music would you use and why? How would your analysis/design maximize the potential of the play on the stage and help the audience fully understand and enjoy the production?

If you were to use the scene in Act II in which Willy Loman talks to Howard about Dave Singleman, Willy's ideal of the successful salesman and the man he hoped to be like, it might be best to have Willy step away from Howard and into a dreamlike setting. Remember that these are merely suggestions to prompt your own thinking. Perhaps fog or smoke could represent that Willy has entered fantasyland, while the part of the stage with Howard grows darker. I might use some sort of dreamy music (you might try to think of a specific piece), have the sound coming as if from far away, and perhaps put a strong spotlight on Singleman. Since Willy thinks of Singleman as representing easy money, it might make sense to have him lolling about in an almost exaggerated way: maybe his green velvet slippers could be a very bright green and oversized and his chair very plush as he makes big deals just talking on the phone. Think about ways you could exaggerate Singleman to show how Willy has built up an exaggerated image of him.
As for who should play Singleman, you would have to use your imagination, but I picture a person like James Gandolfini, who played Tony Soprano, or Jack Black.
All of this would be meant to help the audience understand how much Willy has built Dave and the idea of easy money into an oversized fantasy.
Again, these are all merely suggestions, and you will need to apply your ideas and imagination to fleshing this out more fully. Best of luck with this!

College Algebra, Chapter 7, Review Exercises, Section Review Exercises, Problem 2

Given the matrix $\left[ \begin{array}{ccc}
1 & 0 & 6 \\
0 & 1 & 0
\end{array} \right]$.

a.) State the dimension of the matrix.


$
\begin{equation}
\begin{aligned}

& \text{Matrix} && \text{Dimension} &&&
\\
\\
& \left[ \begin{array}{ccc}
1 & 0 & 6 \\
0 & 1 & 0
\end{array} \right]
&& 2 \times 3
&&& \text{2 rows by 3 columns}

\end{aligned}
\end{equation}
$


b.) Is the matrix in row-echelon form?

Yes, the matrix is in row-echelon form.

c.) Is the matrix in reduced row-echelon form?

Yes, the matrix is in reduced row-echelon form.

d.) Write the system of equations for which the given matrix is the augmented matrix.

The equivalent system of equations of the augmented matrix is


$
\left\{
\begin{equation}
\begin{aligned}

x =& 6
\\
y =& 0

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

I have to write an essay referring to Michel Foucault's "The Subject and Power" and structuralism applied to Jane Austen's Pride and Prejudice. It is a sort of a literary analysis, using examples from the book and applying the theory of Structuralism. Anyone have any ideas, and/or examples in the book, with page numbers? Thanks!

First, as page numbers vary from edition to edition, and you do not specify which edition you are reading, an educator cannot give page numbers for the edition which you are assigned, but we can describe the episode in which a textual evidence is embedded. 
The nature of the essay you have been assigned to write is what is called a "theory/application" essay, in which you are asked to interpret a literary work in light of a specific theory. The point of this type of essay is for the instructor to see how well you have grasped both the theory and the text in a single assignment; applying a theory to a specific work requires you to understand the theory rather than just paraphrasing a summary of it.
There is a fairly standard way to approach this type of essay. The outline below should give you some idea of how to work through the essay.
1. Introduction: Foucault's analysis of power provides an interesting lens on Jane Austen because it allows readers to focus on the mechanisms of social control and power operating as the background to the novel. A structuralist reading foregrounds these implicit assumptions and relationships. You should then add a transition sentence talking about what elements of power you will discuss in the novel.
2. Binary Oppositions: A structuralist analysis reveals that the power structures in the novel are embedded in a series of binary oppositions. One of the most important is gentry/non-gentry. Others include rich/poor, male/female, parent/child, officer/subordinate, older/younger, attractive/unattractive. In each of these cases, the first of the paired qualities are associated with power and are more highly valued in the village. 
3. Control Mechanisms: For Foucault, informal control mechanisms function to enforce power structures. For example, village gossip and the way neighbors constantly watch each other and circulate information makes the village function almost as a panopticon. Note at the ball at Netherfield the way the villagers pay close attention to who dances with whom and how many times. It is also important to note that informal social control mechanisms are used to intimidate those who appear to be overstepping or challenging social norms, as when Lady Catherine tries to prevent Elizabeth from marrying Darcy. Foucault notes that we need to distinguish between violence and power. We can see that illustrated in the way that conformity is enforced by opinion rather than brute force. Lydia and Georgiana Darcy both face social ostracism, but their seductions by Wickham and rescues are not stories of rape or violence, but rather ones of seduction and persuasion and bribery. As you read through the book, you should look for examples of informal control mechanisms that regulate every aspect of behavior from food to dancing to clothing. 
4. Subversion: In many ways, Austen shows resistance to the operation of power in several moments of subversion. Her positive portraits of the Gardiners and the acceptance of them by Darcy and Elizabeth subverts the binary opposition between tradesmen and gentry, and suggests that noble character is not a matter of birth or profession but inner goodness. One can view Elizabeth's marriage to Darcy as ultimately an example of subversion or of assimilation.
 
 
 

Estrangement and "othering" involving race, ethnicity, cultural, and gender divisions have led humans to dehumanize each other and commit great abuses throughout history. Solomon Northup’s account of kidnap, abuse, exploitation, violence, and brutality gives us a firsthand account of the fragility of our ideas of right, equality, and justice. Systems created for the abuse of one group also affect those enforcing this system. The superior and inferior mutually view each other as uncivilized. Using Twelve Years a Slave, analyze how the system of bondage dehumanized and brutalized not only slaves but also those that made a living from the slave economy. How did this mutual "othering" perpetuate and reinforce brutal dehumanization?

Because the prompt asks you to focus on how slavery’s brutality dehumanizes both the slave and the slave owner/seller/controller, I would focus on chapters 12–20 of 12 Years a Slave.  Those are the chapters that cover the ten years that Solomon Northup lives under the tyranny of Edwin Epps.  Edwin Epps is a “nigger breaker,” and Northup is sold to him because of the hatred that Tibeats harbors for Northup.  During those ten years, readers witness the abuse, humiliation, and deprivation that Epps forces upon his slaves.  Epps is able to treat the slaves this way because he simply doesn’t see them as people.  The slaves are property to him.  They are equivalent to tools that are beat on for a purpose and thrown away after breaking.  It’s easy to see how the slaves are dehumanized in this kind of situation; however, Epps is a dehumanized character as well.  The slaves don’t really consider Epps a human because of how inhumane he acts toward the slaves under his control.  Even other slave owners don’t necessarily see Epps as a person.  They see him as a tool to be used to correct deviant slaves.  That’s why he’s known as a “nigger breaker.”  
For a different text that portrays a similar situation to Northup’s experience with Epps, I would choose Narrative of the Life of Frederick Douglass.  Within that text, I would focus on chapters 9 and 10.  Chapter 9 focuses on Douglass’s time with Master Thomas.  After 9 months, Thomas decides that Douglass is too unruly to keep around.  Thomas decides to “lend” Douglass to Edward Covey for one year.  That’s when chapter 10 starts.  
Covey is a well-known slave breaker.  He is considered the best in the area, and Thomas believes that Covey can “train” Douglass to be a better slave.  

Some slaveholders thought it not much loss to allow Mr. Covey to have their slaves one year, for the sake of the training to which they were subjected, without any other compensation.

Like Epps, Covey’s training methods are far from kind.  He mercilessly beats his slaves until they do as they are told no matter what.  Douglass is at first unfamiliar with the tasks that Covey gives him because Douglass is more of a city slave; therefore, Douglass makes simple mistakes.  Instead of teaching Douglass the correct method of doing something, Covey just beats him.  

I lived with Mr. Covey one year. During the first six months of that year, scarce a week passed without his whipping me. I was seldom free from a sore back. My awkwardness was almost always his excuse for whipping me.

Douglass escapes one night, and he returns to Thomas.  Douglass begs for Thomas to do something about the beatings, but Thomas just sends him back.  Thomas does not want to be seen as a man that goes back on a business deal.  

Master Thomas ridiculed the idea that there was any danger of Mr. Covey’s killing me, and said that he knew Mr. Covey; that he was a good man, and that he could not think of taking me from him; that, should he do so, he would lose the whole year’s wages; that I belonged to Mr. Covey for one year....

The conflict in these two chapters shows readers exactly how dehumanizing and brutal the institution of slavery is.  Slaves were regarded as property, not people; therefore, men like Douglass could be bought, sold, traded, and loaned like any other piece of property.  Both Covey and Epps have the opinion that slaves are not people with feelings.  If they did think that, then they wouldn’t repeatedly beat the slaves nearly to death.  I think the fact that Thomas doesn’t take Douglass back is also incredibly important regarding the dehumanizing aspects of slavery.  Thomas can easily see that Douglass has been severely beaten, yet Thomas refuses to go back on his original business deal with Covey.  Douglass is not a human to Thomas.  Douglass is a material good, a commodity, and Covey is supposed to be the kind of person that can make Douglass a more valuable commodity.  Even if Thomas wanted to help Douglass, the institution of slavery has made it more profitable for him to ignore what is happening to Douglass.