Calculus of a Single Variable, Chapter 5, 5.6, Section 5.6, Problem 54

The derivative of y in terms of x is denoted by (dy)/(dx) or y’'
For the given problem: y = xarctan(2x) -1/4ln(1+4x^2) , we may apply the basic differentiation property:
d/(dx) (u-v) = d/(dx) (u) - d/(dx) (v)
Then the derivative of the function can be set-up as:
d/(dx)y =d/(dx)[ xarctan(2x) -1/4ln(1+4x^2)]
y ' = d/(dx) xarctan(2x) -d/(dx) 1/4ln(1+4x^2)

For the derivative of d/(dx)[ xarctan(2x) , we apply the Product Rule: d/(dx)(u*v) = u’*v =+u*v’ .
d/(dx)[ xarctan(2x)] = d/(dx)(x) *arctan(2x)+ x * d/(dx)arctan(2x) .
Let u=x then u' = 1
v=arctan(2x) then dv= 2/(4x^2+1)
Note: d/(dx)arctan(u)= (du)/(u^2+1)

Then,
d/(dx)(x) *arctan(2x)+ x * d/(dx)arctan(2x)
= 1 * arctan(2x) +x * 2/(4x^2+1)
= arctan(2x) +(2x)/(4x^2+1)

For the derivative of d/(dx) 1/4ln(1+4x^2) , we apply the basic derivative property:
d/(dx) c*f(x) = c d/(dx) f(x) .
Then,
d/(dx) 1/4ln(1+4x^2)= 1/4 d/(dx) ln(1+4x^2)
Apply the basic derivative formula for natural logarithm function: d/(dx) ln(u)= (du)/u .
Let u =1+4x^2 then du = 8x
1/4d/(dx) ln(1+4x^2) = 1/4 *8x/(1+4x^2)
=(2x)/(1+4x^2)

Combining the results, we get:
y' = d/(dx)[ xarctan(2x)] -d/(dx)[ 1/4ln(1+4x^2)]
y ' = [arctan(2x) +(2x)/(4x^2+1)] - (2x)/(1+4x^2)
y ' = arctan(2x) +(2x)/(4x^2+1) - (2x)/(1+4x^2)
y ' = arctan(2x) +0
y'=arctan(2x)

Single Variable Calculus, Chapter 2, 2.4, Section 2.4, Problem 17

Show that the statement $\lim\limits_{x \to -3} (1-4x) = 13$ is correct using the
$\varepsilon$, $\delta$ definition of limit and illustrate its graph.






Based from the defintion,


$
\begin{equation}
\begin{aligned}

\phantom{x} \text{if } & 0 < |x - a| < \delta
\qquad \text{ then } \qquad
|f(x) - L| < \varepsilon\\

\phantom{x} \text{if } & 0 < |x - (-3)| < \delta
\qquad \text{ then } \qquad
|(1-4x)-13| < \varepsilon\\

\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}
& \text{But, } \\
& \phantom{x} & |1-4x-13| = |-4x-12| = |-4(x+3)| = 4|x+3| \\
& \text{So, we want}\\
& \phantom{x} & \text{ if } 0 < |x+3| < \delta \qquad \text{ then } \qquad 4|x+3| < \varepsilon\\
& \text{That is,} \\
& \phantom{x} & \text{ if } 0 < |x+3| < \delta \qquad \text{ then } \qquad |x+3| < \frac{\varepsilon}{4}\\


\end{aligned}
\end{equation}
$


The statement suggests that we should choose $\displaystyle \delta = \frac{\varepsilon}{4}$

By proving that the assumed value of $\delta$ will fit the definition...



$
\begin{equation}
\begin{aligned}
\text{if } 0 < |x+3| < \delta \text{ then, }\\
|(1-4x)-13| & = |1-4x-13| = |-4x-12| = |-4(x+3)| = 4|x+3| < 4 \delta = \cancel{4} \left(\frac{\varepsilon}{\cancel{4}}\right) = \varepsilon
\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}

& \text{Thus, }\\
& \phantom{x} \quad\text{if } 0 < |x-(-3)| < \delta \qquad \text{ then } \qquad |(1-4x)-13| < \varepsilon\\
& \text{Therefore, by the definition of a limit}\\
& \phantom{x} \qquad \lim\limits_{x \to -3} (1-4x) = 13


\end{aligned}
\end{equation}
$

Betrayal is a theme introduced at the very beginning of Great Expectations. How does the constant stream of betrayal affect the outcome of the plot, and which characters are most affected by it?

The central betrayal in Great Expectations, as in many of Dickens's novels, is the betrayal of innocent children by adults. The "expectations" of the novel can be interpreted as having a second meaning; as well as the money the title refers to, it also suggests that children can expect love, kindness, honesty, and care from their families. The novel is replete with instances in which adults fail to meet the expectation of proper care for children. We also see here that betrayal exists in cycles: one person's bitterness and disappointment over a betrayal leads that person to betray others in turn. Several characters are involved in betrayals.
Miss Havisham: The great villain of the novel, Compeyson, betrays Miss Havisham by arranging to marry her, defrauding her, and, rather than showing up to the church, sending her a letter jilting her, which she receives after she is already dressed in her wedding gown. She has a mental breakdown and reacts to this betrayal by bringing up Estelle to betray men by breaking their hearts. Pip's love for Estelle in part is impetus for his desire to become a "gentleman."
Arthur: Miss Havisham's half-brother conspires with Compeyson to defraud Miss Havisham.
Magwitch: Magwitch is betrayed multiple times by Compeyson, something that leads to his initial heavy sentence and eventual deportation to New South Wales. There he earns the money that enables Pip to become wealthy. He is also initially emotionally betrayed by Pip, who is disappointed that Magwitch, rather than Miss Havisham, is his benefactor, but eventually, they are reconciled.
Pip: When Pip goes to London and enjoys his newfound wealth, he (temporarily) becomes a snob who betrays his old friends and avoids them; he does not see that true worth is about character—not wealth or class. Eventually, though, he redeems himself as he matures.
Compeyson: Much of the plot is driven by Compeyson's successive betrayals. He first betrays his fiance, Miss Havisham, and then betrays his accomplice Magwich. He is a career forger and con artist whose entire life and career are based on the betrayal of trust.

What duty has Mary Warren been performing in Salem?

In Act Two, Mary Warren tells her employers, who are John and Elizabeth Proctor, that she is now "an official of the court."  She has been going into Salem in order to give testimony against accused witches such as Sarah Good, and she considers this to be her Christian duty.  When John Proctor forbids her to go into Salem to the courts again, she says,

I must tell you, sir, I will be gone every day now.  I am amazed you do not see what weighty work we do.

Despite Mary Warren's evident doubts––after all, she tried to convince Abigail Williams to confess in Act One––she has apparently, now, bought into the lies the girls are telling.  She tells stories about feeling "a misty coldness climbin' up [her] back" as she sat in court while Sarah Good denied the charges against her. Mary also believed that Sarah Good cursed her, after Mary had refused the beggar food and drink one day.  She believes that Goody Good witched her, because she had felt as though her "guts would burst for two days after."  Mary seems to believe in the things she's saying now, and she fully believes it is her Christian duty to go to the courts and provide such testimony during the trials of these people.

What is the genre of The Lady or The Tiger?

The Lady or The Tiger can be considered an anti-fairy tale. Instead of the traditional happy ending, Stockton's short story ends on a somewhat tragic and uncertain note.
The story begins typically enough for a fairy-tale: "In the very olden time there lived a semi-barbaric king..." There is also a princess, but her character veers from archetype. This princess is beautiful; however, she is also decidedly imperious, unabashedly passionate, and violently possessive. This isn't our typically gracious, gentle, and virtuous princess of traditional lore.
Her lover is a commoner, and the intensity of their passion is clear:

This royal maiden was well satisfied with her lover, for he was handsome and brave to a degree unsurpassed in all this kingdom, and she loved him with an ardor that had enough of barbarism in it to make it exceedingly warm and strong.

Again, this isn't our typical fairy-tale, where a princess's erotic inclinations are seldom mentioned (much less alluded to). In Stockton's anti-fairy tale, the princess is both heroine and antagonist. When her lover is presented with a conundrum that threatens to either end in his death or establish him in marital bliss with a beautiful commoner, the princess's possessive nature is exposed.
The story ends on an uncertain note. Stockton doesn't reveal whether the princess's young lover is saved from the tiger or joined in holy matrimony to a beautiful maiden. What is revealed, however, is the princess's violently possessive nature. This revelation highlights the uncomfortable themes of female jealousy, gender conflict, and sociopolitical issues, all elements of the anti-fairy tale.

In his speech before the Second Virginia Convention, what measures does Patrick Henry says the colonists have already tried in their dealings with England?

In his famous March 23, 1775, speech before the Virginia Convention, Patrick Henry made an impassioned argument for independence for Britain's American colonies. In so doing, he firmly positioned himself, as was already established, in the corner of those colonialists prepared to break with the British Crown and to employ violence, if necessary, in defense of that proposition. Henry's position was not, of course, unanimously accepted, as there remained many who favored remaining part of the British Empire. Lest anyone underestimate the gravity of the situation, Henry, early in his comments, makes clear that this is a momentous occasion, but one fraught with great peril:

"The question before the House is one of awful moment to this country. For my own part, I consider it as nothing less than a question of freedom or slavery . . ."

Henry was a gifted orator, and understood the importance of setting forth his case for independence, and that meant reiterating the measures taken to date with regard to the colonies' grievances with the Crown. And, Henry emphasized the military threat imposed upon the colonies by the Crown in response to efforts at reconciliation--efforts that spanned the previous decade. The time had come, he argued, to put diplomacy aside and to fight for secession:

"Shall we try argument? Sir, we have been trying that for the last ten years. Have we anything new to offer upon the subject? Nothing. We have held the subject up in every light of which it is capable; but it has been all in vain. . .Sir, we have done everything that could be done, to avert the storm which is now coming on. We have petitioned; we have remonstrated; we have supplicated; we have prostrated ourselves before the throne, and have implored its interposition to arrest the tyrannical hands of the ministry and Parliament."[Emphasis added]

To all of this, Henry pointed out, the Crown repeatedly responded with indifference at best and with military threats at worst. He remonstrated about the presence among the colonies of increased numbers of soldiers and of British naval vessels off the coast. The answer to the student's question--what measures did Patrick Henry reiterate were taken with regard to the British Crown--are those in the bold print above. Henry was declaring that legitimate forms of petitioning the Crown, and the humiliating process of attempting to appease it, all lead to nothing, and that it was time to take the next step.

Patrick Henry is specific about what the colonies have tried to do to negotiate with Britain.  He points out that the negotiations have dragged on for ten years with no discernible improvement.  He goes on to say that the colonies "have petitioned; [we have] remonstrated; [we have] supplicated; [we have] prostrated ourselves before the throne."  In other words, the colonies have tried to submit signed petitions that demonstrate the will of the people to the ministers of Parliament, they have made forceful protests, begged humbly, and more or less made every gesture of submission to try to effect change in their relationship--all to no avail.  He also implies that the colonies have not shown that they are unwilling to be satisfied; it is Britain who has been behaving unreasonably despite the honest and peaceful efforts of the colonies to work out their differences. 

Single Variable Calculus, Chapter 8, 8.1, Section 8.1, Problem 32

Evaluate $\displaystyle \int^t_0 e^s \sin (t-s) ds$ by using Integration by parts.
If we let $u = \sin (t-s)$ and $dv = e^s ds$, then
$du = - \cos (t-s) ds \quad v = e^s$

So,

$
\begin{equation}
\begin{aligned}
\int^t_0 e^s \sin (t-s) ds &= uv - \int v du = e^s \sin (t -s) - \int e^s \left( -\cos (t-s) \right) ds\\
\\
&= e^s \sin (t-s) + \int e^s \cos (t-s) ds
\end{aligned}
\end{equation}
$


To evaluate $\displaystyle \int e^s \cos (t - s) ds$, we must use Integration by parts once more...

$
\begin{equation}
\begin{aligned}
\text{Hence, if we let } u_1 &= \cos (t -s ) &&\text{ and }& dv_1 &= e^s ds \text{ , then} \\
\\
du_1 &= \sin (t-s) ds &&& v_1 &= e^s
\end{aligned}
\end{equation}
$


So, $\displaystyle \int e^s \cos (t-s) ds = u_1 v_1 - \int v_1 du_1 = e^s \cos (t-s) - \int e^s \sin (t-s) ds$

Going back to the first equation,
$\displaystyle \int^t_0 e^s \sin (t-s) ds = e^s \sin (t-s) + \left[ e^s \cos (t-s) - \int e^s \sin (t-s) ds \right]$

Combining like terms

$
\begin{equation}
\begin{aligned}
2 \int^t_0 e^s \sin (t-s) ds &= e^s \sin (t-s) + e^s \cos (t-s)\\
\\
\int^t_0 e^s \sin (t-s) ds &= \frac{e^s \sin (t-s) + e^s \cos (t-s)}{2}\\
\\
&= \frac{e^s}{2} [\sin(t-s) + \cos (t-s)]
\end{aligned}
\end{equation}
$


Evaluating from 0 to $t$, we have

$
\begin{equation}
\begin{aligned}
&= \frac{e^t}{2} - \frac{1}{2} \sin t - \frac{1}{2} \cos t\\
\\
&= \frac{1}{2} \left( e^t - \sin t - \cos t \right)
\end{aligned}
\end{equation}
$

In the story "The Veldt," why does Ray Bradbury have virtual lions kill real people?

In "The Veldt," Bradbury may have used the virtual lions to kill the parents to emphasize the serious dangers of technology.
In much of Ray Bradbury's science fiction, there is an underlying distrust of technology. What he seems to find the most dangerous is the temptation for people to depend on technology to provide intangibles such as happiness, love, or emotional comfort. This reliance is characteristic of the aptly-named children, Wendy and Peter (characters from the fantasy novel Peter Pan by J.M. Barrie), who have divorced themselves from reality as they attend a plastic carnival rather than dine with their parents. At home, they sequester themselves in their playroom of virtual realities. These children have lost the "human touch" of life. Lydia Hadley bemoans that she is no longer needed as a mother.

"I feel like I don't belong here. The house is wife and mother now, and nursemaid....Can I give a bath and scrub the children as efficiently or quickly as the automatic scrub bath can? I cannot."

Since the physical parental roles have been eliminated, there are few opportunities for George and Lydia to interact with their children. As a consequence, the children are undisciplined and given to indulging their separate interests, as well as thoughts of anger at their parents and vengeance against them. Without this adult supervision, Wendy and Peter gravitate to the enticement of technology's delights. These delights come to dominate their lives and become a force that the passive parents cannot defeat. Within the context of Bradbury's narrative, then, it is line with the theme that the virtual "kings of the beasts," lions, consume the parents.

Where does the king sit in the arena?

The king sits "high up on his throne of state," directly above the opening where the accused enters the arena. Across from the king are the two doors, one of which the accused person must open. In other words, the king has a prime view of the person making the fateful decision, but he cannot be seen by the accused unless the accused turns around.
Because he is so high up and on a throne, the king must be easily visible to his subjects and an important part of the spectacle. His good view of the doors suggests that he likes to be among the first to see the fate of his accused subject. It also suggests that the king is a bit bloodthirsty and might enjoy a good view of those who get eaten by the famished tiger.

The "semi-barbaric" king sits high on his throne directly above the door where the accused subjects enter the amphitheater. On the opposite side of the amphitheater are the two doors, where either a ferocious tiger or lovely woman enters the arena, which randomly depends on what door the accused subject chooses. The king believes that his method of administering justice is perfectly sound, and the institution is very popular throughout the kingdom. When a courtier falls in love with the king's jealous daughter, he is sent into the amphitheater to test his fate by choosing either door on the opposite side of the arena. When the courtier enters the arena, he looks directly at the king's daughter for direction. The princess ends up signaling to the courtier what door to choose, but Stockton does not reveal the courtier's fate.

What is the tone of Lincoln's "Gettysburg Address" speech?

The purpose of the Gettysburg Address was to dedicate a Civil War battlefield. Lincoln helped put the war in a larger context—that it was a war to protect government "of the people" from "perishing from the Earth." Lincoln uses the line "of the people" to frame the war as a war to protect the Founding Fathers' view of the nation. Lincoln takes a reverential tone when he states the people gathered at Gettysburg that November afternoon could not "dedicate" or "consecrate" that land any more than the soldiers who died there the previous July. Lincoln's concise speech always keeps the focus on the soldiers buried there. Also, Lincoln does not differentiate between the Confederate and Union dead—he seems to value them both equally.  
Lincoln gave this speech at a time when, while the Confederacy was losing power, the outcome of the war was in doubt. The war had already killed hundreds of thousands of men on both sides, and many in the Union were asking if the war was worth the cost. By framing the war as a battle to maintain the Founding Fathers' view of the nation, Lincoln states the Union's success is critical.  
https://www.windsor-csd.org/Downloads/Gettysburg%20Address.pdf

How/Why did the annexation of Mexican territory push the united states closer to the civil war?

When James K. Polk ran for president in 1844, he ran on a platform of expansion, specifically promising to secure US claims to the Oregon Territory and to annex Texas, California, and New Mexico. From 1846 to 1848, the US fought Mexico in the Mexican-American War, and the Treaty of Guadalupe-Hidalgo, signed in 1848, granted the US 525,000 square miles of former Mexican territory, including present-day California, Arizona, New Mexico, Colorado, Nevada, Utah, and Wyoming. However, these new acquisitions reignited the long-standing issue of slavery in the United States, specifically the question of whether slavery would be allowed to spread into territories that could one day become states. Since the Constitutional Convention in 1787 and with passage of the Missouri Compromise in 1820, political leaders sought to maintain a balance between free states and slave states in Congress. Adding the new territory from the Mexican-American War opened the opportunity for additional free or slave states to enter the Union. Southerners and pro-slavery Congressmen argued that slavery should not be prohibited anywhere, whereas Northerners and opponents of slavery and its spread argued that slavery should not be allowed in new territories.
This issue came to a head when California applied for statehood as a free state in 1849, threatening to upset the balance between free and slave states. Senator Henry Clay brokered a compromise that revealed the increasing tensions between North and South and free and slave states. California entered the Union as a free state, but in Utah and New Mexico, residents would choose whether or not to allow slavery (it would be decided by popular sovereignty). In addition, the slave trade was outlawed in Washington, DC, and a stricter Fugitive Slave Law was passed. While this compromise temporarily settled the issue, it would reemerge by 1854, when the Kansas-Nebraska Act was passed.

How is the digestive system linked to the circulatory system?

The digestive and respiratory systems are closely linked, and as with all other body systems one cannot function properly without the other.
First, think of the functions of each system separately to help you understand how each system relies on the other.
The digestive system breaks down food to provide energy to the other organs and organ systems in order for those things to do their jobs.  At the cellular level, the digestive system is providing glucose to the cells.  The mitochondria need this glucose as one part of the equation in cellular respiration.  In simple terms, this formula is
Glucose + Oxygen  -----> Water  + Carbon Dioxide + Energy (ATP)
So the digestive system provides one of the things you need in order for your cells to produce energy.
The oxygen is brought into your body by the respiratory system.  Your circulatory system is the delivery system for your body.  It delivers the oxygen from your respiratory system to your cells as well as the glucose from the digestive system.  
Without the circulatory system, your cells could not produce energy because they would not receive the glucose and oxygen they need to function.  Without the glucose provided by the digestive system, your cells could not produce ATP and the circulatory system would not have the energy it needs to do its job. So, the circulatory and digestive systems are closely linked and important to how your body functions.

The circulatory system is actually linked to all of the systems because it is responsible for transporting oxygen, nutrients, hormones, and cellular waste out through the entire body using blood vessels. The digestive system is responsible for converting food into nutrients and other vital components so that the circulatory system can transport them to their proper location in the body. The digestive system begins with the mouth (ingestion) and ends with the large intestine (excretion). In between those points the other organs--pharynx, esophagus, stomach, small & large intestines, pancreas, liver and gallbladder work together to filter food, decide what to keep and what to discard, and transport. It is in the large intestines specifically where the food is broken down and nutrients are absorbed into the blood (circulatory system).

The digestive system is made up of various organs that are all supplied blood by the circulatory system; however, I don't think that is the intended connection that the question implies.  Food enters the digestive system through the mouth, and a combination of mechanical and chemical digestion begins assaulting the food there.  After swallowing, the food travels down the esophagus to the stomach.  Chemical digestion occurs there over the next few hours, and then the food (known as chyme) moves from the stomach into the small intestine.  Chemical digestion continues to occur in the first section of the small intestine (duodenum).  Once the food is fully broken down, it needs to be absorbed into the blood stream in order for those nutrients to be transported to cells all around the body.  This is where the digestive system and circulatory system are linked.  The middle section of the small intestine (jejunum) is covered in tiny folds called villi.  These folds increase the surface area and absorption space of the small intestine.  Each villi contains specialized cells that transport different nutrients into the blood.  Once in the blood, the circulatory system delivers the nutrients to the cells. 
https://livehealthy.chron.com/importance-villi-small-intestine-digestion-nutrients-3923.html

Single Variable Calculus, Chapter 1, 1.2, Section 1.2, Problem 16

It will cost \$2200 to manufacture 100 chairs in one day and \$4800 to produce 300 chairs in one day according to the manager of a furniture factory.



a.) Express the cost as a function of the number of chairs produced, assuming that it is linear then sketch its graph.



$
\begin{equation}
\begin{aligned}
c &= ax + l \text{ where}:\\
c &= \text{cost}\\
a &= \text{slope}\\
x &= \text{number of chairs}\\
k &= \text{other expenses}
\end{aligned}
\end{equation}
$


Given:

$
\text{when } \begin{array}{llllll}
x &=& 100 &c &=& 2200\\
x &=& 300 &c &=& 4800\\
\end{array}
$


Substituting these values to the equation will result to :



$
\begin{equation}
\begin{aligned}
a &= 13\\
k &= 900
\end{aligned}
\end{equation}\\
\boxed{.: c= 13x+900}
$





b.) Find the slope of the graph then state what does it represent.

The slope is 13, it represents the change in cost for every change in the number of chairs.

c.) Find the y-intercept of the graph and state what does it represent.

The $y$ intercept is 900, maybe it represents the charges for the maintenance of the equipment used.

How did the colonists' changing attitudes toward the Native Americans, particularly "Praying Indians," help turn the tide of war? How did Benjamin Church's military strategy show these changing attitudes?

Captain Benjamin Church led the first Ranger force in colonial America; his force eventually became the Army Rangers. During King Philip's War (1675-1678) in colonial New England, Church used Native American tactics against Native Americans. He recruited Native Americans to join his forces, and they became teachers of his troops. These Native Americans were called "Praying Indians" because many had converted to Christianity, and they helped the colonists defeat other Native Americans by following their opponents into swamps and forests and ambushing them. In these places, conventional military tactics were ineffective. These tactics, and the colonists' willingness to fight alongside Native Americans, turned the tide of the war in the colonists' favor. King Philip's War ended when John Alderman, a "Praying Indian," killed King Philip, or Metacomet, a Wampanoag who was the son of Massasoit and who had commanded the opposing Native American forces. 

What is the conflict that drives the action and provides tension in Henry V?

The main conflict in Henry V is, on the surface, the war between the English and French. Both want to govern France, and both kings claim that they have the right to do so so based on their ancestry. The only way to decide the claim is to fight, so Henry takes his men and goes to France to do so. This conflict frames the story.
On a deeper level, however, the conflict concerns whether it is possible to have a just war. Henry's conduct of the war is deeply questionable. He threatens Harfleur with rape and the murder of children if they do not surrender. He instructs his men to kill their prisoners for no apparent reason. The Chorus seems convinced that he is "the mirror of all Christian kings," but if you ask the soldier Michael Williams, you get a very different perspective. In the end, the burden of deciding what to believe about war is on the audience.

In William Shakespeare's Henry V, the main conflict driving the characters is an invasion during the Hundred Years' War, a series of battles in which England attempted to conquer French land. At the beginning of the play, King Henry V decides to launch another invasion of France on the advice of the English nobility. The odds are against Henry's troops; the English army is so much smaller and relatively lacking in technology that the French royals don't even consider the invasion a threat at first. Henry's men struggle to take the town of Harfleur, and many of them fall ill due to the struggle of battle. The French army then sends 60,000 troops to fight against Henry's weakened 12,000. After a brutal day of battle, Henry receives news that his men managed to kill 10,000 French troops- a decisive victory for England. The play ends with Henry courting Katharine, the princess of France, in the hopes of uniting the two countries under a single crown. The conflict is resolved as Katharine's father, King Charles VI, gives Henry his blessing to marry Katharine and signs a peace treaty between the two nations.
 

Discuss why Zinn disputes Kissinger's idea that "History is the memory of states."

In A People's History of the United States, Zinn disagrees with Kissinger's vision of history because he feels that it silences the voices of people's experience.
Zinn feels that Kissinger's version of history is a form of mythology. Zinn believes that when history is told from the nation's point of view, it removes the struggles that different groups experienced.  Highlighting this struggle is Zinn's primary motivation:

My viewpoint, in telling the history of the United States, is different: that we must not accept the memory of states as our own. Nations are not communities and never have been, The history of any country, presented as the history of a family, conceals fierce conflicts of interest (sometimes exploding, most often repressed) between conquerors and conquered, masters and slaves, capitalists and workers, dominators and dominated in race and sex. 

Zinn believes that Kissinger's view of history emphasizes national progress over individual struggle.  Telling history from the point of view of nations eliminates the fight people waged against the Status Quo.  Kissinger's view of history also removes the possibility of the nation being wrong.  For example, Zinn emphasizes how important it is to tell the story of the United States Constitution from the perspective of African-Americans, people that the original document silenced.
Zinn views Kissinger's understanding of history as dangerous.  When we embrace the historical narrative of states or governments over individual people, Zinn feels we are more prone to justify national exercises of power.   For example, if we look at industrialization as simply a time where America advanced, we tend to forget the struggles that took place between workers and management.  As Zinn demonstrates in his chapter "Robber Barons and Rebels," we would forget how American government and industry colluded with one another to deny the interests of the poor.  Zinn believes struggles like this one define the essence of historical scholarship. The historian must be committed to retelling this story of conflict because it encompasses the "people's" stories.
This paradigm is established in chapter 1 of A People's History of the United States.  This is the chapter where Zinn analyzed Columbus's subjugation of the Native Americans.  Kissinger's vision of history would view Columbus as a hero, the man who discovered America. Zinn's embrace of history as the story of the people, the narrative of "conflict," compels him "to tell the story of the discovery of America from the viewpoint of the Arawaks." Zinn does not believe that the nation should be more important than "a people's history."  As a result, he disagrees with Kissinger's perspective on history.

What force is needed to slide a 250-kg crate across the floor at constant velocity if the coefficient of sliding friction between a crate and a horizontal floor is 0.25?

Hello!
Newton's Second law will help us. It states that the (vector) sum of all forces acting on a body is the same as its mass multiplied by its acceleration, vecF = m veca.
There are four forces here: gravitational force mg downwards, reaction force N upwards, traction force F_T horizontally and friction F_f also horizontally but in reverse direction.
The acceleration is zero, because velocity is constant. So we obtain
m vec(g) + vecN + vec(F_T) + vec(F_f) = vec0.
Vertical forces must balance each other and horizontal, too, so in magnitudes we obtain
N = mg  and  F_T = F_f.
Also we know that F_f = mu N, where mu is the coefficient of sliding friction. Hence F_T = F_f = mu N = mu m g. This is the final formula, and numerically F_T approx 0.25*250*9.8 =612.5 (N).
The answer: the force of about 612.5 N is needed.

y = arctanx + x/(1+x^2) Find the derivative of the function

Recall that the derivative of y with respect  to is denoted as y' or (dy)/(dx) .
 For the given equation: y = arctan(x) +x/(1+x^2) ,
we may apply the basic property of derivative:
d/(dx) (u+v) =d/(dx) (u) + d/(dx)(v)
 where we take the derivative of each term separately.
Then the derivative of y will be:
y' = d/(dx)(arctan(x) +x/(1+x^2))
y' =d/(dx)(arctan(x)) +d/(dx)(x/(1+x^2))
To find the derivative of the first term:d/(dx)(arctan(x)) , recall the basic derivative formula for inverse tangent as:
d/(dx) (arctan(u)) = ((du)/(dx))/1+u^2
With u = x and du=dx or (du)/(dx) =1 , we will have:
d/(dx)(arctan(x)) =1 /(1+x^2)
 
For the derivative of the second term:d/(dx)(x/(1+x^2)) , we apply the
Quotient Rule for derivative: d/(dx) (u/v)= (u' * v- v'*u)/v^2 .
Based fromd/(dx)(x/(1+x^2)) , we let:
u = x then u' = 1
v = 1+x^2 then v'=2x
v^2= (1+x^2)^2
Applying the Quotient rule,we get:
d/(dx)(x/(1+x^2)) = (1*(1+x^2)-(x)(2x))/(1+x^2)^2
d/(dx)(x/(1+x^2)) =(1+x^2-2x^2)/(1+x^2)^2
Combining like terms at the top:
d/(dx)(x/(1+x^2))= (1-x^2)/(1+x^2)^2
For the complete problem: 
y' =d/(dx)(arctan(x)) +d/(dx)(x/(1+x^2))
y' =1/(1+x^2) +(1-x^2)/(1+x^2)^2
 
 
 

What does the name of Diana Moon Glampers suggest?

The name "Diana Moon Glampers" is full of allusion and allows a great deal of interpretation that can enrich the meaning of Vonnegut's "Harrison Bergeron." 
First, the name as a whole sounds funny and presents a stark contrast within itself. Diana is a lovely, flowing name that means heavenly, divine, or perfect. But Glampers is a clumsy, ordinary, even ugly name. The contrast corresponds to the society the Handicapper General works for; it is ostensibly perfect because all people are finally equal. In reality, it is a very ugly society that removes everything beautiful its citizens are capable of. The wry humor of the name is menacing in the way that the final joke of the story is more sickening than cheering.
The name Diana is an allusion to the ancient Roman goddess of the moon and the hunt. Diana Moon Glampers is a goddess in the sense that she has supreme power over the subjects of the United States in 2081. She also proves to be an excellent hunter when she takes down Harrison and the ballerina with her "double-barreled ten-gauge shotgun." 
The use of "Moon" as the character's middle name also allows some interpretation. Because the middle name repeats the idea of the first name in a "dumbed down" version, it represents the dumbing down of the society in order to ensure equality. To moon can also have the meaning, as a verb, of pining after someone or something sentimentally. This would be ironic if applied to the Handicapper General because she is anything but sentimental. It could refer to the idea that the society aimed high--aimed for the moon, so to speak--in wanting to create an equal society. 
Finally, Glampers may call to mind the word "clamper." Diana Moon Glampers is the one who must clamp down on those who violate the laws of equality. Because of its inelegant sound, it sounds like someone who runs roughshod over the feelings and rights of others. 
One can read many things into the simple name chosen by Vonnegut for the Handicapper General: Diana Moon Glampers.
https://literarydevices.net/allusion/

England underwent a period of instability and crises both at home and in the colonies during the 1700's. What might have happened in England and her North American colonies had the glorious revolution not taken place? Explain.

The Glorious Revolution was a vital turning point in the history of the UK, which greatly expanded the power of Parliament and reduced the power of the monarchy, and set the UK on the course toward becoming what it is today, which is technically a constitutional monarchy but de facto a representative democracy. Today the Queen has some real power, but Parliament is far more important; this might not have been the case were it not for the Glorious Revolution. Indeed, the effects of the revolution were even broader than that, as they set a global precedent for the expansion of power to broader classes of people. This was a trend that had been going on for centuries (and continues today), but the Glorious Revolution was a turning point, where relatively suddenly elected officials took on more control of a global superpower than the hereditary monarch.Without that turning point, the American Revolution might never have gained steam, for fear that it couldn't possibly succeed; or, on the other hand, it might have occurred even earlier, as it would be even easier to gather outrage against unrepresentative government when that government is led by a king instead of by a parliament. Perhaps even Canada would have launched a revolution under those circumstances. I can therefore imagine either the United States and Canada remaining under the British crown, or neither of them, depending on whether the stronger monarchy was able to hold control or triggered an even fiercer backlash toward democracy. This would also depend in part on how well the British monarchy held itself together against the various political and economic forces that led to the Glorious Revolution in the first place. Still, the winds of change were blowing, and even if there hadn't been the specific incidents (particularly involving Dutch involvement) that led to the Glorious Revolution, I think it is quite likely that Britain's monarchy would have weakened and transitioned toward democracy at some point anyway. This also happened in many other countries in Europe, such as Norway and Sweden, and while each transition had its own unique historical circumstances, they all fit a larger pattern of broadening political power to the people. It could be that without the Glorious Revolution, some other revolution would have simply come along later to take its place.
http://eh.net/encyclopedia/the-glorious-revolution-of-1688/

http://www.bbc.co.uk/history/british/civil_war_revolution/glorious_revolution_01.shtml

https://www.ucl.ac.uk/constitution-unit/what-uk-constitution/what-uk-constitution

What does the narrator of 'The Evil B.B. Chow' realise? And does the realisation change how she behaves, or is it subtler than that? How does it impact the ending?

Maureen, the narrator and protagonist of "The Evil B.B. Chow," writes for a magazine that, among other things, advises women on relationship issues. Despite this, she can never find "The One", or "Mr. Right." Then, out of the blue, up pops B.B. Chow into her life: a gauche, dorky doctor who seems to be anything but the ideal mate.
But there's a certain cute artlessness to B.B. He's so lacking in self-consciousness that it's actually quite endearing. When Maureen meets up with him at a fancy Belgian bistro it's clear that he's somewhat lacking in social graces. And when he shows up to meet her to watch a play at an upscale art space, he looks very out of place.
But Maureen doesn't mind. Why? Because B.B. is completely real. He isn't putting on an act; this is who he really is. This is new for Maureen. Previously, the guys that she's dated have been loudmouths, two-timing jerks, or maybe had commitment issues. But B.B. is different: he compliments Maureen on her feet, telling her how beautiful they are, and he even asks permission to kiss her on the cheek. He makes her feel happy and empowered.
Maureen realizes that maybe the advice she's been giving women for so long is actually true. There are genuine nice guys out there amidst all the jerks and players. But she's quickly disillusioned when she discovers that Brock Blaine, to give him his full name, has dumped her for an ex-girlfriend named Dinah.
Worse still, Maureen realizes something else. Under Dinah's bathroom sink is a large pile of back copies of Woman's Work, the magazine Maureen works for. Her resulting realization is that Maureen has somehow contributed to many women having unrealistic expectations of what can be found in a man. And now, she has fallen victim to the exact same advice she's been dishing out to other women.
Yet as Maureen trudges along the docks she seems in some way resigned to her fate: "There is so much time in this life for grief. So many men lying in wait." We get the impression that she'll continue in her seemingly never-ending quest for Mr. Right. Also, it seems that she'll continue to advise other women that he really is out there even though she's tired of doing so and no longer truly believes it in her heart of hearts.
 
 

Who gives the reader the first description of Mr. Rochester in these chapters, and how does it affect the story?

The first description Jane and the reader receive of Mr. Rochester is given by Mrs. Fairfax in chapter 11.
Mrs. Fairfax's initial remark that his visits at home were "rare, sudden and unexpected," and that it "put him out to find everything swathed up" leaves Jane with a newfound curiosity to know more about her mysterious and temperamental employer. She asks Mrs. Fairfax numerous questions about the man: Is he exacting and fastidious? Is he generally liked? What is his character? Unfortunately, Mrs. Fairfax turns out to be, as Jane afterwards observes, one of those "people who have no notion of sketching a character," and Jane learns next to nothing about Mr. Rochester from her.
However, it is perhaps Mrs. Fairfax's unintentional evasiveness that serves to influence Jane's subsequent curiosity in her employer's true character, an interest that strongly affects her later actions and therefore the remainder of the story.
For instance, Mrs. Fairfax notes vaguely that her master has "traveled a great deal, and seen a great deal of the world" and that "he is clever." For Jane, who has an unquenchable thirst for learning and who has always dreamed going to far-off lands, this is intriguing to say the least. Jane herself is extremely intelligent, and though she is already growing fond of Mrs. Fairfax and Adele at this point in the book, they are not able to stimulate her intellectually, and she yearns for conversation with someone who can.
Further, Mrs. Fairfax admits that "you cannot be always sure whether he is in jest or earnest, whether he is pleased or the contrary; you don't thoroughly understand him, in short." An introvert with strong intuitive skills, Jane makes a study out of other people's true characters. To come across such a seemingly contrary and puzzling personality as Mr. Rochester's must have aroused her curiosity and surely affected the amount of interest she later showed in him.

In "The Necklace," how do Monsieur Loisel's inner thoughts affect your opionion of Madame Loisel's character?

Monsieur Loisel's thoughts and actions contrast with those of his selfish and querulous wife. 
Whereas he is content with his station in life, Madame Loisel is disappointed.

She grieved incessantly, feeling that she had been born for all the little niceties and luxuries of living. She grieved over . . . things which another woman of her class would not even have noticed.

When M. Loisel comes home, holding a large envelope with pride, he informs his wife that he has something for her. Rather than being delighted when she opens the envelope and sees an invitation to a ball at the Ministerial Mansion Mme. Loisel tosses the card aside and complains that she has nothing to wear for such an elegant occasion. Observing his wife's disappointment, her loving husband asks her how much she needs for a gown; she responds, "I think with four hundred francs I could manage it." M. Loisel turns pale. He has been saving for a rifle so that he could join friends the following summer in a hunting expedition. Unselfishly, though, M. Loisel gives the four hundred francs to his wife for a gown.
When they attend the ball, Mme. Loisel delights in the attention that she receives in her lovely gown adorned with a dazzling necklace that she has borrowed from a former school friend. Even the minister himself takes notice of her. On this night, Mme. Loisel . . .

. . . giv[es] no thought to anything in the triumph of her beauty, the pride of her success . . . of all the awakened longings, of a sense of complete victory that is so sweet to a woman's heart.

She even ignores her husband who has fallen asleep. Finally, she and her husband depart at four in the morning. After they arrive home, Mme. Loisel discovers that she has lost the borrowed diamond necklace. Monsieur Loisel goes back out and retraces their steps to find the necklace, but he has no luck. Madame Loisel is too ashamed of this loss to inform her friend. Instead, she and her husband borrow the money to purchase a replacement and take it to Mme. Forestier. 

[M. Loisel] compromised the rest of his life...and then, terrified by the outlook for the future, by the blackness of despair about to close around him, and all the privations of the body and tortures of the soul,...he went to claim the new necklace.

After this financial setback, Monsieur Loisel, a changed man, labors night and day. Also changed, Madame Mathilde Loisel does the heavy housework and haggles with the grocer and the butcher. Finally, their debt is paid. One Sunday while Mme. Loisel walks on the broad boulevard named the Champs Elysées, she encounters her old friend. Mme. Forestier, who does not recognize her because she is "greatly changed." Mathilde Loisel informs Mme. Forestier that she is to blame for Mathilde's having aged. She explains to Mme. Forestier that she actually lost the diamond necklace and had to purchase another to replace it. To her surprise, Mme. Loisel learns from Mme. Forestier that the first necklace was merely made from glass. Mathilde's selfish pride, which prevented her from informing her friend of the loss, has unnecessarily caused her and her husband untold hardships.

How does Odysseus's retelling of his wanderings to Penelope in book 23 function in The Odyssey?

Odysseus's recounting of his story of his wanderings to Penelope in book 23, the second to last chapter, functions to bring closure to his travels and start winding the book down to its conclusion.
But before Odysseus can get to the point of reuniting with Penelope as her husband, he first has to overcome the obstacle of her disbelief that he is who he says he is. She believes he is a god disguising himself as Odysseus. Given the tendency of the Greek gods to use deceit to obtain sexual access to mortal women, Penelope is wise to be cautious. She also has had many men attempting to marry her over the years.
Even when he appears in fine clothing, Penelope is not sure Odysseus is who he says he is. She tests him by suggesting that they move their wedding bed to a new location. This incenses Odysseus, who knows that the bed is built from a tree that is firmly rooted in the ground and can't be carried from place to place. After he reveals this information in a long speech, Penelope throws herself into his arms.
To help reestablish the intimacy of their marriage, the two share with each other what has gone in their lives for the past decade. Odysseus tells Penelope all that has happened to him. Athena actually has to delay dawn from appearing so that the two can get caught up with each other.

Book 23 of The Odyssey begins in the aftermath of Odysseus's slaughter of the Suitors and details Odysseus's reunion and reconciliation with his wife, Penelope. Of course, it should be noted that Penelope herself is mistrustful of Odysseus and wary that his return amounts to a deception. (And here it must be said that these kinds of deceptions are a recurring theme throughout Greek mythology. When seen within that context, her misgivings are actually entirely valid, and her skepticism displays a shrewdness well-matched with Odysseus himself.) Thus, rather than accepting her husband's return on faith, she instead tests his identity to confirm to her own satisfaction that he is actually the person he claims to be. Even if Odysseus had already returned to Ithaca (and slain the Suitors), it is only after he has passed her test that his marriage to Penelope can be restored.
Towards the end of book 23, then, we observe Odysseus and Penelope recounting their experiences to one another. I do think that there might be an element of emotional catharsis here. At the same time, though, it feels like a point where the entire poem has come full-circle, where those previous threads can be revisited and re-invoked, now that much of the poem's emotional impetus has been resolved.

Odysseus’s retelling of his wandering in book 23 must be seen within the context of the book and the epic poem as a whole. When we do this, we realize something about Penelope’s character: she is smart, knows how to scheme when she has to (think of the burial shroud that she made for four years), and is clever in every sense of the world. She is just like Odysseus, a match made in heaven. So, when there is a man who looks like Odysseus, she must test him. She needs to be persuaded.
In the book, Telemachus is shocked at her mother’s lack of initial warmth towards Odysseus. Penelope is being cautious. Hence, Odysseus's retelling is necessary. He needs to make his case; he needs to persuade Penelope, and he knows it.
The final test, of course, is when Penelope says to her maid servant to move the bed. Both know that it cannot be moved. If Odysseus is the man who he says he is, then he will know as well. He does. Only after passing this test does Penelope believe that this man before her is her husband. In conclusion, the retelling of Odysseus’s story is just a part of a larger test. Both he and she would have it no other way.

Book Twenty-Three is the penultimate book of the Odyssey. Odysseus has survived his many trials and made it home to Ithaca, killed the suitors who had taken over his household, and been reunited with his family. His reunion with Penelope is the final step he must take to complete his homecoming. Odysseus conceals his identity from his wife until after dispatching the suitors, which enables him to return to Penelope's arms as the undisputed lord and master of his household.
Penelope is overjoyed to welcome Odysseus home, and is eager to know what has happened to him in their long separation from each other. Odysseus recounts his experiences to her as they lie in bed together for the first time in twenty years:

Odysseus told of what hard blows he had dealt out to othersand of what blows he had taken—all that story.She could not close her eyes till all was told.

A lot of things have happened during their time apart from each other. Odysseus takes action to undo the situation that has arisen in his absence, for he cannot truly return home while the suitors remain in situ. Penelope, for her part, needs to be able to "fill in the blank" of the past ten years. It is essential to Penelope to understand where her husband has been and what he has been through since the end of the Trojan War. They cannot move on with their life together until Penelope is privy to Odysseus's experiences.
For Homer's audience, this passage also serves as a "recap" of the events of the poem, signalling that the action is over now and the hero will rest from his adventures.

Remembering,[Odysseus] drowsed over the story’s end. Sweet sleeprelaxed his limbs and his care-burdened breast.

Although Odysseus must fulfil one further obligation to discharge Poseidon's wrath, and although there is a temporary threat of violence in Book Twenty-Four, the main story of the Odyssey concludes with Book Twenty-Three, as Odysseus retells his story to his loving wife and then falls asleep in her arms.

How did George Washington make an impact?

George Washington served as Commander-in-Chief of the Continental Army during the American Revolutionary War. After the war ended, Washington was elected to preside over the Constitutional Convention where, along with the other Founding Fathers of our country, he participated in drafting the Constitution of the United States. In 1789, he was elected to serve as the first President of the United States of America. Washington served two terms as president with his second term ending in 1797.
As the first President of the United States, Washington created a path along which others would follow. For example, despite the fact that during his presidency the Constitution did not set a limit to the number of terms that a president could serve, Washington did not choose to run for a third term. Subsequent presidents followed suit by serving only two terms until 1940 when President Franklin D. Roosevelt was elected for a third term. The tradition of only serving two terms was written in the Constitution in the 22nd Amendment.
Washington would set many more precedents during his term as president. For example, he often relied on counsel from heads of departments, which set a precedent for the president choosing his own cabinet members. Washington also practiced executive restraint by not vetoing legislation that may have conflicted with his own beliefs. In his farewell address, he cautioned against foreign involvement in domestic affairs. This philosophy remained unchanged for the next century.
https://www.history.com/topics/us-presidents/george-washington

John Calhoun writes in Slavery a Positive Good that slavery is not that bad because he defends it that the country as a whole kind of needs it. He try to make an argument that try to stop it is bad and compares it as an infection on the country. “As widely as this incendiary spirit has spread, it has not yet infected this body, or the great mass of the intelligent and business portion of the North; but unless it be speedily stopped, it will spread and work upwards till it brings the two great sections of the Union into deadly conflict.” He gives examples of how the new movement or infection starts to attack the ignorant, the weak, the young, and the thoughtless and gradually extend upward till they would become strong enough. He goes on to make it seem like slavery is an upgrade from the situation they were in Africa. He finishes off by making seem that things in the South were more under control compared to the North to make seem that allowing slavery was the reason. What is your opinion on this?

It is important to offer some clarification. The "incendiary spirit" to which John Calhoun refers is that of abolition, or the fervent movement to end slavery, which was dominant in the New England states. He refers to this in the previous paragraph in which he discusses the need to "[arrest] the progress of abolition." He also begins the essay with what amounts to a call of arms: "I do not belong...to the school which holds that aggression is to be met by concession." Interestingly, he asserts that those who do not meet "encroachments" at the beginning are destined "to become slaves." In other words, the South will not cede its way of life, but he also does not want to "[resort] to secession or disunion." His appeal in this speech is one for peace.
To your second point, Calhoun does try to make the argument that "the black race of Central Africa" is better off than before. He says that the conditions for the slave are better than those for the tenants of the work houses "in the more civilized portions of Europe." He seems to be referencing the work houses of the Victorian Era, usually inhabited by those who worked in textile factories. Calhoun claims that the slave has "the kind superintending care of his master and mistress," which allow for him or her to be looked after "in sickness or infirmities of age." 
Anyone with even an elementary knowledge of the antebellum South and the slave system knows that this is a lie. While it is true that not all masters and mistresses were cruel to their slaves, the very fact of owning another human being from birth to death, disqualifies any pretensions of goodness. Conditions for the poor in work houses were, indeed, abominable; and England's strict class structure offered little hope to escape from penury, but these laborers were still free. It is possible that some did have the opportunity to escape from their misery. No such opportunities existed for slaves who could only escape from their condition by running away, which was extremely risky and held no promise of freedom.
Calhoun justifies the plantation system by claiming that "never has yet existed a wealthy and civilized society in which one portion of the community did not, in point of fact, live on the labor of the other." He defends himself with history, while intentionally overlooking, like many Southern sympathizers, the unique project of the United States: to dismantle these ancient hierarchies and to create a nation in which "all men are created equal." 
He does, indeed, make the case that this "neo-classical" order -- that is, one that mimics the hierarchies of Ancient Greece and Rome -- protects the South from the kinds of clashes between ethnic groups which were common in the North at the time: "The condition of society in the South exempts us from the disorders and dangers resulting from this conflict [between labor and capital]."
Calhoun conveniently forgets the bloody insurrection that took place six years before when Nat Turner led a group of slaves to kill around sixty whites in Southampton County, Virginia. While it occurred in one small area, news of the insurrection rippled throughout the South and made slave-holding whites more fearful of future attempts. All was not "so much more stable and quiet" than in the North as he claims; and the stability that did exist was only due to the fierce determination of black people to survive. Clearly, black people were not content with their condition as slaves, but did not know how to get out of it without confronting mortal danger.
Based on what I have outlined, I think that you can form a sensible opinion of Calhoun's speech. His efforts to avoid discord with the North, while also defending the pride of the South, are somewhat noble. On the other hand, his justifications for slavery are dishonest, and rooted both in racism and simplifications of history.

What is release? Describe the process.

In Jonas's community, release is a euphemism for sentencing a person to death. There are several reasons why citizens are released in Jonas's community. If a citizen commits three transgressions, they are released from the community. At the beginning of the novel, a pilot accidentally flies a jet over the community, and it is announced that he will be released for his mistake. The elderly are also released at an old age when the committee decides that it is time for them to die. Also, unhealthy infants are released when the Elders conclude that they will not live healthy lives. In chapter 19, Jonas is traumatized after watching a video of his father releasing an infant. Jonas watches as his father lethally injects the infant with a syringe at the top of its head before placing the dead infant into a container. Discovering the true nature of release disturbs Jonas, which results in his decision to flee the community.

Which character sets the tone of sympathy for Mrs. Wright?

Interesting question! It can be argued that the character who sets the tone of sympathy for Mrs. Wright is Mrs. Hale.
In the play, it is Mrs. Hale who takes control of the narrative by speaking up in defense of Mrs. Wright. When the county attorney makes a disparaging comment about Mrs. Wright's apparent lack of housekeeping skills, Mrs. Hale puts him in his place with a terse response: "There's a great deal of work to be done on a farm."
In the same conversation, the county attorney tries again by criticizing Mrs. Wright's use of "roller towels." Upon hearing this, Mrs. Hale counters with "those towels get dirty awful quick. Men's hands aren't always as clean as they might be."
In a later conversation with Mrs. Peters, Mrs. Hale defends Mrs. Wright's reputation again. Both women are discussing the possibility of Mrs. Wright having played a part in her husband's death. During the conversation, Mrs. Hale defends Mrs. Wright. She argues that a woman who worries about her canned fruit cannot possibly be a murderer as well.
In the play, we get further evidence of how Mrs. Hale sets the tone of sympathy for Mrs. Wright. It is Mrs. Hale who informs Mrs. Peters (and us) of how Mrs. Wright's marriage changed her. Mrs. Hale proclaims that the young Minnie Foster (before she became Mrs. Wright) used to wear pretty clothes and sing in a choir. Later, Mrs. Hale uses the adjectives "sweet," "timid," and "fluttery" to describe Mrs. Wright. These words are contrasted with her description of Mr. Wright, whom she calls a "hard man."
From the above, it can be argued that Mrs. Hale is the character who sets the tone of sympathy for Mrs. Wright.

How does Della speak? Does she have any identifiable speech patterns?

Whenever Della speaks to Jim, she has a tendency to say a lot, all at once, before giving him an opportunity to respond.  In fact, she often asks a question and then continues making statements without actually allowing him any word edgewise.  It seems to convey, in part, her nervousness about his liking her hair and her desire to smooth things over and make him happy.  
When he first gets home, she says,

"Jim dear. . . don't look at me like that.  I had my hair cut off and sold it.  I couldn't live through Christmas without giving you a gift.  My hair will grow again.  You won't care, will you?  My hair grows very fast.  It's Christmas, Jim.  Let's be happy.  You don't know what a nice—what a beautiful nice gift I got for you."

In one speech, Della gives him an instruction, an explanation, a statement of reassurance, asks him a question, gives him further assurance, another instruction, and then, finally, another sort of explanation of the gift.
Then, a short while later, Della tells him,

You don't have to look for [my hair]. . . .  It's sold, I tell you—sold and gone, too.  It's the night before Christmas, boy.  Be good to me, because I sold it for you.  Maybe the hairs of my head could be counted. . . but no one could ever count my love for you.  Shall we eat dinner, Jim?"

Again, Della repeats much of what she has said before in a steady stream of words that do not permit Jim to speak.  She seems so eager to please!

f(x)=root(4)(1+x) Use the binomial series to find the Maclaurin series for the function.

Binomial series is an example of an infinite series. When it is convergent at |x|lt1 , we may follow the sum of the binomial series as (1+x)^k where k is any number. The formula will be:
(1+x)^k = sum_(n=0)^oo (k(k-1)(k-2) ...(k-n+1))/(n!) x^n
or
(1+x)^k = 1 + kx + (k(k-1))/(2!) x^2 + (k(k-1)(k-2))/(3!)x^3 +(k(k-1)(k-2)(k-3))/(4!)x^4+...
To evaluate the given function f(x) = root(4)(1+x) , we may apply radical property: root(n)(x) = x^(1/n) . The function becomes:
f(x)= (1+x)^(1/4)
or   f(x) =(1+x)^(0.25)
By comparing "(1+x)^k " with "(1+x)^(0.25) ”, we have the corresponding values:
x=x and k =0.25
Plug-in the values on the formula for binomial series, we get:
(1+x)^(0.25) =sum_(n=0)^oo (0.25(0.25-1)(0.25-2)...(0.25-n+1))/(n!)x^n
=sum_(n=0)^oo (0.25(-0.75)(-1.75)...(0.25-n+1))/(n!)x^n
=1 + 0.25x + (0.25(-0.75))/(2!) x^2 + (0.25(-0.75)(-1.75))/(3!)x^3 +(0.25(-0.75)(-1.75)(-2.75))/(4!)x^4+...
=1 + 0.25x + (-0.1875)/(1*2) x^2 + (0.328125)/(1*2*3)x^3+(-0.90234375)/(1*2*3*4)x^4+...
=1 + 0.25x -0.1875/2 x^2 + 0.328125/6x^3 -0.90234375/24x^4+...
=1 + x/4 -(3x^2)/32 +(7x^3)/128 -(77x^4)/2048 +...
Therefore, the Maclaurin series  for  the function f(x) =root(4)(1+x) can be expressed as:
root(4)(1+x)=1 + x/4 -(3x^2)/32 +(7x^3)/128 -(77x^4)/2048 +... 

Calculus of a Single Variable, Chapter 8, 8.4, Section 8.4, Problem 39

Recall indefinite integral follows int f(x) dx = F(x)+C
where:
f(x) as the integrand
F(x) as the antiderivative of f(x)
C as the constant of integration.
To evaluate the given integral: int x/sqrt(x^2+6x+12)dx , we may apply completing the square at the trinomial: x^2+6x+12 .
Completing the square:
x^2+6x+12 is in a form of ax^2 +bx+c
where:
a =1
b =6
c= 12
To complete square ,we add and subtract (-b/(2a))^2 :
With a=1 and b = 6 then:
(-b/(2a))^2 =(-6/(2*1))^2 = 9
Then x^2+6x+12 becomes:
x^2+6x+ 12 +9-9
(x^2+6x+9) + 12 -9
(x+3)^2 +3
Applying x^2 +6x +12 =(x+3)^2 + 3 in the given integral, we get:
int x/sqrt(x^2+6x+12)dx=int x/sqrt((x+3)^2 + 3)dx
We may apply u-substitution by letting: u = x+3 or x =u-3 then du = dx .
The integral becomes:
int x/sqrt((x+3)^2 + 3)dx =int (u-3)/sqrt(u^2 + 3)du
Apply the basic integration property: int (u-v) dx = int (u) dx - int (v) dx .
int (u-3)/sqrt(u^2 + 3)du =int u/sqrt(u^2 + 3)du -int 3/sqrt(u^2 + 3)du
For the integral of int u/sqrt(u^2 + 3)du , we may apply formula from integration table: int u/sqrt(u^2+-a^2) du = sqrt(u^2+-a^2) +C
Take note we have + sign inside the root then we follow: int u/sqrt(u^2+a^2) du = sqrt(u^2+a^2) +C .
int u/sqrt(u^2 + 3)du=sqrt(u^2+3)
For the integral of int 3/sqrt(u^2 + 3)du , we use the basic integration property: int cf(x)dx = c int f(x) dx.
int 3/sqrt(u^2 + 3)du = 3int 1/sqrt(u^2 + 3)du
From integration table, we may apply the formula for rational function with roots:
int 1/sqrt(x^2+-a^2)dx = ln|x+sqrt(x^2+-a^2)| +C
With just (+) inside the root, we follow:int 1/sqrt(x^2+a^2)dx = ln|x+sqrt(x^2+a^2)| +C.
3int 1/sqrt(u^2 + 3)du=ln|u+sqrt(u^2+3)|
Combining the results, we get:
int (u-3)/sqrt(u^2 + 3)du =sqrt(u^2+3) -ln|u+sqrt(u^2+3)| +C
Plug-in u = x+3 on sqrt(u^2+3) -ln|u+sqrt(u^2+3)| +C , we get the indefinite integral as:
int x/sqrt(x^2+6x+12)dx =sqrt((x+3)^2+3) -ln|x+3+sqrt((x+3)^2+3)| +C
Recall: (x+3)^2+3 =x^2+6x+12 then the indefinite integral can also be expressed as:
int x/sqrt(x^2+6x+12)dx =sqrt(x^2+6x+12) -ln|x+3+sqrt(x^2+6x+12)| +C

Calculus of a Single Variable, Chapter 3, 3.4, Section 3.4, Problem 28

This function is fully differentiable on a given interval. We can use the second derivative to determine concavity and inflection points. Let's find f'' and where its positive, negative or zero:
f''(x) = -sin(x) - cos(x) = -sqrt(2)*cos(x-pi/4).
This is zero at x-pi/4 = pi/2+k*pi, or x = (3*pi)/4 + k*pi for any integer k. There are two such x at [0, 2pi ], x=(3pi)/4 and x=(7pi)/4.
f''(x) is negative on (0, (3pi)/4), positive on ((3pi)/4, (7pi)/4) and is positive again on ((7pi)/4, 2pi). Therefore f(x) is concave downward on (0, (3pi)/4) and on ((7pi)/4, 2pi), and is concave upward on ((3pi)/4, (7pi)/4).
The points of inflection are (3pi)/4 and (7pi)/4.

int (4x-2/(2x+3)^2) dx Find the indefinite integral

int (4x - 2/(2x+3)^2)dx
To solve, express it as difference of two integrals.
= int 4x dx - int 2/(2x+3)^2dx
Then, apply negative exponent rule a^(-m)=1/a^m .
= int 4xdx - int 2(2x+3)^(-2)dx
For the second integral, apply the u-substitution method. 

u = 2x + 3
du = 2dx

Expressing the second integral in terms of u variable, it becomes:
=int 4xdx - int (2x+3)^(-2) * 2dx
=int 4xdx - int u^(-2) du
For both integrals, apply the formula int x^ndx= x^(n+1)/(n+1)+C .
= (4x^2)/2 - u^(-1)/(-1) + C
=2x^2 + u^(-1) + C
= 2x^2 + 1/u + C
And, substitute back u = 2x + 3
=2x^2+1/(2x+3)+C
 
Therefore, int (4x - 2/(2x+3)^2)dx=2x^2+1/(2x+3)+C .

y = 1/2x , y = 0 , x =2 Find the x and y moments of inertia and center of mass for the laminas of uniform density p bounded by the graphs of the equations.

For an irregularly shaped planar lamina of uniform density (rho)  , bounded by graphs y=f(x),y=g(x) and a<=x<=b ,the mass (m) of this region is given by,
m=rhoint_a^b[f(x)-g(x)]dx
m=rhoA  ,where A is the area of the region.
The moments about the x and y-axes are given by the formula,
M_x=rhoint_a^b1/2([f(x)]^2-[g(x)]^2)dx
M_y=rhoint_a^bx(f(x)-g(x))dx
The coordinates of the center of mass (barx,bary) are given by,
barx=M_y/m
bary=M_x/m
We are given y=1/2x,y=0,x=2
The attached image shows the region bounded by the functions and the limits of integration,
Let's evaluate the area of the region,
A=int_0^2x/2dx
Evaluate the integral by applying power rule,
A=[1/2(x^2/2)]_0^2
A=1/4[2^2-0^2]
A=1/4(4)
A=1
Now let's evaluate the moments about the x and y-axes,
M_x=rhoint_0^2 1/2(x/2)^2dx
M_x=rhoint_0^2 1/2(x^2/4)dx
M_x=rho/8int_0^2x^2dx
Apply the power rule,
M_x=rho/8[x^3/3]_0^2
M_x=rho/8[1/3(2)^3]
M_x=rho/8(8/3)
M_x=rho/3
M_y=rhoint_0^2x(x/2)dx
M_y=rho/2int_0^2x^2dx
Apply power rule,
M_y=rho/2[x^3/3]_0^2
M_y=rho/2[1/3(2)^3]
M_y=rho/2[8/3]
M_y=4/3rho
Now let's find the coordinates of the center of mass,
barx=M_y/m=M_y/(rhoA)
barx=(4/3rho)/(rho(1))
barx=4/3
bary=M_x/m=M_x/(rhoA)
bary=(rho/3)/(rho(1))
bary=1/3
The coordinates of the center of mass are (4/3,1/3)
 

Beginning Algebra With Applications, Chapter 5, 5.5, Section 5.5, Problem 10

The following table shows the length of the humerus (the long bone from the shoulder to the below), in centimeters, and the total wingspan, in centimeters, of several pterosaurs, which are extinct flying reptiles of the order Pterosauria. Write a relation in which the first coordinate is the length of the humerus and the second coordinate is the wingspan. Is the relation a function?

$\begin{array}{c|ccccccc}
\text{Length of humerus, in centimeters} & 24 & 32 & 22 & 15 & 4.4 & 17 & 15 \\
\hline \\
\text{Wingspan, in centimeters} & 600 & 750 & 430 & 300 & 68 & 370 & 310
\end{array} $

The table can be written as the relation

$\{ (24,600), (32,750), (22,430), (15,300), (4.4, 68), (17,370), (15,310) \}$

The relation is a function because no two ordered pairs have the same first coordinate and different second coordinates.

Single Variable Calculus, Chapter 4, 4.3, Section 4.3, Problem 46

a.) Use a graph of $f(x) = x^3(x-2)^4$ to give a rough estimate of the intervals of concavity and the coordinates of the points of inflection.
b.) Use a graph of $f''$ to give better estimates.


a.)


Based from the graph, the function has an upward concavity at intervals, $0 < x < 0.4$ and $ x > 1.3$. On the other hand, the funciton has a downward concavity at interval $x < 0 $ and $0.4 < x < 1.3$. Also the coordinates of the points of inflections can be approximated as $(0,0),(0.4,0.5)$ and $(1.3,0.5)$


$
\begin{equation}
\begin{aligned}
\text{if } f (x) &= x^3(x-2)^4, \text{ then}\\
\\
f'(x) &= x^3 \left[ 4 (x-2)^3 \right] + 3x^2(x-2)^4 && \Longleftarrow \text{(By using Chain and Product Rule)}\\
\\
f''(x) &= x^3 \left[ 12(x - 2)^2 \right] + 3x^2 \left( 4(x-2)^3\right) + 3x^2 \left[4 (x-2)^3 \right]+ 6x (x-2)^4\\
\\
f''(x) &= 12x^3 (x-2)^2 + 12x^2 (x-2)^3 + 12x^2 (x-2)^3 + 6x(x-2)^4\\
\\
f''(x) &= 12x^3(x-2)^2 + 24 x^2 (x-2)^3 + 6x (x-2)^4
\end{aligned}
\end{equation}
$





Based from the graph of $f''$, the function has an upward concavity (where $f''$ is positive) at intervals $0 < x < 0.46$ and $x > 1.28$ On the other hand, the function has downward concavity (where $f''$ is negative) at intervals $x < 0 $ and $ 0.46 < x < 1.28$
Also using the graph of $f''$, the points of inflections (where the slope is 0) are approximately $x = 0.18, \quad x = 0.83, \quad x = 1.57, \quad x = 2$

“Competition is for Losers” The Wall Street Journal, Sept. 12, 2014. Why is it better to build a monopolist rather than a competitive firm? How can a company build a monopoly? If it is so easy, why aren’t all companies monopolies?

There are several reasons why a company can profit from being a monopoly. The most obvious is that a monopoly has the ability to charge prices only limited by what the market will bear, rather than being driven by competition. In a competitive market, sellers try to undercut one another in order to generate sales. This reduces profitability, but one needs to match competitors' price reductions to maintain sales volume. Next, sales are naturally higher if you monopolize a market (as opposed to splitting the market with competitors). Also, as a monopolist, you have lower costs. You can offer lower bids to suppliers, you can invest less in consumer loyalty (especially in a captive market such as a utility), and you can invest less in improving your product because you do not need to compete for market share based on features. Essentially, monopolies can charge high prices for goods it costs little to produce. Additionally, monopolies can take advantage of economies of scale. 
One important part of monopolistic practices in a digital or platform economy has to do with network effects. As more people shop on Amazon, more sellers gravitate to Amazon, attracting even more buyers. The same is true of social media sites; the more people there are on a given site, the more participants are attracted to it. 
There are, though, several arguments against monopolies. The first is obviously that they can be bad for consumers and that they can lead to corruption and rent seeking. The next is that they are vulnerable to disruptive innovation. Even worse, monopolies can become lazy and complacent, meaning that they gradually lose the ability to deal with competition when it inevitably occurs. Consumers may rebel against monopolies and may try to find ways to circumvent them, such as by going off the grid to avoid paying high utility prices, abandoning cable television and landlines for mobile phones, VOIP, and streaming services, and so on.

College Algebra, Chapter 3, 3.6, Section 3.6, Problem 60

Suppose a print shop makes bumper stickers for election campaigns.
If $x$ stickers...
Use the fact that
Profit = Revenue $-$ Cost

To express $P(x)$, the profit on an order of $x$ stickers, as a difference of two functions of $x$.

$
\begin{equation}
\begin{aligned}
\text{Revenue } &= x (0.15 - 0.000002x)\\
\\
\text{Cost } &= x\left(0.095 x - 0.0000005x ^2\right)\\
\end{aligned}
\end{equation}
$

Where $x$ is the number of stickers.
Then

$
\begin{equation}
\begin{aligned}
\text{Profit } &= x (0.15 - 0.000002x) - x \left(0.095 x - 0.0000005x^2\right)\\
\\
\text{Profit } &= x \left[ 0.15 - 0.000002x - \left(0.095x - 0.0000005x^2\right) \right]\\
\\
\text{Profit } &= x \left( 0.15 - 0.000002x - 0.095 x + 0.000000 5x^2 \right)\\
\\
\text{Profit } &= x \left( 0.15 - 0.095002x + 0.0000005x^2 \right)
\end{aligned}
\end{equation}
$

What were the causes of the Renaissance?

While there is no specific singular cause for the Renaissance, there are various factors that have contributed to the commencement of the era. The Renaissance followed the end of the Medieval period. Therefore, events that marked a change in Medieval culture, mentality, technology, and beliefs naturally influenced the beginning of the Renaissance. The evidence of this is aptly reflected in the name Renaissance itself. “Renaiss” derives from the Middle French renaistre (to be born again) and the suffix -ance (indicating an action, state, condition, or quality).
The Renaissance era was characterized by the artistic, literary, and overall cultural influence of Greece and Rome. Following the fall of Constantinople in 1453, a wave of Italians (many of whom were scholars, poets, lecturers, philosophers, artists, scientists, astronomers, etc.) migrated to western Europe. These émigrés brought with them a wealth of teachings, art, and knowledge that would greatly influence the Renaissance. The amalgamation gave birth to a mentality that contrasted notably from the previous thought-process of the medieval way of life. Prior to the Renaissance, ideals were generally monastic, religious, and basically dogmatic. These medieval cultural norms were met with perspectives such as those found in the works of Italian scholar and poet Francesco Petrarch, which glorified the secular and worldly. What became known as “Renaissance humanism” (and a general interest in uncensored and relatable human emotions and conditions being depicted in art and literature) overshadowed the medieval scholasticism that existed prior.
Other notable factors include the invention of the printing press, the effects of the Black Death, and the influence following the advancement of various technologies. The printing press was invented by Gutenberg of Mainz in 1445. This made it far cheaper and easier to create and circulate literary works and further academia in a way never before possible. Europe’s Black Death allowed for the wealth of this era to spread, resulting in more time for the artistic and literary focus of the Renaissance. The invention of more advanced technology (such as the appearance of the telescope in 1608) further allowed for the new perspectives and mentalities regarding science and religion that took shape during the Renaissance.

Who was Alice in Nightjohn?

Nightjohn is a young adult novel by Gary Paulsen. The book is about slavery in the South and is set just before the American Civil War. The book takes place on a plantation, where the protagonist, Sarny, meets a new slave. This new slave, Nightjohn, is older and scarred, and he has a rare skill: he can read. The book follows Sarny and Nightjohn as he teaches her to read. Alice is another young slave girl on the plantation. Characters in the book refer to Alice as being "addled in the head," which means that she is mentally challenged.
Alice is a breeder, a slave who is forcefully used to procreate with male slaves to increase the number of slaves for their master. The horrific breeding process causes Alice to have a mental breakdown. She starts to wander around the plantation aimlessly and gets too close to the master's house. She tries to escape, but the master sends his dogs after her, and she is chained to the side of the house. The master whips her relentlessly. After he is done, he commands Mammy to rub salt in Alice's wounds as torture. After Alice is unchained, Sarny helps Mammy take care of Alice and her wounds. Alice must heal from wounds from the whipping and the dog bites.
Alice serves as a narrative foil to Sarny. She shows Sarny what can happen if she does not follow the rules on the plantation. While Alice's first instinct is to run, Sarny's rebellion leads her to learn more and more.

What Happens while Margot is in the closet?

The sun comes out for one hour, the hour that Margot is locked in the closet.

They surged about her, caught her up and bore her, protesting, and then pleading, and then crying, back into a tunnel, a room, a closet, where they slammed and locked the door.

Ray Bradbury's short story is set in the future, when people live on Venus. There it rains constantly; the sun only emerges once every seven years. Since the children are nine years old, they have no memory of the sun. Because she has moved to Venus from Earth, only Margot remembers what the sun looks like and how it feels warm on the flesh and "like a blushing" on the face, and how it looks "like a penny." She stands apart from the others and does not wish to play their games with them in the underground tunnels of the city, which are artificially lighted. It is because she does not play with the others and because she never sings unless the song is about the sun that the other children hate her for "these reasons of big and little consequence."
When one cruel boy sees in Margot's eyes that she eagerly waits for the hour of the sun, he tells her "It's all a joke!" but she insists that this day is the one which the scientists have determined that the sun will emerge.

"All a joke!" said the boy, and seized her roughly. "Hey, everyone, let’s put her in a closet before the teacher comes!" "No," said Margot, falling back.

The cruel children push Margot into a closet, watching as she throws herself against the door desperately. They smile as they turn and go back down into the tunnel before the teacher arrives. When the sun does come out, the children are ecstatic; they squint at the sun, and they remove their jackets to feel the rays upon their arms.

They put their hands up to that yellowness and that amazing blueness and they breathed of the fresh, fresh air and listened and listened to the silence which suspended them in a blessed sea of no sound and no motion.

And then it is over. A raindrop falls in one girl's hand. Then, another girl utters a faint cry: "Margot." Margot, whose greatest desire was to again see and feel the sun, has been in the closet all the time that the sun was out.

As explained in The Diary of a Young Girl, what was the role of "Kitty," or Anne's diary, during her period of hiding in the annexe?

Kitty, Anne's diary, plays the role of Anne's confidante while Anne is in hiding with her family in the secret annex. Anne's decision to refer to her diary as "Kitty" proves Anne's need for a friend; this need is so strong that Anne names her diary as if it were a real person, and she writes in this diary as openly and emotionally as if she were speaking to someone close to her heart.
Anne confesses all of her secrets to Kitty, Anne's only substitute for a trusted friend while in hiding, and because Kitty cannot respond, Anne cannot feel judged nor misunderstood. Anne experiences relief and satisfaction at her ability to express herself honestly on paper, similar to the relief and satisfaction someone might feel after a long and honest talk with an old friend.

Anne's diary, Kitty, serves as a voice and sounding board for Anne at a time when she was relegated to silence.
Anne's diary, Kitty, allowed her to have a voice.  In both the act of hiding and in her life, Anne lived a life of silence. Literally and symbolically, she was unable to speak. However, Kitty changes that by giving Anne a place where she could speak her mind.  Anne admits this in her opening entry:  "I hope I will be able to confide everything to you, as I have never been able to confide in anyone, and I hope you will be a great source of comfort and support."  In this way, Kitty is a confidant to Anne.  
Anne believes that Kitty provides an opportunity for her to be heard.  Anne feels that Kitty can validate her experience:

Writing in a diary is a really strange experience for someone like me... Oh well, it doesn't matter. I feel like writing, and I have an even greater need to get all kinds of things off my chest.

Anne needs to "get all kinds of things off [her] chest" because she does not have a release.  Kitty's role is to provide this release.  Anne says that she was "prompted to keep a diary in the first place" because she lacks friends. In her role as a friend, Kitty is able to authenticate and validate Anne's voice.

How did the twins Romulus and Remus help shape Roman culture?

Romulus and Remus are two figures of Roman myth and the legendary founders of the city of Rome. As the legend has it, Romulus and Remus are the twin sons of Rhea Silvia and Mars, the god of war. When the twins were born, Rhea's uncle (who stole the throne from her father) stole the babies away and ordered them to be drowned in the Tiber River. Luckily, the infants floated to safety and were looked after by a wolf and woodpecker, then taken in by a shepherd. As young men, the twins get into a fight with some of the king's men, and Remus is captured. Romulus kills the king, who he does not know is his uncle, and rescues Remus, restoring their estranged grandfather to the throne. 
The twins then decide they wish to found their own cities, though they disagree about the location. Romulus decides to build his city on Palatine Hill, and constructs a wall to secure the location. Remus thought building a wall was a silly idea and even tried to prove how ridiculous the wall was by jumping over it. In anger, Romulus killed his brother, and named the city for himself—Rome. This is the foundational myth of Roman culture and how the city got its name.
The myth of Romulus and Remus explains the name for the city, and further details help provide a mythological or historical ground for some of the geopolitical and socioreligious values of Roman culture. It is said that after founding his city, Romulus offered asylum to those who had been kicked out of other places, including criminals, the sick, and fugitives. The population of Rome was overwhelmingly male, and to obtain some brides for his citizens, Romulus invited women from the native, neighboring tribes of Sabines and Latins to come to the city for a festival. There, the women were captured, assaulted, and forced to marry the Roman men. This part of the myth offers a "justification" or societally-grounded inspiration for the continual capture, assault, and forced assimilation of many of the tribes surrounding Rome. Despite forced assimilation, these cultures were heavily incorporated into the new Roman society—for example, many Roman gods are parallels of those worshiped by the Sabines.
In response to the capture and abuse of women and children, these neighboring societies declared war on Rome, but were ultimately defeated. When defeated, their territories were forfeited to the city of Rome, and here we begin to see the development of the Roman Republic. Rome began to include surrounding lands outside of the city wall and transplant "Roman" culture to the farthest reaches of the Republic. 
As we can see, the foundational myth of Romulus and Remus provided not only the name for a city and culture, but a cultural identity grounded in expansion, conquest, and social dominance. Their actions described in the foundational myths of Rome fostered an attitude which grew into the Roman Empire, which included much of Europe and North Africa.
https://www.ancient.eu/Romulus_and_Remus/

https://www.britannica.com/biography/Romulus-and-Remus

https://www.britannica.com/place/Roman-Republic

What was the purpose of King's "Letter from Birmingham City Jail"?

When King wrote his "Letter from Birmingham Jail," the nonviolent mass protests of the Civil Rights movement were at their height and had gained national attention. While there was much vehement opposition to this movement and its goals, there was also a growing number of "sympathetic" people who argued that blacks did deserve more rights, but that it was not the right time. They criticized King's actions and called for him to wait for a better time. This type of argument was not new in American history.
King largely writes this letter in response to this argument. He poignantly points out that black Americans have been told to wait time and time again with little progress being made. He concludes that being told to wait really means "no" to their demands. He affirms his commitment to the Civil Rights movement and refuses to wait for a so-called "better time." Instead, he argues, black Americans deserve full and immediate political, economic, and social equality.

The letter was written by King in response to "A Call for Unity," a statement by a group of white clergymen from Alabama. In the statement the clergymen acknowledged the existence of widespread social injustice, but maintained that justice was best served through the courts. The clergymen were highly critical of King and his methods of waging the struggle for civil rights. They particularly objected to street demonstrations and protests, which they believed to have been whipped up by "outsiders."
King responds by saying that African Americans cannot simply wait for the courts to deliver civil rights; they must continue with their strategy of nonviolent resistance. In other words, justice delayed is justice denied. White Christians like the "Call for Unity" clergymen need to take a firm stand. The issue of civil rights is a moral question, one that has a fundamentally religious dimension.
In writing the letter, King attempted to emphasize the religious nature of the civil rights struggle. He does this in order to take the civil rights movement beyond the inherently contentious world of politics and law and into a realm of timeless truths and eternal justice. He's also encouraging those involved in the civil rights struggle to continue with the fight, to look ahead and see the day when they, and not those such as the clerics who wrote the "Call for Unity," will be hailed as heroes.

What moment in the story describes George and Lydia's failure as parents?

Towards the beginning of the story, while Peter and Wendy are enjoying a helicopter trip, Lydia laments about the nursery and tells her husband that she is afraid of the African veldt, which the children have been watching on an everyday basis in their nursery. Bradbury provides a clue that depicts George and Lydia's failure as parents when George mentions that Peter and Wendy threw a temper tantrum last month when he locked the door to the nursery for a few hours. This comment is significant and reveals that George and Lydia bow to their children's demands. The fact that George allows his son and daughter to throw tantrums and is willing to leave the nursery unlocked indicates that he lacks control and authority in his home.
At dinner, Peter and Wendy mention that they are too full to join their parents, because they have been eating hot dogs and ice cream all night. They also lie to their parents about the African veldt, and Wendy purposely deceives her father by quickly changing it before he enters. Allowing Peter and Wendy to consume junk food, skip dinner, and lie to their faces are additional examples that depict their bad parenting skills. Later that night, George admits to his wife that they have failed as parents by telling her:

"We’ve never lifted a hand. They’re insufferable—let’s admit it. They come and go when they like; they treat us as if we were offspring. They’re spoiled and we’re spoiled" (Bradbury, 8).

After Peter and Wendy return from the carnival, they lie to their parents about the African veldt playing on the view screens in their nursery. They say they are not watching Africa, and they actually change what is playing to try to deceive their parents. George, however, finds his chewed wallet in the nursery, and it smells of the African veldt. 
It is after this episode that the parents decide they have failed. George says that children need to stepped on occasionally, but George and Lydia have spoiled their children. George then locks the nursery and says it will stay locked. He also decides to invite Dr. McClean over to determine whether the children are emotionally healthy.
All of this indicates a family in crisis. However, the parents will fail again when they allow the nursery to be unlocked because the children beg them to do so.

How do the people in Brave New World see art?

The short answer is that the people of the Brave New World do not see art. No art is created in the present, and the World Controllers have done everything they can to erase the past. They have closed all the museums, blown up the historical monuments, and banned "all books published before A.F. 150."
Unusually for the Brave New World, there appears to be no difference between the castes in this respect. The Alphas are just as ignorant of high art as the Deltas and Epsilons. There may be some exceptions at the very top of the hierarchy: Mustapha Mond appears to be familiar with art and literature, as he is with science, but this can be chalked up to the fact that the censor himself has to have some idea of what he is censoring in order to work efficiently.
Mond points out that the different castes are necessary to social order. A society composed entirely of Alphas would be a disaster, because

An Alpha-decanted, Alpha-conditioned man would go mad if he had to do Epsilon Semi-Moron work—go mad, or start smashing things up.

However, he does not make the connection with art that Huxley, a paragon of polymath sophistication, certainly did. A highly educated person cannot happily do mind-numbingly tedious work. For the same reason, they cannot endlessly consume shallow ersatz entertainment. The semi-pornographic feelies may satisfy the Epsilons, but is is evident from the text that they cannot and do not satisfy the minds and hearts of men like Bernard and Helmholtz. Where art is not seen, it is felt as an absence by those whose lives are shallow and unsatisfying without it.

The vast majority of people in the World State are satisfied with shallow, pornographic art that gives them fleeting pleasure and doesn't cause them to think. It simply reflects back to them the world they know.
The classics of the past are banned. When John the Savage questions Mond about art, and why nobody is allowed to read Shakespeare anymore, Mond says:

Because it’s old; that’s the chief reason. We haven’t any use for old things here.

Mond goes on to explain that the World State has been engineered to make what is called "high art" obsolete. After the Nine Years' War, people craved stability and happiness above all else. They have a stable world, and that kind of world makes real art incomprehensible. Mond says:

you can’t make tragedies without social instability. The world’s stable now. People are happy; they get what they want, and they never want what they can’t get.

According to Mond, sacrificing high art, such as Shakespeare, was a necessary and beneficial trade off. If people are stimulated to think, they will be unhappy, and that will cause social instability. Social instability has to be avoided at all costs.

The society of Brave New World does not value art at all. Their prime mode of entertainment are the "feelies" (probably a play on the 1920s/1930s term "talkie," which described sound films which obviously introduced a new sensory element to the previously silent cinema), films which incorporate touch and smell. These films are less interested in compelling stories and characters than they are in indulging the baser fantasies of their audience. They are usually pornographic in nature.
John the Savage is told outright by Mustapha Mond that art has no place in the modern world because true art is not focused solely on pleasure. Tragic plays make people sad and in the future, any unpleasant feelings are considered dangerous and bad rather than cathartic and ennobling.

The citizens of Aldous Huxley's Brave New World have been conditioned to only enjoy low, vulgar art which promotes the self-indulging values of this society.
Children are given electric shocks when they touch books in order to condition them to hate literature. They are provided with synthetic, absurd pop-songs for music. The films they watch are called feelies, which are movies that the viewer is able to experience with all the senses. The storylines of these films are terribly simple, but the crude, sensuous plot is another way that the people experience pleasure and physical satisfaction. This art is not meant to stimulate any sort of intellectual or emotional depth, only to satisfy the desires of the moment and endorse the values the citizens have been conditioned to believe in.
Poetry and rhyme are exclusively used for propaganda. This is one of the reasons why Helmholtz is banished from the community. He wants to create poetry to express his innermost feelings, which is a dangerous thing. He tells Bernard,

I feel as though I were just beginning to have something to write about. As though I was beginning to be able to use that power I feel I've got inside me—that extra, latent power.

After John, Helmholtz, and Bernard have been arrested, Mustapha Mond explains why popular art in this society is so crude and vulgar:

that's the price we have to pay for stability. You've got to choose between happiness and what people used to call high art. We've sacrificed the high art. We have the feelies and the scent organ instead.

In order to appreciate high art like Shakespeare, people must be able to experience instability, loss, grief, pain, and love. The people of this society are satisfied and comfortable without these deep thoughts and emotions. Because of this, only low, self-indulgent art is accepted in Brave New World.

How do the other characters in the Twelfth Night view Feste?

Feste is a professional fool, or jester. This places him in a position where he is permanently isolated, estranged from so-called polite society. As a fool, he's been granted the fool's pardon, which allows him to say things about other characters that he wouldn't otherwise be allowed to express. He's also a highly intelligent man; indeed, he's arguably the most intelligent character in the play. His acute intelligence gives him a great insight into the myriad flaws and foibles of everyone else, an insight which he then passes on to us, the audience.
Despite this, Feste isn't really taken all that seriously by anyone else in Twelfth Night. At best, he's a source of entertainment and amusement; after all, that is his job. But the prevailing social hierarchy is so rigid that no one can really look upon at Feste as an equal, cannot really accept him as a fellow human being in the fullest sense of the word. For all his sparkling wit, inventive wordplay, and winning personality, he is still a servant, and as a servant must work hard for his keep.
Feste finds himself torn between the dictates of a free-spirited soul and the sometimes onerous responsibilities of his role as court jester. Every so often, Feste feels the overriding need to take off, to break out from his socially-imposed role, even if it means running the serious risk of being punished by his mistress Olivia.
It's tough being a fool, especially when no one takes you seriously as a person. It's even worse when your jesting skills appear to be slipping, as Malvolio indicates:

I marvel your ladyship takes delight in such a barren rascal. I saw him put down the other day with an ordinary fool that has no more brain than a stone. Look you now, he’s out of his guard already. Unless you laugh and minister occasion to him, he is gagg’d. (Act I Scene V)

Once a fool stops being funny, there's no further use for him. Feste's isolation in the rarefied world of Twelfth Night is confirmed at the play's ending when he's left all alone. He doesn't belong with Olivia and her lovers, but nor does he belong with Sir Toby and Maria, Sir Andrew or Malvolio. He is an entirely separate entity, complete in and of himself, but destined to be forever defined by the onerous, wearisome burden placed upon his shoulders by a society that steadfastly refuses to acknowledge his individuality.

In To Kill a Mockingbird, what are examples of Jem being responsible?

Since To Kill a Mockingbird can be considered a bildungsroman, a coming-of-age story, Jem certainly has his moments of immaturity. On the other hand, he learns to be responsible in the instances in which he cares for others or must make up for his immature actions. In chapter 6, for example, Jem and Dill go over to the Radley house to see if they can catch a glimpse of Boo. Unfortunately, Mr. Radley hears them in the backyard and comes out shooting his gun in the air. As the kids are slipping under a fence to get away, Jem's pants get caught, and he has to leave the pants there in order to escape in time. In an effort to cover his tracks, Jem goes back in the middle of the night to fetch them. One might say that this action does not show responsibility because Jem is doing this to avoid getting in trouble. Furthermore, Scout argues that Jem should "take a lickin'" rather than go back to the house and risk death. Jem argues, "Atticus ain't ever whipped me since I can remember. I wanta keep it that way" (56). In his own way, Jem takes responsibility for keeping his clean streak alive and goes after his pants.
Another act of responsibility shows Jem taking care of his sister during Maudie's house fire in chapter 8. For the first few chapters, Jem seems to be either bothered by his sister's existence or at odds with Scout about something else. When a crisis arises, though, Jem steps up and takes care of his little sister without argument. Additionally, he tries to soothe her and keep her calm during the chaos:

Jem put his arm around me. "Hush, Scout," he said. "It ain't time to worry yet. I'll let you know when" (69).

Scout later mentions that her father says the same thing to her when she is scared, so when Jem says it, it helps calm her down. Jem not only knows this, he also puts his arm around his sister to show that he is there for her. This is a great example of taking responsibility on Jem's part.
One more example of Jem taking responsibility is after he attacks Mrs. Dubose's flowers in chapter 11. After freaking out and making a complete mess of an old woman's yard, Jem promptly admits to his father about what he did when he is asked. Jem could have lied or tried to justify his actions to throw all the responsibility on Mrs. Dubose's rude humor, but he does not do that. He looks his father in the eye and admits with complete honesty what he did and why he did it. As a result, he has to go read to the old woman every day for a month. He does this without any prompting from anyone else. Jem takes responsibility for his actions and does not try to hide or justify them. That is a sign of true growth right there.

Read the article detailing discrimination against pregnant women and share your thoughts: Please keep it no more than 300 words https://www.theatlantic.com/business/archive/2014/09/when-bosses-discriminate-against-pregnant-women/380623/

In "When Bosses Discriminate Against Pregnant Women" by Darlena Cunha, the issue of discrimination against pregnant women and how their work compares to childless women and men is discussed. Though the article doesn't go into much depth about the issue and mostly includes anecdotes from unnamed sources, the strength of Cunha's argument rests on studies that indicate that women with children are evaluated unfairly by others at work -- and that it affects their income.
Cunha links a study published in the American Journal of Sociology to explain that women suffer from discrimination after they get pregnant and once they've given birth. The study also discusses the pay gaps mentioned later in the article. Including it directly strengthens her argument by providing hard evidence -- something the article would lack if it was all anecdotes.
While the anecdotes that Cunha uses to make her case are compelling, they are still anecdotes. Personal experience is valid, but it isn't stronger than the linked studies. Since the two line up, Cunha's reliance on personal anecdotes doesn't weaken the article. Instead, it illustrates the problem and adds a touch of human interest to the piece. 
One thing that complicates the issue -- as Cunha points out -- is that it's difficult to prove discrimination at work. People who witness it may fear for their own jobs; they may be too afraid to speak out when it can easily result in retaliation against them. Discrimination can appear normal from the outside and women may not even realize they're experiencing it at the time. Still, the article says that discrimination cases filed with the EEOC increased more than 30 percent from 1996 to 2006.
Ultimately Cunha's article makes the point that discrimination against pregnant women is a real world thing and has serious consequences for those that experience it. 
https://www.theatlantic.com/business/archive/2014/09/when-bosses-discriminate-against-pregnant-women/380623/