College Algebra, Chapter 4, 4.5, Section 4.5, Problem 24

Factor the polynomial $P(x) = x^4 - 625$, and find all its zeros. State the multiplicity of each zero.

To find the zeros of $P$, we set $x^4 - 625 = 0$, by factoring


$
\begin{equation}
\begin{aligned}

x^4 - 625 =& 0
\\
\\
(x^2 - 25)(x^2 + 25) =& 0

\end{aligned}
\end{equation}
$


Thus, the zeros are $x = \pm 5$ and $x = \pm 5i$.

By factorization,


$
\begin{equation}
\begin{aligned}

P(x) =& (x - 5) \left[ x - (-5) \right] (x - 5i) \left[ x - (-5i) \right]
\\
\\
=& (x - 5)(x + 5)(x - 5i)(x + 5i)

\end{aligned}
\end{equation}
$


We can say that each factors have multiplicity of $1$.

What might Irving have been trying to say about the true impact of the Revolutionary War? What about the nature of democracy?

Irving might be suggesting that the American Revolution brought about great changes to the country. Rip Van Winkle falls asleep for twenty years and misses the entire American Revolution. When he wakes, he is shocked by the ways in which America has been transformed. For example, people no longer serve under the British king but are loyal to their president, George Washington. In addition, people are voting, which is something he has never done before.
Irving implies that having missed just these twenty years makes someone hopelessly out of date in America, as it has changed so greatly in that time period. It has gone from being part of the British empire to being its own democratic nation. Rip is completely out of date and can't fathom the immense changes that his country has undergone while he was sleeping.

One of the observations which stands out in reading "Rip Van Winkel" is the sheer contrast which Irvings makes between colonial life and the post-Revolutionary War era. Life in the colonial era is described as largely tranquil (with the notable exception of Winkel's wife). Also, consider the small inn and the personage of Nicholas Vedder, described in the tale as "a patriarch of the village," surrounded by "his adherents . . . (for every great man has adherents)." Just as the George III (whose image hangs on the wall) rules the empire, so does Vedder rule the inn. There does, then, seem to be a kind of static peacefulness in this time period, which is joined with a kind of aristocratic traditionalism.
Contrast that with the scene that follows as Rip Van Winkel returns from his sleep in the Catskills. The scene is suddenly much more vibrant. The town is described as larger, with new houses and faces that are unfamiliar to Rip. As Irving writes, "the very character of the people seemed changed. There was a busy, bustling tone about it, instead of the accustomed drowsy tranquility." It is far more active, the people are more passionate and opinionated, with a sharp and passionate interest in politics. That aristocratic quality has been replaced with a more democratic spirit, which can risk becoming unruly—consider the distress Van Winkel is put under when they start suspect him of being a Tory, for example, and how the crowd nearly dissolves into a frenzy. Nevertheless, it's clear within Irving's account that the entire town has undergone a startling transformation, becoming much more animated (politically and emotionally) than it had been before the war.

Iriving's story illustrates that the Revolutionary War and the democracy it brought woke people up. It roused them from the deep sleep or stupor in which they had been living under British rule.
Rip van Winkle is the symbol of the sleepy old ways. He drifts through life without any ambition, lets his wife (like Britain with the colonies) push him around, and would rather sit in front of the inn talking than do anything useful. Finally, he literally falls asleep for twenty years.
By the time he wakes up, America has won the Revolution and democracy is in place. Apathetic people like him are obsolete. He comes back to a village that is newly bustling and bursting with life exactly because its men have become citizens of a republic and participants in a democracy. They are energized by an upcoming election and the chance to have their voices heard in a representative government.
Irving is contributing in this tale to building the American mythology. Democracy and the break from Great Britain are depicted as all good. The Revolution was nothing but positive because it brought men (it would be men only participating with the vote in this democracy) from an apathetic stupor to vigorous activity.

Why is Leslie from Bridge to Terabithia so brave?

I would say that the text gives several good examples of Leslie being brave; however, the text does not offer much explanation as to why she is as brave as she is.  It could be a genetic trait, and she was simply born brave.  But I don't believe that a person is entirely determined by their genetic nature.  A person's environment plays a large role in shaping a person's behavior too.  This would be their nurture.  I believe that Leslie is brave because her parents have taught her to be brave.  Whether it was intentional or not is unknown, but Leslie's parents have a huge impact on her.  Both of Leslie's parents are well educated people.  Consequently, Leslie is a well educated young girl too.  That education builds self-confidence, and self-confidence often looks like (or is) bravery.  
Leslie's bravery might also be a coping mechanism to a new environment.  She has just been moved to a new city and a new school.  She's smart enough to know that if she wants to make friends, she is going to have to be brave and make an effort at it.  If she stands in the background of things, she might never make any new friends.  That could be why she gravitates to the running races in the first days of school.  She likes running, and she is good at running.   Those two things give her the bravery and the confidence to try and break into the recess races.  Her bravery works too.  It doesn't net her a lot of friends, but it nets her a wonderful friend in Jess.  

Single Variable Calculus, Chapter 4, 4.8, Section 4.8, Problem 16

Use Newton's Method to approximate the positive root of $2 \cos x = x^4$ correct to six decimal places.

Rewrite the equation in Standard Form

$2 \cos x - x^4 = 0$

Therefore, let $f(x) = 2 \cos x - x^4$. Then,


$
\begin{equation}
\begin{aligned}

f'(x) =& 2 \frac{d}{dx} (\cos x) - \frac{d}{dx} (x^4)
\\
\\
f'(x) =& 2 (- \sin x) - 4x^3
\\
\\
f'(x) =& -2 \sin x - 4x^3

\end{aligned}
\end{equation}
$


Using Approximation Formula


$
\begin{equation}
\begin{aligned}

x_{n + 1} =& x_n - \frac{f(x_n)}{f'(x_n)}
\\
\\
x_{n + 1} =& x_n - \frac{2 \cos x_n - x_n^4}{-2 \sin x_n 4x^3_n}
\\
\\
x_{n + 1} =& x_n + \frac{2 \cos x_n - x^4_n}{2 \sin x_n + 4x^3_n}


\end{aligned}
\end{equation}
$









To find the initial approximation $x_1$, we graph $y = 2 \cos x$ and $y = x^4$.

Based from the graph, it appears that they intersect at a point in $x$-coordinate where they are very close to -1 and 1. We have $x_1 = 1$ and $x_1 = -1$ as the initial approximation.

So we get


$
\begin{equation}
\begin{aligned}

x_2 =& x_1 + \frac{2 \cos x_1 - x_1^4}{2 \sin x_1 + 4x_1^3}
&&
\\
\\
x_2 =& 1 + \frac{2 \cos(1) - (1)^4}{2 \sin(1) + 4(1)^3}
&& x_2 = -1 + \frac{2 \cos (-1) - (-1)^4}{2 \sin (-1) + 4(-1)}
\\
\\
x_2 \approx & 1.014184
&& x_2 \approx - 1.014184
\\
\\
x_3 =& 1.014184 + \frac{f(1.014184)}{f'(1.014184)}
&& x_3 = - 1.014184 + \frac{f(-1.014184)}{f'(-1.014184)}
\\
\\
x_3 \approx & 1.013958
&& x_3 \approx - 1.013958
\\
\\
x_4 =& 1.013958 + \frac{f(1.013958)}{f'(1.013958)}
&& x_4 = - 1.013958 + \frac{f(-1.013958)}{f'(-1.013958)}
\\
\\
x_4 \approx & 1.013958
&& x_4 \approx -1.013958

\end{aligned}
\end{equation}
$


Since $x_3$ and $x_4$ agree to six decimal places, therefore $x \approx 1.013958$ and $x \approx -1.013958$

The North Atlantic Treaty Organization (NATO) and the Warsaw Pact were two important Cold War organizations. Describe their purpose and function as they relate to the Cold War.

The United States and 11 other Western nations formed the North Atlantic Treaty Organization (NATO) in 1949 as a way of standing together against further Communist expansion around the globe. In response, the Soviet Union and the nations in Eastern Europe under its influence signed the Warsaw Pact, the Communist equivalent of NATO, in 1955. Both organizations aimed to create a coordinated defense in order to deter an enemy attack against any one of their member states, creating two opposition alliances that would face off against each other in the emerging Cold War.
NATO reflected an important change in US foreign policy after World War II, as the nation departed formally from a policy of isolationism and linked its national security and defense to that of its allies in Europe. From its original member states of Belgium, Britain, Canada, Denmark, France, Iceland, Italy, Luxembourg, the Netherlands, Norway, Portugal, and the United States, NATO membership expanded during the Cold War era to include Greece and Turkey, West Germany, and Spain. While the Warsaw Pact was responding indirectly to NATO’s formation, its signers (including Albania, Bulgaria, Czechoslovakia, East Germany, Hungary, Poland, and Romania) were more directly motivated by the rearmament of West Germany and its inclusion in NATO in 1955.

NATO was formed in 1949 as a consequence of the realignment of Europe into eastern and western camps after World War II ended. Eastern European nations had become communist satellite states of the Soviet Union, behind what Winston Churchill called the “iron curtain.” Western European democracies and the United States responded by signing the North Atlantic Treaty, the charter for NATO. Its Article Five included a collective security commitment by all NATO members. They pledged to view any attack on a single NATO country as an attack on the entire alliance. NATO cemented the transatlantic partnership of Western Europe with the United States and ensured the U.S. would use the threat of its nuclear arsenal to deter, or prevent, the outbreak of a new war against Soviet Russia.
When West Germany was admitted into NATO in 1955 and promised to re-arm, the Soviet Union—which by then had become a nuclear weapons state—and the Eastern European countries in its sphere of influence responded by creating their own collective security agreement, the Warsaw Pact. Through the remaining decades of the Cold War, the two organizations geographically represented the tenuous balance of power (or, considering the nuclear threat, the balance of terror) by which Europe kept the peace.

Both NATO (the North Atlantic Treaty Organization) and the Warsaw Pact were collective security treaties created during the Cold War. Basically, if a country within one of these treaties was attacked, all member nations of that respective treaty would rise in its defense and declare war against the attacker.
NATO was formed in 1949 against the USSR in an effort to stop the spread of Communism. The USSR was gaining power at this time and was using its strong forces to capture satellite countries. Member nations of NATO would defend each other from the possibility of the USSR taking control of their country.
In 1955, the USSR and other Communist nations in Eastern Europe formed a rival alliance, the Warsaw Pact. The Warsaw Pact was a symbol of Soviet dominance in Eastern Europe. The USSR could use the pact as an excuse to keep Soviet troops in other Eastern European countries and keep a close eye on its satellite states.
The creation of these two alliances made it difficult for the US and USSR to directly attack one another as this would lead to another World War. Thus, the US and USSR could not engage in direct confrontation or a “hot” war and instead fought one another through proxy wars in Non-Aligned countries like Afghanistan and Vietnam.
Interestingly enough, these collective security treaties were what gave rise to terms like "first-world", "second world", and "third world" when describing countries. First world countries referred to NATO member nations, while second world countries referred to Warsaw Pact member nations. Third world countries, on the other hand, were not part of either treaty and thus often fell victim to proxy wars.

Both Nato and thee Warsaw pact were the collective defense and deterrence organizations from both "blocks" during the Cold War, Nato was formed as a defense organization by the United States and the countries of Western Europe to thwart the advances of communism both in the European continent and abroad, while the Warsaw pact was formed by the Soviet Union as a counter to the Western Capitalist powers both in Europe and around the world.
Both organizations were charged with similar goals, albeit being ideologically opposed, as both acted as deterrent against the other succesfully creating a balance of power during the Cold war, coupled with Nuclear deterrence this collective security organizations served their purpose by keeping the war "Cold" instead of it going "hot", while they never had a direct confrontation agains one another they engaged in various proxy wars around the world succesfully shaping the International System during the second half of the 20th century.
One of the most important aspects of both NATO and the Warsaw Pact was the standarization of military procedure and equipment on their respective areas of influence, NATO on one hand modelled made the Allies adopt standard equipment, procedure and terminology on Europe, modeled of course after US military apparatus which meant that if the need arised the whole European and US military could mobilize in uniformity and coordination. The Warsaw pact on the other hand while not really standirizing the military as a coordination effort like NATO helped developing and modernizing the military apparatus of countries in the "Buffer Zone" as well as providing aid to other ideologically aligned governments, guerrillas, and movements around the world like the case of the Cuban Revolution were the rebels were armed and funded by the Warsaw pact or the case with "Las FARC" on Colombia were the guerrillas were trained, armed and funded by the Soviet Union.

In the novel Fahrenheit 451, who is Montag's greatest ally?

There are several characters throughout the novel that aid Montag in his search to find meaning in life and engage in intellectual pursuits. However, I feel that Faber is Montag's greatest ally because he explains why books are important and willingly risks his safety to help Montag challenge the authoritative regime. When Montag visits Faber's home for the first time, Faber gives Montag insight into the importance of literature and allows him to take a two-way communication device. From the safety of his home, Faber gives Montag advice via the green bullet. After Montag kills Captain Beatty, Faber offers Montag refuge in his home while the authorities search for him. Faber also helps Montag flee the Hound and tells him where to find a group of traveling intellectuals. Faber's advice and selfless support make him Montag's greatest ally throughout the novel.

Discuss the role and responsibilities of line managers in regard to human resource management.

One distinction often made in management science is that between a line (or direct) manager and a "project" manager. A line manager directly supervises people, although those people may be assigned to work as parts of teams on specific projects, with tasks assigned or supervised within the project context by "project managers."
The responsibilities of line managers vary depending in the specific workplace, but they share certain common attributes. First, line managers are middle management with respect to human resources, and they are responsible for implementing policies that are passed down from executives. Line managers report to higher-level managers or executives. Line managers rarely create human resources guidelines, but they are responsible for implementing them and often interface with both the employees they supervise and human resources departments.
Line managers work closely with human resources in hiring and firing employees. They are usually responsible for conducting regular performance reviews and facilitating appropriate coaching or training. They often mentor employees and are tasked with monitoring and improving employee performance and productivity.

Simply put, a line manager's job is to supervise the people who work under then and to report on the department's activities to their seniors. A line manager can also be referred to as a supervisor, direct manager, or team leader.
A line manager's responsibilities include ensuring that deadlines are met, making sure that their team has everything that they need to do the work, and bridging the gap between upper management and less senior members of staff. By assuming responsibility for the team and its output, the line manager protects their team and prevents mistakes from being made. They can be considered the first level of supervision over entry-level employees.
In addition to this, the line manager is responsible for selecting, recruiting, inducting, and training new team members.
https://www.thebalancecareers.com/role-and-challenges-of-a-line-manager-2275752

Line managers are essentially the direct managers for certain employees (their direct reports are the next in line in terms of hierarchy and leadership). They have managerial duties over their direct reports, which extend to many human resources functions.
The main functions line managers take on with their reports involve commendation, reprimanding, wages, and time management. If their employee does a good job at something, they are commended, potentially with a bonus or some other perk, and this comes from their direct line manager. Reprimanding works the same way—since the direct line manager works with them closest, they are the ones in charge of reprimanding them for poor performance.
In terms of wages, the line manager handles performance reviews and recommends/approves of raises and bonuses for their employees. Additionally, the line manager is responsible for verifying the timekeeping and absences/vacations of their employees to ensure that they are reported correctly to human resources.

A line manager, also called a direct manager, is responsible for the direct supervision and management of employees in their work. The line manager reports to higher managers and plays a crucial role in human resource management.
The line manager is often responsible for the following functions:
hiring employees
supporting and training employees
coaching employees and providing feedback on their performance
helping teams meet department or company-wide goals
reporting to managers about individual employees' performance and about progress towards meeting department goals
providing performance reviews to employees
deciding on promotions or raises for employees
identifying the need for changes in the management of department goals or performance
working with other direct or line managers
While managers provide overall goals for a department or company, it is up to line managers to oversee teams and individuals to ensure that these goals are met. A line manager plays a critical role in recruiting and hiring employees, in motivating and coaching them to achieve department or company goals, and in communicating company-wide goals to them. Often, an employee's level of motivation depends on his or her relationship with a direct manager, and a line manager plays a vital role in keeping employees motivated and retaining talent. A line manager can also play a critical role in retraining or cross training employees to carry out additional tasks. Line managers are critical in implementing the goals of management and helping their employees meet these goals.

What is Zoroastrian religion?

The Zoroastrian religion, or Mazdayasna, is the pre-Islamic religion of Iran. It was founded sometime before the 6th century B.C.E. by the prophet Zarathustra (known to the Greeks as Zoroaster).
Zoroastrianism is a dualistic religion; that is, it ascribes to a worldview in which the universe is composed of polar opposites, such as Light and Darkness, Good and Evil, and Order and Chaos. Both the physical and spiritual realms exist in a state of constant tension between these opposing forces. Spiritually, these opposites are embodied in the benevolent supreme god, Ahura Mazda, who represents goodness, creation, and life, and his nemesis, the chaotic spirit Ahriman, who represents evil, destruction and death. It is the duty of every person during their lifetime to "fight" for Ahura Mazda to help the god overcome the forces of chaos represented by Ahriman.
Ahura Mazda is omnipotent and omniscient, but he does not rule the universe alone. To aid him, he created six beings known as the Amesha Spentas, or "Bounteous Immortals." These beings are similar in nature to the angels of the Abrahamic faiths, but they are also metaphors for spiritual goals each person should try to attain. The Amesha Spentas are:

Vohu Manah — Good mind and good purpose.

Asha Vahishta — Truth and righteousness.

Spenta Ameraiti — Holy devotion, serenity and loving kindness.

Khashathra Vairya — Power and just rule.

Hauravatat — Wholeness and health.

Ameretat — Long life and immortality.
People must work to achieve the Amesha Spentas every day. When a person dies, their soul will be judged according to their deeds in their lifetime. Those who performed more good acts than evil acts will enter Heaven, while those who performed more evil acts than good ones must go to Hell. Zoroastrianism also accounts for a concept of Purgatory, where the souls of those people whose good and evil acts precisely balance each other are sent.
Ahura Mazda and Ahriman are constantly at war, both in the larger world and in the soul of each person. Ultimately, this war will lead to a final confrontation—an apocalypse—in which Ahura Mazda permanently defeats Ahriman, after which all beings will live in bliss and harmony. Before this final war, there will be periods in which Ahriman seems to be prevailing, but Zarathustra predicted that "sons," or descendants, of his would appear in the world at these periods just in time to tip the balance back in favor of Ahura Mazda.
The belief in a final battle makes Zoroastrianism an eschatological religion, while Zarathustra's predictions about his descendants appearing to save the world make Zoroastrianism a messianic religion. These features, as well as Zoroastrianism's fundamental dualism, heavily influenced the development of both Christianity and Islam.
Zoroastrianism is a living tradition, although since the advent of Islam, it has dwindled to a very small community of fewer than 200,000 people worldwide. Most of the community is based outside of Iran, in India, Iraq, Kurdistan, and Central Asia.
https://www.britannica.com/topic/Zoroastrianism

How does Mercutio die in Romeo and Juliet?

Mercutio dies when he is stabbed by Tybalt who reaches under Romeo's arm. After this Tybalt flees with his followers.
In Act III, Scene 1, Mercutio, Benvolio, a page and servants enter a public place. Because of the heat and because the Capulets are also walking around Verona, Benvolio urges Mercutio to "retire" to their homes so that they will not become involved in a brawl. But, Mercutio, who is very short-tempered on this hot day, accuses Benvolio of getting angry at almost nothing when he is in a mood to be angry, so he should not criticize any one else.
This argument between friends sets a threatening tone for the scene. Then, as Benvolio and Mercutio quarrel, Tybalt enters with some other men. He asks to have a word with Benvolio and Mercutio. Annoyed by Tybalt's intrusion, Mercutio taunts him with puns until Romeo enters. Tybalt then turns his attention to Romeo, calling him "a villain," but since Romeo has married Juliet and is now related by marriage, he speaks kindly to Tybalt, saying that he "tender[s]" the name Capulet and loves him. Not knowing why Romeo says these things, Mercutio is incensed--"Oh, calm, dishonorable, vile submission!"(3.1.44), and he draws his sword. He and Tybalt exchange insults and Tybalt draws his sword, too. With the intention of ameliorating things, Romeo steps between them, urging them not to fight because the Prince has forbidden "this bandying in Verona streets" (3.1.56), but Tybalt reaches under Romeo's arm and fatally stabs Mercutio.

Single Variable Calculus, Chapter 6, 6.5, Section 6.5, Problem 14

Determine the numbers $b$ such that the average value of $f(x) = 2 + 6x - 3x^2$ on the interval $[0, b]$ is eqaul to 3.


$
\begin{equation}
\begin{aligned}

& f_{ave} = \frac{1}{b - a} \int^b_a f(x) dx
\\
\\
& 3 = \frac{1}{b - 0} \int^b_0 (2 + 6x - 3x^2) dx
\\
\\
& 3b = \left[ 2x + \frac{6x^2}{2} - \frac{3x^3}{3} \right]^b_0
\\
\\
& 3b = \left] 2(b) + \frac{6 (b)^2}{2} - \frac{3 (b)^3}{3} \right] - \left[ 2(0) + \frac{6(0)^2}{2} - \frac{3(0)^2}{3} \right]
\\
\\
& 3b = 2b + 3b^2 - b^3
\\
\\
& b^3 - 3b^2 + b = 0
\\
\\
& \text{We have,}
\\
\\
& b = 0 \text{ and } b^2 - 3b + 1 = 0
\\
\\
& \text{By applying Quadratic Formula}
\\
\\
& b = 2.6180 \text{ and } b = 0.3820

\end{aligned}
\end{equation}
$


Therefore, the values of $b$ are..

$b = 0, b = 2.6180$ and $b = 0.3820$

Intermediate Algebra, Chapter 3, 3.5, Section 3.5, Problem 32

Determine the domain and range of the given graph below.



According to the vertical line test, if every vertical line intersects the graph of a
relation in no more than one point, then the relation is a function. So, the given graph fails
the vertical line test, since the same $x$-value corresponds to two different $y$-values, and is not the graph of a function.


Moreover, the arrow heads indicate that the line extends indefinitely to the right, as well as up and down.
So the range is $(-\infty, \infty)$. However, there is a least $x$-value of $3$, the domain includes all numbers greater than
or equal to $3$, written as $[3,\infty)$

Single Variable Calculus, Chapter 7, 7.8, Section 7.8, Problem 26

Determine the $\displaystyle \lim_{x \to 0} \frac{\sin x - x}{x^3}$. Use L'Hospital's Rule where appropriate. Use some Elementary method if posible. If L'Hospitals Rule doesn't apply. Explain why.
$\displaystyle \lim_{x \to 0 } \frac{\sin x - x}{x^3} = \frac{\sin 0 - 0}{0^3} = \frac{0}{0} \text{ Indeterminate}$

Thus, by applying L'Hospitals rule,
$\displaystyle \lim_{x \to 0} \frac{\sin x - x}{x^3} = \lim_{x \to 0} \frac{\cos x - 1}{3x^2}$
If we evaluate the limit, we will still get an indeterminate form, hence, we need to apply L'Hospitals Rule once more, so...

$\displaystyle \lim_{x \to 0} \frac{\cos x - 1}{3x^2} = \lim_{x \to 0} \frac{(-\sin x)-0}{6x} = \lim_{x \to 0} \frac{-\sin x}{6x}$

Again, by applying L'Hospital's Rule for the third time, since we still get indeterminate form.

$
\begin{equation}
\begin{aligned}
\lim_{x \to 0} - \frac{\sin x}{6x} &= \lim_{x \to 0} - \frac{\cos x}{6}\\
\\
&= \frac{-\cos(0)}{6}\\
\\
&= \frac{-(1)}{6}\\
\\
&= \frac{-1}{6}
\end{aligned}
\end{equation}
$

I have been assigned to write an essay about Kathy Knapp's analysis of T. C. Boyle's The Tortilla Curtain. She says the novel "captures the ethos of the gated community." I need help understanding how Knapp defines that ethos.

Kathy Knapp writes in "Ain't No Friend of Mine" (see the source below) that the gated community in The Tortilla Curtain "embodies in miniature the nation's schizophrenic relationship with its undocumented community" (page 122). Knapp states that homeowner associations, such as the gated community where Delaney and Kyra Mossbacher live in the novel The Tortilla Curtain, generally allow undocumented immigrants into the community to perform chores such as housework and gardening. In other words, the white community only recognizes undocumented workers when they want work done, such as having their children cared for or having their pool cleaned.
In the novel The Tortilla Curtain, Cándido Rincón and his wife, América, undocumented immigrants from Mexico struggling to survive around Los Angeles, are invisible to the wealthy suburbanites in the Arroyo Blanco gated community. When Delaney Mossbacher, a resident of Arroyo Blanco, hits Cándido with his car, Delaney gives Cándido $20, later stating that it's sufficient compensation because the man is Mexican. In other words, Cándido's life is of little value to Delaney. However, residents of the Arroyo Blanco gated community employ América as a cleaning lady and pay her very little in return for her work, and they employ other undocumented immigrants as gardeners. The characters in the novel practice the ethos that Knapp discusses as they only value and see undocumented immigrants when the immigrants can be helpful to them as very low-paid workers. Otherwise, the characters do not recognize or try to help undocumented immigrants such as Cándido Rincón and his pregnant wife, América.
Source:
Knapp, Kathy. “‘Ain’t No Friend Of Mine’: Immigration Policy The Gated Community, And The Problem With The Disposable Worker In T. C. Boyle’s Tortilla Curtain.” Atenea 28.2 (2008): 121-34. Print.

College Algebra, Chapter 4, Chapter Review, Section Review, Problem 18

Graph the polynomial $P(x) = -2x^3 + 6x^2 - 2$ by using a graphing device. Find the $x$ and $y$ intercepts and the coordinates of all local extrema. Describe the end behavior of the polynomial.







Based from the graph, the $x$ intercepts can be approximated as $-0.5, 0.65$ and $2.95$. On the other hand, the value of the $y$ intercept is $2$. Also, the coordinate of the local maximum is $(2, 6)$. While the coordinate of the local minimum is $(0, -2)$. More over, the function has end behavior of $y \to - \infty$ as $x \to \infty$ and $y \to \infty$ as $x \to - \infty$.

Discuss the legacy of Christopher Columbus and his voyages to the New World.

During the era of Christopher Columbus in the 15th Century, Europeans were very interested in the markets of India and the East.  Countries like Portugal, England, and Spain were interested in finding routes to the East that would avoid the exorbitant fees being charged by Muslim middlemen.  The Portuguese established a route by sailing south along the coast of Africa.  Christopher Columbus believed that he could sail to the West and reach India in that direction.  Naturally, this was not possible without slamming into the Americas. Columbus initially landed on an island in the Bahamas.  He also would travel to a number of other islands and also Hispaniola.  Columbus managed to create interest in the European colonization of this vast wealth of land.   As a result of Columbus's voyages, Spain was able to claim a large empire in the New World and benefited economically from the looting of gold and silver from the land.  
https://www.history.com/topics/exploration/christopher-columbus

The issues of politics and administration dichotomy first raised by Woodrow Wilson continue to generate debate among scholars of public administration in the modern time. People think that his idea was useful, but others think it was impossible. Is that distinction practical and workable, and are there advantages to using such a dichotomy today as a way to advance that field of study?

It is understandable why, during Woodrow Wilson's time, the distinction between politics and administration was clear and distinct. The federal administrative state was nowhere near as big as it is today, and civil service reforms had just been enacted following the assassination of President Garfield by a disgruntled civil service job applicant. The belief was that the administration of government should be separate from the politics required to gain elected office.
However, as the administrative state has grown, and presidents, governors, mayors, and other elected officials have gained more power as a result, the line between politics and administration has blurred. At the federal level, Congress's abrogation of its legislative power and the growing prominence of executive orders and administrative rulemaking have led presidents, under political pressures, to appoint more partisan candidates to administrative bodies.
The recent debate over Net Neutrality is an example of politics invading and erasing the dichotomy with public administration. Until 2015, the Federal Communications Commission determined that it had no authority to regulate the internet, but under political pressure from the Obama Administration, it issued unprecedented rules changing the classification of the internet. Two years later, thanks to a change in the White House, and under the influence of different political pressures, the FCC rescinded the 2015 rules and returned regulation of the internet to the status quo ante.
As we see administrators subject to more political pressure because of their increased authority, we can expect to see more and more rule-making subject to the changing winds of politics until the legislative bodies provide clearer direction, removing the ability for administrators to play politics with the rules.
https://sites.duke.edu/niou/files/2011/05/Rosenbloom-The-Politics-Administration-Dichotomy-in-U.S.-Historical-Context.pdf

In "Everyday Use," what things did the characters find important or worthwhile? Why were those items important to them?

In the story, both Maggie and Dee desired two family heirloom quilts for themselves, but they have very different reasons for wanting them.
The quilts contained pieces of clothing worn by relatives all the way back to the Civil War. To Dee, these hand-stitched quilts represent a priceless artistry that is worthy of preservation, and she feels she is the best person to showcase the quilts to their glory.
Maggie was promised the quilts by Mama as a wedding gift. To Maggie, the quilts represent her mother's love and her memories of her grandmother. Unlike Dee, Maggie appreciates the quilts for their sentimental value. Dee finds the quilts worthwhile for a different reason. To Dee, the history of her family's struggles for equality and autonomy (as evidenced by the small piece of Great-Grandpa Ezra's Civil War uniform on the quilt) was secondary to her need to highlight her sophisticated tastes.
Similarly, Dee's fascination with the churn top and the dasher demonstrates her self-absorption. She viewed these two items as valuable from an artistic perspective, not a sentimental or historic one. On the other hand, both Maggie and Mama hold the same views in regard to the items, particularly the quilts.
While Dee imagines Maggie is "backward enough to put them to everyday use," Maggie knows the quilts are more than just artistic showpieces. Because of her own physical suffering, Maggie can appreciate the historical sacrifices and trials African-Americans have had to endure on the road to freedom. This is why she initially consented for Dee to take the quilts. Her words "I can 'member Grandma Dee without the quilts" demonstrate her introspective nature, one which places more emphasis on authenticity than superficiality.

Does the big bang theory or the steady state theory explain the origin of the universe better? Why?

The big bang theory is currently the best theory of how the universe was created. 
The steady state model concluded that the observable universe was of a constant density because there was a source of matter in the universe generating new energy. At the time, the concept of matter being neither created nor destroyed was still new and contested. The theory of the big bang states that there is a constant amount of energy in the universe. All of this energy was created in the moment of the big bang.
There are several reasons the steady state theory is discounted. The first is the fact that the universe is changing. By looking through telescopes into deep space, we can see effectively into the past of the universe. At the furthest reaches of observable space, things are different. Radio wave-emitting stars, forming galaxies, and more varieties of stars can be found, suggesting a changing universe over time. 
The steady state theory is also discounted because of cosmic microwave background radiation. This field of radiation is almost strictly uniform in wavelength and direction, showing no point of origin. This implies there is no point where matter is being generated and no point where energy is being created. It also aligns with the theory of a cooling blackbody, which the big bang theory suggested.
Newer data today still refutes the concept of steady state. The recent discovery of gravitational waves is evidence of colliding supermassive black holes from the time after the big bang. Even the concept of Hubble's Law refutes the steady state theory, as stars can be observed to have velocities away from the point of observation proportional to the distance away.
The big bang theory explains the origin of the universe far better than the steady state theory.

College Algebra, Chapter 2, 2.5, Section 2.5, Problem 32

The Boyle's Law states that the pressure $P$ of a sample gas is directly proportional to the temperature $T$ and inversely proportional to the volume $V$.
a.) Write an equation that expresses this relationship.
$\displaystyle P = \frac{kT}{V}$

b.) Find the constant of proportionality if $100 L$ of gas exerts a pressure of $332 kPa$ at a temperature of $400 K$.

$
\begin{equation}
\begin{aligned}
33.2 kPa &= \frac{k(400K)}{100L} && \text{Solve for } k\\
\\
k &= 8.3 \frac{kPa \times L }{K}
\end{aligned}
\end{equation}
$


c.) If the temperature is increased to $500K$ and the volume is decreased to $80 L$. What is the pressure of the gas?

$
\begin{equation}
\begin{aligned}
P &= \frac{kT}{V} && \text{Model}\\
\\
P &= \frac{\left( 8.3 \frac{kPa \times L }{K} \right)(500 K)}{(80 L)} && \text{Cancel out like terms, solve for } P\\
\\
P &= 51.875 kPa
\end{aligned}
\end{equation}
$

Who is Portia in Shakespeare's The Merchant of Venice?

Portia is one of the main characters in the play, and we are introduced to her in name quite early in the play. Bassanio tells Antonio and audiences that he has his love sights set on Portia because she is super attractive and super rich.

In Belmont is a lady richly left,
And she is fair and—fairer than that word—
Of wondrous virtues. Sometimes from her eyes
I did receive fair speechless messages.
Her name is Portia, nothing undervalued
To Cato’s daughter, Brutus' Portia.

Apparently, she is so rich and so good looking that many men from around the world know about her and are trying to obtain her as their trophy wife.


Nor is the wide world ignorant of her worth,
For the four winds blow in from every coast
Renownèd suitors, and her sunny locks
Hang on her temples like a golden fleece,



Fortunately, Shakespeare creates a much more vibrant and deep character with Portia than a static, beautiful and empty headed character. Audiences will discover that Portia is incredibly intelligent and unafraid to go after what she wants. This is why she rigs the casket lottery to make sure that Bassanio picks the right casket. She's also intelligent enough to manipulate and twist the law in her favor in order to rescue Antonio out of Shylock's clutches.

Portia is the intelligent, beautiful heroine of the play The Merchant of Venice. She is a wealthy heiress who lives in Belmont and is forced to obey her father's will by marrying the suitor who wins the lottery. At the beginning of the play, Portia complains to Nerissa about her situation and the awful suitors who have attempted to marry her. However, Portia is respectful to the suitors from Morrocco and Arragon; still, though, she is pleased that they did not choose the correct casket. Portia instantly falls in love with Bassanio and selflessly gives him her fortune after he chooses the correct casket. She also allows Bassanio to return to Venice to visit Antonio and saves Bassanio's close friend by dressing up as a man and intervening in Antonio's trial. Portia is magnanimous, sympathetic, and witty throughout the play. She not only marries the man that she loves but also intelligently conducts a plan to save his friend Antonio.

Intermediate Algebra, Chapter 1, 1.4, Section 1.4, Problem 42

Complete the statement so that the indicated property is illustrated. Simplify the answer if possible.


$
\begin{equation}
\begin{aligned}

9y - 6y =& \underline{(9 - 6)y = 3y}
\qquad \text{(distributive property)}

\end{aligned}
\end{equation}
$

When the narrator says that Shelia is "out of reach" what does he mean?

In "The Bass, the River, and Sheila Mant," the narrator is a young fourteen-year-old boy that develops a crush on Sheila Mant. Sheila's family is spending the summer in a cottage at the same lake as the narrator. As Sheila sunbathes, the narrator learns all of her moods by watching her body language and expressions. Other suitors seem to be aware of her moods as well, knowing just the right time to approach her.
The narrator describes Sheila as the "middle daughter—at seventeen, all but out of reach." What he means by this comment is that because Sheila is a beautiful, older girl, he feels that he doesn't stand much of a chance with her. He shares that he has many "false starts" on his way to her house, often becoming too nervous to complete the journey. He eventually works up the courage to ask her out.

According to Annabeth, did Percy really have ADHD and dyslexia? What was her explanation?

Percy tells readers very early on in the story that he struggles in school, and he tells us that the school counselor believes his struggles are the result of suffering from dyslexia and ADHD. Percy is beginning to believe that his struggles and disorders make him less of a competent member of society.

What was so great about me? A dyslexic, hyperactive boy with a D+report card, kicked out of school for the sixth time in six years.

Then, in chapter 6, Annabeth gives Percy some important information about his supposed "disorders." Annabeth and Percy are talking, and Annabeth states that Percy has to be a son of a god. Percy simply can't believe that, and he claims that Annabeth can't possible know anything about him. Annabeth then describes Percy perfectly.

"No?" She raised an eyebrow. "I bet you moved around from school to school. I bet you were kicked out of a lot of them."
"How—"
"Diagnosed with dyslexia. Probably ADHD, too."

Percy can't believe what he is hearing, and Annabeth quickly explains what ADHD and dyslexia have to do with being the son of a god. She tells Percy that the letters get mixed up because his brain is wired differently (built to understand ancient Greek), and his constant need to move is a symptom of conditioned battlefield reflexes that exist to keep him alive. The attention problems are due to the fact that his eyes and brain are taking in far more information that a mere mortal could take in.

Taken together, it's almost a sure sign. The letters float off the page when you read, right? That's because your mind is hardwired for ancient Greek. And the ADHD—you're impulsive, can't sit still in the classroom. That's your battlefield reflexes. In a real fight, they'd keep you alive. As for the attention problems, that's because you see too much, Percy, not too little. Your senses are better than a regular mortal's.

In Percy Jackson and the Olympians: The Lightning Thief, Percy is a sixth grader who has issues in school, partially because he has trouble focusing and reading. In the world of mortals, these problems have been attributed to Percy having ADHD and dyslexia.
When Percy gets to Camp Half-Blood and finds out that he's a demigod, he uncovers a lot of truths about his life. Annabeth Chase, a demigoddess with a lot of experience at Camp Half-Blood, tells Percy that his diagnoses of dyslexia and ADHD are wrong, and that many demigods are told that they have the same learning disorders. The reason he has trouble reading English is because his "mind is hard-wired for ancient Greek," and he can't sit still and pay attention in school because he has "battlefield reflexes" and his senses are "better than a regular mortal's." Percy realizes that Annabeth is telling the truth later on when she begins teaching him Ancient Greek, and he starts learning how to read in the language pretty easily.

How did the universe form?

There are a number of theories that attempt to explain the origin of our universe, however, the Big Bang Theory is the most commonly accepted model.
According to the Big Bang model of our universe, it all started from an infinitesimally small point (a singularity) in space. In a very-very short span of time (much less than even a fraction of a second), the universe expanded at a rate faster than the speed of light itself. The expansion of our universe is still continuing, however, the speed of expansion is very slow as compared to the beginning.
It has been hypothesized that as the universe expanded and cooled (as compared to its initial state), various elements were formed and over time, stars, planets, and other heavenly bodies were formed.
The discovery of the cosmic microwave background (CMB) in 1965 is the conclusive evidence of this theory.
Hope this helps.

When do you get the feeling that the story is changing or going in ways you did not expect?

The first moment I begin to feel as though the story changes unexpectedly is when the narrator describes the scene outside Louise Mallard's window, after she's shut the door in order to gain some privacy. At this point, she "sank" down into a chair with an "exhaustion that haunted" her body—so far, all these words sound appropriate to describe the feelings and actions of a grieving woman. However, the next lines present a significant change in the story's mood:

She could see in the open square before her house the tops of trees that were all aquiver with the new spring life. The delicious breath of rain was in the air [...]. The notes of a distant song which some one was singing reach her faintly, and countless sparrows were twittering in the eaves. There were patches of blue sky showing here and there through the clouds that he met and piled one above the other in the west facing her window.

She has just learned that her husband has died tragically; I would not expect the first thing she notices to be signs of "new spring life"—this presents a hopeful scene rather than something more mournful sounding. Further, to describe the air after the rain as "delicious" is another incredibly positive word choice given the emotional state in which we would expect Louise to be. Moreover, someone is "singing" and flocks of birds are "twittering." These are also words that possess a happy connotation, rather than a sad one. Finally, the narrator points out the "blue sky," rather than any gray patches that might be left after a rain. In short, the descriptions of what Louise sees are all hopeful, full of life, and happy, even though she has just heard of a death that we would expect to affect her—and the story's mood—in quite the opposite way. I think these lines present our first clue that not all is as it seems in Louise's first reaction to the news.

The fact that Louise Mallard retreats to her room upon hearing that her husband Brently has been killed in a railroad accident is unsurprising to the reader. Her husband's friend Richards and her sister, Josephine, are in the house, but Louise wants solitude to process her emotions. Louise's desire for privacy is completely understandable after her breakdown in Josephine's arms. In fact, Louise continues to sob occasionally when she is on her own.
Eventually, it begins to occur to Louise that Brently's death means that her life will change in ways about which she begins to feel elated. These lines mark the turn in the story to the surprising feelings of elation that Louise develops:

When she abandoned herself a little whispered word escaped her slightly parted lips. She said it over and over under her breath: "free, free, free!"

The story continues to surprise readers today, but not nearly as much as it did upon its publication in 1894.

In "A Bird came down the Walk--" by Emily Dickinson, what does the phrase "too silver for a seam" mean? What do you think is suggested by the color silver?

This poem is a beautiful example of Dickinson's style, which often employs radically unique syntax and diction to craft images of astounding poetic quality. Unfortunately, because they are so tightly and uniquely crafted, Dickinson's images are often extremely difficult to interpret. The quote you've referenced is no exception to this rule. 
First, let's look at the quote in context:

... [the bird] unrolled his feathers, 
And rowed him softer Home -
 
Than Oars divide the Ocean,
Too silver for a seam,
Or Butterflies, off Banks of Noon, 
Leap, plashless as they swim. (15-20)

Based on the context the quote comes in, it seems like Dickinson is describing the fluid motion of the bird taking flight. Moreover, it seems like the phrase "Too silver for a seam" is meant to be a description for "the Ocean." The ocean that Dickinson has in mind appears to be seamless or smooth, as the absence of a seam is indicated by the phrase's syntax. Based on this assumption, we can assume that the phrase is meant to conjure images of a smooth ocean's surface, while "silver" is probably meant to evoke both a fluid but unbroken liquid form (such as might be found in mercury or "quicksilver," for instance), and to describe the color of the ocean's surface. As such, the phrase is basically comparing the motion of a bird taking flight to an ocean that is smooth and silver, although Dickinson characteristically complicates this interpretation with her unusual diction.  
 
As with all of Dickinson's poetry, this phrase is hard to interpret, and so my take on it is somewhat unstable and unsure. Taking my interpretation into account, apply it to the poem and see if it works, or whether or not your own opinion requires some more interpretive work.  
https://www.poetryfoundation.org/poems/56593/a-bird-came-down-the-walk-359

What is the setting of the novel The Mailbox?

There are two books you could be referring to, coincidentally both set in the South.
The Mailbox by Audrey Shafer is a mystery set in Virginia. After the death of his uncle, a boy decides to keep the situation secret to avoid the foster care system. The mailbox portion comes into play as he receives mystery notes that threaten his situation even more after his uncle's body disappears.
The Mailbox by Marybeth Whalen is set on the coast of contemporary North Carolina, specifically a place called Sunset Beach. The mailbox here is a place for the main character to deposit her feelings and letters throughout her life. It is my understanding that this revolves around a real landmark out there on the beach. This book is the first in a series of modern romance novels.
https://www.goodreads.com/book/show/145310.The_Mailbox

https://www.goodreads.com/book/show/7443281-the-mailbox

Draw resonance structures for each the following compounds or ions, and use formal charges to indicate which resonance structure will make the largest contribution to the true structure, namely, which of the resonance structure most closely approximates the true structure of that compound or ion. Show your calculations. a. SCN-1 b. SO2 c. NO2 -1 d. OH e. BF3 f. CO2

I have attached an image file showing resonance structures. Equivalent resonance structures are not drawn in every case; I will leave it to you to recognize and add those as appropriate. I have left off the formal charges, but I will explain them.
a) thiocyanate
Numbers of valence electrons: S-6, C-4, N-5, plus 1 for the -1 charge. Sulfur can have more than an octet, but carbon and nitrogen must have 8 electrons total in any good Lewis structure.
Formal charges on the atoms are found by taking the atom's original number of valence electrons (which is equal to the atom's core charge) and subtracting 2 for each lone pair and 1 for each shared pair (covalent bond).
In the structure on the left, the formal charges are
S: 6-6-1=-1; C: 4-0-4=0; N: 5-2-3=0.
In the middle structure, we get
S: 6-4-2=0; C: 4-0-4=0; N: 5-4-2=-1
In the right-hand structure, we have
S: 6-6-1=-1; C 4-3=+1; N: 5-4-2=-2
The best structure normally has the least charge separation, and if there is a negative charge, it will be on the most electronegative atom. Nitrogen is the most electronegative of the three, so the center structure is expected to most closely approximate the "true" structure of the ion.
b) sulfur dioxide
Number of valence electrons = 6+6+6 = 18. Sulfur can accommodate more than an octet, but oxygen cannot (Period 2 of the periodic table; no close-lying d orbitals available).
Left structure:
O (left): 6-4-2=0; S: 6-2-4=0; O (right): 6-4-2=0
Middle structures (equivalent but calculation is for the upper one—reverse numbers for the lower one)
O (left): 6-6-1=-1; S: 6-2-4=0; O (right): 6-2-3=+1
Right-hand structures (again equivalent—reverse numbers for the lower one)
O (left): 6-6-1=-1; S: 6-0-4=+2; O (right) 6-4-3=-1
The preferred structure here will be the left-hand structure with no charge separation.
c) nitrite
Total valence electrons = 6+5+6+1=18.
Here the left and middle structures are equivalent. The left has
O (left): 6-4-2=0; N: 5-2-3=0; O (right): 6-6-1=-1
Right-hand structure:
Both oxygens are the same, with 6-6-1=-1, while N has 5-2-2=+1. The equivalent left and middle structures are preferable; the ion has the negative charge distributed between the two oxygen atoms.
d) I presume you meant a hydroxide ion, OH-. This ion has 6+1+1 (8) valence electrons, and hydrogen will have a filled valence shell with only two.
Left-hand structure has
O: 6-6-1=-1; H: 1-0-1=0.
Right structure has
O: 6-8-0=-2; H: 1-0-0=+1.
The left-hand structure, with less charge separation, is preferable.
e) boron trifluoride
Total valence electrons = 3 + 7 + 7 + 7 = 24.
In the left-hand structure, all fluorines are equivalent. This structure, however, violates the octet rule, with only 6 valence electrons on boron. Formal charges are
B: 3-0-3=0; F: 7-6-1=0.
The right-hand structure is one of three equivalent structures having double bonds to different fluorines. It obeys the octet rule. Formal charges are
B: 3-0-4=-1; F (single bonded): 7-6-1=0; F (double bonded): 7-4-2=+1.
This would lead to partial positive charges on all three fluorines and a negative charge on boron—not likely considering the high electronegativity of fluorine. The left-hand structure, despite violating the octet rule, is preferable.
f) carbon dioxide
Total valence electrons are 6 + 4 + 6 = 16.
The left-hand structure has all partial charges equal to 0. The other two each have a partial charge of +1 on the carbon, -1 on the singly-bonded oxygen, and 0 on the doubly-bonded oxygen.
Because oxygen is significantly more electronegative than carbon, the structures showing negative charge on oxygen are considered to contribute significantly. If your assignment is to choose a single structure, however, we know that the molecule is nonpolar and the two oxygen atoms are equivalent, so the best choice would be the left-hand structure.

Which two pairs of lines from Shakespeare's Romeo and Juliet show that Lord Capulet thinks Juliet is too young to get married?

Early in the play, Paris requests permission to marry Lord Capulet's daughter, Juliet. Lord Capulet reveals that he thinks Juliet is too young to get married by telling Paris,

"My child [Juliet] is yet a stranger in the world. She hath not seen the change of fourteen years. Let two more summers wither in their pride Ere we may think her ripe to be a bride" (Shakespeare, 1.2. 8-11).

When Paris responds by telling Lord Capulet that some women get married at an even younger age, Lord Capulet tells Paris to take his time with Juliet and attempt to win her heart naturally. Lord Capulet is initially portrayed as a sympathetic, understanding parent when he informs Paris that his permission is only part of Juliet's decision. He then proceeds to invite Paris to his ball later that night and encourages him to charm Juliet. Lord Capulet's initial attitude regarding his daughter's marriage is dramatically different from his stance later in the play. In act 4, scene 3, Lord Capulet informs Paris that he will make Juliet marry him and even threatens to disown her in the following scene if she does not follow his instructions to marry Paris.

What is an explanation of the following lines: "What devil art thou that dost torment me thus? / This torture should be roared in dismal hell. / Hath Romeo slain himself?"

When the nurse arrives with the rope ladder that was meant to permit Romeo to climb to Juliet's bedroom on wedding night, she must deliver the news that Romeo has slain Tybalt. However, she is not very good at delivering news: she describes someone's dead body, without saying whose exactly, and then she cries, "Romeo!" Thus, Juliet interprets this to mean that Romeo is dead, and she begins to panic. She calls the nurse a "devil" because she is tortured by the woman's inability to be specific, by the way the nurse fails to be clear about what has happened and who has been affected. She says that not knowing if Romeo is dead or alive is actually worse than being in hell. She vows that she will become deadlier than a snake if he is dead.

In this scene, the Nurse has just explained to Juliet that her new husband, Romeo, has killed her beloved cousin, Tybalt. Juliet, who knows Romeo is not prone to fighting, cannot believe that her true love would kill someone so dear to her. She turns on the Nurse, asking her what kind of devil she is to say such horrible things, and goes on to claim that the Nurse's news is more agonizing than the tortures of Hell.

Hath Romeo slain himself? Say thou but “ay,”
And that bare vowel I shall poison more
Than the death-darting eye of cockatrice.

Here, Juliet is saying that if the Nurse tells her Romeo has killed himself, Juliet will be so deep in her own grief as to become dangerous to others. She is not only afraid of losing Romeo, but also of losing her humanity.

Precalculus, Chapter 1, 1.1, Section 1.1, Problem 32

Plot the points $A = (-6,3), B = (3,-5)$ and $C = (-1,5)$ and form the triangle $ABC$. Verify that the triangle is a right triangle. Determine its area.








$
\begin{equation}
\begin{aligned}

AB =& \sqrt{[3-(-6)]^2 + (-5-3)^2}
\\
=& \sqrt{81 + 64}
\\
=& \sqrt{145}
\\
BC =& \sqrt{(-1-3)^2 + [5-(-5)]^2}
\\
=& \sqrt{16 + 100}
\\
=& \sqrt{116}
\\
AC =& \sqrt{[-1- (-6)]^2 + (5-3)^2}
\\
=& \sqrt{25+4}
\\
=& \sqrt{29}
\\
(AB)^2 =& (AC)^2 + (BC)^2
\\
(\sqrt{145})^2 =& (\sqrt{29})^2 + (\sqrt{116})^2
\\
145 =& 29 + 116
\\
145 =& 145

\end{aligned}
\end{equation}
$


Thus, $\Delta ABC$ is a right triangle.
The area of $\displaystyle \Delta ABC = \frac{1}{2} AC \cdot BC$,


$
\begin{equation}
\begin{aligned}

\Delta ABC =& \frac{1}{2} (\sqrt{29}) (\sqrt{116})
\\
\\
=& \frac{58}{2}
\\
\\
=& 29 \text{ square units}

\end{aligned}
\end{equation}
$

What role does love play in "A Retrieved Reformation"?

Love as a motivating factor plays a major role in O. Henry's "A Retrieved Reformation."
When Jimmy Valentine receives a pardon from his prison sentence for robbery, the warden admonishes Jimmy to reform.

"Now, Valentine," said the warden, "you'll go out in the morning. Brace up, and make a man of yourself. You're not a bad fellow at heart. Stop cracking safes, and live straight."
"Me?" said Jimmy, in surprise. "Why, I never cracked a safe in my life."

This response of Jimmy's strongly suggests that he has no intention of reforming as the warden has encouraged him. In fact, on the day that he is released, Jimmy heads to the depot and takes a train. Three hours later, he returns to his room. "Everything was just as he had left it." From behind a wall, Jimmy pulls out his suitcase containing his burglar's tools. In a short time, Jimmy leaves his room, "dressed in well-fitting clothes." He carries his suitcase, now dusted and cleaned.
After a week there is a report of a safe-burglary in Richmond, Indiana. Like other recent robberies, there are no clues left behind. Later, more bank robberies occur. The losses become so great that Ben Price, the detective who previously captured Jimmy, is called upon to conduct an investigation. However, an abrupt end to safe-burglary occurs. The cause of this termination is love. Jimmy Valentine has fallen in love after he stops in a small town in Arkansas. There he goes by the alias of Ralph D. Spencer, and he adores Annabel Adams, the daughter of the bank's owner. Because of his love for Annabel, he goes into business in Elmore, Arkansas, opening an exclusive shoe store.

Mr. Ralph Spencer, the phoenix that arose from Jimmy Valentine's ashes—ashes left by the flame of a sudden and alternative attack of love—remained in Elmore, and prospered.

By the end of a year, Ralph Spencer is part of the community and has won the respect of many; further, "Annabel's pride in him almost equaled her affection." Jimmy even writes to a friend in St. Louis one day, offering him his suitcase of "tools" if he will meet Jimmy at a certain place. His friend accepts this generous offer, so Ralph tells his betrothed that he is going to Little Rock to order his wedding suit and to buy something for Annabel. But Annabel wants him to first accompany her and members of her family to the bank where a new safe and vault have just been installed.
As the adults talk, nine-year-old May playfully shuts little Agatha in the vault. She even "shot the bolts and turned the knob of the combination" as she has seen one of the bank workers do. While this is going on, Ben Price enters the bank. Hearing the bolts, Mr. Adams tugged at the door. Then, he says, "The door can't be opened. . . . The clock hasn't been wound nor the combination set." This announcement creates hysteria in Agatha's mother. Annabel turns to Jimmy, "her large eyes full of anguish. Can't you do something, Ralph?—try, won't you?"
Again, Ralph's love for Annabel wins over his heart. Knowing that he will return to prison if he reveals his tools and skills in safe-breaking, he, nevertheless, does what he can to save little Agatha. After the safe is opened, it is Jimmy Valentine who puts on his coat and walks toward the front door. Once again, however, love supersedes all other matters. Waiting at the door for Jimmy is Ben Price. Acknowledging the detective, Jimmy says with resignation, "Well, let's go." But, love moves Ben Price because he says, "Guess you're mistaken, Mr. Spencer. . . . Don't believe I recognized you. . . . " In the end, love saves him.

Write a brief evaluation of Macbeth as a typical tragic hero. Do you think he is an otherwise noble figure with one tragic flaw, or do you find him less noble overall than a tragic hero should be?

A tragic hero is traditionally a protagonist or antagonist of noble birth with heroic qualities who is fated by some supernatural force to fail or endure extreme suffering. This suffering can create sympathy from the audience for the tragic hero. A tragic hero also has a personality flaw that results in the character's downfall. Throughout the play, Macbeth would be considered a typical tragic hero. He is initially the Thane of Glamis and a noble warrior, who valiantly serves King Duncan. Following his brave exploits in battle, Macbeth earns the title, "Thane of Cawdor," which was prophesied by the witches. Macbeth is misguided by the Three Witches and encouraged to commit regicide by his wife. The audience initially sympathizes with Macbeth because he is persuaded by his malevolent, ambitious wife to murder King Duncan. Macbeth is quickly manipulated by his wife after he initially rejects the thought of murdering King Duncan. Macbeth's immediate feelings of guilt following his crime also reveal his conscience. Macbeth then begins to hallucinate and see his friend's ghost after Banquo is assassinated. Similar to many tragic heroes, Macbeth also has a tragic flaw, in his case, unchecked ambition. In every aspect, Macbeth meets the criteria of a typical tragic hero. In my opinion, Macbeth is a noble individual with one tragic flaw. Unfortunately, he is manipulated by his wife into murdering King Duncan.
https://www.csus.edu/indiv/s/santorar/engl190v/trag.hero.htm

Will a rough surface have a greater or lesser sliding force and static friction compared to a smooth surface?

Friction is resisting force - a type of force that resists movement. The type of friction that resists movement between two objects in contact with each other is dry friction. There is dry friction between a book and a table, or the wheels of a car and the road.
Dry friction can be divided into two. Objects in contact against each other can be moving with respect to one another or stationary. When the objects are stationary, the friction between them is called static friction. Static friction resists movement. Imagine a box full of books on a floor. Initially, when you try to push the box, you struggle. This is because of the static friction between the box and the floor that resists the force you apply. Overcoming this, it becomes easier. Once the box starts to move, there is sliding friction. Sliding friction is the type of friction between objects moving relative to one another, and always opposes the acting force. Thus, it resists the movement as well as you push the box. 
Friction - whether static or sliding, or any other type of friction - depends on the type of material and the degree of contact between objects. In general, rougher surfaces tend to have higher coefficients of friction - which means they will tend to have higher sliding and static friction. Rough surfaces are surfaces that are highly uneven - maybe because of parts of it sticking out, or just scratched surface. These increases the surface area of contact between two objects, and could contribute to an increase in friction. Imagine the box on a cemented floor. The cemented floor is rough and it will be hard to either start pushing the box or continue pushing it. This is true when compared to pushing the box on an ice rink - where friction is lower and hence, the task is easier.
While this is the general case, it is not always true. For instance, two glasses are very hard to slide against each other. This is because of adhesion between the molecules. There is a point where when two objects are really smooth, friction increases due to adhesion. In general, however, smoother surfaces have less friction, while rough surfaces have greater friction.
http://hyperphysics.phy-astr.gsu.edu/hbase/frict.html

In "The Old Man at the Bridge," does Hemingway tell you directly what you should think about the old man?

In the story, Hemingway does not tell us directly what we should think about the old man. He does, however, hint indirectly that the old man will die if he chooses to stay in the area.
The narrator tells us it is his job to "cross the bridge, explore the bridgehead beyond and find out to what point the enemy had advanced." From his words, we can deduce the narrator is a soldier or army scout who has been sent out to determine the direction of the enemy's advance. When the narrator notices the old man, he questions him.
The old man says he was the last to leave his hometown of San Carlos. In the rush of leaving, he was ordered to leave behind the animals under his care. The old man admits he worries about the safety of the cat, two goats, and the four pairs of pigeons he had to leave behind. The narrator, a little distracted, assures him the animals will probably come through fine. He strongly advises the old man to move on if he can.
Meanwhile, the old man tries to stand up but finds he cannot quite keep his balance. At this stage, we get the impression that the old man is too worn out to travel any further. We recognize the inevitability of his death, as he mutters to himself about taking care of his animals. The last paragraph indirectly reinforces our immediate verdict and intuition about the old man's possible fate:

There was nothing to do about him. It was Easter Sunday and the Fascists were advancing toward the Ebro. It was a gray overcast day with a low ceiling so their planes were not up. That and the fact that cats know how to look after themselves was all the good luck that old man would ever have.

Please respond to the following questions: What do the portrayals of Walter Lee and Beneathea In “A Raisin in the Sun” suggest about identity within the Black community during the late 1950's? How would you describe the tone of Dr. King's "A Letter from a Birmingham Jail"? Do you think his tone is effective given that he is addressing a white audience? What does Malcom X mean when his says it is either the ballot or the bullet? Why does he think Black Nationalism is the solution to the Black community's issues? Why is poetry not a luxury for Audre Lorde? How might Black women find it a useful tool? What is the "Black Aesthetic"? In your opinion does this aesthetic empower or hinder Black writers during the Black Arts Movement? What is Alice Walker saying about Back women's creative expression? Why must we acknowledge this creative expression for what it is?

This question covers a lot of ground. Let's go through each of the six prompts and discuss how you might answer them, citing a few useful examples to help you craft your own responses.
1.   A Raisin in the Sun. There's a lot to say about these two characters in the play and what the playwright, Lorraine Hansberry, shows the audience about Chicago's black community in the late 1950s. Both characters are ambitious and forward-thinking, dreaming of better things for themselves and their family. The family has recently received an insurance payout after the death of the patriarch, and there's disagreement about what to do with the money. Walter Lee wants to help the family rise up out of poverty by investing in a liquor store. Beneatha wants to go to medical school, even though her brother doesn't think it's a realistic dream. Her sarcastic response shows Beneatha's defiance of her brother:

And forgive me for ever wanting to be anything at all! (Pursuing him on her knees across the floor) FORGIVE ME, FORGIVE ME, FORGIVE ME!

Despite their differing views, neither character wants to continue the cycle of poverty. These are modern characters, and they represent the aspirations of young black Americans coming of age in mid-century America. 
2. "A Letter from a Birmingham Jail." This open letter was also called "The Negro is Your Brother," which gives us a clue about the tone. Though the letter is an argument, King's tone is warm and conciliatory, not aggressive. Right off the bat, and throughout the speech, King attempts to find common ground with a white audience both in content and form. He addresses his audience as “My Dear Fellow Clergymen" and "my friends."
3. "The Ballot or the Bullet." Malcolm X's speech was addressed to an African-American audience. He urged them to exercise their right to vote for politicians who would represent their interests (and civil rights in general). But there's another layer to the speech that's intended for a wider audience. If the African-American population continues to have their rights curbed by legislation and discrimination, he warns, they'll have to resort to another form of power (the bullet). His point isn't only about race. It's about human rights. He believes that black people must come together to fight corruption and oppression:

Now in speaking like this, it doesn't mean that we're anti-white, but it does mean we're anti-exploitation, we're anti-degradation, we're anti-oppression. And if the white man doesn't want us to be anti-him, let him stop oppressing and exploiting and degrading us. 

4. Audre Lorde herself answers this question best:

For women, then, poetry is not a luxury. It is a vital necessity of our existence. It forms the quality of the light within which we predicate our hopes and dreams toward survival and change, first made into language, then into idea, then into more tangible action. Poetry is the way we help give name to the nameless so it can be thought. The farthest horizons of our hopes and fears are cobbled by our poems, carved from the rock experiences of our daily lives.

For Lorde, poetry isn't a "luxury," which is to say it's not something that would be nice to have but isn't quite necessary. It is an essential form of expression, especially for women and moreover for black women, whose voices aren't always heard. Poetry is a platform for expressing important ideas and thoughts that would otherwise stay inside people.
5. "Black Aesthetic." Many art critics and scholars believe that the development of a Black Aesthetic, an art movement that went hand in hand with Black Power, was essential to the development of African-American artistic tradition in the late 1960s. The Black Aesthetic introduced many important African-American figures in music, art, and culture to a wider audience, as their faces and figures were represented in murals; public artworks, like those murals, helped foster a sense of community among black artists and the neighborhoods they lived and worked in. 
This question asks for your opinion, so it's up to you to decide. 
6. I'm not sure if you're referring to a particular text here, so let's talk about Walker's views in general. She invented the term "womanism" to describe "black feminism," as she believed that feminism (as it was originally defined) did not include or fully encompass the perspectives of black women. Clearly, her advocacy for black women, whether in or out of a creative field, is important to her work.

No person is your friend who demands your silence, or denies your right to grow.
The most common way people give up their power is by thinking they don't have any. 

Some of her most frequently cited statements, like the two above, speak to her belief in the importance of black women (and of all women, and all people) to express themselves—and why those expressions shouldn't be censored or edited for any purpose. She demands equality for black women, and urges them to demand it for themselves.


 

In chapter 4, where do Moose and his family take Natalie? How does Moose feel about this?

Chapter 4 is entitled "American Laugh Nosed Beet." Natalie scrambles the name of an American leaf-nosed bat to create the title of this chapter. Natalie is Moose Flanagan's younger sister, and she has autism. The answer to the question of where the family takes Natalie in this chapter is the Esther P. Marinoff school. The family has moved to Alcatraz Island specifically so that Natalie can attend this school. Moose's father is a guard at the prison on Alcatraz, and Natalie's school is located just a twelve-minute ferry ride away on the shore of San Francisco. The Marinoff school is a boarding school, so Natalie will live there. It is designed for students who have similar disabilities to Natalie. Moose is unhappy about the move and indicates that his sister has attended multiple schools. Readers can infer that the family has moved a lot as a result of this.

How is a comedy different from a tragedy?

These terms, adopted from Aristotle’s Poetics, serve as both dramatic taxonomy and as general terms for aesthetic judgments. As genres, they differ in their motives and “rules” of construction. Tragedies are carefully defined by such requirements as “a great man falls from a high place” due to “a tragic flaw” in his character, causing a national catastrophe (represented by a “chorus” of citizens,), etc.  Comedy has often been defined as “tragedy avoided.” In modern terms, tragedies are unhappy (tragic) occurrences from any cause (heredity, natural disaster, etc.), while comedies are stories with “happy outcomes,” reconciled dramatic twists, etc.—often humorous and/ or romantic, with likable characters and everyday, non-serious dilemmas. The passages of Aristotle’s descriptions of types of drama that deal with a definition of “comedy” have been lost to posterity.

How are gender stereotypes illustrated in Emma?

An example of gender stereotyping is provided by the relationship between Emma and Mr. Knightley. Mr. Knightley is presented as unfailingly calm, rational, and sensible, in contrast to Emma's immaturity and self-confessed foolishness. Knightley takes Emma in hand, adopting a paternalistic attitude towards her, acting as a kind of surrogate father and teacher.
Their relationship reflects the prevalent understanding of gender roles at the time, with men placed in a position of control over their womenfolk. Throughout the novel, Emma has been presented as something of a free spirit, slightly unconventional in her behavior. Yet, the message seems to be that there's a limit as to how much freedom a woman should have.
What Austen appears to be suggesting here is that at some point in a woman's life she needs to settle down with a nice husband and devote herself to his well-being. Although Knightley is a kind and honorable man, it's clear he is the dominate partner in his relationship with Emma, which is exactly what would've been expected in society at that time.

Jane Austen uses stereotypes as the frameworks on which to build characters that rarely conform completely to narrow views. The title character of Emma is a gossipy, meddlesome upper-class girl who might easily be dismissed as shallow. Austen shows, however, that Emma’s good heart and well-protected innocence are also factors in her behavior. She is easily swayed by Frank Churchill because she does not realize that people can be so malicious.
Emma also accepts her class status, and thus she assumes that she should “help” Harriet obtain a higher-status husband. In that regard as well, Austen plays with the stereotype of women as fundamentally oriented toward pursuing matrimony.
In addition, the author introduces Mr. Elton’s bride as a flat character whose flaws are bold exaggerations of Emma’s minor negative tendencies. Her critical, bossy personality makes her a stereotypical shrewish wife who is matched up with a hen-pecked husband.

Emma conceives of herself as a kind of stereotype, and her opinions of other characters in the book serve to stereotype them as well. As the head of Highbury society, she thinks herself immensely clever at matchmaking, but she is mistaken about almost everyone around her. Emma constructs a kind of stereotypical story around Frank Churchill, who she thinks is pursuing her (because she is so desirable!). But Frank is not the stereotypical lover Emma imagines -- he is in love with Jane Fairfax, not her! Emma similarly stereotypes Harriet, whom she conceives of as well connected, when in fact Harriet's mysterious parent turns out to be a tradesman. Her stereotyping of Knightley as family friend blinds her to his growing attachment. None of the people around Emma assume the roles she assigns to them, and the conclusion of the novel works to show that the story Emma thought she was the protagonist of (the story where Emma gets the dashing young lover and secures for her friends their due place in society) is not the story of her life at all.

Austen uses gender stereotypes to show how people in Highbury treat other people unfairly based on gender.
For example, Emma treats Miss Bates unkindly based on the stereotypes she holds about older single women. At times Miss Bates may act silly, but Emma seems not to comprehend that Miss Bates is a poor woman who needs to be friendly to everyone to survive. At Box Hill, Emma ridicules Miss Bates, causing Mr. Knightley to scold her for her insensitivity. Emma needs to learn that even poor older women have feelings and should be treated with compassion.
Austen also attacks a gender stereotype that treats it as permissible to allow women to be ill-educated. Emma is a good case in point. Because she has had a scattershot and undisciplined education under the direction of a too kindly governess, dabbling a bit in reading, art, and music, she tends to jump to conclusions, overestimates her own abilities to read other people, and, in general, behaves cluelessly. This causes trouble for the people around her, such as Harriet Smith, and pain to Miss Fairfax.

when did the sugar act start

The Sugar Act, also known as The American Revenue Act, was passed by the British Parliament in 1764. It was a modified version of a previous piece of legislation, the Sugar and Molasses Act of 1733. Under the original Act, a tax of sixpence per gallon was placed on the importation of foreign (i.e. non-British) molasses into the American colonies. The point of the legislation was to protect British trade by making it more expensive for American merchants to buy molasses from the French West Indies.
However, the 1733 Act was widely ignored and evaded by American merchants, who continued to buy cheaper molasses from elsewhere, thus depriving the British Treasury of much-needed tax revenue. The Sugar Act was an attempt to remedy the situation. The provisions of the new law were based on a carrot and stick approach. On the one hand, the tax on imports was reduced from sixpence a gallon to threepence. On the other hand, a much more rigorous system of customs enforcement was put into effect to prevent merchants from evading their responsibility to pay tax.
More controversially, the Sugar Act also extended the number of foreign goods liable to pay customs duty. This proved to be a deeply unpopular measure as it severely restricted the number of countries and territories with which American colonists could trade. Inevitably, the new measures disrupted the colonial economy and made America more economically dependent on Britain. The Sugar Act generated an enormous amount of resentment, which only increased further in the wake of other ill-advised pieces of legislation such as the Currency Act, and the most notorious one of all, the Stamp Act. 
 
https://www.britannica.com/event/Sugar-Act

What is the central idea of the story "Marriage Is a Private Affair"?

The central idea of the story “Marriage Is a Private Affair” reveals that choice-based marriages can prove successful, even in societies where arranged marriages are the norm, when there is love and commitment between the parties involved. Indeed love can conquer anything.
The story is based on an Ibo society, whose marriage customs require that couples are matchmade. Nnaemeka thus faces stiff opposition from his family, and village at large, about his plans to marry Nene, a woman he has met in the city of Lagos. His father Okeke is so furious that he decides to erase the memory of his son from his mind, especially after Nnaemeka marries Nene in spite of his and the clan’s objections. Okeke even bans his son from his home. Over the years, however, an undeterred Nene works hard to gain the approval of the clan. She makes friends with her husband’s village mates, who are living in the city. She even writes a letter to her father in law, begging him to reconsider their situation, as their children would really want to visit the village to see their grandfather. This letter really touches the old man’s heart. The story ends, with Okeke in a remorseful mood, thinking about his innocent grandchildren and how he just might die “without making it up to them”.

What was the impact of the Cold War?

The Cold War affected the Soviet Union and the United States profoundly.  The United States invested trillions of dollars in its defense that could have been used on domestic spending.  To this day the United States does not trust Russia.  Thousands of young men have died fighting proxy wars against Communism in Korea and Vietnam.  A great deal of our scientific research in space and atomic energy was driven by an urge not to fall behind Russian scientists.  
In the Soviet Union, distrust of the United States led to the nation's slow rebuild from WWII.  The Soviet economy never quite fully recovered from the war, while Western Europe received Marshall Plan funds.  The Soviet Union expanded into Eastern Europe, and to this day, the economies of those countries still lag behind the West.  Soviet paranoia led to crackdowns on political and religious dissenters that killed or imprisoned millions during the Cold War era.  Even today, there are older people in Russia who do not trust the West due to the propaganda of the Cold War.  

What does conflict theory tell us about income inequality? What does the functionalist perspective tell us about wealth inequality? What does the interactionist perspective tell us about the black and white income gap in the US?

The conflict theory in sociology states that income inequality arises from the ways in which the societal elite are systemically able to control and manipulate the poor. For example, the elite are able to perpetuate their wealth through tax dodges that allow them to pay a lower percentage of their income to taxes, while the poor toil at jobs which earn so little that they cannot hope to educate themselves or their children or gain the capital to ascend the economic ladder. These factors keep the working class poor.
From the functionalist perspective, parts of the society are meant to work together to contribute to the overall functioning of the society. Therefore, although an income gap exists between rich and poor, each person has their role to play, knitting society into an interdependent whole. Although the poor might earn less, there are also charities, both public and private, to help them, as all of society works together.
From the symbolic interactionist perspective, the white-black income gap persists because white people feel that they should retain the more highly paid positions in society. In this view, white peoples' interaction with black people is fraught with deeper meanings, including the idea that black people do not deserve access to power or money. Hence, these symbolic readings of race translate into racism and fewer economic opportunities for black people in society. 

First, the conflict perspective says that all aspects of our society come about through conflict between groups.  Groups compete to create the rules of our society.  When a group wins, it is able to set society up in a way that it likes (at least with regard to the issue it was competing over).  We can say that income inequality comes about because of conflict between the rich and poor/non-rich.  We could argue that the rich have won this battle.  An example of this would (arguably) be the fact that we have all sorts of free trade agreements with other countries.  We can say that the rich benefit from free trade while many poorer people lose their jobs because of it.  Therefore, if we have free trade, it is because the rich have won their conflict with the other classes.
Second, the functionalist perspective says that all aspects of our society play a part in keeping our society alive and stable, just as every part of our body plays a part in keeping us alive and healthy.  In this view, wealth inequality could come about because it gives people an incentive to better themselves.  If we all had the same amount of wealth regardless of how hard we worked to get ahead, many people would not work hard and our society would become much poorer.  Since some are rich and some are poor, everyone has the incentive to strive to achieve wealth and avoid poverty.
Finally, symbolic interactionism emphasizes the ways in which individuals perceive the world.  We assign meanings to all the things we see in our society.  The meanings that we assign affect how we interact with the aspects of our society, thus creating the society in which we live.  In this perspective, the important thing about racial income inequality is that we have, as individual members of society, chosen to believe that there is such a thing as race and that it matters. We have chosen to interpret skin color and other aspects of race as meaningful things that make us fundamentally different from one another.  In terms of economic inequality, an example of this could be the various studies that have shown that people with “white” names get more calls for interviews than people with “black” names when identical resumes are sent out with only the names changed.  Because people have defined race as something that matters, they treat these identical resumes differently on the basis of the race they associate with each.

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

To apply Root test on a series sum a_n , we determine the limit as:
lim_(n-gtoo) root(n)(|a_n|)= L
or                         
lim_(n-gtoo) |a_n|^(1/n)= L
Then, we follow the conditions:
a) Llt1 then the series is absolutely convergent.
b) Lgt1 then the series is divergent.
c) L=1 or does not exist  then the test is inconclusive. The series may be divergent, conditionally convergent, or absolutely convergent.
In order to apply Root Test in determining the convergence or divergence of the series sum_(n=1)^oo (1/n -1/n^2)^n , we let: a_n =(1/n -1/n^2)^n.
We set-up the limit as: 
lim_(n-gtoo) |(1/n -1/n^2)^n|^(1/n) =lim_(n-gtoo) ((1/n -1/n^2)^n)^(1/n)
Apply the Law of Exponents:(x^n)^m= x^(n*m) .
lim_(n-gtoo) ((1/n -1/n^2)^n)^(1/n) =lim_(n-gtoo) (1/n -1/n^2)^(n*1/n)
                                    =lim_(n-gtoo) (1/n -1/n^2)^(n/n)
                                     =lim_(n-gtoo) (1/n -1/n^2)^1
                                     =lim_(n-gtoo) (1/n -1/n^2)
Evaluate the limit by applying the limit property: lim_(x-gta)[(f(x))-(g(x))] =lim_(x-gta) f(x) -lim_(x-gta) g(x) .
lim_(n-gtoo) (1/n -1/n^2)=lim_(n-gtoo) 1/n -lim_(n-gtoo) 1/n^2
                            = 1/oo - 1/oo^2
                            = 1/oo - 1/oo
                            = 0 -0
                            = 0
The limit value L=0 satisfies the condition: L lt1 since 0lt1 .
Conclusion: The series sum_(n=1)^oo (1/n -1/n^2)^n is absolutely convergent.

Amir and Hassan have a favorite story. Does the story have the same meaning to both men? Why does Hassan name his son after one of the characters in the story?

Amir and Hassan share a love and fascination for the short story “Rostam and Sohrab,” but for different reasons. In the story, Rostam kills Sohrab in battle, not knowing that he is his son. Hassan cries after he hears Amir read the story to him, and Amir notes that he didn’t understand Hassan’s reaction. Amir wonders if all fathers have a desire to kill their sons. For Amir, this story is a lens though which he can try to understand his own dysfunctional relationship with his father, who secretly blames Amir for murdering his wife after she died giving birth to him. In contrast, Hassan reads the story about Rostam and Sohrab as a tragedy that he can’t fully appreciate, as his father, Ali, adores and protects Hassan as his most prized possession. Hassan likely names his son after Sohrab because he was a character from a story that had great significance in his childhood, but it is also a clue from the author of Hassan’s appreciation for and instinct toward sacrifice for one’s family members.

Amir and Hassan enjoyed readings from the Shahnamah, with special emphasis on the story about Rostam and Sohrab. In the story, Rostam killed Sohrab only to learn Sohrab was his son. The emotions evoked by the story brought tears to Hassan’s eyes, but Amir did not know who the tears were for, Rostam or Sohrab.
The story was interpreted differently by the two boys. Amir saw himself as Sohrab, the young warrior, and his father as Rostam. The story reflects his relationship with his father. Amir does not comprehend Rostam’s grief or fate.

Personally, I couldn't see the tragedy in Rostam's fate. After all, didn't all fathers in their secret hearts harbor a desire to kill their sons?

Hassan’s interpretation is not explicitly given, but his emotions suggest he understands the situation between the father and his son. He goes on to name his son Sohrab because he was his favorite character in the story.

In "A Rose for Emily," who was the author writing for, and to what purpose?

It is difficult to pinpoint a single audience or purpose for most literary works, and William Faulkner's "A Rose for Emily" is no exception. First, it may be useful to think about the narrative voice and themes of the story.
The narrator is a sort of communal "we" representing the townspeople who know (or know of, at least) the title figure, Miss Emily Grierson. The narrative voice reports, in a non-chronological order, the major events of Emily's life, as observed from the outside by the town. The story begins with Miss Emily's death and the opening of her home to mourners. Most of the townspeople have never been in the home before this, and they join in the procession mainly out of curiosity. We then hear some background on Emily's relationship with her father and with the town, in which her family was once important and powerful. Eventually, hints are dropped about Emily buying rat poison and a stench coming from her home. At the end of the story, the town discovers that Emily has apparently poisoned a former suitor and kept his body in a bed where she has seemingly slept with him for a number of years. All of the information is presented in an almost gossipy tone. The townspeople talk about Emily but not to her. Their knowledge of her life is based on speculation, rumor, and detached observation. The narrative voice could be addressing any kind of audience. The reader need only be interested in hearing about Emily's story (while also understanding that the story is an interpretation of the character and not necessarily a factual account).
Purpose is another tricky term that seems related to the slippery concept of authorial intent. Many authors do not have one intended purpose, meaning, or message when writing a complex literary text. However, we can discuss some of the themes that emerge from the story and can infer that some of the purposes may be to have the reader think about those themes. First, Emily and her family are considered a tradition in the town, and the outward respect citizens show her is mostly based on her family's previous influence and standing. Now, the house is decrepit and the family is dying out with Emily's demise. The world around the Griersons has evolved and modernized, but Emily tries desperately to hold on to the past. This is seen in several examples but in none more clearly than her symbolic attachment to Homer's dead body. Faulkner is, in large part, drawing our attention to humans' desire to hold on to what they have, particularly when what they have is power and money. Further, in context, Faulkner seems to suggest a larger message about the South trying to hold on to the prosperous society and economy they enjoyed in the antebellum period. More generally, the story could also suggest how little humans really know about one another's lives or psychologies. The story could also possibly be lamenting the human impetus to scapegoat or exile others who are mysterious or different. 

In Rules of the Game, Waverly's mother says the "strongest wind cannot be seen." What does she mean by this? How does this idea show up in the story?

Waverly says she learned the art of invisible strength from her mother. The invisible strength of the strongest wind means she does not always say what she is thinking and she acts as a hidden threat. This is one of the ways she is able to become so successful at chess. She watches and learns. No one really expects a little girl in ribbons to be a chess champion.
Waverly was good at chess because she was intelligent enough to learn from what others taught her. Her mother realizes the value of Waverly becoming good at chess and allows her to play with the men in the park. Waverly watches them.

I learned why it is essential in the endgame to have foresight, a mathematical understanding of all possible moves, and patience; all weaknesses and advantages become evident to a strong adversary and are obscured to a tiring opponent. I discovered that for the whole game one must gather invisible strengths and see the endgame before the game begins.

The wind becomes a metaphor for Waverly's inner voice. She listens to her instincts, the wind inside of her, and she becomes more and more successful. She uses these insights to secretly sneak up on her opponents.

"Blow from the South," it murmured. "The wind leaves no trail." I saw a clear path, the traps to avoid. The crowd rustled. "Shhh! Shhh!" said the corners of the room. The wind blew stronger. "Throw sand from the East to distract him." The knight came forward ready for the sacrifice.

The concept of the strongest wind does not just apply to chess. Waverly uses her wind to give herself a voice. In a way, she was following her mother's own advice when she told off her mother. She just did not quite follow it in the way her mother intended. Waverly was just a little too rude. She was independent, but forgot to be strong and silent.

Did the isolation of the Island of the Blue Dolphins affect its inhabitants?

The Island of the Blue Dolphins focuses on a group of people living on an isolated island off the coast of California. The story is based on the life of a real woman who lived alone on a California island until 1853. During this time period, it would have been more difficult to find and map this tiny island. This causes the characters in The Island of the Blue Dolphins to be cut off from modern advances and technology. For example, they refer to the Russians' ship as a "giant canoe" because they are unaware of the correct term for it.  
The island's inhabitants also rely on hunter-gatherer roles, in which men hunt and women take over more domestic duties. This means that when Karana is left alone on the island in the story, she has to take over the more "male-oriented" responsibilities.    

Single Variable Calculus, Chapter 1, 1.3, Section 1.3, Problem 66

If $g$ is an odd function, let $h = f \circ g$. Is $h$ always an odd function? What if $f$ is odd? What if $f$ is even?


$
\begin{equation}
\begin{aligned}

\text{Let } g(x) =& x^3\\
f_1(x) =& x^5\\
f_2(x) =& x^6\\
\\
h_1 =& f \circ g\\
h_1 =& (x^3)^5\\
h_1 =& x^{15}\\
\\
h_2 =& f \circ g\\
h_2 =& (x^3)^{16}\\
h_2 =& x^{18}

\end{aligned}
\end{equation}
$



It's unpredictable, we must know first the function $f$ ; if $f$ is odd, $h$ will be odd also. On the other hand, if $f$ is even, $h$ will be even as well.

What is the verse form of the poem "The Solitary Reaper" by Wordsworth?

William Wordsworth's poem "The Solitary Reaper" has a mixed rhyme scheme, with the first and last stanzas following an abcbddee pattern and the middle stanzas following an ababccdd pattern. More importantly, the poem is written in iambic tetrameter. Similar to iambic pentameter, iambic tetrameter is slightly more compact, as it uses only four feet per line, rather than five. A foot is a group of two syllables, one of which is stressed and one of which is not stressed. Each line in Wordsworth's "The Solitary Reaper" contains four of these groupings, thus ensuring that a constant, reliable rhythm runs throughout the verse and holds the whole composition together. 
Understanding poetic feet can be difficult at first, so here's a trick to start figuring it out: when looking at a line of poetry, count the number of groupings of two syllables. The ending number will be the total number of feet. Once you get the hang of this, it will be much easier to also identify stressed and unstressed syllables, and also whether something is written in iambic pentameter or not. Try it out with the lines in "The Solitary Reaper," and aim to identify four feet per line. 
https://www.poetryfoundation.org/poems/45554/the-solitary-reaper

In "The Devil's Highway" by Luis Urrea, how and why do you think Urrea describes illegal immigration as "a game"?

In any game, there are always two opposing sides; this is certainly the case in the area of illegal immigration.
In the book, Urrea discusses how the Border Patrol agents (La Migra) often find themselves at odds with the Coyotes (human smugglers) who facilitate the migration of illegals across the Mexican-United States border. Urrea characterizes the conflict between the Border Patrol agents and the Coyotes as a game.
While the Coyotes aim to guide their charges across the border unseen, the Border Patrol agents are paid to "see the invisible." In this daily game of cat-and-mouse, Urrea tells us that the Coyotes "score" when they successfully guide their clients across the border. On the other hand, the Border Patrol agents get to "score" when they manage to stop the Coyotes on any given day. In this dangerous "game," there is a formidable referee, and it is La Muerte (Death). Urrea describes Death as a "masked invader who regularly storms the field to disrupt the game."
With two opposing sides and a referee of sorts, illegal immigration is a game of wits at best and a vicious game of survival at worst. Both sides (as in any game) depend on trusted strategies to win the conflict. The Coyotes and their charges tape blocks of foam rubber to their shoes so as to leave no prints. They also utilize what they call the "brushout." This is when the last man in any group walks backwards and uses a branch to wipe away the footprints of those who've gone before him.
Meanwhile, the Border Patrol relies on in-ground sensors buried in places known only to agents. The agents "cut" the land (checking the sensors) in search of illegal immigrants who've lost their way; so, these agents are the "cutters" in search of "walkers" (the illegals). In their line of work, cutters know that illegal immigrants often cross the Mexican-United States border between the hours of 11pm and 3am. Thus, they scrutinize the tracks left by the migrants as they track them across the border.
Often, the agents rely on signs left by small animals that trample over the footprints just before dawn. The animals make what are known as "bug-signs." If the bug-signs cross over the footprints, Border Patrol agents know that migrants crossed nearer to midnight than to dawn. On the other hand, if the footprints appear to crush out the bug-signs, agents know that migrants may have recently crossed and are probably nearby. If so, with a new day beginning, these migrants will be in trouble once the blazing sun powers its merciless rays against their backs.
Most of time, by using the in-ground sensors, the agents are able to corral the walkers into a tight area, where they can then apprehend them. At other times, as with the Yuma 14 who perished in the desert, walkers can unwittingly wander way "off the map," where La Muerte eventually claims them for his own. So, from Urrea's point of view, illegal immigration often results in a perilous game of life and death.