Why do we have a tremendous degree of social inequality in our own country? Do we live in a class or caste system?

Social inequality seems to be a universal feature of societies that have undergone the neolithic transition. Unlike people in hunter-gather societies, those who produce food by domestication of plants and animals have a strong incentive towards private property. In such systems, it is only worth cultivating land if one owns what is produced on that land or the fruits of one's labor. Because those who control land produce surplus food, they become wealthy and accumulate capital which they can continue to re-invest to become wealthier, leading to income inequality. 
In modern societies, there are two types of capital, one cultural (including education) and one material (money, land, possessions, etc.). Ownership of these forms of capital allows one to give one's children great advantages in the forms of inheritance of wealth and also access to cultural capital. As people tend to practice assortative mating (taking spouses within their own class) this results in something almost like a caste system with little social mobility even in countries which putatively have classes rather than castes. 
In advanced economies, several other factors contribute to income inequality as well:
Inequality of skills and education leading to increasing wage inequality
Shift of wealth production from labor to capital and forms of rent-seeking
Technology making certain skills obsolete and even replacing workers with machines
Government policies which provide subsidies to wealthy rather than to the poor
Educational systems in which there is inequality of opportunity (e.g. poor students being crowded into worse schools)
Globalization reduces inequality between countries but may increase inequality within countries
Lack of social safety net (in the US, lack of a national single payer health care system is a major contributor to inequality)
 
 
https://www.economist.com/united-states/2014/02/08/sex-brains-and-inequality

https://www.imf.org/external/pubs/ft/sdn/2015/sdn1513.pdf

Single Variable Calculus, Chapter 1, 1.3, Section 1.3, Problem 51

Evaluate each expression using the graph given below. If it is undefined, explain why.









$
\begin{equation}
\begin{aligned}
& \text{(a)} f(g(2))\\
& \qquad \text {Referring to the graph given} f(g(2)) =f(5) = 4.\\

& \text{(b)} g(f(0))\\
& \qquad \text {Referring to the graph given} g(f(0)) = g(0) = 3.\\

& \text{(c)} (f \circ g)(0)\\
& \qquad \text {Referring to the graph given} (f \circ g)(0) = f(3) = 0.\\

& \text{(d)} (g \circ f)(6)\\
& \qquad \text {Referring to the graph given} (g \circ f)(6) = \text{undefined because $f(6) = 6$ is not a domain of $g$.}\\

& \text{(e)} (g \circ g)(-2)\\
& \qquad \text {Referring to the graph given} (g \circ g)(-2) = g(1) = 4.\\

& \text{(f)} (f \circ f)(4)\\
& \qquad \text {Referring to the graph given} (f \circ f)(4) = f(2) = -2.

\end{aligned}
\end{equation}
$

what challenges does odysseus face on his journey back to ithica

Odysseus's journey back to Ithaka at the end of the Trojan War is fraught with seemingly endless difficulties, which he describes to his Phaiakian hosts in Book IX of the Odyssey.
After leaving Troy, Odysseus and his men land at Ismaros and raid the city there. They stay long enough for the inhabitants to muster a counterattack, and Odysseus loses many of his crew before they can flee the island.
They sail for nine days, buffeted by storm winds, until arriving at the island of the Lotus Eaters. The lotus was used in the ancient world as a powerful narcotic, and the Lotus Eaters are addicted to it. Anyone who takes the drug becomes completely indifferent to life, and wishes only to have more and more lotus, forever. Three of Odysseus's men eat the lotus and he has to drag them back to his ships to get them off the island.
The crew sail on to the land of the Kyklopes, where they encounter Polyphemos, who eats several of Odysseus's men before Odysseus manages to blind the giant by stabbing him in his one terrible eye. Unfortunately, as Odysseus makes his escape, he can't help letting Polyphemos know exactly who outwitted him, and Polyphemos calls upon his father, the god Poseidon, to curse Odysseus. Poseidon's wrath towards Odysseus causes Odysseus to eventually lose all his ships and crew and remain trapped on Calypso's island for years.
The crew then sails to the island of Aiolos, the King of the Four Winds, who gives Odysseus a leather sack containing the winds, which Odysseus can use to drive his ships directly back to Ithaka. They are within landfall of the island when one of his men opens the leather sack and lets all the winds out at once. A terrible storm arises and blows the ships all off course, so Odysseus limps back to Aiolos and asks him if he can fill the leather sack again, but Aiolos refuses, saying Odysseus has clearly incurred the wrath of the gods.
Making their painful way back toward Ithaka, this time with no winds at all in their sails, Odysseus's crew sails up a strange fjord in a silent country. Odysseus sends a scout out to see if there are any inhabitants who might spare them some food. Alas, they've come to the land of the Laistrygonians, vicious cannibals who pour out of the seemingly silent landscape and manage to kill most of Odysseus's crew before he can escape with just one ship.
Odysseus and his remaining men next land on Aiaia, where the beautiful witch Kirke turns some of the men into pigs. Odysseus manages to overcome Kirke and forces her to undo her enchantment, and she becomes a friend and ally to him. They stay on Aiaia for a year to rest and recuperate before sailing onwards.
Their next destination is the land of the dead, for Odysseus must speak to the ghost of Tireisias, the old blind prophet of Thebes, in order to determine how to get home to Ithaka. Odysseus speaks to many ghosts, including Tireisias, who warns him that whatever happens, his men must not eat the Cattle of the Sun.
On their way back from the land of the dead, the crew stops at Aiaia again, and Kirke warns Odysseus of the perils of the Sirens, the monster Skylla, and the whirlpool Kharybdis.
Odysseus takes Kirke's warnings to heart and manages to get past the deadly Sirens by blocking his men's ears with beeswax so they cannot hear the Sirens' song. The monster Skylla manages to eat several of Odysseus's men as they skirt the edge of the whirlpool Kharybdis, but this fate cannot be avoided.
Having passed the monster, the ship lands at Thrinakia, where the Cattle of the Sun dwell. Odysseus warns the men never to kill these cattle, no matter how hungry they are, but once the food stores run out, the men get desperate, and kill the cattle and eat them. Odysseus immediately sets sail from the island, but his ship is destroyed by a lightning bolt, and he is the only survivor.
Cast adrift on the ocean in a terrible storm, Odysseus washes up on the island of the nymph Calypso. She takes care of him and falls in love with him, and keeps him prisoner on her island for seven years. She only lets him go when the gods order her to. She gives Odysseus a raft and provisions, and Odysseus sets sail once again. He nearly drowns in a storm sent by Poseidon before washing up on the Phaiakian shore.
The Phaiakians give Odysseus food, shelter, and many gifts and take him safely back to Ithaka in one of their own ships. It has taken Odysseus ten full years to reach Ithaka's shore.

Calculus: Early Transcendentals, Chapter 4, 4.4, Section 4.4, Problem 43

lim_(x->0) cot(2x)sin(6x)
The function cot(2x)sin(6x) is undefined at x=0. So to take its limit, let's apply the L'Hospital's Rule. To do so, express it as a rational function.
=lim_(x->0) cos(2x)/sin(2x) * sin (6x) = lim_(x->0) (cos(2x)sin(6x))/sin(2x)
Then, take the derivative of the numerator and denominator.
=lim_(x->0) ((cos(2x)sin(6x))')/((sin(2x))')=lim_(x->0) (cos(2x)*cos(6x)*6 + (-sin(2x))*2*sin(6x)) / (cos(2x)*2)
=lim_(x->0) (6cos(2x)cos(6x) - 2sin(2x)sin(6x))/(2cos(2x))=lim_(x->0) (3cos(2x)cos(6x) - sin(2x)sin(6x))/(cos(2x))
And, plug-in x=0.
=(3cos(2*0)cos(6*0)-sin(2*0)sin(6*0))/cos(2*0)=(3*1*1-0)/1=3

Therefore, lim_(x->0) cot(2x)sin(6x) = 3 .

What was the Emancipation Proclamation? How did it impact our country, both during the Civil War and now?

From the beginning of the Civil War, President Lincoln defined the war as one being fought for preservation of the Union (the United States), not as one to abolish, or end, slavery. In his first Inaugural Address, prior to the outbreak of war, Lincoln stated that he would not abolish slavery where it existed, as he felt he could not constitutionally do so. He also made this promise in an attempt to diffuse the increasing tensions in the South after his election. Although Lincoln opposed slavery, he also knew that it would be controversial to frame the war as one fought for abolition. Lincoln knew that many Northerners would not support a war to free slaves. In addition, Lincoln could not lose the support of the border states. The border states were Maryland, Delaware, Kentucky, and Missouri. These were states that allowed slavery, yet chose not to secede with the Confederate states during the Civil War. Lincoln feared that if he made the Civil War a fight to end slavery, these states would defect to the Confederacy.
Lincoln also felt constricted by the Constitution. Technically slaves were considered property, and the Constitution protected property. The Fugitive Slave Clause in the Constitution also stipulated that “no person held to service or labor in one state” could earn freedom by escaping to another state, and the controversial Fugitive Slave Law of 1850 required individuals and states to return escaped slaves to their owners. Lincoln therefore took steps throughout the war as commander in chief to slowly chisel away at slavery. As commander in chief of the armed forces, Lincoln could seize property being used to wage war. He therefore passed a series of contraband acts, arguing that because slaves provided labor for the Confederate Army, they could be seized by the Union Army as contrabands of war. Lincoln effectively used the South’s own argument against them—in considering slaves property and using them in the war effort, Southerners opened up the opportunity for Lincoln to free slaves seized by the Union Army.
As the war progressed, emancipation became more and more necessary to weaken the Confederacy and to gain support of European nations. In Europe, especially in places such as Italy, and among workers and lower classes in Britain, the war was seen as a war over slavery, even if no one in the United States would admit it. The Confederacy was attempting to gain the support and alliance of Great Britain and France; however, these countries would not support a war for slavery. As long as the Confederacy could frame the Civil War as a war for independence and states’ rights, they could potentially gain the support of European countries. Lincoln therefore also felt an increasing need to change the purpose of the war in order to dissuade European support for the Confederacy.
The Battle of Antietam in 1862 provided Lincoln an ideal opportunity to issue the Emancipation Proclamation. The Union secured a much needed strategic victory at this battle, stopping General Lee’s powerful Army of Northern Virginia. In his proclamation, which Lincoln issued as an executive order, Lincoln stated that all slaves in seceded states would be freed on January 1, 1863. Therefore, slaves in border states were exempt because they were still part of the Union. Nevertheless, the proclamation proved hugely significant, as it changed the purpose of the war from preserving the Union to preserving the Union and ending slavery in the South. The proclamation also allowed escaped slaves to serve in segregated units of the Union Army. Thousands of slaves responded by fleeing the South and joining Union troops, making vital contributions to the Union war effort and to their own freedom.
Lincoln, a lawyer, knew that he still faced a constitutional battle after the war. Once the war ended, the proclamation might no longer be valid—he knew he needed a constitutional amendment in order to permanently end slavery. In 1864, after fierce debates in Congress, the 13th Amendment to the Constitution was ratified, declaring “neither slavery nor involuntary servitude … shall exist within the United States.”
https://guides.loc.gov/emancipation-proclamation

The Emancipation Proclamation was actually an Executive Order issued by President Abraham Lincoln, effective January 1, 1863. The order was issued in order to free those people that were held in slavery in southern states. Although history now looks favorably on the order, it was clearly quite controversial at the time. Lincoln had already been elected under contentious circumstances and the issuance of the Proclamation served to further divide the country and incite even more anger among many in the south. Southern landowners, and others, saw slavery as a critical resource to the southern economy and perceived Lincoln's actions as inflammatory against their economic and social stability. Prior to Lincoln issuing the order, slavery had been considered a secondary issue in the already underway Civil War. However, the issue of slavery became one of the objectives of Union armies after the Proclamation was issued. Although the long term impact of the Emancipation Proclamation had clear positive impacts on the socio-economic trajectory of the United States, the ramifications were pronounced. Particularly in the ten southern states identified by the order, the abolishing of slavery led to decades of social unrest, segregation, and institutional disregard for federal laws. Historians and sociologists continue to analyze the varied effectiveness of equality efforts around the country.

What does Old Scratch offer Tom Walker and what does Old Scratch want in return?

In "The Devil and Tom Walker," Old Scratch is the devil. Tom Walker is in pursuit of riches, particularly the Pirate Kidd's treasure, and the devil knows where it is. He offers to give it to Tom Walker so that he can be wealthy for life if Tom will serve him. Old Scratch sets the terms; first of all it is implied that when Tom dies, his soul will belong to him. Moreover, he wants Tom to use the money in his service and proposes that Tom outfit a slave ship and engage in slave trafficking. Ironically, Tom refuses this request on moral grounds. Old Scratch then proposes that Tom become a money lender, or usurer, and charge exorbitant interest rates; he tells Tom "you shall extort bonds, foreclose mortgages, drive the merchants to bankruptcy." Tom enthusiastically agrees, asserting that he will raise the interest rate even higher than the devil suggests.

When Old Scratch and Tom Walker first meet, they discuss the topic of the hidden pirate treasure. Old Scratch, being in complete control of the treasure, offers to give it to Tom on one condition. This condition is not explicitly stated in the story, but the reader can infer that Old Scratch wants Tom's soul. Tom, however, does not agree to this deal and returns home.
Later in the story, Old Scratch and Tom talk terms again. This time, Old Scratch offers Tom the pirate's treasure but, in return, Tom must use the money to make Old Scratch a profit. Old Scratch suggests Tom would make lots of profit if he became a slave trader, but Tom does not agree to this occupation. Instead, he agrees to become a moneylender.
Once the deal is struck, Tom takes the pirate treasure and uses it to set up his moneylending business in Boston. Here, he becomes a very rich and successful moneylender.

Calculus of a Single Variable, Chapter 9, 9.7, Section 9.7, Problem 21

Maclaurin series is a special case of Taylor series that is centered at x=0 . The expansion of the function f(x) about 0 follows the formula:
f(x)=sum_(n=0)^oo (f^n(0))/(n!) x^n
or
f(x)= f(0)+(f'(0))/(1!)x+(f^2(0))/(2!)x^2
+(f^3(0))/(3!)x^3+(f^4(0))/(4!)x^4 +(f^5(0))/(5!)x^5+...
To determine the Maclaurin polynomial of degree n=5 from the given function f(x)=1/(x+1) , we may apply Law of Exponent: 1/x^n = x^(-n) . The function becomes:
f(x) = (x+1)^(-1)
Apply Power rule for differentiation: d/(dx) u^n = n * u^(n-1)* (du)/(dx) to list the derivative of f(x) .
Let u =1+x then (du)/(dx) = 1 for each derivatives.
f'(x) = d/(dx)(x+1)^(-1)
= (-1) *(x+1)^(-1-1)*1
= -(x+1)^(-2) or -1/(x+1)^2
f^2(x)= d/(dx) -(x+1)^(-2)
=-1*(-2 *(x+1)^(-2-1))*1
=2(x+1)^(-3) or 2/(x+1)^3
f^3(x)= d/(dx) 2(x+1)^(-3)
=2*d/(dx) (x+1)^(-3)
=2* (-3*(x+1)^(-3-1))*1
=-6(x+1)^(-4) or -6/(x+1)^4
f^4(x)= d/(dx) -6(x+1)^(-4)
=-6*d/(dx) (x+1)^(-4)
=-6* (-4*(x+1)^(-4-1))*1
=24(x+1)^(-5) or 24/(x+1)^5
f^5(x)= d/(dx) 24(x+1)^(-5)
=24*d/(dx) (x+1)^(-5)
=24* (-5*(x+1)^(-5-1))*1
=-120(x+1)^(-6) or -120/(x+1)^6
Plug-in x=0 , we get:
f(0) = 1/(0+1)
=1/1
=1
f'(0) = -1/(0+1)^2
=-1/1^2
=-1
f^2(0) =2/(0+1)^3
=2/1^3
=2
f^3(0) =-6/(0+1)^4
=-6/1^4
=-6
f^4(0) =24/(0+1)^5
=24/1^5
=24
f^5(0) =-120/(0+1)^6
=-120/1^6
=-120
Plug-in the values on the formula for Maclaurin series.
sum_(n=0)^5 (f^n(0))/(n!) x^n
= 1+(-1)/(1!)x+2/(2!)x^2+(-6)/(3!)x^3+24/(4!)x^4+ (-120)/(5!)x^5
= 1-1/1x+2/2x^2-6/6x^3+24/24x^4-120/120x^5
= 1-x+x^2-x^3+x^4-x^5
The Maclaurin polynomial of degree n=5 for the given function f(x)= 1/(x+1) will be:
P_5(x)=1-x+x^2-x^3+x^4-x^5

Single Variable Calculus, Chapter 3, 3.8, Section 3.8, Problem 16

At what rate is the length of his shadow on the building decreasing when he is 4m from the building?

Illustration







Given:

$\qquad $ height of the man = $2m$

$\qquad $ distance of the spotlight to the wall = $12m$

$\qquad $ horizontal velocity of the man = $1.6 m/s$

Required: the rate how fast is the length of the man's shadow on the building decreasing when he is $4m$ from the building.

Solution:

By applying similar triangles we have,


$
\begin{equation}
\begin{aligned}

\frac{y}{12} =& \frac{2}{12 - x}
\\
\\
y =& \frac{24}{12 - x} = 24(12 - x)^{-1}

\end{aligned}
\end{equation}
$


By taking the derivative with respect to time,


$
\begin{equation}
\begin{aligned}

\frac{dy}{dt} =& \frac{dy}{dx} \left( \frac{dx}{dt} \right) = 24 \cdot \frac{dy}{dx} (12 - x)^{-1} \frac{dx}{dt}
\\
\\
\frac{dy}{dt} =& 24(-1)(12 - x)^{-2} \cdot (-1) \frac{dx}{dt}
\\
\\
\frac{dy}{dt} =& 24(12 - x)^{-2} \frac{dx}{dt}


\end{aligned}
\end{equation}
$


We know that $\displaystyle \frac{dx}{dt} = 1.6$ and $x = 4m$ so


$
\begin{equation}
\begin{aligned}

\frac{dy}{dt} =& 24(12 - 4)^{-2} (1.6)
\\
\\
\frac{dy}{dt} =& 0.6 m/s

\end{aligned}
\end{equation}
$


The length of the shadow is decreasing at a rate of $0.6 m/s$ when the man is $4m$ from the building.

When and where was Romeo and Juliet originally set?

William Shakespeare identifies the setting of Romeo and Juliet in his opening words as the Chorus says, "In fair Velona where we lay our scene."  Romeo and Juliet takes place in Verona, a city in Italy, in the 1300s (although the play itself is believed to have been written around 1592). 
The play consists of both interior and exterior settings during both daytime and nighttime.  One of most significant interior settings from the first act is the ballroom where Romeo and Juliet first see each other.  It is significant that Romeo (who, with his friends, is often seen outdoors) has come to the ball without a proper invitation, on the urging of his friends who hope the beautiful women there will help him to overcome his love for Rosaline. 
Another significant interior setting is Friar Lawrence's cell, where the two lovers meet through the efforts of both the Friar and the Nurse.  There they finalize their plans to marry and to create the ruse of Juliet's feigned death.  It is significant that this is one of the only places Juliet, a sheltered young woman (not yet 14), can venture outside of her home. 
Juliet's bedroom, where the marriage is consummated in secret, is another significant interior setting as is the mausoleum where Juliet (having taken a potion to appear dead) is entombed until Romeo finds her and kills himself (leading, of course, to Juliet's real death). 
The outdoor settings are equally significant.  It is in the outdoor square that Tybalt kills Mercutio and Romeo then kills Tybalt, leading to Romeo's banishment and hastening the plot of marriage and feigned death.  We revisit the same outdoor square when all is revealed as the play ends and the two mourning families finally make peace. 

College Algebra, Chapter 2, 2.4, Section 2.4, Problem 60

Use slopes to determine whether the given points are collinear.

a.) $(1, 1), (3,9), (6,21)$

b.) $(-1,3), (1,7), (4, 15)$

a.) Let $m_1$ be the slope through points $(1,1)$ and $(3, 9)$, $m_2$ be the slope through points $(1, 1)$ and $(6, 21)$, $m_3$ be the slope through $(3, 9)$ and $(6, 21)$.


$
\begin{equation}
\begin{aligned}

m_1 =& \frac{9 - 1}{3 - 1} = \frac{8}{2} = 4
\\
\\
m_2 =& \frac{21 - 1}{6 - 1} = \frac{20}{5} = 4
\\
\\
m_3 =& \frac{21 - 9}{6 - 3} = \frac{12}{3} = 4

\end{aligned}
\end{equation}
$


Since $m_1 = m_2 = m_3$, all the points are collinear.

b.) Similarly, let $m_1$ be the slope through $(-1, 3)$ and $(1, 7)$

$\qquad m_2$ be the slope through $(1,7)$ and $(4,15)$

$\qquad m_3$ be the slope through $(-1,3)$ and $(4, 15)$


$
\begin{equation}
\begin{aligned}

m_1 =& \frac{7 - 3}{1 - (-1)} = \frac{4}{2} = 2
\\
\\
m_2 =& \frac{15 - 7}{4 - 1} = \frac{8}{3}
\\
\\
m_3 =& \frac{15 - 3}{4 - (-1)} = \frac{12}{5}

\end{aligned}
\end{equation}
$


Since $m_1 \neq m_2 \neq m_3$, the points do not lie on the same line.

How is ethos used in Blink: The Power of Thinking Without Thinking?

Basically, throughout this book, Malcolm Gladwell establishes an authoritative tone, revealing himself and his own personality and trustworthiness to the reader; as a result, he creates ethos.
By the way, let’s get clear on this: what is ethos? It’s a strong, trustworthy reputation, something authors attempt to build as a means of bolstering their arguments and persuading their audience.
As another educator has already explained, Malcolm Gladwell calls on various authorities to lend credibility to his argument, a powerful way to build ethos.
But citing other authorities is just one way to create ethos. Another way is for the author to present himself or herself as a trustworthy person. As the argument expert Jay Heinrichs put it, ethos “employs the persuader’s personality, reputation, and ability to look trustworthy” (emphasis added).
So, let’s check out how Gladwell presents himself as an authority, someone you can trust, someone with a good personality and a reliable reputation.
Check out the introduction to the text, titled “The Statue That Didn’t Look Right.” Right away, Gladwell captures our interest with an engaging and true story. He captivates us with the description of the statue and its value:

It stood close to seven feet tall. It had a kind of light-colored glow that set it apart from other ancient works. It was an extraordinary find. Becchina’s asking price was just under $10 million.

Notice how his writing is clear, error-free, and exciting, with careful attention to parallelism and repetition (“It stood… It had… It was…”) as well as the reporting of precise details (“seven feet tall,” “light-colored glow,” “Becchina’s,” “$10 million”).
This guy knows what he’s talking about.
Gladwell maintains that authoritative tone, that powerful storytelling persona, throughout the text. The result? Ethos. We trust him, so we believe him.
There’s more, though! Look out for how Gladwell references himself directly, his own insights and experiences. He even reveals his shortcomings, then shows how he overcame them and achieved understanding. Here’s an example, and you can bet it builds ethos:

I hadn’t realized how much of an issue this was until I tried thin-slicing couples myself. I got one of Gottman’s tapes, which had on it ten three-minute clips of different couples talking. Half the couples, I was told, split up at some point in the fifteen years after their discussion was filmed. Half were still together. Could I guess which was which? I was pretty confident I could. But I was wrong. I was terrible at it. I answered five correctly, which is to say that I would have done just as well by flipping a coin.
My difficulty arose from the fact that the clips were utterly overwhelming.

Finally, notice how Gladwell often uses the words "we," "us," and "our," placing himself alongside us, the readers, treating us as equals, as in this sentence:

Whenever we meet someone for the first time, whenever we interview someone for a job, whenever we react to a new idea, whenever we’re faced with making a decision quickly and under stress, we use that second part of our brain.

What a sneaky way to build ethos! Whenever he does this, Gladwell is playing the kindly professor, the authority on matters who is friendly and good-natured enough to place his arm around our shoulders—metaphorically—and speak to us as if we were his intellectual protégés. That is some truly expert ethos-building.
Let's sum that up. Not only does Gladwell cite outside authorities to build ethos, but he also presents himself as an authority: as a savvy storyteller, as a man of insight and experience, and as a knowledgeable teacher who treats his students with respect and kindness.
https://books.google.com/books/about/Thank_You_For_Arguing_Revised_and_Update.html?id=xzDKMNju-V4C

Ethos involves convincing the audience of the authority or credibility of the person making an argument. Gladwell uses a great number of authorities to buttress his arguments. For example, in the "Introduction," he writes about the psychologist Timothy D. Wilson, author of the book Strangers to Ourselves. Gladwell uses Wilson as an authority about how much information the mind collects in the unconscious, which is one of the premises of Gladwell's book. Gladwell cites Wilson's training as a psychologist and the title of Wilson's book to make Wilson more credible and to appeal to the reader's sense of ethos. In Chapter One, Gladwell cites the research of John Gottman, a psychologist at the University of Washington, to again build a sense of credibility--in this case, about the ability of researchers to understand a marriage by looking at a short videotape of the married couple interacting. Throughout his book, Gladwell cites authorities in different fields to buttress his argument.

What did the February Revolution cause Tsar Nicholas II to do?

It was the February Revolution—which began with a series of protests in Petrograd, ultimately escalating into violent clashes between soldiers and the protesters—that caused Tsar Nicholas II to abdicate his throne. Famously, strikes began on International Women's Day in the city of Petrograd after women rioted, breaking shop windows and taking to the streets in protest against Russian involvement in the First World War and the food shortages which had spread across Russia. The strikes soon became widespread, and unrest became increasingly violent.
Tsar Nicholas offered his abdication in a train car in Pskov. He had been on his way back to Petrograd upon hearing news of the riots, but he never made it back. Instead, representatives of the Duma, the Russian parliament, intercepted his train to tell him that the situation in the city had escalated so badly that they were going to take power into their own hands. Nicholas had little option but to sign his abdication papers as requested.
https://www.smithsonianmag.com/history/abdication-nicholas-ii-left-russia-without-tsar-first-time-300-years-180962503/

In what ways does the setting help portray several themes, motifs, and symbols present in the book Dracula?

The city of London is an important symbol, representing the hub or center of the world in the 1890s. At that time, England was the world's superpower, with an empire on which "the sun never set." London is the crowded, highly populated capital of England and, as the novel illustrates, a center of trade and activity, with ships coming into and out of the Thames at all times. It was a fitting place for the "disease" of the vampire Dracula and his followers to infect the rest of the world. Dracula, fought by doctors and scientists, is able to take on the form of disease-carrying rats and bats. He is very much shown as a sleeping, medieval illness or evil like the bubonic plague. The heroes fight him from modern England using state-of the-art technology, such as blood transfusions.
Dracula's castle at the beginning of the novel—remote, imprisoning, and medieval—is strongly associated with Dracula and symbolizes him as an evil from another age, come to infest the modern world.

What are the characteristics of the contingency viewpoint of management?

Contingency based management essentially is in constant flux. This style of management holds that no single style is better than others but that they are all valuable in different situations. Essentially, the model holds that in the event of an emergency or if your primary management style breaks down, you have a secondary approach, and you can keep cycling through management styles until you find one that is successful.
Primarily, to be successful, the roles must be very well defined between manager and employee, because the relationship may shift while transitioning between management styles, so it is best to have them set in stone beforehand. Additionally, the objectives must be well defined as well because as each management style comes and goes, the approach to find a solution will change, but the objective must remain the same. Finally, the manager needs to be well-versed in different management styles to be able to appropriately incorporate them into their leadership.

Contingency viewpoint management, to put it quite simply, dictates that different situations will inevitably call for different approaches when managing a team. Often times managers will attempt a fair and fool-proof system by adopting rigid guidelines to leadership that they see as "one-size-fits-all" solutions to any possible problem. Contingency viewpoint, however, maintains that solutions that will work in one context may be completely useless in another, and vice-versa, depending on several factors such as employees, jobs, and levels of accountability. Contingency theory acknowledges that there is no one best way to lead an organization, and even a situational "best way" is subject to change. Operating under this sort of management style requires varying positions of leadership with various traits that will be better suited to different situations.

The contingency management approach holds that there are a variety of styles of management and there is no style that is better than the rest. The rationale focuses on the situation, which forces the manager to seek the correct way or style to manage. Thus, the manager is responsible for matching the right style to the right situation. The manager also needs to know their style of leadership in order to accommodate and work with the rest of the employees.
To ensure the management system works, the roles of each member of the organization should be clearly defined, which enhances the level of accountability. In this case, the manager can objectively evaluate the members based on their tasks and deliverables. A good working relationship between the manager and the rest of the staff is essential in a contingency system because it places the manager in control of the organization.
In summary, an organization based on contingency management
Applies different approaches based on the situation it is facing
Is focused on creating synergies between the different members of the organization
Is aimed at adapting to the different circumstances
Appreciates diversity because it results in new ideas and new ways of getting things done
https://www.business.com/articles/contingency-management-theory/

https://www.encyclopedia.com/management/encyclopedias-almanacs-transcripts-and-maps/contingency-approach-management

The contingency viewpoint of management involves a manager weighing many different possibilities when solving an organizational problem. This process appreciates the constantly changing environment in which a problem is solved, as well as the dynamic needs of management and employees. When coming up with possible solutions, a manager considers many variables, including the makeup of the workforce, the organizational culture of the company, the company's size, the company's environment, and other factors. The advantage of this type of solution is that it can produce solutions that are specific to the problem, rather than adopting a one-size-fits-all approach. As the manager has considered many factors in producing the solution, the solution has a better chance of being feasible. The disadvantage of this process is that it can require a great deal of effort and time to produce customized responses to different types of problems that arise in an organization. 

What aspects of the narrator's personality allow him to survive this ordeal?

The narrator is very curious and logical, and his ability to distract himself from his terror by considering his space and how best to understand his situation likely saves him from losing his mind in the dungeon. He's very observant in terms of using his senses to gain information about his surroundings, and he is a good problem-solver, too. The narrator determines a way to map the layout of his cell:

I tore a part of the hem from [my] robe and placed the fragment at full length, and at right angles to the wall. In groping my way around the prison, I could not fail to encounter this rag upon completing the circuit.

Although he falls and then begins to move in the opposite direction from which he started, throwing off his calculations about the size of his dungeon, this activity serves as a constructive one rather than allowing himself to descend into the depths of despair and horror which the idle mind might be more inclined to do.

"The Pit and the Pendulum" by Poe is a story about a victim of the Spanish Inquisition who finds himself at the bottom of a pit. The last thing he remembers is having fainted at hearing he would be sentenced to death. The story follows as the narrator offers his perceptions of the black pit and as he experiences new tortures until he is finally rescued.
While very little explicit information is given about the narrator, indirect characterization allows us to analyze his words and actions in order to get to know him. The two characteristics that best support the narrator's survival are his practicality and resolution.
For evidence of his practicality, we must analyze how the narrator studies his prison and how he outsmarts the officials of the Inquisition. He uses a knife and piece of his clothing as a marker in order to study the size of the pit as he paces around its edges in search of the marker. He drops a fragment of stone down the pit and waits to hear it drop in order to guess at its depth. To break free of rope restraints, he lies still enough for rats to ignore him and crawl onto him long enough to chew through his bindings. This resourceful nature keeps him from carelessly falling into the pit in the dark and allows him to escape the various near-death instances he faces while imprisoned.
The second useful character trait the narrator exhibits is his resolution, his sheer determination to survive. We know that he must be a man of principle, since the Spanish Inquisition only punished those with the courage to oppose the Catholic Church. In the pit, the narrator faces every temptation to give in and let himself die rather than to fight back. He is abandoned in a black hole full of rats and he's given food he supposes to be drugged. He is left strapped on a board while a razor slowly descends toward him at a maddening pace, and after he escapes that, he is surprised by heat emanating from the walls that are inching in closer to him, forcing him toward the pit. The fact that the narrator doesn't give up, doesn't stop trying to survive, is ultimately what keeps him alive long enough to be rescued.

Single Variable Calculus, Chapter 1, 1.1, Section 1.1, Problem 1

Given the graph of the function $f$ evaluate the following:







a.) Find the value of $f(-1)$

By referring to the graph given, the value were $f(-1) = -2$


b.) Estimate the value of $f(2)$

By referring to the graph given, the value where $f(2) \approx 2.9$


c.) For what values of $x$ is $f(x) = 2$

By referring to the graph given, the values where$f(x) = 2$ are $x = -3$ and $x =1$


d.) Estimate the values of $x$ such that $f(x) = 0$

By referring to the graph given, the values where $f(x) = 0 \approx \text{at} x = 0.3$ and $x = -2.5$


e.) State the domain and range of $f$

By referring to the graph given, the domain and range of $f$ are D$[-3,3]$ R$[-2,3]$ respectively


f. ) On what interval is $f$ increasing?

By referring to the graph given, $f$ is increasing at interval $[-1,3]$

Precalculus, Chapter 9, 9.5, Section 9.5, Problem 38

You need to use the binomial formula, such that:
(x+y)^n = sum_(k=0)^n ((n),(k)) x^(n-k) y^k
You need to replace 2/x for x, 3y for y and 5 for n, such that:
(2/x-3y)^5 = 5C0 (2/x)^5 +5C1 (2/x)^4*(-3y)^1+5C2 (2/x)^3*(-3y)^2 + 5C3 (2/x)^2 (-3y)^3 + 5C4 (2/x)(-3y)^4 + 5C5 (-3y)^5
By definition, nC0 = nCn = 1, hence 5C0 = 5C5 = 1.
By definition nC1 = nC(n-1) = n, hence 5C1= 5C4 = 5.
By definition nC2 = n(n-1)/2 , hence 5C2= 5C3 = 10.
(2/x-3y)^5 = 32/x^5 - (240y)/x^4 + (720y^2)/x^3 - (1080y^3)/x^2 + (810y^4)/x - 243 y^5
Hence, expanding the expression using binomial theorem yields (2/x-3y)^5 = 32/x^5 - (240y)/x^4 + (720y^2)/x^3 - (1080y^3)/x^2 + (810y^4)/x - 243 y^5.

“A compassionate but flawed heroine.” Discuss Shakespeare's presentation of Cordelia in light of this statement.

Cordelia is undoubtedly the only one of Lear's daughters who has any genuine love or compassion for her father. But because she isn't prepared to play along with the charade of insincere public flattery, she falls out of favor with him. It's only much later in the play that Lear finally recognizes that Cordelia was the only one of his daughters who truly loved him. But by then, it's too late for both father and daughter.
It could reasonably be argued that Cordelia's tragic flaw is her total honesty. Instead of indulging in the same kind of shameless flattery as her sisters, she believes that the best way of showing love for her father is through actions, not words. And right throughout the play she displays that love, as well as her goodness and integrity, for all to see:

O dear father, It is thy business that I go about; Therefore great France My mourning and importuned tears hath pitied. No blown ambition doth our arms incite, But love dear love, and our aged father’s right. Soon may I hear and see him (Act IV, Scene iv).

But in such a thoroughly dishonest, cutthroat world, virtues like these are of no avail. Cordelia is simply too good, too pure, too noble for such a brutal, unforgiving world. She represents the last chance of redemption for Lear, the last flickering beacon of hope. Once she dies, all hope is gone, and Lear's own death is inevitable.

In Gulliver's Travels by Jonathan Swift, what are Gulliver's feelings when he opens his eyes in Lilliput?

When Gulliver first opens his eyes in Lilliput, he does not really remark on his feelings.  He notes that he is bound by a great many ligatures to the ground, and he cannot get up.  He hears confused noises around him and feels something small advancing up his person.  When he finally sees that it is a humanoid creature, though no more than six inches tall, he "was in the utmost Astonishment."  It is no wonder that he would be surprised: he awakens to find himself tied down, even his hair is bound, and then he feels not just one but forty more such tiny creatures striding up his body.  When one of these creatures begins to speak to Gulliver in a language that he cannot understand, he describes himself as feeling a "great Uneasiness."  This almost seems like an understatement given the situation.  Of course he would be terribly uncomfortable in such a state.  Gulliver also feels "excessive pain" when he attempts to move his head to either side.  It is a rude awakening, to say the least.

How does priming prompt consumers to think about a particular product and help affirm biases about a product? How do marketers use the priming effect to manipulate consumers? What are three examples of print or television ads that utilize the priming effect?

Priming in psychology is the effect that exposing someone to an earlier stimulus has on their response to a stimulus that is introduced later. For example, experiments have found that respondents who are exposed to rude words before an interview are more likely to interrupt the interviewer. Priming in marketing can be used in different ways. For example, a 1999 experiment conducted by North et al. found that grocery shoppers who were exposed to German music in the store bought more German wine, while those exposed to French music in the store bought more French wine. The shoppers were unaware the auditory priming affected their buying behavior. 
Some examples of priming include those that use smiles in their campaigns. Using a smile has been shown to increase the amount of liquid people drink. For example, in 2015, Coke used a "Laughter Mob" video in Belgium as part of its #ChooseHappiness campaign. This video featured a man laughing on a train and others laughing as a result. The priming effect was using laughter to influence people to buy and drink Coke. Laughter can also be used to promote other types of buying behavior, not just those related to drinking. For example, it could be used to influence people to visit a restaurant or resort.
According to an article in Health Psychology, food has been found to have an effect on eating behaviors (see the link below). Many ads show food, such as the Chips Ahoy! S'mores TV Ad, "Camping Trip," which shows the chocolate center of the cookie. In this case, just seeing food is intended to influence someone to buy it. This priming effect of showing food could also be used to get someone to buy healthy food. 
Music also has a priming effect. For example, a Volkswagen ad uses the lyrical Allison Krauss and Union Station song "When You Say Nothing At All" to prompt people to buy a Volkswagen. The priming effect is using music to make people feel lyrical and loving so they will associate that feeling with Volkswagen and want to buy one of the company's cars. This priming effect could also be used to promote other buying behaviors, such as purchasing a loving greeting card. 

In An Unquiet Mind by Redfield Jamison, does the author make the point that mental illness is very common? Are there are any quotes to support this? I know she emphasizes treatment and medicine, but does she clearly make the point that mental illness is much more common than people think (that many more people are affected than was thought)?

Redfield Jamison makes the point that mental illness is very common. For example, she writes that women are often not diagnosed with mania because depression is "more in line with society's notions of what women are about: passive, sensitive, hopeless, helpless, stricken..." (page 123). However, she writes that while depression is twice as common in women as in men, "manic-depressive illness occurs equally often in women and men, and, being a relatively common condition, mania ends up affecting a large number of women" (page 123). In other words, while women are not perceived as having mania, many of them do, as mania is very common.
She later writes that it might be impossible to split mood disorders into manic and depressive states and that such a distinction "minimizes the importance of mixed manic-and-depressive states, conditions that are common, extremely important clinically" (page 183). In other words, mania and depression are often mixed, and these conditions are very common.
The author also writes about the increased public knowledge of mental disorders and the fact that mental health advocacy groups have increased support for people with mental illness and their families by convincing members of Congress, "many of whom themselves suffer from mood disorders or have mental illness in their families" (page 184). The author notes that many public figures have mental illnesses, including mood disorders, as do many people in society. People and their families often suffer from mental illness as a result. 

Did Miss Emily kill Homer Barron?

Faulkner never states outright that Miss Emily killed Homer Barron, but that's the beauty of modern writing; it follows Hemingway's "iceberg theory," wherein the writer focuses on that which is on the surface (the part of the iceberg that people see above the water) without discussing the underlying elements (the rest of the iceberg that floats under the water). 
But even though Faulkner does not state that Miss Emily killed Homer, there are plenty of clues. The most obvious clue is the arsenic that Miss Emily buys at the drugstore. When she comes into the store, Faulkner writes,

[S]he was over thirty then, still a slight woman, though thinner than usual, with cold, haughty black eyes in a face the flesh of which was strained across the temples and about the eyesockets as you imagine a lighthouse-keeper's face ought to look.

Her looks suggest that she is under extreme stress, perhaps brought on by the rumors about Homer leaving town without proposing marriage to her. And when the druggist asks for the reason she needs the poison, she only stares at him. The druggist is the one to write "[F]or rats" on the bottle.  Afterward, when Homer returns, once Miss Emily's relatives leave, the town never sees him again, even though "[A] neighbor saw the Negro man admit him at the kitchen door at dusk one evening." 
Another clue that Miss Emily killed Homer is the smell that lingers at her home. While the story is not told in chronological order, Faulkner writes that after Homer disappeared, Miss Emily was not seen outside of her house for six months, and that was the time when the men came over to sprinkle lime around her yard to rid the smell...probably of a decaying body!
And finally, the final clue, is Homer's dead body found in Miss Emily's room after her death. Again, while the text does not outright state that the body is Homer Barron ("The man himself lay in the bed"), the reader assumes that it is indeed Homer.

How has the Republican Party transformed in values from Abraham Lincoln's era to current times?

In Lincoln's era, the Republican Party was newly formed by anti-slavery Democrats, Free-Soilers, and Whigs, which dissolved as a party in the 1850s. Their main concern at this time was the abolition of slavery. After that was achieved with the Emancipation Proclamation in 1863, the Republicans focused on Reconstruction, but quickly ended this project with their concession to the South in the form of the Compromise of 1877, signed by Republican President Rutherford B. Hayes.
Until the 1930s, most blacks either did not vote (black men did not gain the right until the Fifteenth Amendment was ratified in 1870; black women did not gain the right of suffrage until 1920) or tended to vote Republican, due to the party's association with abolition. Of course, voter intimidation was very common in the South, which was a stronghold for the Democratic Party. This affiliation persisted, even after the sweeping reforms created by the New Deal. Republicans, however, were opposed to Roosevelt's economic plan.
By this time, the Republican Party became the favored party among those in the West, of wealthy people, and of those who lived in the growing suburbs. Most importantly, Republicans were overwhelmingly white Anglo-Saxon Protestants. Meanwhile, urban areas became more heavily Democratic. This shift coincided with the migration of blacks to Northern cities at the beginning of the twentieth century, as well as the influx of immigrants from Southern and Eastern Europe and Asia. These new citizens, particularly blacks, relied on Franklin D. Roosevelt's reforms, even though, arguably, they were not most directly intended for these groups.
The realignment in the Republican Party in the 1930s -- from a party formed to address a social injustice to a party that became increasingly anti-immigrant and staunchly anti-union -- is directly related to Roosevelt's policies and to changes in demographics. The Republican Party's association with white Anglo-Saxon Protestant citizens has persisted to date with few exceptions.
This is not to say that Democrats were more enlightened. During the Civil Rights era, many Southern Democrats, known as "Dixiecrats," were firmly opposed to advancements for blacks. Meanwhile, some Republicans, like former New York governor (and, later, Vice President) Nelson Rockefeller, made great strides against discrimination towards blacks and women in areas such as housing and education. However, Rockefeller was a moderate Republican serving from the mid- to late-1960s, a considerably progressive era, due to Lyndon B. Johnson's leadership. 
Under Johnson, the Civil Rights Act of 1964 was signed, followed by the Voting Rights Act of 1965. Johnson famously said that, with the stroke of his pen, the Democratic Party, to which he belonged, would lose the South forever. His premonition came true. The South, with the exception of West Virginia, became firmly Republican. The spiteful exit of the South from the Democratic Party (though, today, a couple of states have returned and others may soon return) forced a shift in values in the Republican Party. While the party retained its anti-labor platform and its distaste for higher taxes on the wealthy, it also absorbed a more socially conservative strain, drawn from Fundamentalist values that are more intrinsic to the South and parts of the Midwest.
These values became centralized in the Republican Party with the election of Ronald Reagan in 1980. The social values platform on which Republicans claimed to stand remains pertinent to them today. Platforms related to the rights of immigrants, blacks, and women, which began to be addressed in the 1930s, remain more closely associated with the Democrats -- the pro-slavery party of Lincoln's time.
 

Calculus of a Single Variable, Chapter 6, 6.2, Section 6.2, Problem 19

The rate of change of N is the derivative of N with respect to t, or (dN)/(dt) . If the rate of change of N is proportional to N, then
(dN)/(dt) = kN , where k is the proportionality constant. This is the differential equation we need to solve.
To solve it, separate the variables:
(dN)/N = kdt
Integrating both sides results in
lnN = kt + C , where C is another constant. This can be rewritten in exponential form as
N = e^(kt + C) = N_0e^(kt) . Here, N_0 = e^C and it equals N(t) when t = 0.
When t = 0, N = 250, so
N(0) = N_0 = 250 and N(t) = 250e^(kt) is the solution of the differential equation above with the initial condition N(0) = 250.
To find k, we can use that when t = 1, N = 400:
N(1) = 250e^(k*1) = 400
e^k = 400/250 = 8/5 = 1.6
k = ln(1.6)
Plugging this back into N(t), we get
N(t) = 250e^(t*ln(1.6)) = 250*1.6^t .
Then, for t = 4, N(4) = 250*1.6^4 =1638.4
So, the solution of the equation modeling the given verbal statement is
N(t) = 250*1.6^t and for t = 4, N = 1638.4.

What is a karyotype?

Karyotype is a term used in cytogenetics to describe chromosomes in terms of number, size, and shape. In other words, the term refers to both the chromosomal count as well as chromosomal physical appearance. Karyotype also means the procedure through which a photographic representation of the chromosomes is developed. Here, the chromosomes are induced, stained, and observed under a microscope, and a photograph is taken. This photograph is then cut into pieces, arranged and numbered according to the sizes of the chromosomes beginning with the largest to the smallest.
Karyotypes are important for two major reasons; first, they enable detection of chromosomal anomalies, which is critical for diagnosis. Secondly, they offer an in-depth understanding of the root causes of genetic disorders, birth defects, and in recent years, cancer.

The prefix karyo- (from Greek, “nut” or “kernel”) refers to the nucleus of a cell. The suffix -type is used for many printing or photographic processes (daguerreotype, linotype). A karyotype is the number and visual appearance that identifies the different chromosomes in a person’s cells.
Doctors create depictions of karyotypes from cells drawn in a blood sample, by swabbing the inside of the cheek, or from a bone marrow sample. When testing the chromosomes of a fetus still in the womb, they’ll draw some of the amniotic fluid that contains the fetus’s cells.
Karyotypes will reveal the gender of an unborn baby. They help doctors determine if a birth defect is present in a fetus or if someone is carrying a gene that would create birth defects in their children. They can also be used to indicate the best treatment for certain types of cancer, though this isn’t always accurate, because cancer tends to damage chromosomes.
https://www.webmd.com/baby/what-is-a-karyotype-test

What do the kite/bench and dance metaphors mean in this book? I need quotes to back up an explanation. I need help forming two paragraphs explaining both of these. I need at least one quote as well.

In the play, dancing represents the only freedom that Willie and Sam, as black men in South Africa, are able to have. They dream of competing in a dance contest, as dancing involves forgetting their troubles and existing in a temporary fantasy world. In the excerpt below, Sam reminds Willie that he must seem romantic when dancing with his partner, Hilda, and must imagine that she is Ginger Rogers: 




SAM: You got it. Tapdance or ballroom, it's the same. Romance. In two weeks' time when the judges look at you and Hilda, they must see a man and a woman who are dancing their way to a happy ending. What I saw was you holding her like you were frightened she was going to run away.
WILLIE: Ja! Because that is what she wants to do! I got no romance left for Hilda anymore, Boet Sam.
SAM: Then pretend. When you put your arms around Hilda, imagine she is Ginger Rogers.
WILLIE: With no teeth? You try.

Hally, the white boy whose mother owns the tearoom where Sam and Willie work, bursts Sam and Willie's bubble. He says the following about their dancing:

Do you want to know what is really wrong with your lovely little dream, Sam? It's not just that we are all bad dancers. That does happen to be perfectly true, but there's more to it than just that. You left out the cripples.




While dancing is a fantasy in which people move about with grace, in real life, there is no such grace and beauty. Instead, as Hally says, people are bad dancers, and the fantasy of Sam and Willie's perfect dance is just that, a fantasy. Hally, a white boy, reminds Sam and Wilie that they are not really free and that dancing is not real life.
The kite symbolizes a dream of racial unity that Sam and Hally shared when Hally was a young boy. Sam constructed a makeshift kite for Hally, and, to Hally's surprise, it actually flew. Hally says, remembering that episode from his youth, "Little white boy in short trousers and a black man old enough to be his father flying a kite. It's not every day you see that." In other words, a black man and a white boy being together and flying a kite is a rare sight and a rare moment of racial solidarity in South Africa.
Hally expresses disappointment that Sam left him to fly the kite on his own, but Hally had not realized that Sam was not allowed to sit on the bench, which was reserved for whites. Sam tells Hally,

I couldn't sit down there and stay with you. It was a "Whites Only" bench. You were too young, too excited to notice then. But not anymore. If you're not careful . . . Master Harold . . . you're going to be sitting up there by yourself for a long time to come, and there won't be a kite in the sky.

The bench symbolizes the reality of a racially divided South Africa, one in which people are prevented from making connections to each other. Sam warns Hally that he will be back on this bench, this place of loneliness and division, if he continues to be hateful. Sam says that there will be no kites in the sky, meaning no moments of peace and unity. To write two paragraphs, start with a topic sentence that expresses what you think is the meaning of each of the symbols. Then include and analyze relevant quotations from the play.

When asked at a seminar at the University of Virginia about the meaning of the title "A Rose for Emily," Faulkner replied, "Oh, it's simply the poor woman had no life at all. Her father had kept her more or less locked up and then she had a lover who was about to quit her, she had to murder him. It was just 'A Rose for Emily'—that's all." In another interview, asked the same question, he replied, “I pitied her and this was a salute, just as if you were to make a gesture, a salute, to anyone; to a woman you would hand a rose, as you would lift a cup of sake to a man.” What do you make of Faulkner’s response? What else might the title suggest?

It is true, as Faulkner said, that Emily lives a life of unhappiness. Her only apparent lover, Homer Barron, deserts her, and she deserves some compensation for her life of unrequited love. However, the title could also suggest that giving Emily a rose is akin to paying homage to a lost time. Miss Emily lives in the only house left on a street that has now been turned over to garages. She is representative of decayed gentility. Faulkner writes, "Alive, Miss Emily had been a tradition, a duty, and a care; a sort of hereditary obligation upon the town." She is a responsibility that they must care for, so they let her get away with not paying her taxes and don't question her when she mysteriously purchases arsenic. She is someone people still feel that they must pay obeisance to, and that is what the title could suggest—paying homage to her as a relic of bygone days.

Where is the Maycomb jail in To Kill a Mockingbird?

In chapter 15 of To Kill a Mockingbird, Scout narrates that the Maycomb jail is "wedged between Tyndal's Hardware Store and The Maycomb Tribune office."
Scout describes the jail as appearing ridiculous because it is a "miniature Gothic joke" designed in imitation of much more expansive and impressive structures. Incongruously, its "ecclesiastical windows" have thick steel bars in front of them. Unlike the Gothic structures of history, it stands upon no hill by itself to be seen and admired but it is instead squeezed between two "square-faced" stores. This odd little building has become a conversation piece of Maycomb's citizenry as some feel that it provides the town with a "respectable look" while others disagree, calling it a "Victorian privy" along with other derogatory descriptions. Despite its unique appearance, it does little more than house many of the black citizens inside it.
Uncharacteristically, Atticus announces that he is going downtown for a while on the same day after the men have come to talk with him, and he takes the car rather than walk as he usually does. Later, Jem decides to look for Atticus, explaining to Scout, "I've just got this feeling . . . just this feeling" as his reason for going out. Scout and Dill accompany him, and they find Atticus outside this miniature Gothic structure where a threatening scene soon takes place.

What is a symbol in A Good Man is Hard to Find? How does it advance or reinforce the plot?

Flannery O'Connor's short stories are teeming with symbolism, and A Good Man is Hard to Find is no exception. There is an overall theme of good versus evil in the story, and symbols push this theme forward. 
After the family has had their car accident, the sky is described as being both sunless and cloudless—clear and empty. It is almost as if the family is caught between night and day, which could translate to being caught between life and death (as they are about to be killed), or perhaps even good and evil. These people, the grandmother especially, have been put in a sort of neutral zone, where their goodness or innocence (whether real or a facade) cannot save them. 
The empty sky also connects to The Misfit. We learn throughout the course of the story that this man, like the cloudless sky, is empty and ambiguous, possessing no regard for what is good or evil. He is in control, just as the sky dominates the setting.

One salient symbol in "A Good Man is Hard to Find" is the shape of a cross into which the grandmother's legs contort after the Misfit shoots her.
This cross made by the grandmother symbolizes her redemption and moment of grace as she has looked at the Misfit and recognized him as one of her children. That is, she has come to know herself as a sinner through what is termed a "redemptive catastrophe." She dies for her sins just as Christ died for the sins of man, and she is redeemed. O'Connor's approach here recalls the idea of the philosopher Martin Heidegger, who was a strong influence upon her. Heidegger, who held a concept called Dasein, or "being-there," felt that death represents the moment when a man's existence becomes complete.
Certainly, for the grandmother grace comes to her in her epiphany at the moment of her brutal death. This is why the Misfit says, "She would have been a good woman if it had been somebody there to shoot her every minute of her life." At the moment of her death, she is redeemed because she finally has enough humility to recognize that she, too, is a sinner--she is "there" with the Misfit--and she abandons her self-righteousness displayed in the car and at Red Sammy's, and thereby receives grace.
This redemptive death acts as the denouement to a plot in which her hypocrisy has been exemplified in her criticisms of others (e.g. her racial remarks when she has set herself up as honest and righteous woman). At the end, she finally recognizes that it is she who has been the greatest sinner and hypocrite.

What were George Washington's ideas and how did they change society?

George Washington's ideas greatly shaped and changed society. Many of his ideas, including his views about the role of the national government, federalism, and the role of the President, became hallmarks of the early American republic.
Washington believed that the new nation needed a strong, centralized government that had supremacy over the individual states (federalism). Washington knew firsthand that the Continental Congress and the Articles of Confederation had been ineffectual at governing the new nation; the Continental Congress had been unable to provide money or supplies for the Continental Army during the Revolution, and the Articles of Confederation (America’s first governing document) could not get money from the individual states (as taxes) for revenue. Washington believed that America needed a strong, centralized government that could bring all of the individual states together for the good of all states. During the Constitutional Convention of 1787, Washington subtly used his influence as President of the Convention to make sure the new Constitution adhered to his particular views and ideas.
During his time as President of the United States (1788-1796), Washington set many precedents for preceding heads of state. This is significant because the Constitution was extremely ambiguous about many of the roles and duties of the President. For example, Washington was the first president to serve two terms. At that point in time, the Constitution did not specify how many terms a president could serve. Washington, rather astutely, stepped down at the end of his second tenure in office. All presidents followed Washington’s example, until Franklin Roosevelt was reelected to an unprecedented third term in 1940. Washington also famously warned his successors to avoid interfering or being drawn into European affairs or alliances, as those relationships could potentially harm the young nation. This advice was generally accepted by all subsequent presidents until the 20th century.
Washington’s ideas shaped many of the ideas and policies of our young republic, and continue to do so today. His nickname of “Father of Our Country” helped to assure that his ideas lived on.

How does the use of diction and structure help achieve the purpose of chapter 7 in The Narrative of the Life of Frederick Douglass? How does it illustrate the concept of intellectual freedom?

Frederick Douglass, who began his life enslaved and without the possibilities of learning to read and write, realized that his path to intellectual freedom lay in the power of literacy. Thus, he began an insatiable quest to learn all he could and through whatever resources he encountered. In chapter 7, Douglass realizes that the poor white boys in the street could provide literacy lessons in exchange for bread.
As his abilities in reading and writing increase, Douglass's diction increases in complexity. Consider the following passage:

Slavery proved as injurious to her as it did to me. When I went there, she was a pious, warm, and tender-hearted woman. There was no sorry or suffering for which she had not a tear. She had break for the hungry, clothes for the naked, and comfort for every mourner that came within her reach. Slavery soon proved its ability to divest her of these heavenly qualities.

Douglass uses strong and precise adjectives, such as injurious, to project not only a voice for those directly held in slavery but those, like his mistress, whose character is forever changed by the damaging tentacles of slavery's reach. Douglass uses a compassionate tone for a woman who owns him and removes from his world any possibility of education. The diction he uses shows how literacy has given him advanced powers of reasoning which includes an incredible compassion for a woman who has oppressed him.
Douglass also illustrates his abilities to create complex structures in this chapter. He shows parallelism in the example above:

She had break for the hungry, clothes for the naked, and comfort for every mourner that came within her reach.

Douglass also shows his ability to construct cumulative sentences, such as this one:

I could regard [my enslavers] in no other light than a band of successful robbers, who had left their homes, and gone to Africa, and stolen us from our homes, and in a strange land reduced us to slavery.

The sentence could end after robbers and still convey a powerful message. However, the additional modifying phrases strengthens the sentence without losing any coherence and paints a strong image of the actions taken against those enslaved in America.
Throughout this chapter, Douglass shows his ability to break free from societal norms of his period in history, forming his independent thoughts about the importance of abolition.

Having been taught to read by Sophia Auld, Frederick Douglass furthered his skills on his own after her husband forbade her to teach a slave. Douglass also taught himself to write, and he wrote with a certain "figurative capacity," as demonstrated in this well-constructed sentence:

...however long I might remain a slave in form, the day had passed forever when I could be a slave in fact. (Ch.7)

Douglass repeats certain words in this sentence for emotional effect, such as slave. In addition, he uses parallelism in order to present ideas equally; the symmetry here emphasizes his meaning.
The diction which Douglass employs is rather formal, perhaps because of the age in which he lived and also because he worked hard to educate himself despite the almost complete lack of opportunity he experienced as a slave.
When Douglass is denied educational opportunities once given to him, he remarks,

The first step had been taken. Mistress, in teaching me the alphabet, had given me the inch, and no precaution could prevent me from taking the ell. (Ch.7)

Here again, Frederick Douglass employs figurative language and parallel structure. He also establishes a tone of dramatic power, self-determination, and intellectual freedom. 
In all of these examples from Chapter 7, Frederick Douglass demonstrates that he has educated himself well, and that he is a man who has attained intellectual freedom mostly through his own efforts. With moving rhetoric he writes of his intellectual freedom:

...the silver trumpet of freedom had roused my soul to eternal wakefulness. (Ch.7)

Single Variable Calculus, Chapter 5, Review Exercises, Section Review Exercises, Problem 18

Find the intergral $\displaystyle \int^1_0 \sin (3 \pi t) dt$, if it exists.
If we let $u = 3 \pi t$, then $du = 3 \pi dt$, so $\displaystyle dt = \frac{du}{3\pi}$. When $t = 0$, $u = 0$ and when $t = 1$, $u = 3\pi$. Therefore

$
\begin{equation}
\begin{aligned}
\int^1_0 \sin (3 \pi t) dt &= \int^1_0 \sin u \frac{du}{3\pi}\\
\\
\int^1_0 \sin (3 \pi t) dt &= \frac{1}{3\pi} \int^1_0 \sin u du\\
\\
\int^1_0 \sin (3 \pi t) dt &= \left. \cdot - \cos u \right|^1_0\\
\\
\int^1_0 \sin (3 \pi t) dt &= \frac{1}{3\pi} \left[ - \cos ( 3 \pi ) + \cos (0) \right]\\
\\
\int^1_0 \sin (3 \pi t) dt &= \frac{1}{3\pi} (2)\\
\\
\int^1_0 \sin (3 \pi t) dt &= \frac{2}{3 \pi}
\end{aligned}
\end{equation}
$

How many soliloquies are there in Hamlet?

A soliloquy is when a character shares his or her thoughts through a speech. The audience is able to hear it, but any other characters that are present are not privy to the words that are spoken. Soliloquies provide insight into what the character is thinking and gives the opportunity for the audience to learn information that cannot be revealed through characters’ conversations. William Shakespeare often uses soliloquies in his plays, and Hamlet is no exception. Throughout the play of Hamlet, there are a total of seven soliloquies. Each soliloquy helps the audience learn more about the character of Hamlet, especially since he’s always honest and his true self during the soliloquies, unlike times when he is speaking with other characters.

Hamlet has seven soliloquies in Hamlet. Their significance lies in their characterizing of Hamlet as an introspective and anguished character. While in a typical Renaissance revenge tragedy, a protagonist would quickly jump into action to try to avenge a death, Hamlet vacillates. Unlike Laertes, who is immediately out for blood when he learns that Hamlet has killed his father, Hamlet carefully contemplates his next steps and wishes he didn't have to face the problem of revenge. What, he wonders, if the ghost he meets has been sent by Satan to tempt him into killing an innocent man? How can he establish in some objective way that Claudius did, in fact, murder his father? 
If Hamlet was already upset about his father death, the ghost's revelation sends him into a tailspin of depression. He indulges in suicidal ideation, wishing in his soliloquies that he could, for example, dissolve like the dew or take his own life, deciding that is only fear of what he might encounter after death that keeps him alive. He later ponders death as the great leveler. 
Hamlet's contemplation of the meaning of life and death, largely through his many soliloquies, elevates this play from another entertaining bloodbath to a haunting meditation on universal questions about mortality, truth and purpose.   

Hamlet, the title character of a 17th-century tragedy by William Shakespeare, speaks seven soliloquies. Recall that a soliloquy occurs when a character in a work is speaking his or her innermost thoughts.  It is similar to thinking aloud.
The first soliloquy occurs in Hamlet in Act 1 scene 2 lines 129-59.  The occurrences during this scene relate to the character Hamlet's suicidal inclinations as he contemplates his late father and his mother's sudden remarriage.
Hamlet's second soliloquy occurs in Act 1 scene 5 lines 92-112. During these lines, Hamlet's confused speech relates to his dislike of the behavior of the characters Claudius and Gertrude and his feelings that he is responsible for avenging the death of his father.
Hamlet's third soliloquy occurs during Act 2 scene 2 lines 546-603.  During this scene, the mood shifts as Hamlet's attitude becomes more determined to channel his rage in order to avenge his father's death.  Shakespeare literary devices like repetition and irony during this soliloquy.
The fourth soliloquy occurs in Act 3 scene 1 lines 56-89.  This is the most famous of the soliloquies in the play and begins with "To be or not to be."  Hamlet is contemplating whether it is better to live in his depressed state or not to live at all.
The fifth soliloquy occurs in Act 3 scene 2 lines 395-406.  The sixth soliloquy occurs in Act 3 scene 3 lines 73-96.  The seventh and last soliloquy occurs in Act 4 scene 4 lines 32-66.
http://modbhamlet.weebly.com/uploads/2/9/4/7/29479151/hamlet_sevensoliloquies.pdf

How you think the graphic format contributes to your understanding of one family that includes a person on the autism spectrum in The Ride Together?

Paul and Judy Karasik use a graphic format in The Ride Together to convey the emotions and perceptions of people in the family, particularly David, the brother with autism. For example, in the top graphic on page 15, Paul Karasik represents the way in which David sees the world. The man on TV is coming toward David, almost as if the man were three dimensional, and David's mother's hand is looming large behind him.  This graphic represents the way in which the real world is distorted in David's mind. In the bottom graphic on page 15, David is shown looking at an oversized clock that is ticking while he is surrounded in black. This graphic shows the concentrated way in which David is fascinated by certain objects, such as the clock, while blocking out everything around him.
The graphic format also shows the reactions of the family members to David in a very clear and affecting way. On page 45, there is a graphic in which the father of the family knocks over David after David attacks the mother. The picture is very large, showing the action of the chair breaking as the father tries to stop David. This graphic makes it clear that the father has understandably lost his temper, resulting in this accident. It shows the physical and emotional reality of what a night at the Karasiks' house is like. On the page before, 44, Paul Karasik draws a bubble that includes all the stimuli that are affecting David, including random names and words that are coming to his mind and clapping sounds. This graphic shows why David is about to explode, as he is pushed over the edge by too many internal stimuli. These graphics show in a poignant and empathic way the perceptions and sensations of a person with autism and the reactions of the people around him. 

Single Variable Calculus, Chapter 1, 1.3, Section 1.3, Problem 56

Assume that an airplane is flying at a speed of $350mi/h$ at an altitude of one mile and passes directly over a radar station at time $t = 0$.



(a) We need to express the horizontal distance $d$ (in miles) that the plane has flown as a function of $t$,

$d = 350 t$

(b) Then express the distance $s$ between the plane and the radar station as a function of $d$,



$
\begin{equation}
\begin{aligned}

s^2 =& 1^2 + d^2\\
s =& \sqrt{1+d^2}

\end{aligned}
\end{equation}
$






(c) And express $s$ as a function of $t$ using composition.


$
\begin{equation}
\begin{aligned}

s =& \sqrt{1+d^2}; && d = 350 t\\
s =& \sqrt{1+(350t)^2}\\
s =& \sqrt{1+122500t^2}

\end{aligned}
\end{equation}
$

Where is the Sahel located in Africa?

The Sahel region is located in the western and north-central region of Africa. It extends from Senegal in the west to Sudan in the east. The Sahel is a transitional zone from one type of ecosystem to another. To the north of the Sahel is the arid Sahara desert, and to the south is the the humid African savannas. As a transitional zone, it blends characteristics of the desert and the savannas. For example, the Sahel does get rain, but the rainy season is limited to just 3-4 months, and rainfall total averages under 10 inches per year. Despite that relatively low rainfall amount, the Sahel has lots of natural pasture areas with low grasses. Additional water sources are a result of flooding from the Niger and Senegal rivers. The Sahel's overall length differs from source to source. Some sources say it is nearly 3,400 miles long, while other sources state it is only 2,400 miles long. Regardless, it's a lengthy region that covers around 1.2 million square miles.
https://www.britannica.com/place/Sahel

https://www.newworldencyclopedia.org/entry/Sahel

The Sahel, meaning “coast” or “shore” in Arabic, is a belt-like region on the southern edge of the vast Sahara desert. It is the transitional zone in Africa between the Sahara to the north and the Sudanian Savanna to the south. It extends 5,400 kilometers (3,360 miles) from the Atlantic Ocean in the west to the Red Sea in the east. Its width varies from several hundred up to a thousand kilometers (620 miles) in different places. It covers a total area of about 3 million square kilometers (1.18 million square miles). There are nine countries in this region from west to east, including Senegal, Mauritania, Mali, Burkina Faso, Niger, Nigeria, Chad, Sudan, and Eritrea. Attached is a picture of the Sahel on the map of Africa.
https://www.worldatlas.com/articles/what-are-the-important-features-of-the-sahel-region-of-africa.html

What is the mood or atmosphere of this story?

The overall mood and atmosphere of Poe's classic short story "The Cask of Amontillado" can be described as disturbing and menacing. At the beginning of the story, the narrator explains to the reader how he got revenge on Fortunato for causing him a "thousand injuries." Montresor proceeds to outline his requirements for committing the perfect crime and elaborates on how he deceived Fortunato into following him down into his family's catacombs. By utilizing dramatic irony, Poe creates an eerie, ominous mood. The reader is aware that Montresor has an evil plan for the unsuspecting Fortunato, who is visibly intoxicated and unaware that he is being deceived by a malevolent enemy. The carnival setting also adds an element of chaos and bizarre to the story's atmosphere, which heightens the suspense and contributes to the unsettling mood. As Fortunato follows Montresor into his family's vaults, the mood becomes increasingly ominous and threatening. The dingy nature of the catacombs and the skeletons surrounding the two characters also contribute to the sinister atmosphere. Once Montresor successfully clasps Fortunato to the back wall of the vaults, Poe creates an atmosphere of danger, panic, and fear as Montresor steadily builds a wall to bury his enemy alive.

The mood of this story is characterized by foreboding and danger. We know from the outset that Montresor is planning to do something terrible to Fortunato. He says, "I would be avenged" and that "I must not only punish but punish with impunity." Therefore, we know Montresor is plotting revenge for the "thousand injuries" Fortunato has done him as well as whatever "insult" Fortunato has offered him. Further, Montresor vows that he must not only exact such revenge, but he must do so without incurring personal consequence for himself. He feels both that he must go unpunished for whatever retribution he exacts as well as that he must make himself known as the author of this retribution. Several times Montresor hints about what he plans to do; the foreshadowing of his later actions lends to the foreboding atmosphere. His calculated coldness—his ability to deceive his victim up until the last moment—helps to create a mood of danger.

Who is Mrs. Mann?

To answer this question, take a look at chapter two. In this chapter, Oliver is sent from the main workhouse to a "branch workhouse" where he, and thirty other children, are placed under the care of an elderly, female superintendent. That superintendent is Mrs. Mann, and it is her responsibility to care for the young Oliver and the other orphans.
From the text, we see that despite her maternal role, Mrs. Mann is neither maternal nor caring towards the children she looks after. In fact, she is far more interested in the financial benefits of this role than in actually tending to the needs of children:

The elderly female was a woman of wisdom and experience; she knew what was good for children; and she had a very accurate perception of what was good for herself.

In addition, we learn that Mrs. Mann is violent towards the children and does not provide them with adequate nutrition. When anybody from the authorities arrives to inspect her establishment, however, Mrs. Mann pretends to be the perfect mother figure. The children are washed, well-dressed, and appear happy. We see this when Mr. Bumble unexpectedly arrives. Mrs. Mann acts as though her only interest is in the children's welfare when, in reality, they are all desperate to escape from her:

That I should have forgotten that the gate was bolted on the inside, on account of them dear children!

However, Oliver's experience in her care shows the very opposite. She is a cruel and financially-motivated woman who shows no love towards those she is paid to look after.

What are the Shakespeare allusions in I Don't Know How She Does It?

In I Don't Know How She Does It by Allison Pearson, the sonnets and romantic works of Shakespeare are often referenced and alluded to.
These allusions are most obviously seen in the sub-plot of Kate's romantic flirtations with the suave American businessman, Jack Abelhammer, who e-mails her Shakespearean sonnets as a method of flirtation. The two also have a discussion about a particular poem in which a man tells his lover than he wishes seven years could be experienced in a single night. Jack suggests the poem to be a work of Shakespeare, but Kate disagrees, attributing the work to Marlowe. Kate humorously writes,

"That's the unfair thing about Shakespeare, though—everything belongs to him whether he wrote it or not!"

Later, Kate also writes that the actor Carey Grant is a contender for the title of "Greatest Englishman with William Shakespeare." Clearly influenced by Shakespeare and other English Literary giants, I Don't Know How She Does It shows an appreciation for the Bard's endlessly rewarding poetry.

In The Help, how does Stockett use fashion as a tool of characterization?

The Help is set in Jackson, Mississippi, in the early 1960s. The author has to convey the times and the settings through descriptions that the readers will understand; and she also has to be true to the very different lives of the white socialites and the black maids. You can first see examples of fashion used as characterization in the opening chapter, which is told by Aibileen. When she comes to terms with her son’s death, she tells us: “I lifted myself up out a bed, I put on my white uniform and put my little gold cross back around my neck and I went to wait on Miss Leefolt cause she just have her baby girl.” We know right away that the black maids wear uniforms to serve the white socialites. We also know that Aibileen sees her religion as being important to her, because she wears a necklace with a cross on it.
Later in the same chapter, Aibileen describes the ladies who come to the Leefolt house for bridge club. About Hilly Holbrook: “Miss Hilly got a round face and dark brown hair in the beehive. … She one a those grown ladies that still dress like a little girl with big bows and matching hats and such.” This clear picture is painted for us. Contrast this to Minny’s first meeting with Miss Celia Rae Foote at the beginning of Chapter 3. Minny describes the person in front of her:

She might be built like Marilyn [Monroe], but she ain’t ready for no screen test. She’s got flour in her yellow hairdo. Flour in her glue-on eyelashes. And flour all over that tacky pink pantsuit. Her standing in a cloud of dust and that pantsuit being so tight, I wonder how she can breathe. … She’s probably ten or fifteen years younger than me, twenty-two, twenty-three, and she’s real pretty, but why’s she wearing all that goo on her face? I’ll bet she’s got on double the makeup the other white ladies wear.

Right away in this scene, we know that Celia is not like the other white socialites of Jackson. No wonder she doesn’t fit in with the group, no matter what she does. And these are just a few examples from the opening chapters of the book. Naturally, all of these appearances and fashions are much more prominent in the movie version. On the screen, we can see immediately the marked differences between races and classes without being given any additional verbal explanations about them.

What are major themes in The Kite Runner that relate to the context of friendship between Amir and Hassan? How does the progression of their friendship develop these themes?

Amir and Hassan's friendship relates to several themes in The Kite Runner. The first is the way in which different ethnic minorities are treated in Afghanistan at the time. Hassan is from the Hazara ethnic minority, while Amir is from the Pashtun group. As Amir reads in a book in his father's study, the Pashtuns have long persecuted the Hazara. It turns out that both Amir and Hassan have the same father (Baba), but their different treatment in society shows the effects of ethnic prejudice on children and their fates.
Another theme related to the boys' friendship is that of redemption. Amir is jealous of his friend and treats him unfairly by trying to make Hassan seem guilty of theft (while Hassan is innocent). Though Amir is not able to redeem himself in Hassan's lifetime, Amir eventually saves and adopts Hassan's son, an act of redemption. The progression of their friendship, even after Hassan has died, allows Amir to eventually try to make amends to his friend.

Some of the major themes that relate to Amir and Hassan's friendship include innocence, sacrifice, and guilt. As innocent children, Amir and Hassan enjoy going to the movies, reading together, and playing in the pomegranate tree on Baba's property. Despite their different ethnicities, the boys live carefree lives and enjoy each other's company. Hassan is depicted as an innocent, morally-upright boy, who makes several sacrifices for Amir as a child. Hassan selflessly defends Amir from Assef by pointing a slingshot directly at Assef's eye, and he also promises Amir that he will return with their opponent's blue kite at the end of the kite-fighting tournament. However, Amir does not sacrifice anything for Hassan as a child and refuses to intervene as he watches Hassan being raped by Assef.
After Hassan is raped, both boys lose their childhood innocence, and guilt negatively affects their friendship. Amir is overwhelmed with guilt and can no longer be around Hassan after he witnesses his friend's assault. Their friendship is eventually destroyed because of Amir's guilt, and Hassan leaves Baba's estate with his father. As an adult, Amir travels back to Afghanistan and atones for his past sins by saving Hassan's son, Sohrab, from a difficult life in Taliban-controlled Kabul. Amir finally frees himself of guilt by sacrificing everything in order to save and adopt Sohrab. Although Amir never had a chance to repair his friendship with Hassan, he finds redemption by sacrificing his comfortable life in America to save Hassan's son.

When did the two kingdoms of Egypt merge to become one?

It’s difficult to pinpoint an exact date for an event that took place so long ago, but we know that the Upper and Lower Kingdoms of Egypt were united sometime between 3150 BCE and 2680 BCE.
It’s generally accepted that King Menes (also known as Narmer) of Upper Egypt was responsible for the unification. The Narmer Palette, which shows his victory over Lower Egypt, has been dated to around 3000 BCE, near the beginning of the First Dynasty. The Palette depicts Menes/Narmer wearing royal crowns in the style of both regions, indicating his rulership over the entire land.
There are two important symbols in Egyptian art which represent the unification of the two kingdoms. The first is the Pschent, a double-crown. (In the attached image the red part shows the crown of Upper Egypt, and the white part of Lower Egypt.) The second is the sema tawy, which shows reeds and papyrus plants being bound together. These images don’t appear in Egyptian art before the unification, so archaeologists use them to help date the art pieces as well as to support their own theories about when the unification actually took place.
https://www.ancient.eu/Narmer_Palette/

Describe the character of the astrologer.

The protagonist in "An Astrologer's Day" is an interesting character because he is a survivor. He came to the big city from one of the many small villages in India and had to find some way to exist without having any formal education or marketable skills. We do not know how he obtained his astrological paraphernalia, but it is possible that he found it somewhere and decided to become an "astrologer" on the spur of the moment. His "professional equipment" consists of

...a dozen cowrie shells, a square piece of cloth with obscure mystic charts on it, a notebook, and a bundle of palmyra writing.

The man who had owned the equipment before him may have been better versed in the pseudo-science of astrology, but he may have lacked the present owner's intelligence, glibness, personality, and "moxie." It is obviously very hard for any astrologer to make a living in this city because most people don't have any money to spare for anything but the bare necessities.
The astrologer's day is a long and precarious one. He has a wife and small daughter waiting for him at home. Even when he encounters Guru Nayak and his life is in danger, he resolutely insists on talking about money. Because of his brains and adaptability, he is able to bring home even more coins than usual. He lives from day to day. He doesn't even want to think about what he is going to do tomorrow. He has gotten through one day and that is enough for him.

"Time to sleep," he said, yawning, and stretched himself on the pyol.

The astrologer might be said to represent the millions of men who are migrating to the big cities of India from the villages. His story is just one of the many stories of these people, whose survival in the cities depends on their adaptability to very difficult living conditions.

He had left his village without any previous thought or plan. If he had continued there he would have carried on the work of his forefathers namely, tilling the land, living, marrying, and ripening in his cornfield and ancestral home. But that was not to be.

It is interesting to see how this nameless man has become transformed into a big-city dweller who deals with great numbers of people every day in order to eke out a living for himself and his tiny family. He needs money to survive and support his family, and he has to get that money from other people by providing something in exchange. The great subcontinent of India is changing in many ways because of globalization, expanding population, and other factors. "An Astrologer's Day" represents the macrocosm in a microcosm, which it what makes it such a memorable short story.

what is the resolution in the story “my brother sam is dead”

The resolution to this story is not a happy resolution; however, it is not a surprising resolution. The book is titled My Brother Sam is Dead, and Sam is very much alive for almost the entire book. Near the end of the story, Sam is accused of being a cattle thief, and he is sentenced to be executed. Readers might really want this to not happen, but based on the book's title, we know it's coming. The end of Chapter 14 is not a great resolution. Sam is shot, and his clothes catch on fire. He is not killed instantly either. Instead, he's writhing around in pain as he burns. Fortunately, another soldier fires another shot and puts an end to Sam's suffering.

They had shot him from so close that his clothes were on fire. He went on jerking with flames on is chest until another soldier shot him again. Then he stopped jerking.

The book does contain a short epilogue that sort of gives readers a happier resolution. The narrator is now 64 years old. He's married and has some kids. His life has been fairly prosperous, and the thinks the United States is a great country; however, the epilogue ends with Tim admitting that he still believes war was not the only way to achieve his country's freedom.

What does it mean to grow up?

Growing up means having to make difficult choices, keep secrets, live with the consequences of one’s actions, realize that the only constant in life is change—and, where the ultimate change is concerned—accept death as a natural part of the life cycle rather than a fearsome inevitability. In Babbitt’s novel, we see what it means to grow up through Winnie’s character.
At the beginning of the story, Winnie, a child who feels oppressed by her family, runs away to the woods. Her decision to do so leads to a fateful meeting with the Tuck family. She learns about the spring of immortality in the woods, and she swears an oath of secrecy about the Tuck family’s unusual condition. As they are immortal, all have been forced to live a life of isolation and secrecy for over eighty years: since they can neither age nor die, they never remain in the same town or place for very long.
Unfortunately, information about the spring’s magical properties has been overheard by a sinister character, the man in the yellow suit, who desires to market the spring water. After bargaining Winnie’s safe return for ownership of the spring, the man returns to the Tuck residence, reveals his plan, and tries to make Winnie drink the water. Mae kills him but she is arrested by the constable shortly thereafter.
Although Winnie helps free Mae to preserve the family’s secret and ultimately, save the world from the ravages immortality would wreak upon its population, she has still broken the law. As such, her crime now forces the Tucks to leave the woods and live their lives on the run. Before they leave, Jesse gives Winnie some of the spring water. Naively believing that she can access the spring any time she wants—the forest and spring will always be there, after all—Winnie chooses not to drink it.
Over time, a lightning strike destroys the woods, and the spring is lost. When the Tucks finally return for a visit, Winnie, who has never partaken of the spring water, has succumbed, as must all who live within the natural order, to time and death.

What sort of prize did Malala receive in 2011?

Malala Yousafzai is well known for battling oppression in her native Pakistan and elsewhere, fighting for the rights of young girls to receive a proper education in places where they are traditionally banned from attending school. She survived an assassination attempt by the Taliban in 2012 and subsequently became a co-recipient of the 2014 Nobel Peace Prize, which made her internationally known.
However, her activism was documented as early as age eleven, as she began blogging anonymously on a local BBC website in January of 2009 about the Taliban's corrupting influence on her home of Swat Valley. Her advocacy for human rights continued, eventually becoming public, and resulted in South African activist Desmond Tutu nominating her from the International Children's Peace Prize in October of 2011, which is awarded each year to a youth who has significantly contributed to advancing the rights and well-being of children around the world.
While Yousafzai didn't win that award, it greatly boosted her public profile and drew the attention of national politicians in Pakistan. Then, on December 19, 2011, when she was fourteen years old, Prime Minister Yusuf Raza Gillani presented her with the country's very first National Peace Award for Youth, which would be given annually to a Pakistani citizen under the age of 18 who contributed to peace and education in the country. The award was accompanied by a 500,000 rupee prize (approximately $5,780 at the time).
https://www.cnn.com/2011/11/24/world/asia/pakistan-peace-prize/index.html

What is Edmund and Fanny's relationship during the play scene like?

At first, Fanny and Edmund are united in their opposition to the idea of doing such a racy play as Lovers' Vows as a family theatrical. Both are, at first, adamant in their refusal to participate.
However, under the influence of Mary Crawford, Edmund decides to participate. Although he goes to the white attic to speak to Fanny about it, and although he wishes she would approve his lame rationalizations for participating, for the first time they are not seeing eye to eye. Fanny continues to think he should not act. She believes he should remember how his father would disapprove of the venture and stand up for his father's principles. She also is jealous of the idea of his playing opposite Mary.
While Fanny is subjected to censure for her refusal to act, she holds her ground, foreshadowing her refusal later to marry Henry Crawford.

Calculus of a Single Variable, Chapter 9, 9.2, Section 9.2, Problem 48

Recall that infinite series converges to single finite value S if the limit if the partial sum S_n as n approaches oo converges to S . We follow it in a formula:
lim_(n-gtoo) S_n=sum_(n=1)^oo a_n = S .
To evaluate the sum_(n=0)^oo 3/5^n , we may express it in a form:
sum_(n=0)^oo 3/5^n =sum_(n=0)^oo 3* (1/5^n)
=sum_(n=0)^oo 3 *(1/5)^n
This resembles form of geometric series with an index shift: sum_(n=0)^oo a*r^n .
By comparing "3 *(1/5)^n " with "a*r^n ", we determine the corresponding values: a = 3 and r =1/5 or 0.2 .
The convergence test for the geometric series follows the conditions:
a) If |r|lt1 or -1 ltrlt1 then the geometric series converges to sum_(n=0)^oo a*r^n = a/(1-r) .
b) If |r|gt=1 then the geometric series diverges.
The r=1/5 or 0.2 from the given infinite series falls within the condition |r|lt1 since |1/5|lt1 or |0.2|lt1 . Therefore, we may conclude that sum_(n=0)^oo 3/5^n is a convergent series.
By applying the formula: sum_(n=0)^oo a*r^n= a/(1-r) , we determine that the given geometric series will converge to a value:
sum_(n=0)^oo 3/5^n =sum_(n=0)^oo 3 *(1/5)^n
= 3/(1-1/5)
=3/(5/5-1/5)
=3/(4/5)
=3*(5/4)
= 15/4 or 3.75

((3-2x)/x^3)/(2/x^2-1/(x^3+x^2)) Simplify the complex fraction.

To simplify the given complex fraction ((3-2x)/x^3)/(2/x^2-1/(x^3+x^2)) , we may look for the LCD or least common denominator.
The denominators are x^3 , x^2, andx^3+x^2 .
Note: The factored form of x^3+x^2 = x^2(x+1).
LCD is the same as getting LCM from the denominators.
We get the product of each factor with highest exponent value,
LCD=x^3*(x+1) .
Multiply each term by the LCD=x^3*(x+1).
((3-2x)/x^3*x^3*(x+1))/(2/x^2*x^3*(x+1)-1/(x^3+x^2)x^3*(x+1))
((3-2x)/x^3*x^3*(x+1))/(2/x^2*x^3*(x+1)-1/(x^2(x+1))x^3*(x+1))
((3-2x)(x+1))/(2x*(x+1)-1*x)
(3x+3-2x^2-2x)/((2x^2+2x)-x)
(-2x^2+3x-2x+3)/(2x^2+2x-x)
(-2x^2+x+3)/(2x^2+x)
Final answer:
((3-2x)/x^3)/(2/x^2-1/(x^3+x^2))=(-2x^2+x+3)/(2x^2+x)

Beginning Algebra With Applications, Chapter 1, Review Exercises, Section Review Exercises, Problem 42

Add: $\displaystyle \frac{-5}{8} + \frac{1}{6}$


$
\begin{equation}
\begin{aligned}

\frac{-5}{8} + \frac{1}{6} =& \frac{3(-5) + 4(1)}{24}
&& \text{Get the LCD}
\\
\\
=& \frac{-15+4}{24}
&& \text{Simplify}
\\
\\
=& \frac{-11}{24}
&&

\end{aligned}
\end{equation}
$

What happens to Charlie's car in That Was Then, This Is Now?

In Chapter 3, Charlie allows Bryon to borrow his car to take Cathy Carlson to the school dance. After Mark ends up getting hit in the head with a bottle during a fight, Bryon rides with him to the hospital and leaves his car at the school. Right before Bryon calls a taxi for a ride home, Ponyboy arrives with Cathy at the hospital in Charlie's car. When Bryon asks Pony how he started the car without a key, Ponyboy tells him that he hot-wired it. At the beginning of Chapter 4, Bryon returns Charlie's car and explains what happened to him. Bryon mentions that Charlie wasn't interested in what he had to say because he just received a draft notice. Later on in the novel, Charlie dies in a gunfight, and the police give Bryon his car. Bryon mentions that he took the car because Charlie would have given it to them. 

What are Susan Glaspell's important contributions to theater?

In addition to her role in the Provincetown Players and The Little Theatre, Susan Glaspell was a very important female writer during the early twentieth century. In a time where it wasn't common, she brought a feminist narrative to theatre and writing. She was known as being a master of dialogue and brought a richness and realness to her characters on stage. She also brought in political and social commentary to her plays, which were set on the backdrop of where she lived: Provincetown and the American frontier. Her experimentation with form and infusing humor into depictions of feminist, social, cultural, and political issues was unique.
Additionally, in the 1930s, the Federal Theatre in Chicago made Glaspell the director of Midwest Play Bureau. In this role, she was able to feature Midwest talent and played an important part in the creation of Living Newspapers, a type of theater form that presented current events to live audiences.
https://muse.jhu.edu/article/47728/summary

https://www.press.umich.edu/14558/susan_glaspell_in_context

Susan Glaspell's contributions to American theater are considerable. She co-founded, with her husband, George Cram Cook, the first American modern theater company, the Provincetown Players, a place for developing plays that would not necessarily have found, at that time, an audience on Broadway. She is credited with discovering American playwright Eugene O'Neill.
Glaspell is considered by many to be the first significant American female playwright, creating fifteen plays, including Trifles (1916), a classic of American drama with themes of feminism, justice, and morality.
Glaspell won the Pulitzer Prize in 1931 for her play Alison's House, a drama said to have been inspired by the poems and life of Emily Dickinson. During the Great Depression, Glaspell was appointed bureau director for the Federal Theater Project, a project sponsored by the government to fund live theater.