"A Gordon LaChance halfway along in the process of losing the shine." This sentence is from the novel named The Body written by Stephen King. What is symbolized by "the shine," and what is the meaning of this sentence?

Gordon LaChance is the protagonist of King's novella The Body. In this line, he is referring to the version of himself that he feels he can still see "behind the lines of print" of the very first story he ever wrote and was proud of. While he knows that this first "whole" story was not very good, being altogether too melodramatic and "undergraduate," it is important to Gordon because it presents him with a view of himself when he was younger, when he was "halfway along in the process of losing the shine."
"The shine" on an object is something that indicates that it is new. The narrator, the current Gordon, sets himself at one end of a scale, with the other end marked by the very young Gordon LaChance, who went along with his friends to see the dead body of Ray Brewer. It is this young Gordon who is the subject of the current story. The Gordon LaChance who wrote the earlier story, the "undergraduate" Gordon, marks the halfway point between the two Gordons.
The young Gordon, we understand, still has the "shine" about him. This indicates that he is young and naive: eager to experience life but not very well informed about what life is really like. Meanwhile, the older Gordon has lost his shine; he is cynical and no longer possesses the earnestness of youth. The Gordon "halfway along in the process" therefore falls somewhere between the two: no longer as naive and eager as his younger counterpart but not yet fully aware of all that life really is.

How does The Gambia’s place in the world economy differ from, say, the place of Britain? How does that place affect The Gambia? What do you think would be necessary for The Gambia to move from “Third World” to “First World”?

First, The Gambia is a very small country, with a tiny economy compared to that of Great Britain or any other European nation of similar size. The country's GDP is very small and has, for several years, been in a state of recession. Its economy is centered around agriculture, which means that it is very susceptible to severe economic downturns in the event of drought or other things that limit agricultural output. There is a relative lack of capital for domestic investment, so the country experiences very high debt relative to its GDP. Like many countries with widespread poverty and with little money to invest in education and infrastructure, The Gambia struggles to maintain even modest economic growth. The economy of Great Britain, on the other hand, is huge. Britain remains a very important player in the world's economy. Its GDP in 2016 was over 2.6 trillion dollars. While British manufacturing is in decline, its economy is highly diversified. The technology and infrastructure that exist in the United Kingdom give it an immeasurable advantage over small, impoverished nations like The Gambia. In order to close this gap, The Gambia would need substantial investment in infrastructure, including roads, communication, and so on. It would also need large amounts of foreign investment. Above all, the economy of The Gambia would have to diversify. This is, of course, very difficult for a small nation like The Gambia.
https://www.worldbank.org/en/country/gambia/overview

https://www.worldbank.org/en/country/unitedkingdom

What are some advantages of consumers having private property?

I'm not really clear on the context in which this question is being asked, since it is listed under "Business," which presupposes a capitalistic system of some sort, I would think. If consumers do not own private property, they are far less likely to want to consume many goods and services, and they have no assets upon which they can draw if need be. If I own a house, I am more likely to buy carpeting and paint to fix it up and buy a few trees and perennials to plant. If I rent, I have no stake in the place I live, and I am not going to acquire a significant number of goods and services to improve the property. If I own a house, I build equity in it, upon which I can borrow, to remodel, to send a child to college, or to finance my senior years. It is difficult to conceptualize an economy in which there are businesses and no one is permitted to own private property.

Who is baby tuckoo in A Portrait of the Artist as a Young Man?

Baby tuckoo is a character from children’s stories that Stephen’s father would tell him as a child. In the story, a mystical “moocow” would come up to the baby and take him to a magical land. This was a common myth from Irish folklore, where children would be spirited away by a magical cow to be trained and groomed into mythical heroes, returning to do incredible feats and deeds on Earth.
James Joyce was frequently called baby tuckoo as a child, and so he chose this familiar phrase for the baby in his book. It echoes the epic coming of age journey the character embarks upon, as if he was taken by the cow to learn to be a hero.

Baby tuckoo is Stephen Dedalus.
When Stephen is little, his father tells him a story about a nice little boy who meets a cow. He says it in the kind of language that many parents would use when talking to a child—a kind of affectionate babytalk. This is how the book opens, with a moocow coming down the road and meeting baby tuckoo.
Then the viewpoint switches, and Stephen remembers seeing his father as he told him the story. He remembers the beard on his face. He remembers the words his father spoke. He says that he, himself, was baby tuckoo.
This introduction takes the reader to the earliest memories that Stephen has. It helps to show the characteristics of his father before showing the rest of his family. It's clear that they're close and warm; his father and the stories he told were important to Stephen in his formative years.

Joyce’s penultimate novel, A Portrait of the Artist as a Young Man, opens with a line from a story Stephen Dedalus remembers being told as a child:

Once upon a time and a very good time it was there was a moocow coming down along the road and this moocow that was coming down along the road met a nicens little boy named baby tuckoo.

Stephen remembers quite well how his father would act out the part of baby tuckoo, as is exemplified by his use of “baby talk” (moocow, for example), and this gives readers their first impressions of Stephen’s father as a kind and involved figure in Stephen’s formative years.
The reason the name baby tuckoo was chosen is because it was a nickname for Joyce himself as a child, and the story itself is an interesting reference as well. As Don Gifford notes in his book Joyce Annotated, the story of moocow and baby tuckoo is rooted in traditional Irish folklore. According to legend, a magical cow takes certain children to an island realm where they are groomed to become heroes before being returned to their astonished parents. This snippet of a story alludes to the traditional “hero’s journey” that Stephen embarks on throughout the novel.
https://books.google.com/books?id=j0OpMmb95KsC&dq=gifford+supernatural+cow+island+realm

Baby tuckoo is a character in a story that Stephen Dedalus remembers being told by his father. It is one of his very first memories, and it is mentioned in the first sentence of A Portrait of the Artist as a Young Man:

Once upon a time and a very good time it was there was a moocow coming down along the road and this moocow that was coming down along the road met a nicens little boy named baby tuckoo.

In the story, Stephen's father acts out the part of "baby tuckoo," which Stephen identifies with. This expression is an example of the kind of baby talk often spoken by parents to their young children. "Moocow" and "Nicens little boy" are other examples of this. The memory is clearly a very pleasant one for Stephen, as he remembers it so vividly. It also introduces us to the jolly, playful figure of Stephen's father, who will have an important role to play in his formative years.

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

int (4x^3+3)/(x^4+3x)dx
To solve, apply u-substitution method. So let:
u= x^4+3x
Then, differentiate it.
du=(4x^3+3)dx
Plug-in them to the integral. 
int (4x^3+3)/(x^4+3x)dx
= int 1/(x^4+3x)* (4x^3+3)dx
=int1/udu
Then, apply the integral formula  int 1/xdx = ln|x| + C .
= ln|u| + C
And, substitute back  u=x^4+3x .
=ln |x^4+3x|+C
 
Therefore,  int (4x^3+3)/(x^4+3x)dx = ln|x^4+3x|+C .

What is the frequency of the light emitted by atomic hydrogen with m = 8 and n = 12? (The Rydberg constant is R =1.097 x 107 m-1, c = 3.00 x 108 m/s) I gotz 2.86*10^13Hz dunno if correct. Show steps please.

  
 
The Rydberg equation is
1/λ = RZ2(1/n12 - 1/n22)
where λ is the wavelength of the photon emitted
R is the Rydberg constant
Z is the atomic number which in this case is 1 since we are dealing with the hydrogen atom
n1 is the same as m which is 8
n2 is  12
So we work out the wavelength of the emitted photon as follows:
 1/λ  = 1.097 x 10^7 (1/8^2 - 1/12^2)
1/λ  = 1.097 x 10^7 x 0.00868
1/λ  =9.522 x 10^4 m^-1
λ= 1.050 x 10^-5m
We then use  f= c/λ to calculate the frequency
              f  = 3.00 x 10^8/1.050 x 10^-5
              f =  2.86 x 10^13 Hz
The wavelength and frequency that we just found tell us that the transition emits energy in the infra-red region of the electromagnetic spectrum. So one would not expect to see a spectral line for a transition from m =8 to m = 12
 
http://chemed.chem.purdue.edu/genchem/topicreview/bp/ch6/bohr.html

Which aspects of social, cultural, and political life in early Roman Empire supported the growth of Christianity and which opposed it?

The Roman Empire was a highly hierarchical, bureaucratic, and authoritarian state where the elites lived comfortably while the urban and rural poor, including peasants, artisans, and slaves, were disempowered, heavily indebted, overtaxed, humiliated, abused, and often subjected to violence by privileged insiders, the wealthy, and especially soldiers and government officials. Chronic insecurity and the frequent arbitrary injustices of the imperial order contrasted with an imperial ideology purporting to benefit the public and support the common good.
In Roman provinces such as Judea, the wealthy and powerful enjoyed the support of the Roman authorities, while people of lower status experienced alienation and despair due to their routine mistreatment, the social fragmentation of local communities, and the growth of inequality. Jesus appealed to these abandoned, humiliated, impoverished, and marginalized masses of the Mediterranean population. Early Christian preaching supported horizontal social solidarity, mutual help, and the equality of rich and poor within new Christian communities that challenged the vertical certainties of the imperial order.
Christian belief in Jesus as the “Son of God” and the “Savior of the World” contradicted the emperor’s cult, which frequently employed similar terms for the divinized emperors. As the Christian message challenged the established powers and values, Christians became subject to persecution by the imperial authorities and the influential local elites. This persecution was sporadic, not continuous or systematic, however. New generations of Christian leaders came increasingly from the educated, urban-residing middle and upper classes; they stressed their loyalty to the ruling emperor and their readiness to abide by imperial laws as long as these laws tolerated their religious convictions.

2x/3 - 4 = 2 Solve

To solve this equation means that we must find out what the value of "x" is. To do this, our task is to isolate "x," or, in other words, get "x" alone on one side of the equation and everything else on the other side of the equation. We know when we've solved the problem when we are left with "x=#(some number)."
The rule to keep in mind is this: if we are adding on one side of the equation, we can subtract that number on the other; and, if we are multiplying on one side of the equation, we can divide by that number on the other side of the equation.
On the left side of the equation, the following operations are in use:
-4 (subtracting 4)
/3 (dividing by 3)
2x (multiplying by 2)
This means we can do the following (opposite operations) on the right side:
+4 (add 4)
*3 (multiply by 3)
/2 (divide by 2)
We can begin by adding 4 to the right side of the equation.

2x/3 = 2 + 4

Now, we can simplify the right side of the equation, because we can add 2 + 4 and get 6.

2x/3 = 6



Next, we can multiply by 3 on the right side of the equation.

2x = 6(3)

And, we can simplify the right side again.

2x = 18


Finally, because 2x means that 2 is multiplied by x, we can divide by 2 on the right side of the equation.

x=18/2

And, for the last time, we can simplify the right side of the equation.

x = 9


To ensure that we have solved this equation correctly, we can write a proof. This means that we begin with the original equation and substitute our answer ("1") for "x" to see if the two sides of the equation are equal.

2x/3 - 4 = 2
2*9/3 - 4 = 2
2 * 9/3 = 6
9/3 = 6/2
3 = 3






We have solved for "x" correctly. x=9. We know this because both sides of the equation (left and right) are equal (3=3) in our proof.

Over the course of his journey, how has Santiago become a wiser individual? Provide text evidence please.

One way that Santiago has become a wiser person by the end of his journey is in his knowledge of the Soul of the World. While Santiago is pursuing his Personal Legend and treasure, his knowledge and understanding of the Soul of the World changes. At first, it is a mysterious force that simply exists as an entity separate from him; however, by the end of the story, Santiago has gained enough wisdom to understand that the Soul of the World is a part of him, and he is a part of it. Everything is connected, and he has the ability to tap into that soul and all of its power. This is fortunate because this knowledge allows Santiago to physically transform himself to escape an almost certain death.

The boy reached through to the Soul of the World, and saw that it was a part of the Soul of God. And he saw that the Soul of God was his own soul. And that he, a boy, could perform miracles.

Name three conflicts Hamlet faces.

One conflict Hamlet faces is how to deal with his uncle, Claudius, who Hamlet suspects has killed his father to usurp the throne of Denmark. Hamlet is also faced with the apparent treachery of his mother, Gertrude, who married Claudius very shortly after Hamlet's father died. Hamlet becomes disenchanted with women in part because of what he feels is his mother's betrayal of his father. Finally, Hamlet questions whether Ophelia, his former beloved, is loyal to him, given the treachery he sees around him and the machinations of her father, Polonius, to help Claudius. Feeling betrayed, Hamlet loses confidence and he ponders, in the "to be or not to be" soliloquy, whether he should passively react to what has happened to his father or take action, which is bound to be bloody, in retaliation for his father's untimely death. 

Precalculus, Chapter 5, 5.3, Section 5.3, Problem 21

tan(3x)tan(x-1)=0
solving each part,
tan(3x)=0
General solutions for tan(3x)=0 are,
3x=0+pin
x=(pin)/3
General solutions for tan(x-1)=0 are,
x-1=0+pin
x=1+pin
so the solutions are,
x=(pin)/3 , x=pin+1

How is Walter Mitty jarred out of his first daydream?

Thurber's short story "The Secret Life of Walter Mitty" was originally published in The New Yorker in March 1939. The story follows Walter and his wife on a normal day as the couple runs typical errands. Walter's daydreams are his way of escaping the humdrum events of the day. Each daydream coalesces events going around him with a more exciting version of himself.
His first daydream begins this pattern. In the daydream, he is driving a hydroplane instead of his car; the audience is introduced to him as a Commander wearing "his full-dress uniform, with the heavily braided white cap pulled down rakishly over one cold gray eye." He is jarred from his dream by the sound of his wife's voice criticizing his driving, “Not so fast! You’re driving too fast!” said Mrs. Mitty. “What are you driving so fast for?” Instantly we meet the real Walter Mitty: a husband on his way to Waterbury with his demanding wife.
Each dream gives us a glimpse of the life Mitty wants, but just like his real day-to-day life he's unable to fully achieve it.

"The Secret Life of Walter Mitty" is a very famous short story by James Thurber, first published in the year 1939. The story follows the titular character, Walter Mitty, as he goes through a very mundane day of driving and errands with his wife and daydreams about extraordinary situations in order to escape from his unsatisfying, humdrum life.
The story actually starts out directly in the middle of one of Walter's day dreams, where he imagines that he's a commander about to steer his "huge, hurtling eight-engined Navy hydroplane" through a hurricane, with his crew is cheering him on. As it turns out, in real life Walter is driving his car with his wife, Mrs. Mitty, in the passenger seat. It seems that Walter's imagination has had an impact on his driving, and Mrs. Mitty jars him out his daydream by yelling, "Not so fast! You're driving too fast!"

Who are the characters in From The Mixed Up Files Of Mrs. Basil E. Frankweiler?

From the Mixed Up Files of Mrs. Basil E. Frankweiler is an award-winning children's book that was published in 1967. It features three main characters: Claudia Kincaid, Jamie Kincaid, and Mrs. Basil E. Frankweiler. 
Claudia Kincaid is the main character. She is the one who decides to run away from home and live in the Metropolitan Museum of Art in New York City, and she is also the one who figures out how to do so. Claudia is also fascinated by a statue that originally belonged to Mrs. Frankweiler, and that part of the story leads to the end of the book. 
Jamie Kincaid is Claudia's little brother. He is financially capable because he saves all his money. This is why Claudia chooses him as her companion on this adventure. 
Mrs. Basil E. Frankweiler is a wealthy widow. She allowed the museum to purchase a statue that could have been by Michelangelo for under $500. She is also eccentric; when Claudia and Jamie show up at her doorstep, using the last of their money, she lets them look in her oddly-arranged files, and they figure out where the information about the statue is. 
There is one ancillary character, Saxonberg, who is Mrs. Frankweiler's lawyer. The book is Mrs. Frankweiler's account to her lawyer for why she wants to leave the statue information to Claudia.

What do Santiago's parents plan for him, and how does he change that plan?

Santiago's parents want him to become a priest, so he attends the seminary until he is sixteen years old. While in the seminary, Santiago learns to read. While it is a great honor and accomplishment for a boy from a poor family to become a priest, Santiago soon realizes he is unhappy at the seminary. He courageously tells his father that he wishes for a life of adventure and travel. After his father tries to convince him that every place is the same and is no better than where he lives, he tells Santiago that the only occupation that will allow a poor person to travel is that of a shepherd. His father relents and gives Santiago three gold coins to allow him to buy a flock of sheep to fulfill his dreams of adventure and travel.

Santiago's parents want him to go to a seminary and train for the priesthood. But Santiago has other ideas; he's determined to follow a different path in life. He wants to travel farther afield, and at that time and in that place, becoming a shepherd was one of the few ways you could do this. Santiago's parents do their best to persuade him to stay—the place where they live is so beautiful, why on earth would anyone want to leave it?—but Santiago is set on exploring the big old world outside. Although Santiago's father is understandably disappointed, he respects his son's decision. He gives him three gold coins to get him started on his new career and buy himself a flock of sheep. Santiago is now able to take the first step on his epic life journey.

What was one key event from the 1850s that escalated tensions between the North and South? How did the push for western expansion impact this event?

One event from the 1850s that heightened tensions between the North and the South was the raid by the abolitionist John Brown on the federal armory at Harpers Ferry, which was then in the state of Virginia.  This raid helped increase tensions because the North and South reacted to it in different ways.
In this raid, Brown and his followers took control of the federal armory.  Their plan, such was it was, was to give out weapons to the slaves who, they were sure, would flock to them.  These slaves would then carry out an armed rebellion.  Brown and his people were defeated and Brown was later executed. 
The “argument” on the part of the North (or at least on the part of many Northerners) was that John Brown was a hero.  Northerners saw Brown as a martyr for his cause.  They felt that he was a courageous man who had stood up for what he believed in.  This infuriated the South.  Their “argument” was that Brown was a killer who was breaking the law in an attempt to get the slaves to rise up and kill the people of the South.  They hated the idea that the North would lionize a man who wanted to cause the massacre of Southern whites.  In this way, the debate between the two sides was not really about the raid, but about how people should perceive Brown.
Westward expansion did not have a great impact on this event. It happened in Virginia, not in any western area.  However, expansion did have one impact.  Westward expansion brought about the Kansas-Nebraska Act and the violence of “Bleeding Kansas.”  John Brown was part of that violence.  He helped lead anti-slavery fighters in Kansas and was involved in an incident now known as the “Pottawatomie Massacre,” in which five pro-slavery men were killed in cold blood.  Although Brown was already an abolitionist, we could argue that westward expansion helped to radicalize him and make him more likely to carry out such an extreme act as his raid on Harpers Ferry.
https://www.ushistory.org/us/32c.asp

Calculus of a Single Variable, Chapter 2, 2.3, Section 2.3, Problem 14

You need to evaluate first y', using the product rule, such that:
y' = (x^2 - 3x + 2)'(x^3 + 1) + (x^2 - 3x + 2)(x^3 + 1)'
y' = (2x - 3)(x^3 + 1) + (x^2 - 3x + 2)(3x^2)
y' = 2x^4 + 2x - 3x^3 - 3 + 3x^4 - 9x^3 + 6x^2
Combining like terms yields:
y' = 5x^4 - 12x^3 + 6x^2 + 2x - 3
You may evaluate now f'(c) at c = 2, replacing 2 for x in equation of f'(x):
y' = 5*2^4 - 12*2^3 + 6*2^2 + 2*2 - 3
y' = 80 - 96 + 24 + 4 - 3
y' = 105 - 96 => y' = 9
Hence, evaluating the derivative of the function yields y' = 5x^4 - 12x^3 + 6x^2 + 2x - 3 and evaluating the value of derivative at c= 2, yields y' = 9.

What is the plot and setting of the movie Act of Valor? Act of Valor is a 2012 American war film directed by Mike McCoy and Scott Waugh and written by Kurt Johnstad.

When Act of Valor was originally conceived, it was planned to be more of a recruitment and documentary film about the Navy SEALs.  Consequently, the film doesn’t benefit from having a tight plot with solid character development.  It plays more like a highlight reel of soldiers blowing stuff up and doing brave acts.  Real grenades were even used in the filming of the movie.  There’s not much Hollywood "fakery" going on in this film.  Real Navy SEALs played the part of the soldiers as well, so all of the action looks completely realistic; however, because the “actors” are not actual actors, the directors focus more on moving the movie from location to location and event to event.  Characters are secondary.
The setting locations are as varied as the action sequences.  Audiences spend time in Coronado, CA, the Philippines, Indonesia, Costa Rica, Somalia, Mexico, a U.S. Navy amphibious assault ship, a submarine, and even a C-130 transport plane.
The movie begins in the Philippines, where a terrorist kills the U.S. ambassador and a bunch of school children (including the ambassador’s son) with an improvised explosive device (IED). The terrorist is a Chechen named Abu Shabal, and he escapes to a terrorist training camp in Indonesia.  
The film then takes viewers to Costa Rica, where CIA operative Lisa Morales is captured and imprisoned by a drug smuggler named Christo.
Next, the film takes viewers to the United States and introduces viewers to the seven SEALs that will be deployed to rescue and exfiltrate Morales. The SEALs parachute into the Costa Rican jungle and rescue Morales.  One of the SEALs is wounded during the rescue operation, and the team is forced to make a hectic escape under heavy enemy fire.  
Aboard the USS Bonhomme Richard, Morales confirms that Shabal and Christo are working together on a terrorist plot that involves extremely thin and powerful explosive vests that cannot be detected by metal detectors. Two of the SEALs (Ajay and Ray) are sent to Somalia to attempt to find out more information about Shabal and an arms deal.
Ajay and Ray parachute from a C-130 and rendezvous with a submarine. The two men confirm Shabal’s presence along with 16 other terrorists.  Shabal and those terrorists then head to an island off of Baja California.  The SEAL team assaults the terrorists, and half of the terrorists are killed. Unfortunately, Shabal escapes.  
At the same time, a second SEAL team successfully captures and interrogates Christo.  Christo reveals that Shabal is planning an attack on the U.S. that rivals the scope of the September 11 attacks.  The team then rushes off to Mexico in order to stop Shabal from entering the U.S. through a tunnel system.  A huge gunfight follows, where several SEALs are either killed or wounded, and Shabal is killed.  The movie ends with a military funeral for the soldiers that were killed.  
https://www.latimes.com/entertainment/la-xpm-2012-feb-12-la-ca-act-of-valor-20120212-story.html

College Algebra, Chapter 3, 3.6, Section 3.6, Problem 8

Evaluate $f + g$, $f - g$, $fg$ and $\displaystyle \frac{f}{g}$ of the function $f(x) = \sqrt{9-x^2}$ and $g(x) = \sqrt{x^2-4}$ and find their domain

For $f+g$,

$
\begin{equation}
\begin{aligned}
f+g &= f(x) + g(x)\\
\\
f+g &= \sqrt{9-x^2} + \sqrt{x^2 - 4}
\end{aligned}
\end{equation}
$

The radicand can't be a negative value. So we factor $9- x^2 = (3-x)(3+x)$ and $x^2 - 4 = (x- 2)(x+2)$. Thus the domain of $f(x) + g(x)$ is $[-3,-2]\bigcup[2,3]$

For $f-g$

$
\begin{equation}
\begin{aligned}
f-g &= f(x) - g(x) \\
\\
f-g &= \sqrt{9-x^2} - \sqrt{x^2 - 4}
\end{aligned}
\end{equation}
$

The radicand can't be a negative value. So we factor $9- x^2 = (3-x)(3+x)$ and $x^2 - 4 = (x- 2)(x+2)$. Thus the domain of $f(x) - g(x)$ is $[-3,-2]\bigcup[2,3]$


For $fg$

$
\begin{equation}
\begin{aligned}
fg &= f(x) \cdot g(x) \\
\\
fg &= \left( \sqrt{9-x^2} \right) \left( \sqrt{x^2 - 4} \right) && \text{Substitute } f(x) = \sqrt{9-x^2} \text{ and } g(x) = \sqrt{x^2 - 4}\\
\\
fg &= \sqrt{(9-x^2)(x^2-4)} && \text{Apply FOIL method}\\
\\
fg &= \sqrt{9x^2 - 36 - x^4 + 4x^2} && \text{Combine like terms}\\
\\
fg &= \sqrt{13x^2 - x^4 - 36}
\end{aligned}
\end{equation}
$

The radicand can't be a negative value. So we factor $9- x^2 = (3-x)(3+x)$ and $x^2 - 4 = (x- 2)(x+2)$. Thus the domain of $f(x) \cdot g(x)$ is $[-3,-2]\bigcup[2,3]$


For $\displaystyle \frac{f}{g}$

$
\begin{equation}
\begin{aligned}
\frac{f}{g} &= \frac{f(x)}{g(x)}\\
\\
\frac{f}{g} &= \frac{\sqrt{9-x^2}}{\sqrt{x^2-4}} && \text{Substitute } f(x) = \sqrt{9-x} \text{ and } g(x) = \sqrt{x^2 - 4}\\
\\
\frac{f}{g} &= \sqrt{\frac{9-x^2}{x^2-4}}
\end{aligned}
\end{equation}
$

The function $\displaystyle \frac{f}{g}$ can't have a denominator equal to zero and the radicand can't be a negative value. So we factor $9-x^2 = (3-x)(3+x)$ and $x^2 - 4 = (x-2)(x+2)$. Thus, the domain of $\displaystyle \frac{f}{g}$ is $[-3,-2) \bigcup (2,3]$

What are the main events in chapter 2 of Night by Elie Wiesel?

In chapter 2, the Jews of Sighet have been rounded up and herded into cattle trucks bound for Auschwitz. Conditions inside the trucks are deplorable—there's no food or water, and the choking, unsanitary air is absolutely stifling due to the extreme heat. But the Jews have no choice; if anyone tries to escape, they'll be shot.
A middle-aged lady called Madame Schaecter starts going out of her mind. She's on board the train with her ten-year-old son and, having been separated from her husband and two older sons, becomes completely unhinged at the grim fate that she believes awaits her and the other prisoners. She begins having frightening visions about a vast, diabolical furnace which she points at through the window. People are understandably scared and unnerved by the woman's outbursts, so much so that they feel that they're about to go mad themselves. Some of the other prisoners descend upon Madame Schaecter, beating her up and trying to gag her. But despite their best efforts, she continues to scream throughout the night, becoming ever more deranged.
When the train finally arrives at Auschwitz, the Jews are told that it's a labor camp and that the conditions are good. This is a total lie, of course, as the Jewish prisoners soon discover to their horror. They also discover that Madame Schaecter's premonitions were frighteningly accurate. The smell of death is everywhere, and there, in the distance, is the notorious crematorium, billowing thick plumes of acrid smoke into the bleak, lightless atmosphere. Ironically, Madame Schaecter now falls silent as her apocalyptic vision materializes before her very eyes.

lim_(x->oo)x^3/e^(x^2) Evaluate the limit, using L’Hôpital’s Rule if necessary.

Given to solve ,
lim_(x->oo) x^3/e^(x^2)
upon x tends to oo we get x^3/e^(x^2) = oo/oo
so, by applying the L'Hopital Rule we get
as for the general equation it is as follows
lim_(x->a) f(x)/g(x) is = 0/0 or (+-oo)/(+-oo) then by using the L'Hopital Rule we get  the solution with the  below form.
lim_(x->a) (f'(x))/(g'(x))
 
so , now evaluating
lim_(x->oo) x^3/e^(x^2)
upon using the L'Hopital Rule
=lim_(x->oo) ((x^3)')/((e^(x^2))')
=lim_(x->oo) (3x^2)/(e^(x^2)(2x))
=>lim_(x->oo) (3x)/(e^(x^2)(2))
now on x-> oo we get (3x)/(e^(x^2)(2)) =oo/oo
so,again by applying the L'Hopital Rule we get
lim_(x->oo) (3x)/(e^(x^2)(2))
=lim_(x->oo) ((3x)')/((e^(x^2)(2))')
=lim_(x->oo) (3)/(e^(x^2)(2)(2x))
=lim_(x->oo) (3)/(e^(x^2) (4x))
now as x-> oo
3/(e^(x^2) (4x)) =3/(e^(oo^2) (4(oo))) =0
so
lim_(x->oo) (3)/((e^(x^2) (4x))) =0
now we can state that
lim_(x->oo) x^3/e^(x^2) =0

How do prose and poetry interact in Tales of Ise?

Ariwara no Narihira's Tales of Ise is a type of Japanese literature called uta monogatari, a sub-genre of monogatari (an epic narrative using extended prose) that combines waka poetry and sections of prose. In this particular case, the poems make up the bulk of the "narrative," with the prose occurring very briefly, usually only to establish the scene, introduce the next poem, or comment on a poem's composition. In many instances, these narratives start with the same beginning: "Long ago, there was a man" (or, "Mukashi otoko arikeri"). Because of the way that it is arranged, the book lacks a traditional plot, and the sections are best connected through the presence of a narrator. The book consists of 125 sections with a total of 209 poems. 

Precalculus, Chapter 7, 7.4, Section 7.4, Problem 22

(x+1)/(x^2-x-6)
Let's factorize the denominator,
x^2-x-6=x^2-3x+2x-6
=x(x-3)+2(x-3)
=(x-3)(x+2)
:.(x+1)/(x^2-x-6)=(x+1)/((x-3)(x+2))
Now let(x+1)/(x^2-x-6)=A/(x-3)+B/(x+2)
(x+1)/(x^2-x-6)=(A(x+2)+B(x-3))/((x-3)(x+2))
(x+1)/(x^2-x-6)=(Ax+2A+Bx-3B)/((x-3)(x+2))
:.(x+1)=Ax+2A+Bx-3B
x+1=(A+B)x+2A-3B
Equating the coefficients of the like terms,
A+B=1
2A-3B=1
Now let's solve the above two equations to get the values of A and B,
express B in terms of A from the first equation,
B=1-A
substitute the expression of B in the second equation,
2A-3(1-A)=1
2A-3+3A=1
5A-3=1
5A=1+3
5A=4
A=4/5
Plug the value of A in the first equation,
4/5+B=1
B=1-4/5
B=1/5
:.(x+1)/(x^2-x-6)=4/(5(x-3))+1/(5(x+2))
Now let's check the above result,
RHS=4/(5(x-3))+1/(5(x+2))
=(4(x+2)+1(x-3))/(5(x-3)(x+2))
=(4x+8+x-3)/(5(x^2+2x-3x-6))
=(5x+5)/(5(x^2-x-6))
=(5(x+1))/(5(x^2-x-6))
=(x+1)/(x^2-x-6)
= LHS
Hence it is verified.

What is Hamlet hoping to accomplish with the speech of the Player Queen to the Player King?

In Act III of Hamlet, Shakespeare presents a play within a play. In the previous act, the ghost of King Hamlet spoke with his son and told him that his death was at the hands of his brother, Hamlet's uncle, Claudius. This revelation leaves Hamlet with even more questions. Was his mother a part of the plan? Did she know Claudius's plan? Hamlet writes extra lines for the players to present in their play "The Mousetrap."
The play within the play begins with the Player King and Player Queen acting out their scene without talking. In this scene, the Player King is killed by a man who pours poison into the king's ear and then steals the crown. The second part of the play has the Player King and Queen discussing their love and what would happen if one of them were to die. The Player King tells his wife to be happy if he dies, but the Player Queen refuses by claiming that if her beloved husband were to die, she could never remarry. She goes so far as to say that marrying another man would be the same as treason and that if she were to go to bed with another man, it would be like killing her first husband over and over.



Oh, confound the rest!

Such love must needs be treason in my breast.

In second husband let me be accursed!

None wed the second but who killed the first.


The instances that second marriage move

Are base respects of thrift, but none of love.
A second time I kill my husband dead

When second husband kisses me in bed.

Hamlet creates the Player Queen's dialogue to lay it on quite thick. Even Queen Gertrude believes that her player counterpart is overacting: "The lady protests too much, methinks." However, Hamlet purposefully uses the dialogue as a test. He wants to gauge the king and queen's reactions to the play. Then he will know if they truly had anything to do with his father's death, and he will learn just how much of a role his mother played in it.

What did Jem realize after Miss Maudie’s house burned down?

In chapter 8 of To Kill a Mockingbird, Miss Maudie Atkinson's house burns to the ground. As we might expect, the scene is one of chaos and confusion. Scout and Jem can only stand and watch as the flames wreak terrible destruction on Maudie's property. It is winter in Maycomb, and it is freezing cold on that terrible night: poor Scout shivers on the sidewalk.
Later on, when Scout is drinking hot chocolate with Atticus, it comes to her father's attention that she is carrying a brown blanket round her shoulders, one that does not belong to them. Scout has no idea whose blanket it is or how it even got there. Jem realizes that it was none other than Boo Radley, who quietly sneaked out of his house and, amidst all the confusion, gently draped the blanket over Scout's shoulders.
We have reached a point in the story when Boo is increasingly starting to reach out to the Finch children; they are his only real connection to the outside world. He has already placed various objects in the knothole of the tree for Scout and Jem to find. Now he is showing his protective side to the children, which foreshadows his act of bravery later on when he saves them from the evil clutches of Bob Ewell.

As Scout looked out from the Radley porch, she regretted that she and Jem never gave Boo anything in return for his gifts, but they did give Boo something. What did they give him?

The main thing the children give to Boo Radley is friendship. Boo Radley had been very lonely. He never left his house, and no one ever seemed interested in caring about him except for Dill, Jem, and Scout, who attempt to reach out to him.
Dill is the one who pushes the hardest for getting Boo to come out of his house. Dill understands loneliness, so that is probably why. He appreciates Boo’s situation and does not consider him a monster.

“All right then. What’d you write him?”
Dill said, “We’re askin‘ him real politely to come out sometimes, and tell us what he does in there—we said we wouldn’t hurt him and we’d buy him an ice cream” (Chapter 5).

Boo Radley really responds to these small acts of friendship. He does not mind the children reenacting his story. He seems to find them amusing and appreciates the attention. This is why he begins leaving the Finch children gifts in the tree. In Boo Radley’s lonely life, Scout and Jem are a breath of fresh air.

Summer, and he watched his children’s heart break. Autumn again, and Boo’s children needed him.
Atticus was right. One time he said you never really know a man until you stand in his shoes and walk around in them. Just standing on the Radley porch was enough (Chapter 31).

Boo Radley is childlike in his own way. He relates to the Finch children because they are kind to him. They reach out to him, so he reaches back. They give him the courage to come out of his house, which he had not done since he was a teenager. He gives them the gift of their lives when he saves them from Bob Ewell, and they give him the gift of friendship.

A ball is thrown upward with an initial velocity of 9.8 m/s. How high does it reach before it starts descending? Choose only one from the three formulas: 1. Vf = Vi + gt 2. dy = Viyt + 1/2gdyt^2 3. Vfy = Viy^2 + 2gdy

To solve, apply the third formula.
v_(fy)^2 = v_(iy)^2+2gd_y
Take note that when the ball reaches the maximum height, its velocity is zero. So plugging in the values 
v_(iy)=9.8 m/s
v_(fy) = 0
g=-9.8 m/s^2
the formula becomes
0^2= 9.8^2 + 2(-9.8)d_y
0=96.04 - 19.6d_y
19.6d_y = 96.04
d_y=96.04/19.6
d_y=4.9
Therefore, the maximum height of the ball is 4.9 meters.
http://zonalandeducation.com/mstm/physics/mechanics/kinematics/EquationsForAcceleratedMotion/Origins/TimeIndependent/Origin.htm

Single Variable Calculus, Chapter 6, 6.3, Section 6.3, Problem 34

Use the graph of $y = x^3 - x + 1, y = -x^4 + 4x - 1 $ to estimate the $x$-coordinates of the points of intersection of the curves. Then, estimate the volume of the solid obtained by rotating about the $y$-axis the region enclosed by the curves.







Based from the graph, the $x$-coordinates of the points of intersection are $x \approx 0.4$ and $x \approx 1.25$. If we use a vertical strips, we can see that there are strips that have a distance of $x$ to the $y$-axis. If we revolve this distance about $y$-axis, you'll have a circumference of $C = 2 \pi x$. Also, the height of the strips resembles the height of the cylinder as $H y_{\text{upper}} - y_{\text{lower}} = -x^4 + 4x - 1 - (x^3 - x + 1)$.

Thus, we have


$
\begin{equation}
\begin{aligned}

V =& \int^b_a C(x) H(x) dx
\\
\\
V =& \int^{1.25}_{0.4} (2 \pi x) \left[-x^4 + 4x - 1 - (x^3 - x + 1)\right] dx
\\
\\
V =& \int^{1.25}_{0.4} (2 \pi x) \left[-x^4 - x^3 + 5x - 2\right] dx
\\
\\
V =& 2 \pi \int^{1.25}_{0.4} \left[-x^5 - x^4 + 5x^2 - 2x\right] dx
\\
\\
V =& 2 \pi \left[ \frac{-x^6}{6} - \frac{x^5}{5} + \frac{5x^3}{3} - \frac{2x^2}{2} \right]^{1.25}_{0.4}
\\
\\
V =& 3.1582 \text{ cubic units}


\end{aligned}
\end{equation}
$

What is the relationship between Hally and his mother in "MASTER HAROLD" . . . and the Boys?

Hally's relationship with both of his parents can be described with the same word. His relationship with his mother and with his father is broken. I might consider that Hally respects his mother just a little bit more than he respects his father, but that is about the only positive thing I could really be convinced of regarding his relationship with his mother. Hally's dad is a deadbeat drunk of a father. His mother is either naive to this fact or unwilling to stand up to it. Hally even angrily explodes on the phone with her that there"is a lot of things you don't know about." He then explains to his mom how his dad tries to sneak and steal money from them to support his habit. Hally isn't making impassioned pleas to his mother to see his point. He's angrily yelling at her about how blind she is. That's not a respectful and loving way to address a mother.

HALLY. (To the telephone) . . . (Loudly) I said I hope you know what you've let us in for! It's the end of the peace and quiet we've been having.

Audiences never get to meet Hally's dad or mom. All we really get to see is Hally and Sam's relationship, and it becomes clear to audiences that Sam has been a great surrogate parent for Hally. Unfortunately, by the end of the play, Master Harold has burned that bridge too.

In Fugard's "MASTER HAROLD". . .and the boys, the relationship between Hally and his mother is weak and seemingly distant. The audience never meets Hally's mother as a present character--she is only referenced in the telephone conversations that Hally has with her while she is at the hospital with Hally's father. But when she calls, she asks Hally to look after his father, which Hally does not want to do. Hally says that his mother allows his father to push her around, and he cannot understand why his mother does not stand up to his father. Both Hally and his mother seem to cower in the shadow of the father, and each wants the other to "solve" the problem. They do not seem to see each other as a support in dealing with the father. Hally wants his mother to be strong so that she can protect him from his father, but his mother does not appear to be in a position to do that for Hally.

How did democracy first develop in Athens?

Athens was originally ruled by kings, who controlled the surrounding region of Attica. By the eighth century BCE, rule by kings had developed into rule by archons (literally "rulers"). The archons were members of the aristocracy; they each served a particular function in ruling the city, and they arrived at decisions by committee.
In the 630s BCE, an aristocrat named Cylon attempted to overthrow the archons and make himself sole ruler of Athens. The other aristocratic families murdered him, and there was social unrest in the city for a while.
About a decade later, the Athenian citizens asked another aristocrat, Draco, to be their ruler and lawgiver. Draco reformed the existing laws of Athens and codified the new ones so that they could be referred to and enforced by a court. He replaced the small council of archons with the Council of Four Hundred, a group of four hundred citizens who worked with the archons to defend the city and enforce the laws.
Draco was a harsh ruler and was eventually exiled from Athens. Another period of social unrest followed, and the Athenians appointed another ruler, Solon, to revise the laws. Solon established the Athenian Constitution, which included the right of any Athenian citizen to a trial by jury and the selection of officials by lot (at random) to avoid the concentration of power in the hands of any particular group. These were prerequisites for the development of Athenian democracy.
Following Solon's death, there was yet another period of social unrest, at the end of which an aristocrat named Cleisthenes emerged as the ruler of Athens. Cleisthenes enacted yet more reforms to Athenian law and political life, the aim of which was to break the power of the aristocratic families and bring all citizens to the same "level" so that no one man had more power than any other. To prevent any person from acquiring too much power, Cleisthenes invented the practice of ostracism, whereby the citizens could vote to exile a dangerous (or unpopular, or overly powerful) individual from the city for a period of ten years.
The various reforms over the years, and particularly those of Cleisthenes, led to the dissolution of the old rule by archons and the establishment of rule by the citizenry, or assembly (ekklesia), which consisted of all free Athenian men over the age of eighteen. Members of the assembly could vote on any topic that affected the citizenry, including military spending, diplomatic matters (treaties, envoys to other nations), allocation of resources (food and money), and the creation of new laws.
You may find the following resources useful:
Aristotle: The Constitution of the Athenians
The Development of Athenian Democracy
Democracy in the Politics of Aristotle

Take one of the main ideologies and examine how it has changed from its classical form. What practical differences do these changes make? What do you see as the main weaknesses of the contemporary form of this ideology?

You may be referring to ideologies such as capitalism and communism. Capitalism has changed significantly since its conception in the late 1700s with Adam Smith's The Wealth of Nations. For example, while Smith imagined a world of perfect competition, economies of scale created monopolies during the Industrial Revolution. In this situation, larger companies had an advantage in the market over smaller companies, and they often pushed smaller companies out of business. In order to facilitate fairer competition, President Teddy Roosevelt used the power of the federal government and courts to regulate monopolies.
In addition, capitalism in its purest form leads to economic inequality. This inequality has effects on society and is in many ways contrary to the principles of democracy. Therefore, at times in American history, the government has stepped in to curb the excesses of capitalism and create more economic and social equality through policies such as graduated income taxes (in which people who have higher incomes pay a greater percentage of their income in taxes).
While governmental policies have restored some degree of fairness to capitalism, there are still weaknesses in the system. Global capitalism has created even greater forms of inequality, and businesses do not always have to pay for the costs of producing their products. For example, companies' production processes may result in pollution, but companies do not always have to assume these costs. These are problems with the contemporary form of capitalism.

Why didn't the sisters ever marry?

Josephine muses, briefly, whether she and her sister might have married if their mother had lived, suggesting that the lack of a mother may have caused them a loss of maternal influence and perhaps the loss of a person who might have encouraged the women to marry or arranged meetings with possible suitors. This idea is quickly dismissed, however, with the statement that "there had been nobody for them to marry." The late colonel had quarreled with his "Anglo-Indian friends," removing them as prospects for marriage to his daughters and presumably meaning that the daughters had no appropriate social set with which to mingle. Josephine muses that she and her sister "never met a single man except clergymen" and had no idea how one met a man, or even how, having met one, it would be possible to become "more than strangers." The sisters have never been pursued, and they have spent most of their time "looking after father." They have never been taught how to behave in male company, except for that of their father, and even he is a frightening figure in the sisters' minds, someone to be kept out of the way of. Now, their father is dead, and Josephine cannot envisage what will come next for them.

How did Hurricane Katrina affect first responders (police, firefighters, and emts)?

First responders involved in Hurricane Katrina, which struck New Orleans in 2005 and was one of the worst natural disasters in American history, experienced mental health problems following the event. The study below, conducted by Osofsky et al. in 2011, studied 1,382 first responders, including fire fighters, police, emergency medical services workers, and workers from the city. The researchers initially screened the first responders 6 to 9 months after the hurricane. The first responders were screened again 13 to 18 months after the hurricane. 
More than one quarter of the first responders who were surveyed said that they had experienced the following traumatic events: damage to home (93%), witnessing injury or death (70%), and injury caused to a friend (25%). The results also suggested that first responders were suffering as a result of their experiences. At least 10% had significant symptoms related to post traumatic stress, and 25% had significant symptoms related to depression. Many (40%) reported increased use of alcohol and conflict with their partner (41%). With the 18 month follow-up, there was not a significant decrease in symptoms of post-traumatic stress or depression. These results suggest that first responders experienced severe trauma during Hurricane Katrina and its aftermath and that these effects were ongoing following the hurricane.  
 
Source
Osofsky, H.J., Osofsky, J.D., Arey J., Kronenberg, M.E., Hansel, T., & Many, M. (2011). Hurricane Katrina's first responders: the struggle to protect and serve in the aftermath of the disaster. Disaster Med Public Health Prep. September 5, 2011. Suppl 2:S214-9. doi: 10.1001/dmp.2011.53. Epub 2011 Aug 24.

Calculus of a Single Variable, Chapter 5, 5.8, Section 5.8, Problem 37

This function is infinitely differentiable on entire RR. The necessary condition of extremum for such a function is f'(x) = 0.
To find the derivative of this function we need the product rule and the derivatives of sine, cosine, hyperbolic sine and hyperbolic cosine. We know them:)
So f'(x) = cosx sinhx + sinx coshx + sinx coshx - cosx sinhx = 2 sinx coshx.
The function coshx is always positive, hence f'(x) = 0 at those points where sinx = 0. They are k pi for integer k, and three of them are in the given interval: -pi, 0 and pi.
Moreover, f'(x) has the same sign as sinx, so it is positive from -4 to -pi, negative from -pi to 0, positive from 0 to pi and negative again from pi to 4. Function f(x) increases and decreases accordingly, therefore it has local minima at x=-4, x=0 and x=4, and local maxima at x=-pi and x=pi.

What choice does Zaroff give to Rainsford in The Most Dangerous Game, and why is there really no choice at all?

Zaroff, an antagonist who hides his savage evil and bloodlust behind a facade of decorum and sportsmanship, illustrates his true nature by giving every man who becomes stranded on his island a choice. The choice that Rainsford is given is to either submit himself to a twisted game in which Zaroff will participate in an island-wide hunt with Rainsford as the quarry or to be savagely beaten by Ivan, Zaroff's gargantuan assistant.
The choice is truly no choice at all, because either situation results in almost certain death. Zaroff is a master hunter—so skilled that he, by his own admission, has grown bored with hunting any sort of prey besides one capable of reasoning on his level, and Ivan is so prodigiously large and strong that any ordinary man would have no hope of surviving being beaten by him.

The maniacal General Zaroff gives Rainsford the choice to participate in the most dangerous game, where Rainsford will be hunted by the general, or to be tortured to death by Ivan, who served as the official knouter to the Great White Czar. Rainsford does not really have a choice because either option endangers his well-being and he risks dying. According to Zaroff's rules for the most dangerous game, Rainsford will be given a small knife, hunting clothes, moccasins, and a supply of food as he is hunted throughout Ship-Trap Island for three consecutive days. If Rainsford manages to survive the three days, he will be allowed to safely leave the island. If Rainsford refuses to participate in the game and allow Zaroff to hunt him, Ivan will torture him to death. After listening to Zaroff's two options, Rainsford has no other choice than to participate in the game. Fortunately, Rainsford outwits Zaroff and survives the three days on Ship-Trap Island before eventually killing Zaroff in hand-to-hand combat.

For every captured man on Ship Trap Island, Zaroff gives two options of which he has to make a choice. One option is to be hunted down by Zaroff, in a highly lopsided contest, considering Zaroff’s excellent hunting skills and knowledge of all the nooks and crannies on the island. To kind of balance the game, Zaroff equips his prey with supplies on which he can survive during the hunt. He also gives him a three-hour head start before he follows his trail. The hunted man wins the game if he is able to elude the hunter for three whole days. The alternative to this choice is a flogging by the giant Ivan. Rainsford is given these options and chooses to be hunted down by Zaroff. However, he is treated in a better manner than the other captured men, who are held in a cellar, which Zaroff refers to as his “training school”, before the hunt.
In Zaroff’s own words, he was yet to lose a hunt on Ship Trap Island, thus playing his quarry is really not a choice as one is sure to lose the game. However, the alternative is even worse as the chance of living through a whipping in the hands of Ivan is quite low.
As the story goes, through many strategies, Rainsford kills one of Zaroff’s best dogs, kills Ivan, and finally kills the general himself.

General Zaroff gives Rainsford a choice between two awful potentials.  Zaroff explains to Rainsford that he gives the men that are trapped on his island a choice.  They can either be whipped to death by Ivan, or they can attempt to survive Zaroff's hunting for three days.  General Zaroff gives Rainsford the exact same choice.  
For most men, the choice really isn't a choice at all.  Thus far, no matter what each man chooses, the end result has been the same.  Death.  The only difference is that choosing to be hunted might give a man a few extra hours of life.  Rainsford chooses to take his chances on the hunt instead of a guaranteed death from Ivan.  Rainsford's choice winds up being a good choice for Rainsford because Rainsford evades Zaroff and eventually ends up killing Zaroff.  

Calculus of a Single Variable, Chapter 7, 7.2, Section 7.2, Problem 19

For the region bounded by y=x ,y=0 , y=4 and x=5 and revolved about the line x=5 , we may also apply the Shell method. we are to use two sets of vertical rectangular strips parallel to the line x=5 (axis of revolution). In this case, we need two sets of rectangular strip since the upper bound of the rectangular strip before and after x=4 differs.
We follow the formula: V = int_a^b 2pi * radius*height*thickness
where:
radius (r)= distance of the rectangular strip to the axis of revolution
height (h) = length of the rectangular strip
thickness = width of the rectangular strip as dx or dy .
As shown on the attached file, both rectangular strip has:
r=5-x
h= y_(above) - y_(below)
thickness =dx
For the rectangular strip representing the bounded region from x=0 to x=4, we may let:
h = x -0 = x
For the rectangular strip representing the bounded region from x=4 to x=5 , we may let:
h =4 -0 = 4
Plug-in the values correspondingly, we get:
V = int_0^4 2pi*(5-x)(x) dx +2piint_4^5 (5-x)(4) dx
or
V =2pi int_0^4 (5-x)(x) dx +2piint_4^5 (5-x)(4) dx
For the first integral, we solve it as:
2pi int_0^4 2pi*(5x-x^2) dx
= 2pi * [ 5x^2/2 -x^3/3]|_0^4
= 2pi * [ (5(4)^2/2 -(4)^3/3) - (5(0)^2/2 -(0)^3/3)]
= 2pi * [ (40 - 64/3) -(0- 0)]
= 2pi * [ 56/3]
= (112pi)/3
For the second integral, we solve it as:
2pi int_4^5 2pi*(20-4x) dx
= 2pi * [ 20x -4x^2/2]|_4^5
= 2pi * [ 20x -2x^2]|_4^5
= 2pi * [ (20(5) -2(5)^2) - (20(4) -2(4)^2)]
= 2pi * [ (100 - 50) -(80-32)]
= 2pi * [ 50 -48]
= 2pi*[2]
=4pi
Combing the two results, we get:
V=(112pi)/3+4pi
V=(124pi)/3 or 129.85 ( approximated value).
We will get the same result whether we use Disk Method or Shell Method for the given bounded region on this problem.

who is Redpenny

Redpenny is a medical student and all-round dogsbody for Dr. Ridgeon. He acts in the capacity of the doctor's laboratory assistant as well as dealing with his voluminous correspondence. The latter is a particularly onerous responsibility given the enormous demand for the doctor's revolutionary new cure for tuberculosis. Redpenny is somewhat immature and idolizes Dr. Ridgeon, believing him to be a scientific genius. As such, he's more than willing to perform any little task for his hero, no matter how menial or tedious.
Though a very minor character in the play, Redpenny epitomizes the unthinking hero-worship often bestowed upon doctors and men of science, especially in the late 19th and early 20th centuries. Society has given Dr. Ridgeon the responsibility to determine precisely who should and should not receive the new cure for tuberculosis he's developed. The doctor's effectively been given the right to play God, and Redpenny is one of his most devoted worshipers.

What private request does Hamlet make of one of the players? What does Hamlet plan to add to the play?

Hamlet first asks the player if the troupe of actors can perform The Murder of Gonzago. He then asks him the following:

We’ll ha ’t tomorrow night. You could, for a need, study a speech of some dozen or sixteen lines which I would set down and insert in ’t, could you not?

The player says he could do that.
The lines Hamlet inserts are lines meant for Claudius's ears, implicating him as the murderer of Hamlet's father. Hamlet wants to watch Claudius's reaction and see if he shows guilt when the lines are recited.
Hamlet is using the empirical method: running an experiment to determine whether the ghost is telling the truth about Claudius or if the ghost is really a devil sent by Satan to tempt him to murder an innocent man.
Ironically, Claudius has been happy about Hamlet's interest in these traveling actors, believing they are helping to rouse his stepson from his melancholic lethargy. If he knew the reasons motivating Hamlet, though, he would not be so happy.

Technically, Hamlet makes two requests of the player: he first asks the actor to put on a play called The Murder of Gonzago and then asks whether he would be able to memorize and insert a short speech (roughly a dozen lines) that Hamlet himself will provide (2.2.563–569).
A few scenes later, of course, Hamlet makes many more demands of the players, specifying in detail how he wants them to perform the speech. His anxiety is understandable, though, given his reasons for adding the speech in the first place: Hamlet has tailored the play to more closely resemble his father's ghost's description of his own murder. By watching Claudius's reactions to the play—particularly the scene in which the murderer pours poison in the king's ear and then courts the widowed queen—Hamlet hopes to prove his uncle's guilt once and for all. The plan works in a sense because Claudius is visibly shaken and runs from the room, but Hamlet's plans to avenge his father are delayed by subsequent events, including his own killing of Polonius.

What kind of relationship do Nora and Helmer have? How would you analyze such a relationship in the context of the story?

Nora herself describes her relationship with Torvald by saying to Torvald that she is "no wife" for him; she is only his "doll" (Act 3).
One of the reasons that Nora contends that she is not a wife to Torvald is the fact that her husband does not appreciate how she has saved his life; instead, he scolds his wife for her crime of forgery and the public embarrassment it has brought him. In Act 3, when she talks with her husband seriously after the party has ended and he has read Krogstad's letter, he calls Nora a "criminal" and a "hypocrite," and he doesn't have any appreciation for her sacrifices to repay the loan.
Nora's forgery is the leading cause of Torvald's ire and her desire to leave him. Because of his lack of appreciation for her saving his life, she also resents his treating her as though she were a child, such as when he forbade her to eat macaroons or scolded her for being a spendthrift. But, whenever he was pleased with her as his "doll," who gave him pleasure, he would call her pet names. She tells him, "You never loved me––...You only thought it was fun to be in love with me" (Act 3). Further, Nora objects to the law that prohibited her from trying to "spare her dying old father or save her husband's life!" (Act 3).
Finally, Nora tells Torvald that she must learn about the society in which she lives. "I have to make up my mind who is right, society or I." (Act 3) Then, she leaves her home and children, saying goodbye to her husband.

What is Holden desperate for?

The answer to this question is not entirely straightforward as Holden seems desperate for quite a few things.
Holden is desperate for authenticity. He expresses his frustration with phony people and their phony behaviors throughout the entirety of the novel. Holden's sister Phoebe is special to him because she isn't phony at all, and perhaps it is her youth that prevents her from being this way.
Holden is also lonely, so he may be desperate for company, but not just any company. He is a rather discriminating character, which means that Holden is selective about his friends and whom he can trust, and people often let him down. Holden is desperate for real friendship and connection.
From an outsider's point of view, Holden might also be desperate for a good therapist who can talk his language and understand him for all of his emotionally intelligent complexity. Without a doubt, Holden has dealt with a lot of difficulty in his young life, between the death by leukemia of his beloved brother to being abused sexually by a trusted adult. His relationship with his parents is challenging and he acts out in worrying ways. He thinks about suicide. All of these reasons might lead someone who knows Holden well to think he desperately needs professional help.

Calculus: Early Transcendentals, Chapter 7, 7.4, Section 7.4, Problem 25

int(4x)/(x^3+x^2+x+1)dx
To solve, apply the partial fraction decomposition.
To do so, factor the denominator.
int(4x)/(x^3+x^2+x+1)dx = int(4x)/((x+1)(x^2+1))dx
Then, express the integrand as sum of proper rational expressions.
(4x)/((x+1)(x^2+1))=A/(x+1)+(Bx+C)/(x^2+1)
Multiply both sides by the LCD.
4x =A(x^2+1)+(Bx+C)(x+1)
4x = Ax^2+A + Bx^2+Bx+Cx+C
4x=(A+B)x^2+(B+C)x + A+C
Express the left side as a polynomial with degree 2.
0x^2+4x+0=(A+B)x^2+Cx+A+C
For the two sides to be equal, the two polynomials should be the same. So set the coefficients of the two polynomials equal to each other.
x^2:
0=A+B (Let this be EQ1.)
x:
4=B+C (Let this be EQ2.)
Constant:
0=A+C (Let this be EQ3.)
To solve for the values of A, B and C, isolate the A in EQ1 and the C in EQ2.
EQ1:
0=A+B
-B=A
EQ2:
4 = B + C
4 - B = C
Plug-in them to EQ3.
EQ3:
0=A+C
0=-B+4-B
0=-2B+4
-4=-2B
2=B
And, plug-in the value of B to EQ1 and EQ2.
EQ1:
0 =A + B
0=A+2
-2=A
EQ2:
4=B+C
4=2+C
2=C
So the partial fraction decomposition of the integrand is:
(4x)/(x^3+x^2+x+1) = -2/(x+1) + (2x+2)/(x^2+1)=-2/(x+1)+(2x)/(x^2+1)+2/(x^2+1)
Then, take the integral of it.
int (4x)/(x^3+x^2+x+1)dx
=int (-2/(x+1)+ (2x)/(x^2+1) + 2/(x^2+1))dx
=int -2/(x+1)dx + int(2x)/(x^2+1)dx + int2/(x^2+1)dx
=-2ln|x+1| + ln|x^2+1|+2tan^(-1)(x) +C

Therefore, int (4x)/(x^3+x^2+x+1)dx=-2ln|x+1| + ln|x^2+1|+2tan^(-1)(x) +C .

Two black holes of mass m=10M_s are traveling at 80% the speed of light and collide head on and merge into a new black hole. If M_s is the mass of our sun, what is the mass of the black hole?

We must apply conservation of relativistic 4-momentum, P^(mu)=[E_(t o t)/c,p] . Where p=gamma*mv is the relativistic spatial momentum.
P_i^(mu)=P_f^(mu)
P_(i,1)^(mu)+P_(i,2)^(mu)=P_f^(mu)
[E_(m,t o t)/c,gamma*mv]+[E_(m,t o t)/c,gamma*m(-v)]=[E_( t ot)/c,0]
Notice the first two black holes have the same momentum but are traveling in the opposite direction. The final black hole has no spatial momentum. Setting the spatial components equal to each other is redundant, so set the zeroth energy components equal to each other.
E_(m,t o t)/c+E_(m,t o t)/c=E_(t o t)/c
2E_(m,t o t)=E_(t o t)
We can use the equation:
E_(m,t o t)=gamma*mc^2
Where gamma is the lorentz factor, for the initial black holes it is:
gamma=1/sqrt(1-v^2/c^2)=1/sqrt(1-(0.8c)^2/c^2)
gamma=5/3
gamma=1 when the object is at rest.
2E_(m,t o t)=E_(t o t)
2gamma*mc^2=Mc^2
Where M is the mass of the final black hole.
2gamma*m=M
Then the final mass of the black hole M is equal to:
M=2gamma*m=2(5/3)(10M_s)~~33.3M_s
This is not merely the sum of the initial two masses. A huge amount of kinetic energy was converted into the final mass and therefore relativity was essential in in the treatment of this problem.
https://en.wikipedia.org/wiki/Lorentz_factor

What is your reaction to Junot Díaz’s “How to Date a Browngirl, Blackgirl, Whitegirl, or Halfie”? Did you enjoy reading the story?

The question is ultimately an opinion question.  As long as you state your opinion and clearly defend why you think what you think, then you are good to go.  
I remember reading this story the first time, and my response was typical of what I see from my students when I have them read this story.  Our initial response is a blend of shock and disgust because of the narrator's unflinchingly blunt description of his tactics to have a girl over and hope for sex.

 If she's a white girl, you know you'll at least get a hand job.  

What's clear at the beginning of the story is that the narrator believes that he has to hide his ethnic background and poverty in order to have the best chances with a girl.  That's why he opens the story with narration about needing to hide the "government cheese."  As the story continues, readers come to see that the narrator also believes that he has to act a certain way in order to impress a girl of a certain race.  The narrator is a chameleon that is willing to transform himself for possible romantic activities.  

Tell her that you love her hair, that you love her skin, her lips, because, in truth, you love them more than you love your own.
She'll say, I like Spanish guys, and even though you've never been to Spain, say, I like you. You'll sound smooth.

The narrative is also offensive because it simply doesn't ever emphasize the fact that girls, of all races, are individual people with their own likes and dislikes.  The narrator simply describes that all girls of one race like things a certain way, and all girls of another race like something different.  That kind of blanket stereotype is crazy.  
To answer the second part of the question, no I didn't like reading this story the first time through it.  I found the narrator's attitude about women offensive, and I thought he was a coward for not trying to "be himself."  Of course my attitude about this story has changed as I have become more familiar with the narrator.  I'm still offended by his thoughts and attitude regarding women and races, but I find his narration much funnier now.  Each time I read the story, I can't help but feel that the narrator is completely full of faked bravado.  He sounds like he knows what he is talking about, but I now believe that the narrator is faking his confidence and pantomiming the actions that he has heard are supposed to work on girls.  

Don't panic. Say, Hey, no problem. Run a hand through your hair like the white boys do . . . 

It's like he's trying too hard to be cool, and that is why my feelings about this story have changed from my initial feelings.  

College Algebra, Chapter 4, 4.5, Section 4.5, Problem 10

a.) Find all zeros of $P(x) = x^4 - x^2 - 2$ of $P$, real and complex

b.) Factor $P$ completely.



a.) We first factor $P$ as follows.


$
\begin{equation}
\begin{aligned}

P(x) =& x^4 - x^2 - 2
&& \text{Given}
\\
\\
=& (w - 2)(w + 1)
&& \text{Factor}
\\
\\
=& (x^2 - 2)(x^2 + 1)
&& \text{Substitute } w = x^2

\end{aligned}
\end{equation}
$


We find the zeros of $P$ by setting each factor equal to :

Setting $x^2 - 2 = 0$, we get $x^2 = 2$ is a zero. More over, setting $x^2 + 1 = 0$, we get $x^2 = -1$, so $x = \pm i$ is a zero. Hence, the zeros of $P$ are $\sqrt{2}, - \sqrt{2}, i$ and $-I$.

b.) By complete factorization,


$
\begin{equation}
\begin{aligned}

P(x) =& (x - \sqrt{2}) \left[ x - \left( - \sqrt{2} \right) \right] [x - i] \left[ x - (-i) \right]
\\
\\
=& \left(x - \sqrt{2} \right) \left( x + \sqrt{2} \right) (x - i) (x + i)

\end{aligned}
\end{equation}
$

Why does Priscilla reject Miles Standish?

"The Courtship of Miles Standish" is a narrative poem written by Henry Wadsworth Longfellow in the year 1858. It is set in the time of early colonists of North America and in an environment of conflict between Native Americans and the pilgrims who settled in Plymouth. Additionally, the story is centered on a love triangle.
Miles Standish, our titular character, and his friend John Alden are both in love with a "Puritan maiden" named Priscilla. In fact, in the beginning, Miles is unaware that John also loves Priscilla, and he asks John to propose to Priscilla on his behalf. Priscilla tells John that because Miles did not make the proposal himself and has never before shown Priscilla that he loves her, she will not marry him. In her own words:

If the great Captain of Plymouth is so very eager to wed me,
Why does he not come himself, and take the trouble to woo me?
If I am not worth the wooing, I surely am not worth the winning!

Additionally, she later says:


This is not right nor just: for surely a woman's affection
Is not a thing to be asked for, and had for only the asking.
When one is truly in love, one not only says it, but shows it.
Had he but waited awhile, had he only showed that he loved me,
Even this Captain of yours — who knows? — at last might have won me,
Old and rough as he is; but now it never can happen.

However, it is pretty clear that Priscilla's main reason for rejecting Miles is that she would rather receive a proposal from John, especially shown when she asks "Why don’t you speak for yourself, John?"

What does the Bicentennial Man have to do to finally be accepted as a man?

Andrew the robot no longer wants to be a servant. He's no ordinary robot and wants to be a human. After he purchases his freedom, he tries as much as possible to make his dream come true. But at every attempt he makes, he is rebuffed by society. No matter how hard he tries to talk, act, and dress like a human, he will never be accepted as one. This is a society that still looks upon robots as inferior to humans, and the abuse of robots is widespread.
So it's not surprising that Andrew chooses to undergo a risky operation that will effectively turn him into a human, albeit one that will live to the ripe old age of 200. Yet even after the operation, society still won't formally accept him as a human. It's only when Andrew goes before the World Legislature and declares that he's sacrificed his positron brain so that, just like a human brain, it will decline over time, that he's finally, and officially, declared a man.

How does the story compare to a safari or journey today?

"A Sound of Thunder" is very different from a modern-day safari trip, hunting trip, fishing trip, etc. in one major way. Modern day vacationers are not capable of traveling back in time. That means modern-day trips do not include hunting dinosaurs. Other than that major difference, the trip in the story is very similar to hunting trips or fishing expeditions that I have been on. In modern times and in the story, people pay a fee in order to go on a guide-led trip. The guide(s) serves as the expert on when and where to go, and he/she takes the paid group members to a spot that will hopefully maximize results. Just like in the story, modern-day hunters or fishermen are not allowed to shoot and kill indiscriminately anything that moves. Only certain species are allowed to be shot or fished, and at times the prey have to be a certain age or even sex. This is why Travis was along. He had to ensure the men on the time safari only killed the dinosaur that had been previously scouted.

College Algebra, Chapter 1, 1.1, Section 1.1, Problem 50

The equation $\displaystyle \frac{1}{x} - \frac{2}{2x+1} = \frac{1}{2x^2 + x} $ is either linear or equivalent to a linear equation. Solve the equation

$
\begin{equation}
\begin{aligned}
\frac{1}{x} - \frac{2}{2x+1} &= \frac{1}{2x^2 + x} && \text{Get the LCD}\\
\\
\frac{\cancel{2}x+1 - \cancel{2}x}{x(2x+1)} &= \frac{1}{2x^2 + x} && \text{Combine like terms}\\
\\
\frac{1}{2x^2+x} &= \frac{1}{2x^2+x}
\end{aligned}
\end{equation}
$


It shows that the equation on the left side is equal to the equation on the right side and that every value of $x$ is a solution. So the two equations will have the same graph.

McDougal Littell Algebra 2, Chapter 5, 5.2, Section 5.2, Problem 33

1. First, let's identify the a, b, and c in trinomial. aq^(2)+bq+c
a=1
b=-7
c=-10
We shouldn't be to concerned about 'a' since it is 1. And, 'b' is what the 2 numbers have to add up to. Last, but not least, 'c' is what the two factors need to multiply up to.
2. We now have to find 2 numbers whose product equals -10 and sum is -7. List out a couple combinations until you find your match.
(-10)(1)=-10 ; -10+1=-9
(5)(-2) = -10 ; 5+(-2)=-3
(-2)(5)= -10 ' -2+5=3
(-1)(10)=-10 ; -1+10=9
However, after listing out the possible combinations, there is no perfect match. Therefore, this equation is not factorable.

What other endings could Ray Bradbury have used in Fahrenheit 451?

In Ray Bradbury's Fahrenheit 451, the nation has changed. Books are now outlawed. If robot-sniffing dogs smell out books in homes, firefighters break in and burn the homeowner's possessions. Montag is one of the firefighters responsible for the book burnings.
His view begins to change when he meets his young neighbor. Her ideas are hard to ignore. When he watches an elderly homeowner burn herself rather than face the loss of her books/freedoms, he starts to question his job. He steals one of her books and brings it home. The problem is that new short attention spans lead to abbreviated books and this full-length book is too hard for him.
Montag seeks the help of an elderly man who was an English professor. The problem is his own wife reports him for having books, and he's ordered by his chief to burn them. He can't do it and sets his chief on fire instead. He's now on the run and meets up with a group of drifters, who also love books and memorize them on the chance future generations embrace books. The group watches as their city is leveled with nuclear weapons.
Fahrenheit 451's ending finds the groups having a meal and planning to return to the city to start anew.
There are many other ways Ray Bradbury could have ended Fahrenheit 451. The group could have given up on the city and started a journey to a new land/area where they would start anew. Montag could have not killed his chief and died in the nuclear bombing. He could have never taken the book from the elderly woman's home in the first place and kept burning books. The question is what would the reader have learned if the book had not ended with plans to form a new world.

College Algebra, Chapter 8, 8.4, Section 8.4, Problem 10

Find the center, foci, vertices and asymptotes of the hyperbola $\displaystyle (y + 5)^2 = -6x + 12$. Sketch its graph.

We can rewrite the equation as $(y + 5)^2 = -6 (x - 2)$. This parabola opens to the left with vertex at $(2, -5)$. It is obtain from the parabola $y^2 = -6x$ by shifting 2 units to the right and 5 units downward. Since $4p = 6$, we have $\displaystyle p = \frac{3}{2}$. So the focus is $\displaystyle \frac{3}{2}$ units from the left of the vertex and the directrix is $\displaystyle \frac{3}{2}$ units to the right of the vertex.

Therefore, the focus is at

$\displaystyle (2, -5) \to \left( 2 - \frac{3}{2}, -5 \right) = \left( \frac{1}{2}, -5 \right)$

and the directrix is the line

$\displaystyle x = 2 + \frac{3}{2} = \frac{7}{2}$

What are the problems of human relations in business?

Although some analysts can try to reduce business issues to a matter of numbers, much of the success of businesses depends on human relations.
First, human relationships are central to human resource management. Hiring and retaining good employees isn't just a matter of salary and benefit packages. Employees who dislike the human side of their work environment will search for other jobs and might perform below peak efficiency in their current roles. Effective management practices also take into account fostering productive collegial relationships.
Next, customer relationships are ultimately human relationships. Everything from brand loyalty to repeat business depends on establishing good relationships with customers. The ubiquity of social media tends to amplify the effects of good or bad relationships with customers, as a single rude or unpleasant interaction can end up going viral and having a negative effect on your company's reputation. 
To foster good human relationships and avoid problems, companies should train employees in issues such as cross-cultural communications and sensitivity to different cultures to avoid inadvertently offending people. 

What happens on the final legs of Vladek's journey?

The final legs of Vladek's journey during and after the Holocaust take place in Maus II. Vladek tells his son—the author of the book, Art—that he was transferred to Dachau. At this point, he has been separated from his wife Anja. They find ways to stay in touch though when Vladek acquires a job that takes him to Anja's camp for work. As he is throughout the Holocaust and even before the family is taken to the camps, Vladek is very resourceful in helping himself and his wife survive. The conditions are awful, but Vladek persists and finds ways to turn horrible elements of his environment to his advantage. Also in the second book, Vladek tells Art how the Nazis take the prisoners on the Death Marches. Many prisoners die on the journey, but Vladek is able to survive. Once the war is over and Vladek has been freed, he must make his way home, and it takes longer than we might expect, but he is eventually reunited with Anja. Unfortunately, both Vladek and Anja have lost most of their family members, including their son Richieu.

what do the crack up and winter dreams by f scott fitzgerald have in common

Both of these works by Fitzgerald deal with "disillusionment," the experience of seeing a false idea or belief that one has cherished over a period of time being destroyed. Though it is a frequent theme in literature, Fitzgerald deals with it in an especially striking and personal way, and there are, unsurprisingly, connections between his treatment of it in these two pieces and in his novels and other short stories.
In "Winter Dreams," Dexter is haunted by not just Judy Jones herself but the image he has created of her. He loves her but is aware of her shallowness, and yet at the end of the story when it's revealed to him that Judy has apparently lost her striking beauty and is stuck in an abusive marriage, his illusion bursts like a bubble. Judy is essentially another version of Daisy in The Great Gatsby. One can include her among people who, as Nick says of Daisy and Tom, "smashed up things," caring little about the consequences. Like Gatsby, Dexter is a social climber, a man from (like Fitzgerald himself) a middle-class, northern Midwestern background who aspires to join the upper crust of society. Dexter becomes a success in business but feels incomplete, even with his engagement to the obviously right-for-him Irene. When he falls for Judy again, he torpedoes, without any real regret, his engagement to Irene and the spiritual comfort it might have given him.
"The Crack-up" deals with the exploding of an illusion, but on a deeper, more transcendent level. Fitzgerald recounts in honest detail the mid-life crisis he experiences after fifteen years as a successful writer. (Eighty years ago, people who were thirty-nine years old did actually think of themselves as being in the "middle" of life.) It is a spiritual self-reckoning compounded by the external changes in the artistic world of the time, in which film is becoming the dominant art form and replacing Fitzgerald's craft, writing. Fitzgerald gives the impression, like Dexter, of having lived in a dream world that collapses when he comes face to face with a new reality. And yet, unlike in "Winter Dreams" where the reality is the end of one's obsession with a woman, Fitzgerald never gives a single, definite explanation of why the crack-up occurs. In all his descriptions, however, there are two statements which to me stand out above the others: "I saw that for a long time I had not liked people and things, but only followed the rickety old pretense of liking;" and "...in a real dark night of the soul it is always three o'clock in the morning, day after day." This is a man confronting an existential dilemma. The incidental things that Fitzgerald mentions as contributing to the crack-up: the exhaustion, the concerns about his health, his annoyance with the trivialities of the world surrounding him like the sound of the radio and the advertisements in the magazines, and the backfiring advice of the woman in his life—these are all symptoms of a more fundamental feeling of insufficiency, of emptiness at the core of a man's life. It's tragic that after writing "The Crack-up" Fitzgerald had only a few short years to live and not enough time to overcome this feeling.
In both "Winter Dreams" and "The Crack-up," dealing as they do with the collapse of illusion, Fitzgerald leaves open the answer to the usual problem of "the meaning of life." In these works, as in his "The Curious Case of Benjamin Button," where a man lives his life backward from old age to the cradle, we are left, after considering the details of each story, with the question, "what was the point of it all?"—apart from the basic fact that life is what it is.

What is the hook in A Wrinkle in Time?

A hook is what makes us curious and keeps us reading in the opening pages of a story. In the first few pages of A Wrinkle in Time, we're introduced to an important story arc, the disappearance of Meg's father, which, of course, makes us curious and drives the rest of the plot. But I would argue that the more important initial story hook is the more generalized sense of mystery, of which the missing father is only a part. Opening with "it was a dark and rainy night" is a cliche, but also signals a mystery, as does Fortinbras's barking, which he only does when a stranger is approaching the house. Then there's feisty Meg feeling like a misfit, the mysterious little brother Charles Wallace waiting for Meg in the kitchen, and the glamorous mother. In a story that's as much about the characters as the adventure, it is ultimately our curiosity about the unusual but close-knit family and what is going to happen to them that hooks us and keeps the pages turning.

Discuss ways in which Homer uses everyday details of Greek life to enhance his tale and give it a familiar feel for his audience.

One key way that Homer employs everyday details in telling his stories is through comparing great actions to day-to-day ones through extended metaphors. (Important terms to know about metaphor include tenor, that is, the literal situation that the writer or speaker is describing, and vehicle, that is, the situation to which it is being compared.) A normal metaphor would be something like "her boyfriend is a clown." The boyfriend (the tenor) is not literally making a living as a clown (the vehicle.) However, he is like a clown because he is a fool or is very funny, depending on the situation. If I were to say, "Her boyfriend is like a clown who trips over his own feet, knocks someone else over, and runs away laughing," you would know that I meant he was a fool. This is an example of an extended metaphor; it is when the writer or speaker expands on the situation described in the basic metaphor to tell you more about the item or situation that is the tenor.
To return to Homer: Homer uses extended metaphors in which the great happenings of the Trojan War or of Odysseus's heroic journey are the tenor, and everyday details are the vehicle. For example:

As ravenous wolves come swooping down on lambs or kids
to snatch them away from right amidst their flock, all lost,
when a careless shepherd leaves them straggling down the hills
and quickly spotting a chance the wolf pack picks them off,
no heart for the fight, so the Achaeans mauled the Trojans.

Homer's hearers might not ever have seen an army destroying another army, but they would be very familiar with the situation Homer describes involving the wolves, the lambs, and the shepherd. This detailed description of a familiar event would allow them to envision something they had never seen before. It is not that the extended metaphors and the daily details they involve make the story itself feel familiar to the listeners; rather, Homer makes use of the familiar to engage his audience's imagination and allow them to see the grand events he is describing—to "enhance his tale," as you say.

Intermediate Algebra, Chapter 4, 4.2, Section 4.2, Problem 42

Solve the system of equations $\begin{equation}
\begin{aligned}

4x + y - 2z =& 3 \\
\\
x + \frac{1}{4}y - \frac{1}{2}z =& \frac{3}{4} \\
\\
2x + \frac{1}{2}y - z =& 1

\end{aligned}
\end{equation}
$. If the system is inconsistent or has dependent equations, say so.

Multiplying each side of equation 2 by $4$ gives equation 1, so these two equations are dependent. Equation 1 and equation 3 are not equivalent, however, multiplying each side of equation 3 by $\displaystyle \frac{1}{2}$ does not give equation 1. Instead, we obtain two equations with the same coefficients, but with different constant terms. Thus, the system is inconsistent and the solution set is $\cancel{0}$.

What is the Giver's favorite memory?

The answer to this question can be found in chapter 16 of The Giver. Jonas actually asks what the Giver's favorite memory is, but then he quickly backpedals and says that the Giver doesn't have to give it to him yet. 

"What is your favorite?" Jonas asked the Giver. "You don't have to give it away yet," he added quickly. "Just tell me about it, so I can look forward to it, because I'll have to receive it when your job is done." 

The Giver responds by saying that he would be happy to share his favorite memory with Jonas. The memory that he shares is a memory of a family at Christmas time. The memory contains a fire in the fireplace, candles on the table, snow falling outside, and lights on a tree that is inside the house. Jonas finds that last detail a bit odd, but that doesn't stop him from thoroughly enjoying the general feeling of the entire memory. Jonas witnesses the family sitting together and enjoying the company. The Giver asks Jonas what he felt, and Jonas describes two specific things. He explains that he felt "warmth" and "family." Jonas also says that he experienced a third feeling that he can't quite describe. The Giver tells him that the feeling is love, and the concept is completely new to Jonas.

"I certainly liked the memory, though.  I can see why it's your favorite. I couldn't quite get the word for the whole feeling of it, the feeling that was so strong in the room." 
"Love," the Giver told him. 
Jonas repeated it. "Love." It was a word and concept new to him. 

Why were the Articles of Confederation not successful?

After the colonists won their independence from Great Britain, they didn’t want to create a federal government that had too much power. As a result, the federal government was a fairly weak institution.
The federal government could not do many things. For example, the federal government could not levy taxes. Thus, it was difficult for the federal government to pay its debts. Since there was no central bank, too much money was printed, causing inflation to occur. Besides the federal government, each state also was able to print money.
The federal government couldn’t make people join the military. As a result, the federal government struggled to deal with aggressive actions that other countries took toward the United States. The Spanish and British interfered with American trade. The British wouldn’t leave forts in the western lands that belonged to the United States. The American military was not in a position to deal with these actions by other countries.
The federal government also had trouble dealing with uprisings within the country. When Shays' Rebellion occurred, it was the state militia of Massachusetts that ended the rebellion, not the American army.
There also was no court system. As a result, there was no place that states could go to resolve disputes that they had with each other.
http://ushistoryscene.com/article/articles-of-confederation/

https://www.history.com/topics/early-us/shays-rebellion

https://www.thoughtco.com/why-articles-of-confederation-failed-104674

When and where was Helen born? What do you know about her family?

Helen Keller was born in the small town of Tuscumbia, Alabama.  It was located in the northern part of the state.  She was born on June 27th in the year 1880.
In her autobiography, The Story of My Life, Helen describes her family background in detail.  Her father was Arthur H. Keller, a Confederate captain turned newspaper editor.  He had been married with children previously, before he had become a widower.  Later, he married the young Kate Adams.  With Kate, they had Helen.  
Casper Keller was a relative of Helen Keller.  He originally hailed from Switzerland before moving to Alabama.  It was through him that Helen was related to"the first teacher of the deaf in Zurich... [who] wrote a book on the subject of their education" (Chapter 1).  Helen found this fact to be "rather a singular coincidence; though it is true that there is no king who has not had a slave among his ancestors, and no slave who has not had a king among his."  She recognized the importance of her ancestor's contributions to the education of the deaf.  Some of these contributions later helped her.  Helen also wrote about her grandparents and other relations who she was descended from.

In what kind of situation is the reputational method the most useful for determining social class?

There are three basic methods that sociologists use to measure social class. These are the objective method, the subjective method and the reputational method. The objective method uses a strict set of data points and criteria for determining class. This often includes income, education and career type. The subjective method asks people what social class they think that they fit into, relying only on the subjects self-perception. The reputational method is based on what class other members of the same social group think that subject belongs to. Often a small set of group members are selected by sociologists to rank the other group members in terms of class relative to the group.
Each of these methods have different situations for which they are useful. The reputational method is most useful in figuring out the social structure of small groups where members of the population know each other. The closer in relationship the members of a community are, the more accurate the class findings. This is a way of understanding the social class of a subject as seen by other members of the same community. While this may differ from how a subject sees himself or herself, it is more reliable than the subjective method when investigating rolls and stratifications within a community as a whole. 
http://www.mccc.edu/pdf/soc101/soc101%20chap%2010.pdf

How is the pelvis of a female different from a male pelvis?

The female pelvis is different from the male pelvis in terms of structure. Usually, the female pelvis is larger and broader, due to a need to facilitate childbirth, while the male's is narrow, long, and more compact. Another difference is found in the distance between the ischium bones—this distance is small in the male pelvis and relatively large in the female pelvis. This difference results in different shapes for the pelvis inlet: the male's is heart-shaped, while the female's is oval. Another notable difference lies in the angle between the inferior pubic rami: 70 degrees for the male pelvis and between 90 and 100 degrees for the female pelvis. Another difference lies in the hip sockets, where the head of the femur fits: the acetabula of the female pelvis are farther apart and more medially located than the male's.
https://courses.lumenlearning.com/boundless-ap/chapter/the-hip/

The pelvis comprises of three bones: the hip bones, the sacrum, and the coccyx. The male and female pelvis differ in several ways in terms of structure and function. To begin with, the male pelvis is smaller and narrower for the purpose of supporting a stronger muscle structure as well as a heavy male body build. The situation is different for the female pelvis, which is wider and larger to enable childbearing.
In terms of structure, whereas the male pelvic bone is heavier and thicker, that of females is denser and thinner. The pubic arch, formed after the fusing of pelvic bones, is V-shaped in males but wider in females. Also, while the coccyx in the male pelvis is projected inwards and rigid, the female one is straighter and more flexible to aid the delivery process. In order to create more space in the pelvic cavity, the female sacrum is shorter, wider, and less curved. That of males is longer and narrower.
https://healthfully.com/the-male-female-pelvic-differences-4423397.html

https://radiologypics.com/2013/04/03/differences-between-male-female-pelvis/

https://www.ncbi.nlm.nih.gov/pubmed/19453039

Who is Tariq in A Thousand Splendid Suns most similar to in The Kite Runner and The Thorn Birds?

I would argue that Tariq is most similar to Dane in The Thorn Birds and Hassan in The Kite Runner.
In A Thousand Splendid Suns, Tariq is the quintessential hero, courageous and always ready to defend those he loves. We get a glimpse of Tariq's fierce loyalty in Part Two, Chapter 18. When Khadim squirts urine all over Laila, Tariq confronts the bully. He takes off his prosthetic leg and beats Khadim with it while hopping on his one good leg. In Part Two, Chapter 25, Tariq fully demonstrates his capacity for loyalty when he pledges to return for Laila, even after she rejects his offer to marry.
There is no bitterness in Tariq because he understands Laila's reasons for rejecting him. He knows that Laila can't "wipe away the obligations of her life" any more than he can his. Tariq's ability to love, forgive, and trust exemplifies his moral stature.
Later, in Part Three, Chapter 44, we get further glimpses of Tariq's sterling nature. At the refugee camp in Nasir Bagh, Tariq's father dies, and his mother almost succumbs to pneumonia. Determined to save his mother from further suffering, Tariq does everything he can to secure employment. His main purpose is to earn enough so that he can move his mother into an apartment in Peshawar, preferably one that has "heating and clean water." However, no one will hire Tariq because of his crippled leg. In the end, Tariq takes on a dangerous job which lands him in prison.
Despite his difficult life, Tariq continues to stay positive. Even when he discovers that his Laila is a married woman, he betrays no ill-will towards the woman he loves. He understands why Laila married Rasheed, and his only regret is that he had to leave Laila behind years ago.
In The Thorn Birds, Dane is most similar to Tariq. Dane is an interesting character, actually. He is morally idealistic and fiercely committed to his Catholic faith. Like Tariq, he harbors deep convictions about life, truth, and religion. While Tariq is obviously Muslim and Dane is Catholic, both are similar in the sense that both are able to love unequivocally and without judgment. Both men are also willing to sacrifice their own comfort for others. In The Thorn Birds, Dane is also the perfect brother to Justine: he's supportive and loving. He loves his sister without reservation.
At the end of the novel, Dane dies of a heart attack after he valiantly saves two German women from drowning. Essentially, Dane made the ultimate sacrifice to his God. While Tariq doesn't die in A Thousand Splendid Suns, he and Dane share a compelling character trait: both are self-sacrificial in nature.
In The Kite Runner, Hassan comes closest to resembling Tariq. We are given glimpses of Hassan's self-sacrificing nature very early in the novel. Hassan serves Amir without reservation despite the latter's private contempt for him. Even after Amir betrays him by neglecting to come to his aid during his moment of greatest need, Hassan never displays any bitterness towards his friend. Like Tariq, Hassan is utterly incapable of holding grudges. In fact, Hassan suffers greatly after Assef rapes him, but he never reproaches Amir for his shameful betrayal. Later, Hassan takes the rap after Amir falsely accuses him of being a thief. Hassan sacrifices himself so that Amir can save his reputation before Baba.
Tariq, Dane, and Hassan exemplify all that is good and moral in the masculine soul; indeed, their collective humanity restores our faith in human nature.

Single Variable Calculus, Chapter 4, 4.1, Section 4.1, Problem 62

a.) Given the function $f(x) = x - 2 \cos x, \quad -2 \leq x \leq 0$, use a graph to estimate the absolute maximum and minimum values.
b.) Use calculus to find the exact maximum and minimum values.

a.)


Based from the graph, the absolute minimum value is approximately $f(-0.5) \approx -2.20$ and the absolute maximum value is approximately $f(-2) = -1.20$

b.) To find the exact value, we take the derivative of the function.


$
\begin{equation}
\begin{aligned}
f'(x) &= \frac{d}{dx} (x) - 2 \frac{d}{dx} ( \cos x )\\
\\
f'(x) &= 1 + 2 \sin x
\end{aligned}
\end{equation}
$


when $f'(x) = 0$


$
\begin{equation}
\begin{aligned}
0 &= 1 + 2 \sin x\\
\\
2 \sin x &= -1 \\
\\
x &= \sin^{-1} \left[ - \frac{1}{2} \right]\\
\\
x &= \frac{-\pi}{6}
\end{aligned}
\end{equation}
$


We have either maximum or minimum at $\displaystyle x = \frac{-\pi}{6}$

when $\displaystyle x = \frac{-\pi}{6}$


$
\begin{equation}
\begin{aligned}
f \left(\frac{-\pi}{6} \right) &= \frac{-\pi}{6} -2 \left(\cos \left( \frac{-\pi}{6} \right) \right)\\
\\
f \left(\frac{-\pi}{6} \right) &= -2.2556
\end{aligned}
\end{equation}
$


Evaluating the function of its interval $[-2,0]$.

When $x = 0$,


$
\begin{equation}
\begin{aligned}

f(0) =& 0 - 2 \cos (0)
\\
\\
f(0) =& -2

\end{aligned}
\end{equation}
$



When $x = -2$,


$
\begin{equation}
\begin{aligned}

f(-2) =& -2 - 2 \cos (-2)
\\
\\
f(-2) =& -1.1677

\end{aligned}
\end{equation}
$


Therefore, the absolute minimum is exactly at $\displaystyle f \left(\frac{-\pi}{6} \right) = -2.2556$ and the absolute maximum is exactly at $f(-2) = -1.1677$.

What is the process by which the Gospels entered the canon?

If you have read the gospels of Matthew, Mark, Luke, and John, you will know that in many cases, they repeat the same stories as each other. There are far more books—called "apocrypha"—that were circulated among the early Christians, also containing broadly similar material, which did not make it into the final, accepted version of the New Testament (the "canon"). We know, however, that the key four gospels, or "Tetramorph," were already generally accepted by 180 AD, when they are referred to by Ireneaus in his writings; the Pauline epistles were also in wide circulation by this point.
By the middle of the third century AD, it is thought that the twenty-seven books of the modern New Testament were widely agreed upon. The process by which this agreement was written down involved a number of church councils, with the Council of Rome famous as key among these. Athanasius, Bishop of Alexandria, was the first to use the word "canon" in relation to the twenty-seven books, which he set out in a letter written at Easter in the year 367. By the time of St. Augustine, the matter of the New Testament canon was regarded as settled, although debate continued over the Book of Revelation and other later sections of the Testament. The gospels themselves, however, were some of the first sections of the Testament to be agreed upon as canon. These had been circulated and debated in the very early church in Rome, and effectively the books considered closest in time to Jesus were accorded privilege; any gospel that appeared to tell contradictory stories was quickly weeded out, although some of these seeded heretical sects which would survive for centuries.

College Algebra, Chapter 4, Chapter Review, Section Review, Problem 46

If $P(x) = 9x^5 - 21x^4 + 10x^3 + 6x^2 - 3x - 1$, then

a.) Find all zeros of $P$, and state their multiplicities.

b.) Sketch the graph of $P$.



a.) To find the zeros of $P$, we apply synthetic division with the possible rational zeros of the factor of $1$ divided by the factor of $9$ which are $\displaystyle \pm 1, \pm \frac{1}{3}, \pm \frac{1}{9}$. Then, by trial and error







Again, by applying Synthetic Division







Again,







Again,








Thus,


$
\begin{equation}
\begin{aligned}

P(x) =& 9x^5 - 21x^4 + 10x^3 + 6x^2 - 3x - 1
\\
\\
=& \left(x + \frac{1}{3} \right) \left( 9x^4 - 24x^3 + 18x^2 - 3 \right)
\\
\\
=& \left( x + \frac{1}{3} \right) (x -1) \left(9x^3 - 15x^2 + 3x^2 + 3 \right)
\\
\\
=& \left( x + \frac{1}{3} \right) (x - 1)(x - 1) (9x^2 - 6x - 3)
\\
\\
=& \left( x + \frac{1}{3} \right) (x - 1)(x - 1)(x - 1) (9x + 3)
\\
\\
=& \left( x + \frac{1}{3} \right) (x - 1)^3 (9x + 3)

\end{aligned}
\end{equation}
$



Therefore, rational zeros of $P$ are $\displaystyle \frac{-1}{3}$ and $1$. Then, the zeros have multiplicity of $1$ and $3$ respectively.

b.) To sketch the graph of $P$, we must know first the intercepts of the function. The values of the $x$ intercepts are the zeros of the function, that is $\displaystyle \frac{-1}{3}$ and $1$. Next, to determine the $y$ intercept, we set $x = 0$ so that


$
\begin{equation}
\begin{aligned}

P(0) =& \left( 0 + \frac{1}{3} \right) (0 - 1)^3 (9(0) + 3)
\\
\\
=& \left( \frac{1}{3} \right) (-1)^3 (3)
\\
\\
=& -1

\end{aligned}
\end{equation}
$



Since the function has an odd degree and a positive leading coefficient, then its end behavior is $y \to - \infty$ as $x \to -\infty$ and $y \to \infty$ as $x \to \infty$. Then, the graph is