Beginning Algebra With Applications, Chapter 6, Review Exercises, Section Review Exercises, Problem 32

Solve by substitution: $
\begin{equation}
\begin{aligned}

7x+3y =& -16 \\
x-2y =& 5

\end{aligned}
\end{equation}
$


$
\begin{equation}
\begin{aligned}

x-2y =& 5
&& \text{Solve equation 2 for } x
\\
x =& 2y + 5
&&
\\
\\
7x+3y =& -16
&& \text{Substitute $2y+5$ for $x$ in equation 1}
\\
7(2y+5) + 3y =& -16
&&
\\
14y + 35 + 3y =& -16
&&
\\
17y =& -51
&&
\\
y =& -3
&&

\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}

x =& 2(-3)+5
\qquad \text{Substitute the value of $y$ in equation 2}
\\
x =& -6+5
\\
x =& -1

\end{aligned}
\end{equation}
$


The solution is $(-1,-3)$.

What do roots in trigonometry mean? Why does solving some trigonometric equations give you multiple solutions?

In solving trig, or other equations, finding the "roots" means to find the solutions.  This also means find the values when "theta" or "x" is zero.  Also known as the x-intercepts.
Trig equations often have multiple solutions because there are multiple angle measurements which give you the same value on a trig graph.  
For instance, consider the trig equation sinx = sqrt(2)/2
Since sin45 = sqrt(2)/2 and sin135 =sqrt(2)/2 so both x = 45 and x = 135 are solutions to the trig equation
There are even more solutions to this equation since trig functions are periodic--meaning that answers repeat themselves every 360 degrees. So x = 45 + 360 = 405 is also a solution. 

College Algebra, Chapter 4, 4.4, Section 4.4, Problem 100

Suppose that an open box with a volume of $1500\text{cm}^3$ is to be constructed by taking a
piece of cardboard $20$cm by $40$cm, cutting squares of side length $x$ can from each corner, and folding up the sides.
Two different ways, and find the exact dimensions of the box in each case.



If the volume of the box is $1500\text{cm}^3$, then

$
\begin{equation}
\begin{aligned}
x(40-2x)(20-2x) &= 1500 && \text{Model}\\
\\
(40 -2x^2)(20-2x) &= 1500 && \text{Distribute } x\\
\\
800x - 80x^2 - 40x^2 + 4x^3 &= 1500 && \text{Apply FOIL method}\\
\\
800x - 120x^2 + 4x^3 &= 1500 && \text{Combine like terms}\\
\\
200x - 30x^2 + x^3 &= 375 && \text{Divide both sides by 4}\\
\\
x^3 - 30x^2 + 200x - 375 &= 0
\end{aligned}
\end{equation}
$

The, by using synthetic division and trial and error with the factor of 375,


Thus,

$
\begin{equation}
\begin{aligned}
x^3 - 30x^2 + 200x - 375 & = 0 \\
\\
(x-5)(x^2 -25x + 75) &= 0
\end{aligned}
\end{equation}
$

So if $x = 5$, then

$
\begin{equation}
\begin{aligned}
40 - 2x &= 30 \\
\\
20 - 2x &= 10
\end{aligned}
\end{equation}
$

Therefore, the exact dimension of the box is $5$ by $30$ by $10$cm.

Who were the sympathetic characters?

The sympathetic characters are those we identify with in a novel. In 1984 these would be Winston Smith and Julia. The story is told through the eyes of Winston, an average outer party member who leads a gray, miserable life like most of the other outer party members. The story opens as he rebels against being forbidden to have independent thoughts. He starts a journal, and we as readers immediately understand his desire to have the freedom of his own ideas. We also immediately feel suspense because we learn that what he is doing is highly subversive and if discovered will get him into deep trouble. 
We sympathize as well with the vibrant, practical, and courageous Julia, who takes the risk of reaching out to Winston even though it is forbidden. It is easy to see how Winston could fall in love her. We sympathize with the simple desires of this twosome to have an ordinary love relationship and an ordinary life of companionship with each other in the room above Mr. Carrington's store. Both characters represent being fully human in a society that is trying to crush their humanity.

Precalculus, Chapter 7, 7.4, Section 7.4, Problem 33

Decompose the denominator:
x^3-x^2-2x+2=x^2(x-1)-2(x-1)=(x^2-2)(x-1)=(x-1)(x-sqrt(2))(x+sqrt(2)).
Therefore the fraction decomposition has the form
x/(x^3-x^2-2x+2)=A/(x-1)+B/(x-sqrt(2))+C/(x+sqrt(2)).
To find A,B and C multiply both sides by the original denominator:
x=A(x^2-2)+B(x-1)(x+sqrt(2))+C(x-1)(x-sqrt(2)), or
x=x^2(A+B+C)+x(B(sqrt(2)-1)-C(sqrt(2)+1))+(-2A-Bsqrt(2)+Csqrt(2)).
Thus A+B+C=0, B(sqrt(2)-1)-C(sqrt(2)+1)=1 and -2A-Bsqrt(2)+Csqrt(2)=0.
A=-(B+C),
B(sqrt(2)-1)-C(sqrt(2)+1)=1,
2(B+C)-Bsqrt(2)+Csqrt(2)=0, orB(2-sqrt(2))+C(2+sqrt(2))=0, orB(sqrt(2)-1)+C(sqrt(2)+1)=0.
Add and subtract these two equations and obtain
2B(sqrt(2)-1)=1, or B=1/(2(sqrt(2)-1))=(sqrt(2)+1)/2 and
2C(sqrt(2)+1)=-1, or C=-1/(2(sqrt(2)+1))=-(sqrt(2)-1)/2.
And A= -(B+C)=-1.

Now check this result:
-1/(x-1)+(sqrt(2)+1)/2 1/(x-sqrt(2)) -(sqrt(2)-1)/2 1/(x+sqrt(2))=
=-1/(x-1)+1/2 ((sqrt(2)+1)x+sqrt(2)(sqrt(2)+1)-(sqrt(2)-1)x+sqrt(2)(sqrt(2)-1))/(x^2-2)=
=-1/(x-1) +1/2 (2x+4)/(x^2-2)=-1/(x-1)+(x+2)/(x^2-2)=
=(2-x^2+x^2+x-2)/((x+2)(x^2-2))=x/(x^3-x^2-2x+2),
which is correct.

How does Squeaky feel about the May Day celebration?

Squeaky finds parts of the May Day celebration frivolous and inappropriate for her inner city neighborhood.
Perhaps because Squeaky has the responsibility of protecting her brother, she has lost some of the imaginative spirit of childhood and is more practical about things. For instance, she feels that the May Pole celebration has no serious value and is hardly worth the purchase of a frilly dress. She cannot understand why her mother is not glad that she is not

prancing around a May Pole getting the new clothes all dirty and sweaty and trying to act like a fairy or a flower or whatever you’re supposed to be when you should be trying to be yourself.

Unfortunately, Squeaky's protection of her brother seems to have caused her to become more skeptical of people's motives and to be concerned with practicalities rather than some of the frivolous, but delightful activities of childhood. She focuses her life on her success as a runner, a success which allows her to be proud of herself and allows some escape from the harsh realities of her life. Before a race, Squeaky allows her imagination the freedom that she does not give it otherwise.

I dream I’m flying over a sandy beach in the early morning sun, kissing the leaves of the trees as I fly by.

During the May Day race, Squeaky notices for the first time how quickly her brother Raymond is capable of running and what an exceptional runner he may become if she trains him. This idea helps to free Squeaky of some of her cynicism, so she smiles and laughs as she considers her new plans to train Raymond and develop other talents that she herself possesses.

Squeaky isn't especially enthusiastic about the May Day celebration. She takes her time getting to the park on May Day because the track meet is the last event of the program, and that is the only event she wants to participate in.
Squeaky especially wants to avoid the May Pole dancing. She thinks that dressing up in a "white organdy dress with a big satin sash" is a waste of time, since the dress will eventually get dirty. Also, May Day occurs only once a year; in Squeaky's opinion, the expense of a pretty dress is unjustified, especially since she won't be able to fit into it the next year. She also doesn't like the idea of dressing up for the sake of pretending to be something she's not.
For example, she relates how she once dressed up as a strawberry in a Hansel and Gretel pageant in nursery school. Squeaky explains that she felt pretty uncomfortable with the whole affair. The reality is that she prefers to run; that's what she's good at, and that's what she prefers to do. So, the only event that makes the May Day celebrations tolerable for Squeaky is the fifty-yard dash.

 

How does Kundera’s novel depict everyday life under Stalinism?

This is Milan Kundera's first novel, originally published in Czechoslovakia in 1967. We get the viewpoints of four different characters, and, together, these give us a full picture of what life was like in Czechoslovakia at that time and the decades beforehand. 
The novel is called The Joke because Ludvik's life was ruined by a joke he made (which the leaders of the Communist party overreacted too) and because the people of Czechoslovakia under Stalinism were victims to "the joke history played on them." Ludvik essentially became a prisoner in "military service," and Jaroslav feels that he is watching Moravian culture fade before his eyes. Even Zemanek, who betrayed Ludvik and got him ousted from the party, eventually becomes a supporter of a more liberal regime. Overall, the novel shows Kundera's view of how strict and unforgiving the communist party became in this country, to the point that most of the people of Czechoslovakia found that repression of their rights and culture was a daily occurrence.
In Ludvik's eyes, everyday life under Stalinism is devastating. 

What are the similarities and differences between the societies in Beowulf and Sir Gawain and the Green Knight?

Comparing the differences between the societies depicted in these two works brings us to a few small problems with a sociological analysis of them. Both Beowulf and the tale of the Green Knight occur in a fantastic realm where story carries more commentary on reality than reality itself. Both provide lessons about heroic acts and choices, offering suggestions to their audiences about how to be a good man. Inferences can be made about the societies that created these myths, even if it may be unproductive to study the limited, fantastic social worlds they contain.
Both the society of Beowulf and the society of the medieval romances believed that bravery and honesty were crucially important to survival. The character of Beowulf, for instance, shows up Unferth, a rival warrior, by pointing out the dishonesty of his words. Beowulf's boasts are grounded in truth, while Unferth skews the truth to make Beowulf look bad. Ultimately, Beowulf's word proves trustworthy, and so Unferth is the one who loses face. Gawain, likewise, makes a point of showing up for his appointment with the Green Knight. An Arthurian knight should keep his word, and he does so. Both Beowulf and Gawain face their enemies fearlessly because they have said they would do so, displaying both the truth of their promises and the courage of their characters.
One glaring difference between the two stories is that in Beowulf, warriors love to boast of their successes in battle, while in the Gawain story, humility is considered wise and honorable. This may relate to the influence of Christian theology. Christianity had only recently been introduced at the time Beowulf was written down, and so we see a mix of Christian and pagan thinking in the epic. In the Middle Ages, however, Christian thinking had long since come to dominate English culture, and so humility (as expressed in Jesus's "Sermon on the Mount") has a more pervasive influence on the literature.
The heroes' reasons for fighting are also quite different. Beowulf goes to Denmark to face Hrothgar's monster because it threatens people's lives, and he faces the dragon in his homeland later in life to save his people from the monster's threats. Gawain's fight, on the other hand, does not stem from the need to protect anyone. The story begins with Arthur asking for an exciting tale from one of his knights' experiences, and the challenge offered by the Green Knight is one Gawain willingly accepts just for the sake of proving himself. No one is in danger from the Green Knight, but Gawain agrees to fight him anyway. When we consider the difference in years—700–800 CE for Beowulf and 1200–1400 CE for Sir Gawain and the Green Knight—it becomes clear that the political and social landscape drastically changed within those several centuries. Ask yourself what type of political context creates a story in which all of the threats are coming from the outside and, if not met, will destroy everyone. Conversely, what type of political context creates a story in which a warrior chooses battles that offer no needed protection but rather a valuable moral lesson?

How does Kipling give advice in terms of language, form, and structure?

Because your question asks for close reference to "the poem," I am going to assume you have miscategorized this question and are asking about Kipling's famous advisory poem, "If."
Kipling's poem, "If," a classic of Victorian stoicism, reflects the values of the society in which it was written. Kipling writes to an unidentified young man, whom he addresses directly: "my son." His choice to write in the second person, addressing the reader directly as "you," lends the poem an immediacy which helps each reader to imagine that it is personal to them; the choice of address fosters an intimacy between speaker and reader which suits the avuncular tone of the poem.
Kipling writes in iambic pentameter, lines with five "beats" or points of emphasis. This is the favored form of Shakespeare, a form extremely familiar to readers of English poetry and one which generally reflects the rhythms of speech. As such, this helps to convey the impression that the advice given in the poem is conversational, passed from one person to another. There is nothing contrived about the form; just as the language is generally straightforward and easy to understand so that the message is not obscured, the form is predictable and reliable, helping to create a sense of trust between speaker and reader, for the most part.
The structure of the poem, with its ABABCDCD rhyme scheme, lends it cohesion and a sense that the conclusion suggested by the repetitive pattern is inevitable if the rules are followed: as in Boolean algebra, if this, so this. The structure is an echo of the content. Only in the first stanza does Kipling deviate from this rhyme scheme: here, we see AAAABCBC. This has the effect of setting the first stanza apart almost as a preamble to what follows. It is particularly interesting to note the word that causes the rhyme scheme to diverge from the later ABABCDCD: the "you" which is repeated at the end of the first three lines. This directs the attention of the reader toward what the poem will privilege. The poem is about "you," the reader, and its focus is upon how to support "you" onward into the rhythmical and metrical stability which the rest of the poem displays.
The literary devices Kipling uses to convey his message in terms of language are effective in their simplicity. Parallelism and repetition emphasize the poem's point that "you" must simply follow the rules consistently in order to eventually "be a man, my son." Anaphora is a key device in the poem: "If you . . . if you . . . " and "Or . . . " are phrases which set up situations in which "you" may find yourself, and then follows the advice as to how one should conduct oneself.
The poem also uses the device of personification to give the impression that the challenges we may encounter in life are almost human, and can be fought as humans can. "Triumph and Disaster," the poet says, are "impostors," while "Will" alone is offered voice: "Hold on!" This suggests that Triumph and Disaster have, ultimately, less agency than the Will within us which will lend us our determination. Interesting, too, is the conversational tone into which the poet sometimes falls, with colloquialisms such as "build 'em up" and "talk too wise" (rather than "wisely") adding to the sense of almost conspiratorial intimacy established between author and reader. What the poet says, he says straightforwardly, which lends a depth of credence to his words. We feel he understands Triumph and Disaster through long experience, and has come to know what Will can achieve by the same means.
This poem is, in fact, one long, run-on sentence. Much of its efficacy lies in the fact that it is all leading, like a crescendo, to the final conclusion reached in the last sentence. The poet lays out every possible situation in which, "if" you behave in a particular way . . . but does not set out what the actual, physical consequence will be of any of this good behavior until the end of the poem. The poem's reliable structure and rhythm, combined with its personalized address, however, mean that the reader cannot be in any doubt that the consequence of if will be positive.

Precalculus, Chapter 6, 6.1, Section 6.1, Problem 41

Given A=150^@, b=8, c=10
Use the Area Formula A=1/2bcsin(A)
A=1/2(8)(10)sin(150)
Area is 20 square units.

How are the both book 11 of the Odyssey and "Ozymandias" related?

The overriding theme of Shelley's "Ozymandias" is the transience of all earthly things. Ozymandias, an Egyptian pharaoh, thought he could achieve immortality by his achievements in this life. Yet his statue lies crumbling in the desert, representing a warning to those foolish enough to think that they can withstand the ravages of time.
A similar theme emerges in book 11 of the Odyssey. Odysseus, on the instructions of Circe, visits the Land of the Dead in order to consult the blind prophet, Tiresias. In Hades, Odysseus is confronted by his own mortality as he meets with the shades of his former comrades-in-arms such as Agamemnon and Achilles.
It is his meeting with the latter that links up with the theme of "Ozymandias." Odysseus always believed that Achilles, like all other great heroes, had achieved immortality through his noble deeds on earth. So Odysseus is somewhat taken aback when Achilles proclaims that he'd rather be a farmer's slave on earth than king of the dead. Evidently, immortality in the Odyssey proves no more desirable than in "Ozymandias."

Explain how Julius Caesar is vain.

There are several examples of how Julius Caesar is vain throughout the play. Julius Caesar not only dismisses his wife's advice about going to the Senate but also rejects the soothsayers' warnings. He is also reluctant to push away the crown when Mark Antony attempts to place it on his head and makes several vain comments when he addresses the other Senators. During Caesar's conversation with Calpurnia in act 2, scene 2, he displays his narcissistic personality by dismissing her warnings, referring to himself in the third person, and telling her,

Caesar shall forth. The things that threatened me Ne'er looked but on my back. When they shall see The face of Caesar, they are vanishèd (Shakespeare, 2.2.10-12).

Caesar goes on to personify danger and compares himself to a lion by saying,

That Caesar is more dangerous than he. We are two lions littered in one day, And I the elder and more terrible. And Caesar shall go forth (Shakespeare, 2.2.45-48).

Later on, Caesar visits the Senate and refuses to yield to the requests of the senators. Caesar displays his vanity by comparing himself to the North Star and says,

If I could pray to move, prayers would move me. But I am constant as the northern star, Of whose true-fixed and resting quality There is no fellow in the firmament (Shakespeare, 3.1.64-67).

Overall, Caesar's vanity is expressed and depicted by his narcissistic comments and exalted perception of himself.

Calculus of a Single Variable, Chapter 8, 8.3, Section 8.3, Problem 12

Recall that indefinite integral follows int f(x) dx = F(x) +C where:
f(x) as the integrand function
F(x) as the antiderivative of f(x)
C as the constant of integration.
For the given integral problem: int x^2 sin(x) dx , we may apply integration by parts: int u *dv = uv - int v *du.
Let:
u = x^2 then du =2x dx
dv= sin(x) dx then v = -cos(x)
Note: From the table of integrals, we have int sin(u) du = -cos(u) +C .
Applying the formula for integration by parts, we have:
int x^2 sin(x) dx= x^2*(-cos(x)) - int ( -cos(x))* 2x dx
= -x^2cos(x)- (-2) int x*cos(x) dx
=-x^2cos(x)+2 int x *cos(x) dx
Apply another set of integration by parts on int x *cos(x) dx .
Let: u =x then du =dx
dv =cos(x) dx then v =sin(x)
Note: From the table of integrals, we have int cos(u) du =sin(u) +C .
int x *cos(x) dx = x*sin(x) -int sin(x) dx
= xsin(x) -(-cos(x))
= xsin(x) + cos(x)
Applyingint x *cos(x) dx =xsin(x) + cos(x) , we get the complete indefinite integral as:
int x^2 sin(x) dx=-x^2cos(x)+2 int x *cos(x) dx
=-x^2cos(x)+2 [xsin(x) + cos(x)]+C
=-x^2cos(x)+2xsin(x) +2cos(x) +C

Describe off the top of your head the external structure of the Royal Ontario Museum located in Toronto, Ontario.

If you were going to describe the Royal Ontario Museum off the top of your head, that would mean you do so without doing research. If you know a lot about architecture, you could apply that, but otherwise, you would be giving impressions of the building, describing what it looks like, what it seems like, and what feelings it gives you.
If I did that, the first thing that I'd say would be a list of words or phrases: jagged. Shiny. Geometrical. Huh? Modern. Probably expensive.
If I had to pull that together into a more rational and coherent response, I'd end up with something like the following:
The Royal Ontario Museum certainly makes an impression. It doesn't look like a museum, but more like the entire thing is a work of art in itself—a work of modern art. The museum's exterior is vivid, geometrical, jagged, and austere. The sharp angles aren't very welcoming, but they do draw the eye and claim space. It kind of looks like an alien spaceship crashed to earth, and half of it is sunk in the ground. It looks like it was designed to stand out and call attention to itself, rather than be welcoming.
https://www.thecanadianencyclopedia.ca/en/article/royal-ontario-museum

If 1.806x10^24 molecules of N2 are produced, how many atoms of sodium metal are also produced?

I am assuming that you are referring to the production of nitrogen gas by thermal decomposition of sodium azide as per the following chemical reaction:
2NaN_3 -> 2Na + 3N_2
In this reaction, the products are sodium atoms and nitrogen molecules.
Remember that each mole of a substance contains an Avogadro's number of particles. In this case, we can say that 1 mole of nitrogen will contain 6.023 x 10^23 molecules. We are given that 1.806 x 10^24 molecules are produced.
In other words, 3 moles (= 1.806x10^24 / 6.023x10^23) of nitrogen is produced.
From the chemical reaction, 3 moles of nitrogen is produced along with 2 moles of sodium by using 2 moles of sodium azide.
Hence, along with the production of 3 moles ( or 1.806 x 10^24 molecules) of nitrogen, 2 moles of sodium will also be produced.
This is equal to 1.2046 x 10^24 (= 2 x 6.023 x 10^23) atoms of sodium.
Hope this helps.

Why did the warden call Stanley a 'caveman' in Holes by Louis Sachar?

The warden called Stanley by his nickname, Caveman.
All of the boys are called by nicknames instead of their real names at Camp Green Lake.  The warden is less interested in the boys’ development than finding buried treasure.  When the warden addresses Stanley by his nickname, which the boys have given him, she is catering to the boys in a way.  She wants them to find her treasure.
Stanley does not even realize that he is Caveman at first.  He is one of the bigger boys.

"The Caveman's one tough dude," said Squid, and he lightly punched Stanley's arm.
Stanley leaned back against the torn vinyl upholstery. Despite his shower, his body still radiated heat. "I wasn't trying to start anything," he said. (Ch. 9) 

He says he doesn’t want to get into a fight with Caveman, because Caveman is kind of a scary nickname.  It isn’t until he realizes that the boys are talking to him and calling him Caveman that he understands that is his nickname.  It sounds tougher than Stanley. 
Stanley decides he likes his nickname.  Having a nickname means that he is one of the guys. It isn’t even that bad of a nickname like Barf Bag.  The nickname means "they accepted him as a member of the group."
When Stanley finally meets the warden, everything about her surprises him.  First of all, he had no idea she was a woman.  She is also meaner to the counselors than the boys, and seems to be more interested in treasure than character-building. 

The Warden turned to Stanley. "Caveman, will you come here, please?"
Stanley was surprised she knew his name. He had never seen her. Until she stepped out of the truck, he didn't even know the Warden was a woman. (Ch. 13) 

When the Warden calls him over to fill his canteen with water, she is making a point to Mr. Pendanski.  This is one of the reasons she used his nickname.  She was being sweet to the boy and mean to Mr. Pendanski.  He contradicted her when he said that he had just filled the canteens, and she did not like being contradicted.  Stanley found the whole incident unsettling.

Please discuss and summarize the relationship of Federalist No. 79–82 to criminal law.

"Federalist No. 79" discusses the importance of an independent judiciary. Hamilton says that judges should serve for life, rather than serving at the whim of politicians. He also says that their salary should not be decreased. In "Federalist No. 80," Hamilton lays out the jurisdiction of the federal judiciary, which includes cases that arise from the laws of the United States as written in the Constitution, cases involving public figures and ministers, cases involving maritime law, cases involving the United States itself as a party, and cases between citizens of different states. In "Federalist No. 81," Hamilton establishes the structure of the judiciary with the Supreme Court at the top and other inferior courts set up by Congress. In "Federalist No. 82," Hamilton writes that the states will retain powers not given to the federal government. This is the basis of our federalist system.
The principles in this section of the Federalist Papers on the judiciary became part of our Constitution and have effects on the practice of criminal law today. For defendants and plaintiffs to receive fair trials, the judiciary must be free of political influence in that judges are appointed to the Supreme Court for life. In addition, the court system establishes a hierarchy in which local courts try cases first and then other courts hear cases on appeal. The Supreme Court only hears cases, including criminal cases, in which the decision of lower courts has been appealed. The Supreme Court hears cases that affect the interpretation of the Constitution, including its provisions for defendants in criminal trials. 

What are the arguments against person-centered counselling?

Person-centered therapy consists of a therapist who acts as a sounding board in a conversation with a patient who takes the lead in their own narrative. By allowing the patient to guide the conversation, s/he experiences self-discovery, helping to find the best solution for their individual mindset, mental abilities, and needs.
While there are various benefits to person-centered counseling, some experts argue that the form has limitations for patients experiences particular issues or with specific histories.
In person-centered therapy, the world is seen from the patient's point of view, often discounting the disparity of power, racial, cultural, and socioeconomic differences that can contribute to people's lives. While person-centered counseling attempts to lead people to a solution of how they can take responsibility for their lives and change things, this negates the possibility that an external force, such as an abuser, is ultimately the one responsible for the issues at hand.
Person-centered counseling often allows a patient to grow his or her self-esteem and sets them up for success in challenging their own expectations and results. Some patients with problems attempting things outside of their capabilities may not be served well by this kind of therapy.
Some researchers fear that person-centered therapy allows the patient to hide or ignore evil tendencies in themselves in favor of an optimistic and hopeful view of humanity. The many benefits of person-centered counseling become detriments when supplied to patients with deep psychological problems to solve.
https://www.psychologytoday.com/us/therapy-types/person-centered-therapy

What is the purpose of telling the Finch family history at the beginning of the novel?

Harper Lee's inclusion of the Finch family history at the beginning of her novel serves several purposes. Not only does it give the reader a sense of the known heritages the Finches can claim, but also illuminates their social class and status within the town, and even within the region.
Not only does it display this to the reader, it also clearly shows what Scout, as the narrator, knows about her family history and how the Finch family is regarded. She's been taught, by members of her extended family, that she needs to take pride in her heritage and her Aunt Alexandra expects her to live up to these demands. This high sense of propriety is in contrast to the casual way that Scout addresses her father by his first name, Atticus.
On an even larger scale, Lee uses this family history to put this story in a very specific time and place. It does not begin in a "Once upon a time" land or have nameless characters. These are specific people who lived in a certain town during a specific era. These are all intentional choices, as the rest of the story cannot hang together without these aspects. When it is all put together, the history makes the people, and the story more real, as none of it is perfect or glossed over, but all of it relatable in some way--no family is perfect, and no history is perfect either, even Aunt Alexandra's Finch relatives.

At the beginning of the novel, Scout elaborates on her family's history. This is significant to the exposition of the story and reveals important background information about her family's status in the small town of Maycomb. Scout discusses how her ancestor, Simon Finch, immigrated from England and established a homestead named Finch's Landing on the banks of the Alabama River. Following the Civil War, the Finch family lost much of their wealth but managed to save their homestead. Though Atticus chose to travel to Montgomery to study law and his brother moved to Boston to study medicine, Alexandra remained on Finch's Landing, where the family gathers each Christmas. Atticus ended up moving back to the small town of Maycomb, where he became a well-known lawyer. Scout's family history not only identifies their revered social status in the community, it also corresponds to Aunt Alexandra's obsession with heredity. Scout's description of her family's history explains Alexandra's affinity for heredity and sense of familial pride. One of the main themes Harper Lee explores throughout the novel is social class and status. By elaborating on Scout's family history at the beginning of the story, Harper Lee subtly begins to emphasize the themes of social status and class.

What are some predictions for the future of each character (Amanda, Laura, Tom, and Jim) in Williams' The Glass Menagerie?

The Glass Menagerie follows the closely intertwined lives of Amanda Wingfield and her adult children, Tom and Laura. Jim, Tom's coworker and Laura's former classmate, joins the family for dinner and the play continues by delving into the illusions each of the four main characters uses to survive in a harsh reality. While the play itself ends on a somber note with Tom leaving his family, as Amanda always feared he would, and Jim admitting that he is engaged and unable to court Laura, the final scene is very open-ended. This open-endedness has resulted in significant speculation on the future of each of the main characters.
Laura and Jim
Towards the end of the play, Jim tells Laura that she should be more confident in herself before kissing her. Although he soon after apologizes and admits that he is engaged, the depth of the conversation shared by these two characters gives reason to suggest that they might reconnect in the future. Jim does not seem fully happy in his relationship with his fiancee, and he is so taken with Laura's gentle spirit and kindness that it is conceivable that he will have a change of heart and pursue a relationship with her in the future. The play closes before we can determine what the impact of Tom's departure will have on the family, but it is certain that Laura and Amanda will continue to search for someone who can provide for them. The play ends on a somewhat hopeful note with Laura blowing out the candles, which is often a literary symbol for making a wish. In the future, Laura's wish for a stable life with Jim or someone else who appreciates her for who she is could come true.
Amanda
The play ends with Amanda's fantasy of Laura living the life she previously led as a sheltered Southern belle being shattered. It is heavily implied that she will continue to retreat into this fantasy world, remaining unable to accept the fact that Laura is disabled and she no longer belongs to the world of glamor and sophistication she grew up in. If Todd's abandonment forces Amanda to stand on her own, she may once again become part of reality and find her own way in the world. If not, it is likely that she will continue turning inward to her memories and that Todd will replace her ex-husband as the person she blames, somewhat rightly, for her sufferings in life.
Todd
As the primary character in the play, Todd's future is easier to speculate about than his family's and Jim's futures. At the end of the play, Todd leaves to pursue a career as a Merchant Marine, but guilt and memories of the family he left behind plague his new career from the beginning. It is reasonable to speculate that, given what we know of Todd's character, he will eventually return to his mother and sister. The Glass Menagerie is an autobiographical account of Tennessee Williams' own life and struggle to build a future for himself, despite being haunted by the needs of his family and his disabled sister. Williams viewed his sister as both a source of guilt and inspiration in his own career, so it is likely that Todd will develop a similar perspective as he continues through life.
As a whole, it is likely that the future for Todd, Amanda and Laura will be mixed with sadness as well as triumph. Todd's choice to leave will either be a catalyst for Amanda and Laura to carve out futures of their own or to become lost in their fantasies forever. Amanda's fantasy world is the decadence of her past, while Laura's is in her collection of glass animals and records. In this sense, Todd's future is far more certain than that of the two women in the play. His ability to move through the world as an able-bodied man, capable of controlling his own destiny, makes his future easier to predict, while Amanda and Laura must either succumb to the habits and misfortunes that have characterized their lives throughout the play or find a way to succeed in life against the odds that are stacked against them.

Summarize the book Newjack: Guarding Sing Sing.

In Newjack: Guarding Sing Sing, a journalist decides to work as a prison guard in a New York prison so that he can write about his experiences and the life of the inmates there. He finds that he's changed by the experience.
Ted Conover gets a job at Sing Sing after being denied access to write about it through standard channels. He goes through the application process and training and then gets into the thick of it in the real job.
He starts the process at the Albany Training Academy, where Sing Sing guards learn to handle the demands of the tough job. There, he makes connections and builds relationships with other correctional officers. He also realizes how difficult the job will be because the training is grueling and physically demanding.
When he actually arrives at Sing Sing, he finds that the job is as hard emotionally as it is physically. The days feel long, and he gets little respect. He doesn't enjoy the way most of the other officers do their jobs. The one person he does like and tries to emulate is a correctional officer who treats the inmates with respect and is willing to joke around with them. He clearly sees them as more than their crimes.
Conover works on the floor, in the gym, in the psych unit, and, at times, in the place where inmates are sent for solitary confinement. He has to deal with finding contraband items and deciding when he should push the rules and when he should relax. It's a balance between keeping the inmates settled and maintaining his authority as an officer.
Conover also tells some of the stories of the men who are imprisoned at Sing Sing. They're often tragic and show intelligent or mentally disturbed people who aren't getting the care, treatment, or stimulation they need to improve their lives. At the same time, though, some are dangerous, and many inmates and officers are hurt in altercations during Conover's time at Sing Sing.

Early in journalist Ted Conover's nonfiction account of the year he spent as a corrections officer in New York State's Sing Sing prison, Newjack: Guarding Sing Sing, he meticulously describes the prison's decrepit condition, noting that "If the whole structure were radically shrunk, the uninitiated might perceive a vaguely agricultural purpose; the cages might be thought to contain chickens, or mink." Conover's point is that the American criminal justice system has failed miserably and that the conditions in which the nation's prison population is housed and treated represents a serious failure to understand the nature of crime and punishment; it also represents a collective failure to adopt a penal system consistent with the country's principles. The prisoners he helped guard were housed like animals, and it should, he concludes, come to little surprise that they responded accordingly.
Newjack is not only a depiction of life inside Sing Sing. It is also a history of the prison itself, from its initial construction during the 1820s to the present. It also serves as a critical analysis of America's criminal justice system. One of the topics covered by Conover, in addition to descriptions of his responsibilities as a prison guard with an emphasis on both the mundane nature of the job and the terror that is inherent in having to confront dangerous, violent convicts daily, is the long unsuccessful history of implementing prison reform. 
Thomas Mott Osborne was warden of Sing Sing in the early part of the 20th century. Osborne had—like Conover a century later and for a much briefer time—checked himself into a prison with his identity concealed so that he could see for himself the conditions in which the United States housed its inmates. Passing himself off as a convict, Osborne was appalled by what he witnessed and was determined to reform the correctional system in New York State. He failed and Conover's observations during his time as a prison guard mirrored those of Osborne. This further illuminates the inability or unwillingness of the United States to adopt measures to reduce the prison population (like many others, Conover is critical of mandatory sentence guidelines and the excessive use of incarceration for nonviolent drug offenses) and to address the problem of recidivism. 
Conover’s examination of the criminal justice system and firsthand observations of life inside a particularly notorious penal institution was intended to illuminate the shocking contradictions between American values and the way it treats over one million of its citizens. The United States, he declares, has failed to create a criminal justice system that rehabilitates those it incarcerates and it does nothing to make our cities safer.

How did the Tet Offensive alter the course of the Vietnam War?

The Tet Offensive, in many ways, failed to achieve the ends for which it was designed by the North Vietnamese. Indeed, the North Vietnamese sustained heavy casualties, and the attacks on South Vietnam did not ultimately stir up the level of anti-American feeling the North Vietnamese had hoped for. Originally, they had conceived of the offensive as a means of breaking up the alliance between the Americans and the South Vietnamese by demoralizing the South Vietnamese and forcing the Americans to leave. This did not happen.
Despite these apparent failures, however, the Tet Offensive did deliver a strategic blow on the part of the North Vietnamese in a way that would change the course of the Vietnam War. The Vietnam War had never been a popular war in the US. However, news had been spread at home that the war would soon be over and that the North Vietnamese could be readily defeated if only the US hung on for long enough. Television footage showing the massive scale of the fighting between the US and the North Vietnamese, however, eroded public support for the war still further: the imagery was often extremely graphic. What successes the Vietcong did have, furthermore, were particularly demoralizing for the American people, who watched as the Vietcong attacked the American Embassy in Saigon.
Generally, the North Vietnamese, who lost ten times as many soldiers as the US and South Vietnamese combined, suffered worst in the fighting, as they simply were not militarily strong enough to achieve the success they had aimed for. Their failure to inflict huge South Vietnamese losses, furthermore, meant that the South Vietnamese did not move to dissolve their alliance with the US. However, the great success of the Tet Offensive lay in the fact that it made clear to those at home in the US that the Vietnam War was not "almost over." Indeed, after the offensive, US Commander William Westmoreland put in a request for over 200,000 new men in order to launch a counterattack. This was a significant number, which could be interpreted at home as evidence of fear. It also suggested that Westmoreland was by no means certain the war could be easily won.
The Tet Offensive by no means meant the end of war in Vietnam. However, it encouraged Lyndon B Johnson to begin de-escalating American participation in the region, minimizing the extent of bombing in response to public outrage and growing dissent among American politicians. Johnson announced that there would be no more bombing about the 20th parallel. The war at this point moved from being simply divisive, to one that was more generally unpopular than popular. The Tet Offensive brought American public attention to what was really going on in Vietnam, and the reality turned them away from it decisively.
https://history.state.gov/milestones/1961-1968/tet

https://www.history.com/topics/vietnam-war/tet-offensive

How is irony expressed in the story “One Thousand Dollars”?

There are three instances of irony in O. Henry's story "One Thousand Dollars":
It is ironic that Young Gillian does not grumble about inheriting only one thousand dollars when he has been entirely dependent upon his uncle's wealth.
It is ironic that Young Gillian is unselfish in his efforts to spend the money, rather than spending it on himself as has been his habit.
It is ironic that when seemingly self-gratifying Gillian learns that his act of being unselfish will earn him a larger inheritance, he falsifies his report so that the young woman he loves will be given the money instead.
1. After Gillian is told by the lawyers that he must "render...an account of the manner of expenditure of this $1000 as soon as you have disposed of it," he goes to the men's club and asks Old Bryson what he should do with the money, and Bryson suggests that he buy Miss Lotta Lauriere, an actress, a diamond necklace.
2. When Gillian asks her if she would like a pendant for a thousand dollars, Miss Lauriere alludes to another actress she knows who has received a necklace that is worth much more. Defeated, Gillian leaves, but he asks the cab driver what he would do with $1000. When he does not like the man's answer, Gillian then asks a blind man how he would spend the money. The man shows Gillian a bank deposit book with more than a thousand dollars in entries; Gillian returns the book and re-enters the cab.He then goes back to the law offices and inquires if Miss Hayden has been left anything besides a ring and $10. Lawyer Tolman replies in the negative. So, Gillian has the cab take him to the house of his dead uncle where Miss Hayden is seated, writing letters in the library. Gillian tellsher that the old lawyers have found a codicil to the will and she is to receive one thousand dollars. Further, he tells her that he was driving this way and lawyer Tolman asked him to bring it to her. Blanching, Miss Hayden can only utter, "Oh!" and repeat "Oh!" Gillian declares his love for Miss Hayden, but she responds, "I am sorry," and takes the money.
Going into the next room, Gillian writes out the account of his expenditure:

Paid by the black sheep, Robert Gillian, $1000 on account of the eternal happiness, owed by Heaven to the best and dearest woman on earth.

Slipping this into an envelope, Gillian departs.
3. Gillian returns to the offices of Tolman & Sharp with his written accounting of how he spent the $1000. He tosses the white envelope upon the table before Mr. Tolman, saying, "You will find there a memorandum, sir, of the modus operandi [method] of the vanishing of the dollars."
Without looking in the envelope, Mr. Tolman calls his partner and together they explore the inside of a huge safe. Finally, they bring out a very large envelope sealed with wax; then they explain that there is a codicil to his uncle's will. When Bobby Gillian has spent his $1000, then this document is to be read. The lawyer reads,

"If your disposal of the money in question has been prudent, wise, or unselfish, it is in our power to hand you over bonds to the value of $50,000, which have been placed in our hands for this purpose....But, if....you have used this money as you have used money in the past—I quote Mr. Gillian—in reprehensible dissipation among disreputable associates,—the $50,000 is to be paid to Miriam Hayden....I will examine your account in regard to the $1000....I hope you will repose confidence in our decision."

As Mr. Tolman reaches for his envelope, Bobby Gillian grabs it first; he tears it into strips and places it into his pocket. He tells the old gentlemen they need not bother to read his account of his itemized bets. "I bet the thousand dollars at the races. Good-day to you, gentlemen." Mr. Tolman and Mr. Sharp shake their heads in disapproval as they watch Gillian depart, whistling happily in the hallway as he goes toward the elevator.

How does Reverend Hale test John Proctor? Does Proctor pass the test?

Reverend Hale is unusual among the leaders of the witch-craze in that he actually wants to get to the truth. He takes his role as lead investigator very seriously indeed, so much so that he goes to the trouble of interviewing the Proctors in person. What Hale's hoping to do here is to ascertain their characters, to see whether they're the kind of people who'd normally get involved in all manner of dark, diabolical activities.
As part of the interview, he asks Elizabeth Proctor to recite the Ten Commandments. She does so without hesitation. John, however, embarrassingly flunks the test. He remembers nine of the commandments, but tellingly the one he omits is the one relating to adultery. As we know, John's already committed adultery by having an affair with Abigail Williams. He didn't pay much heed to "Thou shalt not commit adultery" then, and it seems to have slipped his mind now.

In act 2, Reverend Hale arrives at the home of John and Elizabeth Proctor.  Elizabeth's name has been mentioned in court, so he comes to conduct an informal interview of the couple to ascertain their characters for himself.  During this questioning, Hale asks Elizabeth if she can name all Ten Commandments, and she answers—quite confidently—that she can.  When asked the same question, however, John is less confident and even hesitates a bit in his response.  Hale says to him, "Let you repeat them, if you will."  John begins to recite the Commandments, counting them on his fingers as he goes.  He accidentally repeats the rule about graven images twice, and then he cannot remember the rule about adultery. This is terribly ironic given his recent adultery and the fact that he and Elizabeth were literally arguing about it moments before.  He does not, therefore, pass the test.

Single Variable Calculus, Chapter 4, 4.4, Section 4.4, Problem 14

Determine $\displaystyle \lim_{t \to -\infty} \frac{t^2 + 2}{t^3 + t^2 - 1}$


$
\begin{equation}
\begin{aligned}

\lim_{t \to -\infty} \frac{t^2 + 2}{t^3 + t^2 - 1} \cdot \frac{\displaystyle \frac{1}{t^3}}{\displaystyle \frac{1}{t^3}} =& \lim_{t \to -\infty} \frac{\displaystyle \frac{t^2}{t^3} + \frac{2}{t^3}}{\displaystyle \frac{\cancel{t^3}}{\cancel{t^3}} + \frac{t^2}{t^3} - \frac{1}{t^3} }
\\
\\

=& \frac{\displaystyle \lim_{t \to -\infty} \left( \frac{1}{t} + \frac{2}{t^3}\right) }{\displaystyle \lim_{t \to - \infty} \left( 1 + \frac{1}{t} - \frac{1}{t^3} \right) }
\\
\\

=& \frac{\displaystyle \lim_{t \to - \infty} \frac{1}{t} + \lim_{t \to - \infty} \frac{2}{t^3} }{\displaystyle 1 + \lim_{t \to - \infty} \frac{1}{t} - \lim_{t \to - \infty} \frac{1}{t^3}}
\\
\\

=& \frac{0 + 0}{1 + 0 - 0}
\\
\\

=& \frac{0}{1}
\\
\\
=& 0

\end{aligned}
\end{equation}
$

In what ways did the Know Nothing Party and the Free Soil Party contribute to the breakup of the Union in 1860?

For much of the history of the United States there have been two major political parties, and at the start of the 1850s those two parties were the Democratic Party (1828-Present) and the Whig Party (1834-1854). The Democratic Party had established itself as the major party after the death of the Federalist Party (1791-1824) and under the leadership of Andrew Jackson after his election as president in 1828. The Whig Party emerged in the 1830s as an opposition party, essentially for those that despised Andrew Jackson. During the 1840s and 1850s the Whig Party fragmented over the tensions surrounding the issue of slavery and its expansion into the western United States; in particular the passage of the Kansas-Nebraska Act of 1854.
In the turbulent period of the 1850s both the Know Nothing Party (1844-1860) and the Free Soil Party (1848-1854) emerged as single issue parties as the Whig Party began to decline and die. The Know Nothing Party, or as they were officially known the American Party, was a nativist party or group focused on anti-immigrant policy. The target of their anti-foreignism was primarily Irish Catholics whose numbers had increased due to the famine in Ireland which reached its peak in 1848. The Free Soil Party grew out of the short-lived Liberty Party (1840-1848), which was also a single-issue party; their issue was the abolition of slavery. A more palatable form of political anti-slavery was limiting the expansion of slavery through a free-soil ideology. For the supporters of the Free Soil Party, free men owning and cultivating free soil represented a more ethical and financially sound system to slavery.
As the political tensions surrounding the issue of slavery in the 1850s increased a new party emerged, the Republican Party (1854-Present). The 1856 slogan of the party was “free soil, free labor, free men.” The Republican Party platform in 1860 supported the ideology of free soil. Supporters of the Republican Party came from both the Free Soil Party and many of the northern members of the American (Know Nothing) Party who increasingly saw slavery as a cancer on American society. So, the Know Nothings and Free Soilers contributed to the breakup of the Union in 1860 by providing members of the Republican Party who elected Abraham Lincoln, which precipitated the call for secession by South Carolina about a month after the election.

The Know Nothing Party had essentially dissipated by 1860. It emerged in the 1850s after the Whig party collapsed in the wake of Bleeding Kansas, and its main cause was espousing anti-immigrant and anti-Catholic sentiments. There was a large influx of immigrants to the US at this time, especially due to the Irish Potato Famine. After the Dred Scott decision in 1857, the party largely merged with the Republican Party due to increasing opposition to slavery.
The Free Soil Party, like the Know Nothing Party, was a single-issue party that had mostly died out by 1860. Free Soilers opposed the expansion of slavery into new territories in the west. They arose mainly in the aftermath of the Mexican-American War, when the US added new territories that could potentially become states. With each new addition, the question of whether or not to allow slavery brought up fierce debates. In order to avoid the divisive nature of abolition, many Free Soilers instead argued that slavery should be banned from the west because it would mean fewer opportunities for freemen and was therefore economically detrimental. This party largely died out after the Compromise of 1850 temporarily eased tension over the extension of slavery. Many Free Soilers instead joined the Republican Party.

Please give three reasons with justifications in favor of a pacifist United States. Is being a pacifist the same as being neutral in war?

A pacifist United States would save a lot of money on its military.  If a nation renounces the use of force, as Japan did in its Constitution following World War II, then it has little reason to spend on its military-industrial complex.  A great deal of the United States' budget goes toward defense.  Without this, the money could be spent on internal improvements or social welfare programs.  
A pacifist United States would possibly have a better reputation abroad.  The United States is in favor of human rights, but many civilians die in attacks aimed at killing terrorists.  The drone program has been especially controversial as of late in the United States, as these devices kill as many civilians as surgical bombing campaigns.  If the United States adopted a policy of peace, it might develop a better reputation in the Middle East.  
A pacifist United States might save American lives.  Thousands of men and women in uniform risk their lives for the United States daily.  By cutting down on these numbers, these men and women can take their talents into the civilian world.  While it is uncertain what other nations would do if the United States took on a pacifist foreign policy, it is certain that another nation would have to take the lead in sending in troops.  
A pacifist nation is not necessarily "neutral" in times of war.  A pacifist nation refuses to take part in wars, whereas a neutral nation only refuses to take sides.  The United States has professed neutrality many times but has still traded with the belligerents.  This happened in both the War of 1812 and World War I with the same result—the United States was drawn into the war after attacks on American shipping.  A pacifist nation would not have traded with the belligerents at all since it does not believe in war.  

To what extent could economics be useful in determining how managers should deal with staff?

Economics is integral to workplace productivity in a capitalist society. The ways in which managers can use economic incentives to increase productivity, maintain control, and foster improved employee relations are numerous, and when implemented properly, incentives can benefit those on all sides of the supply chain. Here are ten ways managers can use economics to effectively handle their staff:
1. Clearly define economic incentives from the outset and be clear on how they are linked to productivity. Employees who understand the remunerative benefits of their labor are more likely to proactively engage in their work or be willing to move to a position that better aligns with their qualifications.
2. Design economic incentives so that employees at every level of the company can benefit from them. Lower-level workers who feel as though they are being short-changed at the expense of higher-level workers can induce resentment, animosity, and strife within the ranks, resulting in decreased productivity.
3. Align individual economic incentives with the performance of a company division or the overall performance of the company itself. Employees who feel that their efforts are being recognized and rewarded vis-à-vis the accelerated performance of the company will foster better relations between the ranks and a greater incentive to produce.
4. Use economic measurements such as base salary, overtime, benefits packages, and union fees in relation to actual employee output in order to determine the number of employees and what qualifications they should have. A careful analysis might determine that three skilled union employees cost less in aggregate and have higher levels of overall productivity than seven unskilled nonunion employees.
5. Use economic measurements to determine whether automation is a viable path to increased productivity and profitability, including an assessment of how it would affect the time management spends dealing with flesh and blood staff. Automation might be a viable and cost-effective way to complement human labor and create new job positions rather than simply replace human labor.
6. Seek employee input or feedback on salaries, bonuses, stock options, and other components of their benefits package. Management's willingness to let staff be a contributing factor in setting fair wages and benefits will lead to increased morale and therefore higher levels of productivity.
7. Investing in employee training programs may be beneficial to the company in certain circumstances, such as when the job positions are especially skilled, the labor market is tightening, or there are a dearth of qualified individuals in the market seeking those positions.
8. Management should set up protocols to reward innovation. Employees who feel that their bright ideas will be listened to, taken seriously, and potentially rewarded will be less likely to take their intellectual capital elsewhere, particularly if the company is in a position to invest much larger sums of capital into the idea than the employees would be likely to raise on their own.
9. Provide additional or outside support for employees who truly need it. While this may be a matter of perspective, often times a small investment in third-party support services or even assistant-level labor can increase productivity in multiples and lead to less turnover from employees who otherwise might feel as if they have been placed in a position to fail.
10. Regular evaluations by management of all relevant economic factors as they relate to company performance and employee morale—including staff salaries and benefits, working hours, real output, and financial return—will allow the company to better pivot in an ever-changing global marketplace by making economic adjustments as necessary.
https://www.forbes.com/sites/victorlipman/2013/03/18/5-easy-ways-to-motivate-and-demotivate-employees/

https://www.forbes.com/sites/victorlipman/2013/06/17/7-management-practices-that-can-improve-employee-productivity/

https://www.nap.edu/read/2135/chapter/6

How would you describe Biff and Happy from Death of a Salesman? Who is more sympathetic?

I would argue that Biff is the more sympathetic of the two. He once had a chance to be someone in life, but his old man blew it for him with his unrealistic expectations and the affair he conducted with a secretary, which completely traumatized Biff when he found out about it. To some extent, Biff inhabits the same delusional fantasy world as Willy, but only because his old man put him there; he's never really had a chance to escape.
Happy, on the other hand, is unburdened with his brother's psychological baggage. With his good looks and charm, he's just the sort of "well-liked man" that meets with Willy's approval. But instead of striving for success, he just breezes through life without a care in the world, happy to share his old man's deluded worldview, unwilling to change or develop as a human being.

Biff is Willy Loman's oldest son, and he is an insecure man without a steady job or relationship. In the play, Biff returns home and is depicted as a lost, confused, desperate individual. As an adolescent, Biff excelled at sports and was a popular, enthusiastic boy. Unfortunately, Willy did not instill the proper values in his son and instead praised his popularity. Biff's dreams of playing college football came to an end after he failed a high school math course and discovered that his father was having an affair. As the play progresses, Biff comes to terms with the reality of his situation and life. By the end of the play, Biff refuses to live a delusional life and lie to himself. He accepts the fact that he is a deceitful thief and leaves home hoping to change the trajectory of his life for the better.
Happy is Willy's youngest son, and he is a delusional, dishonest man. Happy is a few years younger than Biff and works as an assistant (although he claims to be the assistant buyer of the company). He brags about sleeping with the executives' fiancées and thrives on sexual gratification. Unlike his brother, Happy is unapologetic and refuses to accept reality by taking responsibility for his actions. Happy's arrogance and lack of self-reflection make him a less sympathetic character than Biff. Happy does not feel bad about engaging in affairs and is content with living a lie. Unlike Biff, who has a tortured soul from years of being selfish, Happy refuses to acknowledge his faults.

In Death of a Salesman, Willy's elder son Biff is uncertain, insecure, and haunted by struggles with his father's expectations. As a child, Biff's parents believed he had more potential than his brother, but once he reached adulthood Biff struggled to hold down a stable job. He dreams of working as a farmer and feels his father and the expectations of his family only serve as obstacles to his desires. Once he discovers his father's affair, Biff loses faith and respect for him and begins to question his values and dreams.
Happy is Willy's younger son who has managed to hold down a modest job as an assistant after a lifetime of living in his brother's shadow. He is interested in career advancement and gaining his parents' approval. He always defends his family members, but his womanizing lifestyle disappoints his mother.
In the play, Biff is written more sympathetically than Happy. Happy shares his father's habit of deluding himself into ignoring how miserable he feels; he lacks insight into his feelings. Biff, on the other hand, is a character with complex feelings who develops throughout the story. Happy is more of a static character, but Biff has complicated feelings about his life, career, and father that develop throughout the course of the play.

What were two big reasons as to why Anti-federalists opposed the idea of the Constitution? What was promised to Anti-federalists to eventually sway enough to support the Constitution?

The Anti-Federalists opposed the Constitution because they thought it vested way too much power in the hands of the federal government. The American colonists had just fought a war against what they saw as British tyranny. The last thing they wanted to see was one kind of tyranny replaced by another. The American Revolution had been fought on the principles of radical republican liberty, which meant, among other things, limited government and the primacy of states' rights. Both of these principles were thought by the Anti-Federalists to be undermined and threatened by the Constitution.
Anti-Federalist hostility to the Constitution was also based on economic grounds. The Anti-Federalists tended to represent agrarian interests and believed that the framers of the Constitution were too close to the banking and commercial sectors of the economy. They were concerned that the federal regulation of commerce would mean central government overriding the concerns of rural folk, who were, after all, the vast majority of the country at that time. Anti-Federalists looked upon their opponents as unashamed elitists concerned only with protecting the interests of a wealthy minority.
The very real concerns of the Anti-Federalists led to the passing of the Bill of Rights; in essence, this was a compromise on the part of the Federalists to try and reassure opponents of the Constitution. Anti-Federalists felt that not enough attention had been paid in the Constitution to the inalienable rights for which countless Americans had recently fought and died. Rights were implied, not explicitly set out. So they demanded, and eventually got, a formal guarantee of those rights, clearly enshrined in the Constitution as the Bill of Rights.
https://teachingamericanhistory.org/resources/bor/fed-antifed-debate/

I have to analyse Ann Patchett's Bel Canto. I have been asked to write an analytical response to pages 56 and 57. Could you please help me with ideas for a good analysis, and different situations that I should use in my analysis to provide a healthy and strong analysis?

On pages 56–57 in my edition, the prisoners are in a state of transition, and the Russian Fyodorov lights a cigarette. Finally, Messner the translator returns.
I would suggest focusing on three elements in analyzing this passage: what has changed in the minds of the prisoners? Patchett states it clearly early on in the passage and it is a very significant change in their mindset: they realize something and this begins to change their behavior. Second, why does Fyodorov light his cigarette? (It directly relates to the change in mindset.) What does this tell us about the character of Fyodorov? Is he cowardly or brave? How do we know? Does he come from a background of poverty or wealth? How do we know? What does the "minion" do who is supposed to stop the smoking? What does this indicate about the terrorists/rebels who kidnapped them? Why does the woman, do you think, feel emboldened to yell that she won't take this? Finally, why is it important that Messner the translator returns? What does all of this foreshadow about what will happen? What does it tell us about the rebels? Are they cold-blooded killers or are they more humane? 
As you answer these questions, you will be analyzing key points about this important passage, which focuses on a transition. Be sure to back up your points with quotes from the text to support what you are saying.

Who were the individuals involved in the Massy Family murder, and what were their social standings?

In February 1915, an English maid named Carrie Davies shot and killed Charles "Bert" Massey as Massey was returning to his house in Toronto, Canada. Davies, who was 18 at the time, told the police that Massey had tried to rape her the day before. Davies was from a working-class British family; her father had died when she was a teenager, and she went to work in Canada to support her mother, who was partially blind, and her three younger sisters. Massey, on the other hand, was from a well-to-do family who owned a company that manufactured farm equipment.
The criminal trial that ensued gained a great deal of public attention. Davies's lawyer defended her as a virtuous young woman whose employer had repeatedly made advances towards her and who, like other young domestics, had no way to protect herself. The jury found her not guilty after only a half-hour deliberation. Davies later married a Canadian farmer, with whom she lived in modest circumstances and had two children before her death in 1961. 

The Massey murder took place on February 18, 1915. Charles Massey was shot to death by his maid, Carrie Davies. There was never any question as to who did it, but Davies claimed it was in self-defense because she believed Charles Massey was going to sexually assault her. She was 18 at the time.
The Masseys were an extremely wealthy family in Toronto, Canada at the time. They employed many people from the town and they belonged to all of the elite social circles. According to CBC, the Masseys felt because of their wealth and status, they would have no trouble convicting Carrie Davies of the murder. That was not the case, however, as the jury believed Davies' testimony and found her not guilty of all charges.
According to CBC (Canada Broadcasting Company), the families still dispute over the facts of the case. Descendants of Charles Massey believe that Davies got away with murder, whereas Davies' relatives believe she did indeed act in self-defense. 
 
 

What "service" has Farquhar been performing in "An Occurrence at Owl Creek Bridge" and why?

Peyton Farquhar has been working in service of the South to disrupt the Northern war effort. In Part II of the story, a Federal scout stops at Farquhar's plantation, and Farquhar, of course, does not realize that this man dressed as a Confederate is really a Union soldier. This man tells Farquhar the Yankees are fixing the railroads and already made it to Owl Creek Bridge; he also says that the commanding officer of that regiment has ordered the hanging of anyone who interferes with these fixtures. This allows Farquhar to understand how important they are and how much damage he could do to the Northern effort if he disrupted the railroad line on this bridge. He asks, "Suppose a man. . . should elude the picket post and perhaps get the better of the sentinel. . . what could he accomplish?" The soldier informs him a recent flood washed a great deal of wood against the bridge, and it is now dry and very flammable. We can assume, then, that this is the crime for which Farquhar is being hanged at the beginning of the story, and his attempt to burn the bridge was the "service" he tried to perform because he is "ardently devoted to the Southern cause" in the war.

Intermediate Algebra, Chapter 2, 2.3, Section 2.3, Problem 68

Problem A:
Jack has $\$800$ invested in two accounts. One pays $5\%$ interest per year and other pays $10\%$
interest per year. The amount of yearly interest is the same as he would get if the entire $\$800$ was
invested at $8.75\%$. How much does he have invested at each rate?

Problem B:
Jill has $800$ L of acid solution. She obtained it by mixing some $5\%$ acid with some $10\%$ acid. Her final
mixture of $800$ L is $8.75\%$ acid. How much of each of the $5\%$ and $10\%$ solutions did she use to get her final
mixture?

a.) Solve Problem A
b.) Solve Problem B
c.) Explain the similarities between the processes used in solving Problems A and B

In problem (a), let $x$ represent the amount invested at $5\%$ interest, and in problem (b), let $y$ represent
the amount of $5\%$ acid used.

a.) Step 1: Read the problem, we are required to determine the amount invested at each account.
Step 2 : Assign the variable. Then organize the information in the table.
Let $x = $ amount invested at $5\%$ interest.
Then, $800 -x =$ amount invested at $10\%$ interest.


$
\begin{array}{|c|c|c|c|c|c|}
\hline
& \rm{Principal} & \cdot & \text{Interest rate} & = & \rm{Interest} \\
\hline
5 \% & x & \cdot & 0.05 & = & 0.05x \\
\hline
10\% & 800 - x & \cdot & 0.10 & = & 0.10(800 - x) \\
\hline
\end{array}
$

Step 3: Write an equation from the last column of the table
$0.05x + 0.10 (800 -x) = 0.0875(800)$

Step 4: Solve

$
\begin{equation}
\begin{aligned}
0.05x + 80 - 0.10x &= 70\\
\\
-0.05x &= 70 - 80\\
\\
-0.05x &= -10\\
\\
x &= 200
\end{aligned}
\end{equation}
$

Then, by substitution
$800 - x = 800 - 200 = 600$

Step 5: State the answer
In other words, the amount invested at $5\%$ and $10\%$ interest rates is $\$250$ and $\$600$ respectively.

b.) Step 1: Read the problem, we are required to determine quantity of each solutions used.
Step 2 : Assign the variable. Then organize the information in the table.
Let $x = $ amount of $5\%$ acid used.
Then, $800 - y =$ amount of $10\%$ acid used.


$
\begin{array}{|c|c|c|c|c|c|}
\hline
& \text{Liters of solution} & \cdot & \text{Percent Concentration} & = & \rm{Quantity} \\
\hline
5\% & y & \cdot & 0.05 & = & 0.05y \\
\hline
10\% & 800 - y & \cdot & 0.10 & = & 0.10(800 - y) \\
\hline
\end{array}
$

Step 3: Write an equation from the last column of the table
$0.05y + 0.10 (800 - y) = 0.0875(800)$

Step 4: Solve

$
\begin{equation}
\begin{aligned}
0.05y+ 80 - 0.10y &= 70\\
\\
-0.05y &= 70 - 80\\
\\
-0.05y &= -10\\
\\
y &= 200
\end{aligned}
\end{equation}
$

Then, by substitution
$800 - y = 800 - 200 = 600$

Step 5: State the answer
In other words, the final mixture she must use is $200$ L of $5\%$ acid solution and $600$ L
of $10\%$ acid solution.

c.) In general, solving part A and B is similar in a way that the total amount or quantity
is equated with the sum of the individual amounts or quantities of each condition.

A block of mass 1.5 kg is placed on a rough table (horizontal) and is pulled by a constant force of 1.2 kgf. The coefficient of friction between the block and the surface is 0.3. Find the acceleration produced in terms of 'g'.

Hello!
By Newton's Second law, the acceleration is equal to the net force divided by the mass of a body. The net force is the vector sum of all forces acting on a body.
These forces in our problem are the traction force (horizontal), the friction force (horizontal), the gravity force mg and the reaction force R (both vertical).
Because the movement is horizontal, the acceleration and the net force are also horizontal. So the vertical forces are balanced, R = mg. Next, the friction force is 0.3R = 0.3mg = 0.45g (in Newtons).
The traction force is 1.2 kgf = (1.2g) Newtons. Thus the net force is equal to 1.2 g - 0.45 g = 0.75 g (N), and the acceleration is (0.75 g)/1.5 = 0.5 g.
So the answer in terms of g is 0.5.
 
 

how is the theme of the monkeys paw and sylvester and the magic pebble similar

"The Monkey's Paw" and "Sylvester and the Magic Pebble" are both stories that involve an element of magic as well as a hint of darkness. The theme of each of these stories is to be careful what you wish for.
In "The Monkey's Paw," the visitor, Sergeant-Major Morris, warns Mr. and Mrs. White as he is telling them about the paw. He states of the man who put a magic spell on the monkey's paw, "He wanted to show that fate ruled people’s lives, and that those who tried to change it would be sorry." Mr. and Mrs. White learn that their first wish is granted at the expense of their son's life. Theirs is not a happy ending.
In "Sylvester and the Magic Pebble," Sylvester, a donkey, wishes to become a rock to save himself from a hungry lion. Once the wish comes true, he learns that since he is no longer holding the magic pebble, he cannot wish again to be a donkey. Sylvester almost gives up hope and resigns to just be a rock. However, the ending of this story is a happier one as Sylvester is able to become a donkey again and reunite with his parents.

What are some study notes for "Unready to Wear"?

"Unready to Wear" by Kurt Vonnegut Jr. is a short story that features a male narrator, Herb; his wife, Madge; and the inventor of being amphibious, Dr. Konigswasser. Herb describes his life as an "amphibious" being. To be "amphibious" in the new sense of the word means that Herb, and many others like him, can exist just as a thought or a soul for most of the time, and he can choose to inhabit a human body when he wants to. He explains, however, that most of the time being in a body is annoying because it has so many practical wants and there are so many things you need to do to maintain it. Bodies "are pure nuisances when you stop and think about them" (Vonnegut, 147). They make people tired, hungry, sick, irritable, and so on. Since bodies make people feel insecure, feeble, weak, or just plain annoyed, they also cause problems between people. At a big event, for example, when many "amphibians" are occupying bodies, "people couldn't help being out of sorts, stuck in sweltering, thirsty bodies for hours" (Vonnegut, 150).
Dr. Konigswasser first discovered how to become amphibious and wrote a book about it that changed the world. Herb and Madge decided to become "amphibious" because Madge was so sick that her body was going to die soon anyway. Everyone who is "amphibious" appears to love it, but humans who still occupy bodies are afraid of the "amphibians" and are at war with them. They end up trapping Madge and Herb with some booby-trapped bodies and put them on trial. They accuse them of deserting humanity and shirking their duties as humans. During the trial, Herb reaches the conclusion that because people are afraid of having their bodies be uncomfortable or captive or destroyed, fear is the only weapon humans have. Without fear of capture, pain, or destruction, they are powerless. Herb uses this fear to make the court afraid and escapes with Madge.
Some of the major themes of the story include the following:
The drudgery of human life and how much people have to go through to simply survive.
Fear as a motivator in human behavior.
Body image and its ties to self-esteem, value, and worth.
Body competition and the envy and conflict it creates between people.
The inability to let go of material worth and material possessions.
The debate between staying and fighting for what you believe in or abstaining from the struggle.
The value of the mind versus the body, action versus thought, and pure reason versus emotion.

I need help finding the elevation points for each point on image 1. The following questions are for image 2: What is the contour interval? What are the elevations of lines A and B? Provide an approximate elevation for points W (point is inside the circle), X, and Y (point is on the line).

Contour maps can be intimidating to look at. A helpful trick is to find two index contours that are somewhat spaced apart, in order to count how many contour lines are between the two index contours. Once that is known, you can figure out what the map's contour interval is. For map 1, the 6,000 foot marker is just south of the red circle. Follow that down and around to the east and then back north, until you are parallel with point "X." Directly underneath "X" is the 5,750 index contour. Based on the number of lines between the 6,000 line and the 5,750 line, the contour interval of the map is 50. Going west of the 5,750 line to point X gives a rough elevation of between 5,950 and 6,000.
Point "W" is much easier. It's right on the 5,750 line. Point "Z" is also right on the 5,750 line. Point "Y" is just a bit west and downhill from "Z." It's past the next contour line, so it has to be below 5,700, but it's also above 5,650, because there isn't another contour line before that point.
Map 2 is simpler to interpret, because it's not so "crowded- looking" with contour lines. The index contours are 100 feet in elevation different. Using that, along with the number of lines between the indexes, gives us the contour interval of 20 feet per line. Point "Y" is right on the 400 line. Point "W" is inside the 300 line, but no other lines appear. This means it has to be greater than 300 and less than 320. Points "A," "B," and "X" are on or near special contour lines, with little perpendicular stubs hanging off of them. Those signal a depression in the ground. This means that point "B" is at an elevation of 60. "A" is at 80. "X" is somewhere between 40 and 20.
https://getoutside.ordnancesurvey.co.uk/guides/understanding-map-contour-lines-for-beginners/

https://www.backpacker.com/gear/reading-topo-maps-understanding-contour-lines

Discuss the Ethics of Aristotle.

Aristotle, like most thinkers of his period, divides thinking about morality into three categories.
Moral actions with respect to the city-state (polis) as a whole, or politics
Moral actions with respect to the household (oikos) or economics
Morality as pertaining to the individual character (ethos) or ethics proper
Aristotle writes about these topics in several works, most notably the Nicomachean Ethics, but also the shorter Eudemian Ethics as well as the Politics and Rhetoric.
Aristotle's account of ethics is often called "eudaimonian" from a a Greek word "eudaimonia" sometimes translated as "happiness" but which means something closer to flourishing or well-being. This refers to flourishing of humans qua humans rather than simply to momentary pleasure. For Aristotle, eudaimonia is something aimed at for itself, an end rather than a means to an end. Since humans, for Aristotle are by nature "political animals" (meaning that they gather in cities or "poleis"), ethics necessary involves considering humans in social and political context rather than merely as isolated individuals. 

How many states had to ratify the Constitution?

Article VII of the Constitution states that in order for the Constitution to become law, at least nine states needed to ratify it. The article is only one sentence long and states, “Article VII. The ratification of the conventions of nine states, shall be sufficient for the establishment of this Constitution between the states so ratifying the same.” Article VII is the last article of the United States Constitution. The states began to ratify the Constitution on December 7, 1787, and each state needed to hold a convention to debate the Constitution and either ratify or reject it. It took ten long and difficult months for the first nine states to approve the document. The ninth state, New Hampshire, ratified it on June 21, 1788, and the new Constitution went into effect on March 4, 1789. The first nine states to ratify the document were Delaware, Pennsylvania, New Jersey, Georgia, Connecticut, Massachusetts, Maryland, South Carolina, and New Hampshire.

How is the injustice overcome?

In this novel, there are two key injustices. One is the problem of Dana Matherson bullying Roy Eberhardt, who is the main character. The other injustice is the plight of the burrowing owls on the construction site of the Mother Paula's All-American Pancake House.
The problem of Dana is overcome by a combination of factors. First, Roy stands up to Dana, which temporarily deters him. After his injuries heal, Dana is out for revenge until he encounters Beatrice "The Bear" Leep. Beatrice is loyal to Roy because of his help with her stepbrother, Napoleon Leep. Beatrice intercepts Dana's bullying attempts twice, and the piece de resistance is that she ties Dana to a flagpole in only his underwear. He is literally stripped of his power.
The plight of the owls is that they are going to be destroyed if the pancake house is built. Napoleon Leep, also known as "Mullet Fingers," goes on a vigilante mission to bring justice to them. But when Roy gets involved, he has a more legal way of solving the problem. Through the help of his father, Roy learns that companies have to file an environmental impact statement before building. He lets a reporter know that the environmental impact statement is missing, and the conspiracy is uncovered. The mayor had received hush money to make the report disappear because it found that there were mated pairs of burrowing owls on the property. The burrowing owls are a protected species in Florida. Chuck Muckle, the company's vice president, is consequently demoted. The company's stock takes a nosedive after the story hits The Wall Street Journal, and to save face the company donates the site as an owl sanctuary. Justice is served.

Single Variable Calculus, Chapter 5, 5.4, Section 5.4, Problem 40

Find the integrals $\displaystyle \int^8_1 \frac{x-1}{\sqrt[3]{x^2}} dx$

$
\begin{equation}
\begin{aligned}
\int\frac{x-1}{\sqrt[3]{x^2}} dx &= \int \left( \frac{x}{\sqrt[3]{x^2}} - \frac{1}{\sqrt[3]{x^2}} \right) dx\\
\\
\int\frac{x-1}{\sqrt[3]{x^2}} dx &= \int \left( \frac{x}{x^{\frac{2}{3}}} - \frac{1}{x^{\frac{2}{3}}} \right) dx\\
\\
\int\frac{x-1}{\sqrt[3]{x^2}} dx &= \int \left( x^{\frac{1}{3}} - x^{\frac{-2}{3}} \right) dx\\
\\
\int\frac{x-1}{\sqrt[3]{x^2}} dx &= \int x^{\frac{1}{3}} dx - \int x^{\frac{-2}{3}} dx\\
\\
\int\frac{x-1}{\sqrt[3]{x^2}} dx &= \frac{x^{\frac{1}{3}+1}}{\frac{1}{3}+1} - \frac{x^{\frac{-2}{3}+1}}{\frac{-2}{3}+1} + C\\
\\
\int\frac{x-1}{\sqrt[3]{x^2}} dx &= \frac{x^{\frac{4}{3}}}{\frac{4}{3}} - \left( \frac{x^{\frac{1}{3}}}{\frac{1}{3}} \right) + C\\
\\
\int\frac{x-1}{\sqrt[3]{x^2}} dx &= \frac{3x^{\frac{4}{3}}}{4} - 3x^{\frac{1}{3}} + C\\
\\
\int^8_1 \frac{x-1}{\sqrt[3]{x^2}} dx &= \frac{3(8)^{\frac{4}{3}}}{4} - 3(8)^{\frac{1}{3}} + C - \left[ \frac{3(1)^{\frac{4}{3}}}{4} - 3(1)^{\frac{1}{3}} + C \right]\\
\\
\int^8_1 \frac{x-1}{\sqrt[3]{x^2}} dx &= \frac{3\left[(8)^{\frac{1}{3}}\right]}{4} - 3 (2) + C - \frac{3}{4} + 3 - C\\
\\
\int^8_1 \frac{x-1}{\sqrt[3]{x^2}} dx &= \frac{3(2)^4}{4} - 6 - \frac{3}{4} + 3 \\
\\
\int^8_1 \frac{x-1}{\sqrt[3]{x^2}} dx &= 12- \frac{3}{4} - 3\\
\\
\int^8_1 \frac{x-1}{\sqrt[3]{x^2}} dx &= \frac{33}{4}
\end{aligned}
\end{equation}
$

College Algebra, Chapter 3, 3.3, Section 3.3, Problem 32

Below is the graph of $f$.

"Please refer in the textbook."

(a) Determine all the maximum and minimum values of the function and the value of $x$ at which each occurs. (b) Find the intervals on which the function is increasing and on which the function is decreasing.

a.) Based from the graph, the maximum values 2 and 1 occurs when $x$ is -2 and 2 respectively. On the other hand, the minimum value -1 occurs when $x$ is 0.

b.) Based from the graph, $f$ is increasing on the intervals $(- \infty, -2)$ and $(0, 2)$. On the other hand, $f$ is decreasing on the intervals $(-2, 0)$ and $(2, \infty)$.

Describe the significance of the title of the poem “Does It Matter" by Siegfried Sassoon.

The significance of this poem's title hinges on its historical context: Siegfried Sassoon was one of a number of early twentieth-century writers whose work rose out of their experiences fighting in World War I. In much of Europe, this war created a sense of profound disillusionment with the modern world, both because of the role that modern nationalism had played in sparking the fighting and because modern weaponry had led to an unprecedented and horrific loss of life. On the broadest level, then, Sassoon's question echoes the pervading mood of the postwar era. The "it" in the poem's title is non-specific; although Sassoon goes on to mention several things it could refer to (lost limbs, blindness, etc.), we can also read it as a stand-in for the entire post-WWI world, where nothing seems to matter.Digging deeper, however, it is clear that Sassoon thinks the war and its effects do matter. The repeated juxtaposition of the somewhat flippant question "does it matter?" with brutal images of war's violence (e.g. "losing your legs") is intentionally jarring; we instinctively feel that something so awful does matter, and we stop short (1). Sassoon further heightens our discomfort by writing in a sing-song (mostly anapestic) meter and employing words that feel trivial, empty, or overly cheerful in context; read against "losing your sight," for instance, the description of the available work as "splendid" comes across as sarcastic (6, 7). The poem's title, then, is bitter and ironic; Sassoon suggests that the things he describes do matter, as much as people would like to explain them away or minimize them as noble, patriotic sacrifices.

Why is violet in lowest part of rainbow?

Rainbows are usually visible after rain - or after watering plants using a hose! Rainbows are a product of light hitting water, in simple terms.
Light, though we usually perceive it as yellowish (sun) or whitish - though we can't actually see light - , is actually a combination of all colors (while black is when there isn't one). Each color of light corresponds to a certain wavelength - and a certain energy. That is, light is a combination of waves of different energies and wavelengths, and as humans, our eyes perceive this as difference in color. We cannot see every wavelength of light. We can only perceive those of a certain wavelength, referred to as the visible wavelength - the range 390-700 nm. There's more light beyond this - infrared, ultraviolet are one common terms you might hear.
When passing through a prism, light refracts and is separated into it's different components in a continuous manner. The prism separates the light into individual components, and bends them differently according to the wavelength of that component. Longer wavelength components get refracted less, and the shorter ones get refracted the most - or in other words, shorter ones get bent more than longer ones. Rainbows are formed when light hits water droplets in the atmosphere, which act as tiny prisms. Light is refracted, and we can see it's individual components as the colors of the rainbow. It is in this particular order - ROYGBIV - because of how light is refracted. Red has a wavelength of 700nm, Violet has a wavelength of around 390nm. Hence, red is refracted less and violet the most as they are at the ends of the visible spectrum. The other colors are of intermediate lengths and go from longer to shorter from orange to indigo. Hence, violet, as it is diffracted the most, is perceived to be at the bottom of a rainbow.
 
---In brief:
Rainbow is created by the refraction of light as it hits water droplets that act as prism. Violet has a short wavelength and is refracted more - red has a long wavelength and is refracted less. The arrangement of the colors of the rainbow is due to the difference in the extend to which they are dispersed or 'bent'. Violet is at the short end of the visible spectrum and red at the longer end and hence, they are at the ends of the rainbow - top and bottom.