How is the first paragraph of the story important to the passage as a whole?

The first paragraph of the story goes a long way toward setting the mood for the text. There is something sad about the statement that none of the men "knew the color of the sky." It is as if there is nothing more in the world than what one can see before oneself, no chance of a higher power or redemption, second chances, or even purpose. The waves are the color of "slate," a dark and oppressive gray; this color feels impenetrable and heavy, like the stone for which it is named. Further, the narrator says that

The horizon narrowed and widened, and dipped and rose, and at all times its edge was jagged with waves that seemed thrust up in points like rocks.

This description of the horizon changing uncontrollably and unpredictably contributes to the idea that life is both uncontrollable and unpredictable. Further, the negative connotation of a word like "jagged" and the description of the water that looks like pointed and dangerous rocks, adds to the unknowability of a world where water can seem like sharp stone. The mood is heavy and menacing, as though there is always some danger awaiting on the horizon, a horizon that is ever-changing.

I have to write an argumentative paper on history of organized crime. I want to discuss how immigrants arriving in this country in hopes of the American dream, upon realizing how difficult it was, might turn to organized crime. My focus would be specifically Italian immigrants. I am struggling with developing a thesis for this paper.

In discussing this, your first job should be to distinguish between facts and myths. The actual reality, for the past century, has been that immigrants, on the average, have been more law-abiding than American citizens, and less likely to commit and be convicted of crimes. On the other hand, a story, for example, of a tailor and his wife who moved from Italy to the United States, opening a dry cleaning and tailoring shop, and had a couple of kids who grew up and went to college doesn't make for a thrilling movie, while stories of Mafia bosses are dramatic and exciting. 
Like most immigrant communities, the Italian-Americans of the early twentieth century were, overall, hard working and law abiding, although, as within any group, there were among them a few who turned to crime. The precipitating factor for the growth of organized crime was 18th Amendment to the U.S. Constitution, or Prohibition, which made the sale of alcohol illegal. The response to this was a growth in organized crime, both among ethnic groups in urban centers and the renowned moonshiners of Appalachia. The Sicilian Mafia, an existing organized crime group in Italy that was under pressure from the fascist dictator Mussolini, saw this as an opportunity to expand operations into the United States. 
Thus your thesis might focus on how Prohibition led to the growth of organized crime, and how after alcohol was legalized, and profits from bootlegging disappeared, organized crime moved into dealing other illegal substances and other activities. You might conclude by speculating on how legalization and regulation of drugs may actually reduce organized crime by taking away its most profitable business. 
https://www.history.com/topics/crime/mafia-in-the-united-states

Why does HCl, being a covalent compound, dissociate in water?

Strong acids or bases can dissociate completely when placed in a solution of water. HCl is a strong acid with a pH value between 0 and 2. Pure water has a pH of 7. When placing HCl into solution with water, it will shift the pH by increasing the number of Hydrogen ions (H+) in solution. When HCl dissociates, it will add H+ ions along with Cl- ions to the solution.
Actually, because the compound HCl contains H atoms bound to the nonmetal Chlorine, this type of compound is known as a nonmetal hydride. When placed in water, the HCl acts as a source of H+ ions thus lowering the pH of the solution.
To summarize, when HCl dissolves in water, its components dissociate into H+ ions and Cl- ions when the covalent bond is broken between them. Water molecules are polar with oxygen atoms negatively charged and the hydrogens positively charged. This helps make water an excellent solvent for polar compounds like HCl due to the attraction of opposite charges.
https://www.biologycorner.com/worksheets/acids_bases_coloring.html

In Macbeth, how does Macbeth betray Lady Macbeth?

One could argue that Macbeth betrays Lady Macbeth by completely distancing himself from her after Duncan's assassination, neglecting her psychological and emotional needs, and acting independently without informing her of his wicked plans. After Macbeth informs his wife about the witches' favorable prophecies, Lady Macbeth formulates a seemingly foolproof plan to help her husband successfully assassinate King Duncan with impunity. Lady Macbeth not only plots King Duncan's murder but also participates in the assassination by placing the bloody daggers back into the king's chamber and acting surprised. Despite her going to extreme lengths to help her husband attain the Scottish throne, Lady Macbeth is immediately betrayed by her husband when he assumes complete authority, refuses to take her advice, and commits horrendous crimes behind her back. Macbeth does not inform Lady Macbeth of Banquo's murder or his orders to slaughter Macduff's entire family. In addition to acting independently, Macbeth also emotionally neglects his wife. While Lady Macbeth sleepwalks and hallucinates, Macbeth distances himself and completely focuses on destroying his political enemies. In act 5, Macbeth learns of his wife's suicide and is unfazed by the news, which emphasizes his callous nature and complete disregard for her well-being. Overall, Macbeth betrays his wife by acting independently, neglecting her emotional needs, distancing himself from her at crucial moments, and refusing to inform her about his bloody orders.

Macbeth betrays Lady Macbeth in his total withdrawal from her. He loses empathy for her by the end of the play, although he once loved her and was deeply influenced by her opinion of him.
After Macbeth murders Duncan, however, his heart begins to harden. Macbeth starts to make decisions without consulting his wife. It is evident by act 4 that he is not spending much time with her because it is her servants who first discover she is sleepwalking and muttering dangerous words in her sleep.
Finally, in act 5, when he hears the scream that means she has committed suicide, Macbeth doesn't even recognize it as the voice of his once beloved spouse. He merely says that sounds such as shrieks used to startle and unnerve him but now have no effect. When he is told it was Lady Macbeth who screamed as she died, all he can say, indifferently, is that she would have died sooner or later anyway:

She should have died hereafter.

Lady Macbeth envisioned the two of them sharing the throne and enjoying its power and prestige together. Instead, she is psychologically betrayed by a husband who turns hard-hearted and self-obsessed.

He betrays Lady Macbeth in the sense that he dispenses her advice and starts to act unilaterally. Lady Macbeth, more than anyone else, is responsible for her husband's rise to power; she made him what he is. She planned King Duncan's murder; she questioned Macbeth's manhood, goading him into committing the wicked act; she even drugged Duncan's guards and planted bloody daggers on them to avoid the merest hint of suspicion. But as soon as Macbeth's on the throne, he starts acting on his own initiative. Hubris takes over Macbeth's character, dissolving what had previously been very much a power marriage. Puffed up with such overweening pride, Macbeth carries out a series of increasingly vicious murders, showing that whatever "milk of human kindness" there may have been in his soul has now turned rancid.
To some extent, Lady Macbeth has helped create a Frankenstein's monster which is now completely out of control. As the bodies start piling up, and Macbeth wades deeper and deeper through blood, Lady Macbeth cannot handle the immense psychological strain that her husband's murderous rampage has unleashed upon her fraying mind. Wicked though it was, at least Lady Macbeth's plot to murder Duncan had a certain rationale behind it. But there appears to be no such justification for Macbeth's murder of Macduff's family, for example. Crucially, Macbeth is defying fate, whereas Lady Macbeth's plot to murder Duncan was entirely in keeping with the Weird Sisters' prophecy. Macbeth, in defying fate, is also betraying his wife, leading directly to her psychological breakdown and eventual death.
 
 

How does Pip attempt to change his life in Great Expectations by Charles Dickens?

After going to Satis House as a young boy and being ridiculed and called "common" by Estella, Pip feels the sting of being from the lower class and desires from then on to better himself.
Pip feels that good fortune comes to him when Mr. Jagger arrives at the forge and brings Pip the "astonishing news" that he has "Great Expectations." Pip is elated,

My dream was out; my wild fancy was surpassed by sober reality; Miss Havisham was going to make my fortune on a grand scale. (Ch. 18)

Pip then leaves the forge after having been released from his apprenticeship to Joe, and he arrives in London with the promise of becoming a gentleman. There he rooms with the former "pale young gentleman" whom Pip fought as a boy on his initial visit to Miss Havisham's, Herbert Pocket. From Herbert, Pip learns proper table manners, and Herbert's father, Matthew Pocket, acts as Pip's tutor.
In his efforts to become a gentleman, however, Pip seeks to elevate himself by rejecting all that is associated with his lowly childhood. Sadly, he rejects Joe because of his crude manners and discomfort when he comes to London to visit. Further, Pip is critical of his childhood friend Biddy; in short, Pip changes into a snob, rather than a true gentleman, who appreciates quality in anyone who has it. Pip also seeks to ingratiate himself with Miss Havisham and Estella in his desperate love for her, perceiving her as having "indescribable majesty....and charm." He has confessed earlier to Biddy, "I admire her dreadfully and want to be a gentleman on her account." (Ch.17)
Of course, Pip makes the grave mistake of placing material values above spiritual, as he rejects the genuineness and love of Joe, he is repulsed that his benefactor is the grateful, but criminal Magwitch rather than the dysfunctional, but aristocratic Miss Havisham, and he finds Estella rather than the sweet and kind Biddy admirable. Nevertheless, he does change his life, as he learns important lessons in London from Herbert and Wemmick and even Magwitch, lessons that bring him back to the forge to renew his relationship with Joe and revive his love for the kind and worthy man along with the genuine and good Biddy.

Question 1 Suppose that you want to test the claim that the mean salary of veterinarians is $91,350. You collect salary information from a sample of 60 veterinarians and find that the mean salary in the sample is $90,350. The standard deviation is $5,000. Part (a) At a level that would be understandable to a senior in high school, explain why it is necessary to carry out a hypothesis test for this claim (rather than rejecting the claim outright since the observed sample mean is clearly different from the claimed population mean). Part (b) Using a level of significance α of 0.1, test the null hypothesis H0: µ = $91,350 using the 6-step procedure.

We are asked to test the claim of the mean salary being $91,350 (mu = 91350 ) using a sample of 60 salaries with a mean of $90,350 ( bar(x)=90350 ) and a population standard deviation of $5000 (s=5000.) ** I will recalculate if this is a sample standard deviation at the end.**
(a) The sample mean is not the sought after population mean, but we do not reject the claim outright. We would not expect the sample mean to be exactly 91350; there is some variability expected. If we were to do another sample of 60 salaries it is unlikely that the mean of this new sample would be 90350.
However, we do expect the sample means to be "close" to the population mean. In fact an application of the central limit theorem tells us that as the sample size grows, the means of the samples will be forced closer to the true population mean.
We use hypothesis testing to determine if the sample mean is outside of the expected range of sample means assuming that the population mean is actually 91350. Hypothesis tests take into consideration the size of the sample and how confident we want to be on accepting/rejecting the claim.
(b) You may need to adapt this to your 6-step process:
H_0:mu=91350 This is the null hypothesis and our claim.
H_1:mu != 91350 This is the alternative hypothesis.
With alpha=.1 we compute the critical value(s):
Since the alternative is two-tailed (we allow for the actual mean to be above or below 91350) we look for the z-value with area .95 to the left (or .05 to the right.) Here z=1.645 (Some texts will use 1.64 or 1.65.) ((This number can be acquired from a standard normal table or from technology.))
The critical values are z=+- 1.645
We now compute the test value. We have n=60,sigma=5000,bar(x)=90350, mu=91350 so the test value is z=(90350-91350)/(5000/sqrt(60))~~-1.549
Since the test value is within the noncritical region (-1.549>-1.645) we do not reject the null hypothesis.
There is insufficient evidence to reject the claim that the mean salary is $91,350.
**********************************************************
If this was the sample standard deviation we run a t-test: The sample is large enough that the critical values and test values are virtually the same with the same answer.
http://mathworld.wolfram.com/HypothesisTesting.html

What are two moments in the book Night that gave you hope?

There are few moments throughout the novel that inspire hope in the reader as Elie recalls his horrific experience surviving the Holocaust. During the selection process in chapter 5, the reader has hope after Elie's father survives the first selection despite his dire conditions and waning health. Elie is excited that his father has passed the first selection, and a few days go by before the Blockälteste reports that some prisoners will be forced to endure another round of selections. Before Elie's father leaves for the second selection, he gives his son a knife and spoon, which Elie refers to as his inheritance. The reader is filled with anguish and sympathizes with Elie's difficult situation. Fortunately, Elie's father miraculously survives the second selection, and the reader is filled with a sense of hope. Elie says,

Were there still miracles on this earth? He was alive. He had passed the second selection. He had still proved his usefulness. . . . I gave him back his knife and spoon (Wiesel, 76).

Toward the end of chapter 5, the Russian Army closes in on the concentration camp, and the Jewish prisoners have hope that the Russians will arrive before their evacuation. The reader is also filled with a sense of hope that the Russian Army will capture the camp and liberate the Jewish prisoners. Unfortunately, Elie and the rest of the Jewish prisoners are forced to evacuate the camp in the middle of the night before the Russian Army arrives and liberates them.

Please summarize about the roles in prison in reducing recidivism from the link https://www.huffingtonpost.com/entry/if-we-want-fewer-prisoners-we-need-more-compassion-when-they-re-enter-society_us_55ad61a5e4b0caf721b39cd1

This article addresses the need for programs which help prisoners re-assimilate to society. Many prisoners are released without money or resources; the challenge of emerging into society without money and without much-needed counseling can result in many returning to prison very quickly. To combat this, some states have special re-entry programs aimed at assisting their former offenders and reducing recidivism rates.
In Louisiana, where the incarceration rate is very high, there is a program providing anger management classes and helping prisoners learn a trade. Recidivism rate has dropped, although it is not possible to correlate this directly with this particular program. San Quentin Prison in California offers college educations to its inmates. The National Criminal Justice Reference Service found in a 2013 study that programs like this do lower recidivism rates, and also that those who pursue college education in prison are likely to survive longer on the outside before reoffending.
Of course, there are those who oppose these programs as a poor use of tax dollars. However, given that a college education "inside" greatly minimizes recidivism rates, more money is being directed toward this initiative.
Another program being run in Washington State offers much-needed support to those who have been recently released, including housing, interview training, job skills, help with substance use disorders, and so on. This program is helping address the six "basic needs" a person must have to be a valuable member of society: livelihood, residence, family, health, criminal justice compliance and social connections. With these needs met, recidivism rates decline. Even picking up inmates upon their release from prison and helping them readjust has been shown to have a significant positive effect.
Often, it seems that ex-offenders simply need more compassion and understanding in order to readjust to the real world.

Explain the roles and actions of different levels of government in relation to trade.

I am assuming that your question is about United States government and relates to international trade, not trade within the United States.  The only level of government that has control over the United States trade with foreign nations is the federal government, as mandated by the Constitution. Other levels of government have no power at all. 
Article I, Section 8 states that Congress regulates commerce with other countries.  There are a few different options that can be exercised in foreign trade.  One is to impose a tariff on in-coming goods, which makes them more expensive for Americans to buy, thus encouraging people to buy American-made goods instead.  This runs the risk of other nations doing the same, which means that fewer people will buy American-made goods. Another option is to have no tariff at all, which is pure "free trade," so that goods move freely over borders without any taxation.  Finally, an embargo can be imposed, which is generally done for political reasons, although one could certainly be imposed for a situation in which unsafe products from other countries were being sold.  We have had an embargo against Cuban products for a very long time. And while no one discusses this, I am sure that we are not supposed to be purchasing any goods from North Korea.
State and local governments are not permitted to enter into trade agreements with foreign countries, and it is easy to see why.  It would destroy the cohesion of the country.  If New York had a trade agreement with France, and Pennsylvania imposed tariffs upon French goods, it would be a disaster.  French goods would be routinely smuggled from New York to Pennsylvania. And that is just one small example.  To be a nation, there must be one cohesive policy that covers all the states. 
None of this stops anyone in any state from selling to or buying from other countries. It simply means that whatever rules apply to the situation, they have been decided upon by Congress, and they apply to all the states.

What's the difference between the state and federal government?

The United States features a division of powers between the fifty states and the national government. This division of power is called federalism. Both governments are similar in form and act directly on their respective citizens, but they occupy different spheres of responsibility.
When the United States was founded, and through most of the nineteenth century, the locus of most government activity was the states. The federal government maintained the army and navy, delivered the mail, and did little else. That balance between state and national governments has been substantially changed, if not reversed, with the federal government entering more and more areas that were formerly the province of the states.
The states and the national government are very similar in form. All fifty-one governments are divided into the three familiar branches: legislative, executive, and judicial. Forty-nine of the fifty states have bicameral (two house) legislatures like Congress, Nebraska being the exception. But the state governments often differ from the national government in important respects. For example, all executive branch officers of the national government are essentially agents of the president, assisting him in carrying out his constitutional responsibility to “take care that the laws be faithfully executed.” In the states, by contrast, certain executive officers, such as the attorney general or state comptroller, are often independently elected officers not dependent on the governor for their authority.
The national government is a government of limited powers. It may exercise only those powers granted to it by the Constitution. By contrast, the state governments pre-date the Constitution and therefore do not derive their powers from the Constitution. They are, however, subject to limitations imposed by the Constitution. Some of these restrictions are found in the original Constitution, such as the prohibition on bills of attainder (conviction of crime by legislative action), ex post facto laws (laws punishing an act that was not illegal when committed), or laws impairing the obligation of contracts in Article I, section 10. Others have been added by the amendments to the Constitution, such as the requirements that no state deny any person the right to vote because of race, color, or previous condition of servitude, or sex, contained in the Fifteenth and Nineteenth Amendments. The Courts have also found implicit limitations. For example, the Constitution in Article I, section 8, grants Congress the power “To regulate Commerce with foreign Nations, and among the several States, and with the Indian Tribes.” The Supreme Court has interpreted this grant of power as imposing an implicit limitation on the power of the states to enact legislation that affects interstate commerce.
Whereas the national government is a government of limited powers, the state governments exercise the three great powers of government: police, taxation, and eminent domain. The police power is the most extensive of these powers. It is the power to legislate to promote the health, safety, morals, and welfare of the people. The power of taxation is the power to compel exactions from the populace for the support of the government. And the power of eminent domain is the power to seize property, upon payment of fair compensation, for government use. The federal government exercises the latter two powers. But the national government does not enjoy the police power. Because of expansive definitions of its delegated powers, such as its power to regulate interstate commerce, however, the federal government has been able to enact much police power type legislation. The regulation of food and drugs is an example of a police power–type regulation enacted pursuant to Congress’s power over interstate commerce.
Both governments enact and enforce criminal laws. Sometimes these laws conflict, and conduct that is illegal under the law of one government is legal under the law of the other. For example, marijuana is classified as a schedule I controlled substance under federal law and is illegal to possess or distribute. On the other hand, several states, including California, have made possession and use of marijuana legal. Theoretically, Californians who take advantage of their state law to possess marijuana can be prosecuted in federal court. The federal Department of Justice has, however, declined thus far to prosecute such violations in states where marijuana possession is permitted. That is a policy decision, however, and is subject to change at the discretion of the president and the attorney general.
Under the federal system, the states and the federal government are each supreme in their own spheres. But in case of a conflict, federal law triumphs by virtue of the Supremacy Clause in Article VI of the Constitution. That clause says that the Constitution, the laws enacted pursuant to the Constitution, and treaties made under the authority of the United States are the supreme law of the land and thus take precedence over contrary state laws. This precedence applies where there is an explicit conflict between state and federal laws, as well as to certain situations when federal law preempts even non-inconsistent state law because the subject requires national uniformity.
In sum, the states, although much diminished, still exercise important governmental powers. They are independent actors and not merely administrative organs of the federal government. The national government has expanded well beyond the scope envisioned by the framers of the Constitution by liberal interpretation of the powers granted Congress in Article I and has probably supplanted the states as the agency of government most important to the average person. But the recent decision in the Obamacare case, limiting the interstate commerce power, suggests a halt to the ever-expanding scope of those powers, if not an actual retrenchment. Federalism may be on life support, but it still survives.

The United States of America is a Federal Nation. Federalism is a framework of the Constitution designed to promote governance and democracy. It provides for a system in which the governance powers are divided between the Federal (National) Government and the State Government. Both of these governments have their own separate Legislative, Executive and Judicial branches. Although the Constitution of United States does not specifically define the term 'Federalism', but it incorporates several provisions that specify the power domain of the Federal and the State governments.

Section 8 of Article I of the Constitution of U.S. grants exclusive powers to the Congress (Federal Government) to levy and collect taxes, to declare war, to make laws for carrying into execution the powers conferred upon it under this provision. Section 9 of Article I of the Constitution prohibits the Congress from taking certain decisions such as suspension of privilege of the writ of Habeas Corpus. The Federal government is also exclusively empowered to enter into treaty, alliance or confederation with other countries or organizations. In addition to these expressed powers, the Congress also assume certain inherent powers emanating from the Preamble such as to defend from foreign and domestic enemies (Powers inherent to a sovereign nation), regulate telecommunications etc.

On the other hand, the Constitution also grants various powers to the State governments. The Tenth Amendment to the U.S. Constitution specifically provides that the powers not granted to the Federal government are reserved for the States and the People. The States governments have the same model as that of the Federal government. They can enact their own laws and constitution, have their own administrative system and set up their own judicial system.

There are certain powers which are concurrently exercised by the Federal government and the State government such as taxation powers, power to take general welfare measures etc.

However, despite of the division of powers between the Federal government and the State Government, Article VI of the U.S. Constitution provides for the supremacy of the Federal law over the State law. The Federal law and the Constitution take precedence over the State laws and their Constitution.

For example, several States in the United States allow legalization of Marijuana. On the other hand, the Federal law bans Marijuana. As the Federal law prevails over the State law, the Supreme Court of United States in the case of Gonzales v. Reich (2005) upheld the law of the Federal government.

Conclusively, the Federal government and the State governments emanate from the concept of Federalism. As discussed above, there are certain domains in which the Federal government exclusively exercises the powers. The reserved powers are exercised by the State governments. The concurrent powers are exercised by both the governments. However, in case of any inconsistency, the Federal law prevails over the State law. Thus, the Federal and the State Governments in the United States differs in terms of the powers which can be exercised by them according to constitutional provisions.

A sector of a circle of radius 8cm subtends a 90 degree angle at the center of the circle. If the sector is folded without overlap to form the curved surface of a cone, find the: [i] base radius of the cone [ii] height of the cone.

Hello!
Denote the radius of the original circle as R and the base radius of the cone as r. Then the length of the original circle is 2piR , and the given sector is a one quarter of the entire circle, hence the length of its curved part is (piR)/2.
And this length becomes the length of the entire base of the cone. This means (piR)/2 = 2pir, thus r = R/4 = 2 cm. This is the answer for [i].
The height of the cone, denote it h, forms a right triangle with a base radius of the cone and its slanted height. The slanted height is obviously R, and h^2 + r^2 = R^2, so h = sqrt(R^2-r^2) = sqrt(60) = 2sqrt(15) (cm). This is the answer for [ii].

what type of character is gandalf

There are several ways literary scholars classify, or group, characters. Sometimes we talk about protagonists (main characters) and antagonists (opposing characters). Other times we talk about static characters—characters who don't change much in a story and often play a short role. Finally, we talk about changing or dynamic characters, which are individuals who shift and change, often playing a more significant role in a story.
Gandalf is not a protagonist in our story; the story does not focus on him. He's a supporting character who comes alongside Bilbo and his friends on their journey to the Lonely Mountain. He plays a very significant role in the plot by encouraging Bilbo to accompany the dwarves and to act as their jewel thief. Gandalf constantly shows that he believes in Bilbo, though Bilbo begins the story with minimal courage. One time when we see Gandalf's belief in Bilbo's strength is when he says:

"In fact I will go so far as to send you on this adventure. Very amusing for me, very good for you -- and profitable, too, very likely . . ." (ch. 1)

Gandalf chooses Bilbo to go on this adventure to the Lonely Mountain. Even when the dwarves look down upon Bilbo, saying, "He looks more like a grocer than a burglar!" (ch. 1), Gandalf defends him.

"You asked me to find the fourteenth man in your expedition, and I chose Mr. Baggins. Just let any one say I chose the wrong man or the wrong house, and you can stop at thirteen and have all the bad luck you like, or go back to digging coal" (ch. 1).

Gandalf is continually supportive of Bilbo, reminding the dwarves that he has more bravery and strength than anyone initially thinks.
Gandalf accompanies them for portions of their journey, and he rescues them from their enemies at several points. For example, he protects Bilbo and the dwarves from the trolls, Bert, Tom, and Bill, who are trying to eat them in chapter 2.
Overall, Gandalf is a supporting character. He's important but not a protagonist. Gandalf is consistently good, selfless, and helpful to those around him. He does not change significantly in the novel, so we would consider him a static character. Even so, he plays a very important roll in The Hobbit.

Gandalf is a good wizard, a kind, often humorous, but wise leader. He recruits Bilbo, an unassuming Hobbit, to join a group of Dwarves on a journey because he discerns that Bilbo has potential. Gandalf is a very powerful wizard who could solve almost all problems himself if he wanted, but he prefers to develop the talents of other creatures when he can. 
Gandalf has a marked tendency to flit here and there to take care of other responsibilities. This leaves Bilbo on his own to cope with dangerous situations without his help. While this may seem unreliable on Gandalf's part, it allows Bilbo to learn to think for himself and hone his leadership skills. 
Adventure always seems to emerge alongside of Gandalf. As the text says:

Gandalf! If you had heard only a quarter of what I have heard about him, and I have only heard a very little of all there is to hear, you would be prepared for any sort of remarkable tale. Tales and adventures sprouted up all over the place wherever he went, in the most extraordinary fashion.

How does Austen present love throughout the book?

Austen presents love as something which is vital to a good marriage.  We see that the Bennets' marriage is a loveless one: Mrs. Bennet is a ridiculous gossip who is well-known for being socially inappropriate; Mr. Bennet can hardly stand her and retreats to his study to escape her whenever he can.  He admits that it wasn't love that brought them together, and look at where they've ended up.  Likewise, the marriage between Lydia and Mr. Wickham isn't founded on love.  Near the end of the novel, the narrator mentions that it doesn't take long for them to completely tire of one another. 
The relationships between Jane and Mr. Bingley, and Elizabeth and Mr. Darcy, however, are founded on love and both take some time to come to fruition.  In this way, Austen also presents love as something that takes time to develop.  The best, most egalitarian relationships in the book, then, are founded on love, and because love is something that takes time to grow, these loving relationships also require time.

Single Variable Calculus, Chapter 5, 5.4, Section 5.4, Problem 58

A particle moves along a line so that its acceleration of time $t$ is $a(t) = 2t + 3$ $\left( \displaystyle \text{ measured in }\frac{m}{s^2} \right)$ with the initial velocity $v(0) = -4$.
a.) Find the velocity at time $t$

$
\begin{equation}
\begin{aligned}
\int a(t) dt &= \int (2t + 3) dt\\
\\
\int a(t) dt &= 2 \int t dt + \int 3 dt\\
\\
\int a(t) dt &= 2 \left( \frac{t^{1+1}}{1+1} \right) + 3 \left( \frac{t^{0+1}}{0+1} \right) + C\\
\\
\int a(t) dt &= \frac{\cancel{2}t^2}{\cancel{t}} + 3t + C\\
\\
\int a(t) dt &= t^2 + 3t + C
\end{aligned}
\end{equation}
$

We know that $a(t) = v'(t)$, so

$
\begin{equation}
\begin{aligned}
v'(0) &= (0)^2 + 3(0) + C = -4\\
\\
C &= -4
\end{aligned}
\end{equation}
$


Then the velocity at time $t$ is
$v(t) = t^2 + 3t - 4$

b.) Find the distance traveled during the time period $0 \leq t \leq 3$ we know that $v(t) = t^2 + 3t - 4 = (t+4)(t-1)$, then $(t+4)(t-1) = 0$
$t = - 4$ and $t = 1$
Only $t = 1$ is in the interval $[0,3]$, thus the distance traveled is...

$
\begin{equation}
\begin{aligned}
\int^3_0 |v(t)| dt &= \int^1_0 - v(t) dt + \int^3_1 v(t) dt\\
\\
\int^3_0 |v(t)| dt &= \int^1_0 \left( -t^2 - 3t + 4 \right) dt + \int^3_1 \left( t^2 + 3t - 4 \right) dt\\
\\
\int^3_0 |v(t)| dt &= \left[ -\frac{t^3}{3} - \frac{3t^2}{2} + 4t \right]^1_0 + \left[ \frac{t^3}{3} + \frac{3t^2}{2} - 4t \right]^3_1\\
\\
\int^3_0 |v(t)| dt &= \frac{-(1)^3}{3} - \frac{3(1)^2}{2} + 4(1) - \left[ \frac{-(0)^3}{3} - \frac{3(0)^2}{2} + 4(0) \right] + \frac{(3)^3}{3} + \frac{3(3)^2}{2} - 4(3) - \left[ \frac{(1)^3}{3} + \frac{3(1)^2}{2} - 4(1) \right]\\
\\
\int^3_0 |v(t)| dt &= \frac{-1}{3} - \frac{3}{2} + 4 + 9 + \frac{27}{2} - 12 - \frac{1}{3} - \frac{3}{2} + 4\\
\\
\int^3_0 |v(t)| dt &= \frac{89}{6} \text{ meters} \qquad \text{or} \qquad \int^3_0 |v(t)| dt = 14.83 \text{ meters}
\end{aligned}
\end{equation}
$

What are the arguments that were put forward against the change of the social services 1946 referendum in Australia?

The 1946 Constitutional referendum in Australia defined the ability of the legislative branch to pass laws related to social services, including unemployment insurance, allowances for pregnant women and widows, medical services, pharmaceutical aid, and benefits for students. Many of these social services already existed in Australia prior to the referendum, but its passage clarified the extent to which the government could provide aid, and made the existence of the laws constitutional. One concern about the expansion of social services powers was the increase of revenue granted to the Commonwealth relative to the states; in 1942, the Commonwealth became the sole government entity responsible for collecting income tax, taking some responsibility away from the states. Some Australians were concerned about the increasing centralization of taxation, especially when the Commonwealth increased taxes to allow benefits for the sick and unemployed. Another argument against the referendum was that the increase in autonomy granted to the Commonwealth would subvert its constitutional role. Those against the referendum argued that it would grant the Commonwealth too much legislative power, in addition to providing it with an increase in tax revenue. Overall, the opponents of the 1946 referendum were primarily concerned about how it would provide both more tax income and more legislative power than the Constitution had allowed at the time, and promoted conforming to the Constitution's existing allowances rather than changing it to protect these new powers. However, the referendum passed with 54% of the vote, and the Constitution was amended.
https://www.abs.gov.au/Ausstats/abs@.nsf/Lookup/8E72C4526A94AAEDCA2569DE00296978

Single Variable Calculus, Chapter 2, 2.5, Section 2.5, Problem 11

Show that the function $f(x) = (x + 2x^3)^4$ is continuous at the number $a = -1$ using the definition of continuity and the properties of limits.

By using properties of limit,

$
\begin{equation}
\begin{aligned}
& \lim \limits_{x \to -1} (x + 2x^3)^4 && = (\lim \limits_{x \to -1} x + 2 \lim \limits_{x \to -1} x^3)^4
&& \text{Apply sum and power law}\\
\\
& \phantom{x} && = [-1 + 2(-1)^3]^4
&& \text{Substitute the given value of $a$}\\
& \phantom{x} &&= 81

\end{aligned}
\end{equation}
$


By using the definition of continuity,
$\lim \limits_{x \to a} f(x) = f(a)$




$
\begin{equation}
\begin{aligned}
& \lim \limits_{x \to -1} (x+2x^3)^4 && = f(-1) = [-1+2(-1)^3]^4\\
& \phantom{x} && = 81
\end{aligned}
\end{equation}
$


Therefore, by applying either of the two, we have shown that the function is continuous at -1 and is equal to 81

Do you think Kitty’s punishment is too severe?

Kitty's "punishment" of not going to Brighton is not too severe. It is not a punishment at all but sensible parenting. Elizabeth had earlier begged her father not to allow Lydia to go to Brighton, where the regiment of soldiers were moving. Elizabeth had warned that Lydia would be an embarrassment with her flirting and would be entering into a dangerous environment that would invite scandal. When Lydia does actually seriously jeopardize both herself and the family reputation by running off with Wickham, Mr. Bennet finally comes to his senses.
Up until that crisis, Mr. Bennet has taken a cavalier attitude toward his parental responsibilities, basically letting his daughters do whatever they want. He withdrew from a disappointing marriage to the books in his library. This worked with the older two daughters, Jane and Elizabeth, who were intelligent and sensible, but not with the younger three.
Seemingly all his life, Mr. Bennet has been ruled by the idea that everything will work out somehow. For this reason, he doesn't put aside money for his daughters to have dowries or curb his wife's embarrassing matchmaking tendencies. Only after his permissiveness leads to near disaster does Mr. Bennet wake up.
Although Kitty takes the restraints put on her as the end of the world, in fact, Mr. Bennet is doing her a favor by keeping her away from Brighton and the temptation to run away with a dashing young officer who would love her and leave her—leaving her as tainted goods in a society in which, for the unmarried female, sexuality purity was the highest value. Not getting to go to Brighton is no punishment: most sixteen-year-olds from good homes would not be allowed to go to such a place—especially while it is swarming with army officers—any more than most sixteen-year-old girls today would be allowed to fly down to Florida to hang out with the college frat guys during spring break.
We can be sure that some of Mr. Bennet's other declarations are exaggerations and that Kitty will be allowed to circulate as any well-brought-up young lady would, only without a freedom that could lead to scandal.

If we were to take Mr. Bennet's punishment of Kitty seriously, then it would be a bit extreme. After Lydia runs away from Brighton with Mr. Wickham, Kitty tells her father that she would not behave in such a manner were she lucky enough to go. He swears that "No officer is even to enter into [his] house again." None of the girls will ever be allowed to go to a ball unless they dance with one another only, and Mr. Bennet tells Kitty that she will not be allowed to leave their home until she can prove that she has been logical and coherent for at least ten minutes a day.
Now, Mr. Bennet is hardly a disciplinarian, and it is difficult to imagine that he would want to be around his family for enough hours in the day to actually enforce his new "rules." He spends most of his time in his den, attempting to escape his wife and daughters. Chances are that Kitty will never get the chance to go to Brighton, not without her parents' supervision at any rate, but it is unlikely that this punishment will come to anything more excessive than that.

Precalculus, Chapter 6, 6.2, Section 6.2, Problem 37

Given: a=8, b=12, c=17
Heron's Area Formula A=sqrt[s(s-a)(s-b)(s-c)]
where s=[a+b+c]/2
s=[8+12+17]/2=37/2=18.5
A=sqrt[18.5(18.5-8)(18.5-12)(18.5-17)]
A=sqrt[18.5(10.5)(6.5)(1.5)]
A=sqrt(1893.94)=43.52
The area is 43.52 square units.

Calculus and Its Applications, Chapter 1, 1.6, Section 1.6, Problem 6

Take the derivative of $F(x) = 3x^4(x^2 - 4x)$: first, use the Product Rule; then,
by multiplying the expression before differentiating. Compare your results as a check.
By using Product Rule,

$
\begin{equation}
\begin{aligned}
F'(x) = \frac{d}{dx} \left[ 3x^4 (x^2 - 4x) \right] &= 3x^4 \cdot \frac{d}{dx} (x^2 - 4x) + (x^2 - 4x) \cdot \frac{d}{dx} (3x^4)\\
\\
&= 3x^4 (2x - 4) + (x^2 - 4x)(12x^3)\\
\\
&= 6x^5 - 12x^4 + 12x^5 - 48x^4\\
\\
&= 18x^5 - 60x^4
\end{aligned}
\end{equation}
$


By multiplying the expression first,

$
\begin{equation}
\begin{aligned}
F(x) &= 3x^4 (x^2 - 4x) = 3x^6 - 12x^5 \\
\\
F'(x) &= \frac{d}{dx} \left[ 3x^6 - 12x^5 \right] = 18x^5 - 60x^4
\end{aligned}
\end{equation}
$


Both results agree.

How is the theme of discrimination prominent in the poem "The Ballad of the Landlord"?

In Langston Hughes's poem "The Ballad of the Landlord," an African-American tenant is complaining to the landlord about the repairs needed in his run-down apartment. The tenant has a leaky roof and broken steps, but the landlord does nothing to fix them. Instead, the landlord threatens the tenant with eviction, turning off the tenant's heat, and throwing him out on the street. These are all crimes on the landlord's part, but it is the tenant who is thrown in jail for threatening the landlord. The poem shows the effects of discrimination, as the African-American tenant is denied proper and well-kept housing but is jailed when he tries to complain. Society has deemed that the landlord, who is likely white, has the right to jail the tenant and does not have to provide sufficient housing to him.

Single Variable Calculus, Chapter 3, 3.6, Section 3.6, Problem 47

Show that the family curve $y = cx^2 , x^2 + x^2 + 2y^2 = k$ are orthogonal
trajectories of each other, that is, every curve in one family is orthogonal to
every curve in the other family. Sketch both families of curves on the same axes.



Taking the derivative of the function $y = cx^2$ implicitly we have

$\displaystyle \frac{dy}{dx} = 2cx$

So the slope of the tangent line to this curve at point $x_1, y_1$ is

$\displaystyle \frac{dy}{dx} = 2cx_1 $

Similarly, on the other curve $x^2 +2y^2 = k$


$
\begin{equation}
\begin{aligned}

2x +4y \frac{dy}{dx} =& 0
\\
\\
\frac{dy}{dx} =& \frac{-x}{2y}


\end{aligned}
\end{equation}
$


So the slope at point $(x_1 , y_1)$ is

$\displaystyle \frac{dy}{dx} = \frac{-x_1}{2y_1} $

but $y_1 = cx_1^2$, so the slope of the second curve is

$\displaystyle \frac{dy}{dx} = \frac{-x_1}{2cx_1^2} $

$\displaystyle \frac{dy}{dx} = \frac{-x_1}{2(cx_1^2)} = \frac{-1}{2cx_1}
$


We know that if the two curves are orthogonal to each other, their tangent lines are perpendicular at each point of intersection, that is, the product of their slopes is equal to $-1$. Multiplying the slopes we get..

$\displaystyle (\cancel{2cx_1}) \left( \frac{-1}{\cancel{2cx_1}} \right) =
-1$


Therefore, the curve must be orthagonal.

How does Swift establish himself as an authority on the subject in "A Modest Proposal"?

One must first, and this is important, distinguish between Swift, who wrote the essay, and the clueless narrator he invents who comes up with the "modest" proposal of killing and eating the offspring of the poor in Ireland. Swift wants the reader to understand that his narrator is ridiculous—and dangerous—because he lacks a moral compass. The narrator treats the Irish poor not as people but as things.
Nevertheless, Swift's narrator establishes (or attempts to establish) his authority on the basis of how thoroughly he has researched his subject. For his instance, he points out that he has consulted expert opinion:

I have been assured by a very knowing American of my acquaintance in London, that a young healthy child well nursed, is, at a year old, a most delicious nourishing and wholesome food, whether stewed, roasted, baked, or boiled . . .

He also has all the facts and figures at his fingertips. He has already worked out the cost of feeding a child for year and the probable price he would fetch on the market. He spells out the figures in detail:

I have already computed the charge of nursing a beggar's child (in which list I reckon all cottagers, laborers, and four-fifths of the farmers) to be about two shillings per annum, rags included; and I believe no gentleman would repine to give ten shillings for the carcass of a good fat child, which, as I have said, will make four dishes of excellent nutritive meat . . .

The narrator tries to persuade his audience by showing he has already thought his proposal through and done his homework on its profitability and so-called benefits.

In "Notes," what happens to Bowker? What does he feel happened to him Vietnam? What does he ask O’Brien to do?

O'Brien starts the chapter titled "Notes" stating that "three years later [Norman] hanged himself in the locker room of a YMCA in his hometown in central Iowa," which finishes the story from the story just before, "Speaking of Courage."
Bowker wrote a letter to the narrator where he talked about how meaningless life now seemed after the war. He detailed how he couldn't keep a job for longer than two months, how he tried college but found it "too abstract, too distant, with nothing real or tangible at stake, certainly not the stakes of a war."
Bowker confesses to O'Brien that the day Kiowa died, a part of Bowker died, too. Seeing his friends and buddies die in horrific ways affected Bowker in a way that most people now attribute to PTSD (post-traumatic stress disorder). And O'Brien feels he must tell this story, especially because he did not experience the same as Bowker, but he (O'Brien) deals with his experiences by telling the troops' stories. And so he tells the story of Bowker, changing his name as Bowker asked.

In "The Soldier," how does the narrator present his views on dying for his country?

The speaker of Rupert Brooke's poem "The Soldier" presents dying for England during the First World War in bittersweet terms. The poem does not glorify death in patriotic terms but does lament that it might be necessary. The opening lines demonstrate the nationalist sentiment of the speaker:

If I should die, think only this of me:That there's some corner of a foreign fieldThat is for ever England.

The focus on how the speaker's body and soul are "wholly English" forms the main subject-matter of "The Soldier." The remaining lines in both stanzas discuss the profound influence that England has had on the speaker as an individual. The implication is that the speaker owes a debt to his native land; although he does not seek death, he would be willing to die for his country.
"The Soldier" is unique because it doesn't quite fit the categories typically created for war poetry. The poem is not anti-war but neither is it patriotically pro-war. The nuance and ambiguity of the poem are some of the primary reasons for its enduring popularity. On a relevant side note, Rupert Brooke died of an infected mosquito bite before he even saw combat. He is buried in Greece. ​

Unlike his contemporary, Wilfred Owen, Brooke paints an idealistic picture of war in this poem. Brooke does not go into the horror or devastation of war. Rather, he celebrates the gesture of making the sacrifice for his country.
He expresses the idea that it is honorable to die for one's country, particularly England. In the first stanza, Brooke says that "if" he should die in a foreign land, then that land (place of his death and/ or burial) will be "for ever England." England made him who he is. He and his native England are materially and spiritually linked. Wherever he happens to end up, that land will have this inherent connection to his sacrifice and his idealized vision of England.
Brooke clearly shows his patriotism in this poem. He was prepared to die for England in this war, and he did die in 1915. He believed if he should die, his spirit would give back what England gave him. These are the thoughts, sights, sounds, and dreams that Brooke attributes to England. His description of England goes beyond patriotism. He gives it such lofty praise that phrases like "English heaven" are no surprise because his England has an almost Edenic aura about it.

How should I go about writing an essay on a literary group in British poetry?

One possibility is to write about the Romantics, who included the poets William Wordsworth, Samuel Taylor Coleridge, Lord Byron, William Blake, John Keats, and others. The movement is considered to have begun when Wordsworth and Coleridge published Lyrical Ballads, a collection of poems, in 1798. Their focus was on rejecting reason in favor of emotion, and they also focused on the subjective experiences of the individual. Many of their poems, such as those of Wordsworth, concentrated on finding inspiration in nature, in reaction to the growth of cities during Industrialization in England. William Blake's poems, for example, in Songs of Innocence and Experience, contrasted the corruption and dirtiness of London with the purity and innocence of the countryside. Rural areas were seen as an outgrowth of the purity of nature. In addition, Blake (who is also seen as a Pre-Romantic) and several of the other poets celebrated youth as a time of inspiration and innocence, as opposed to the corruption of adulthood. 

How is morality explored in Moll Flanders?

In his preface to Moll Flanders, Defoe states that his intention is to convey a serious moral. Yet, explicit moralizing is notable by its absence in the relating of Moll's bawdy, picaresque adventures. Right throughout the story, Moll becomes caught up in all manner of escapades, none of which are in any way illustrative of the Christian moral life.
Moll is a serial thief and prostitute; worse still, from a moral point of view, she is an unrepentant serial thief and prostitute. Yet she does live by a moral code of sorts, often trying to rationalize her socially unacceptable behavior.
For instance, after she's robbed a drunken rich man she's just slept with, she convinces herself that perhaps the experience will prove instructive to the unfortunate gentleman. Perhaps, she reasons, he'll be less likely to cheat on his wife in future. Not surprisingly, that doesn't happen, but we can at least understand how Moll's mind is working. Essentially, she seems to believe that good can come from bad, moral actions from immoral ones.
Moll tests out this principle again when she steals from a young girl walking home by herself:

"I had given the Parents a just Reproof for their Negligence in leaving the poor little Lamb to come home by it self . . . ” (p.154)

In other words, it's not her fault that this little girl has been robbed; it's her parents' fault that they let her walk home all by herself, carrying such valuable objects. Maybe this unfortunate incident will teach them a salutary lesson.
Defoe was intelligent enough to know that treating Moll Flanders's story as an extended homily wouldn't have been anywhere near as interesting for the reader. Moll is his protagonist. As such, it's necessary for her to be made recognizably human. We cannot sympathize with Moll's criminal dishonesty, nor with her disingenuous self-justifications. Defoe doesn't expect us to.
However, we can at least understand her actions, even if we don't in any way accept them. In other words, we are induced to feel empathy, not sympathy. Defoe's method of telling the tale is all the more effective for being descriptive rather than prescriptive. It also provides us with a much more honest, more realistic portrayal of the criminal sub-culture in which Moll lives, moves, and has her being.

How was life at Montag’s house very different from that of Clarisse‘s house?

Montag and Clarisse have drastically different lives when they initially meet at the beginning of the novel. Life in Montag's home is mundane, unexciting, and routine. Mildred spends the majority of her time watching her loud, meaningless interactive television shows on her parlor walls while Montag sits idly by and remains silent. Montag's home is also dark, and there are no signs of life, which is typical in Bradbury's dystopian society. He rarely has conversations with Mildred, and their marriage suffers. In contrast, Clarisse's home is well lit, and one can tell from the street that people are awake inside doing something. When Montag asks Clarisse what is going on in her home, she tells him that her family is having a conversation. Something as simple as having a discussion and enjoying family time is unheard of in their society. Clarisse comes from an introspective, curious family that enjoys learning, having conversations, and experiencing nature. After having several enlightening conversations with Clarisse, Montag begins to analyze his meaningless, superficial life and wishes to make a change.

Based on the Preface, Introduction, and Chapters 1-4 of Ian Haney López's "Dog Whistle Politics: How Coded Racial Appeals Have Reinvented Racism and Wrecked the Middle Class, what were the views of the Supreme Court in the 1960s and 1970s on "color blindness"? Why, today, is "color blindness" the dominant behavior when discussing race?

First, colorblindness refers to the disregard of race in the public arena. The idea is that the Constitution is colorblind and therefore, cannot favor any one group of people over another. Based on this form of reasoning, affirmative action policies are unnecessary to ensure the complete integration of black Americans into the public sphere. This view of absolute colorblindness was steadfastly rejected by the Supreme Court in the early 1960s.
Initially, civil rights champions like Martin Luther King welcomed the idea of absolute colorblindness. However, as the 1960s progressed, it became clear that informal efforts against integration prevailed despite laws against segregation. So, the civil rights movement changed course; leaders began demanding that race be considered in efforts to integrate black Americans into every social sphere. However, by the mid 1960s, the Supreme Court reversed its earlier position. It now championed the view that it was just as wrong to compel integration as it was to force segregation. Lopez argues that such a notion of colorblindness renders civil rights gains obsolete and promotes dog whistle politics.
He maintains that the notion of absolute colorblindness protects whites in their efforts to derail the full integration of minorities into mainstream society. So, today, "colorblindness" is dominant in the race discussion because there is disagreement about how to pursue racial cohesion in American society. While some argue that integration shouldn't be enforced by violent means or by affirmative action policies, others argue that raced-based policies should be in place to reverse centuries of material hardship. So, a working interpretation of "colorblindness" is central to the debate about racial harmony.

Single Variable Calculus, Chapter 3, 3.3, Section 3.3, Problem 84

Find constants $A,B$ and $C$ such that the function $y= Ax^2+Bx+C$
satisfies the differential equation $y''+y'-2y=x^2$.


$
\begin{equation}
\begin{aligned}
y &= Ax^2+Bx+C\\
y' &= A \frac{d}{dx} (x^2) + B \frac{d}{dx} (x) + \frac{d}{dx} (C)\\
y' &= A(2x) + B(1) + 0\\
y' &= 2Ax+B\\
y'' &= 2A \frac{d}{dx}(x) + \frac{d}{dx}(B)\\
y'' &= 2A(1)+0\\
y'' &= 2A
\end{aligned}
\end{equation}
$


Substituting these values to the differential equation,

$ y'' + y' - 2y =x^2$


$
\begin{equation}
\begin{aligned}
2A+2Ax+B-2(Ax^2+Bx+C) = x^2\\
2A+2Ax+B-2Ax^2-2Bx-2C = x^2\\
-2Ax^2+(2A-2B)x+(2A+B-2C) = x^2
\end{aligned}
\end{equation}
$

Equating each power we get,
For $x^2$:

$
\begin{equation}
\begin{aligned}
-2A &= 1\\
A &= \frac{-1}{2}
\end{aligned}
\end{equation}
$


For $x$:

$
\begin{equation}
\begin{aligned}
2A-2B &= 0\\
\cancel{2}A &= \cancel{2}B\\
B = A &= \frac{-1}{2}
\end{aligned}
\end{equation}
$


For constant,

$
\begin{equation}
\begin{aligned}
2A + B - 2C &= 0\\
2\left(\frac{-1}{2}\right) + \left(\frac{-1}{2}\right) -2C &= 0\\
C &= \frac{-3}{4}
\end{aligned}
\end{equation}
$

What is the main conflict in Unwind by Neal Shusterman?

I suppose that different readers might choose slightly different "main" conflicts in the story. I'll highlight a few of the major conflicts that are present in Unwind.  
For me, the most central conflict in the story is a person/people vs. society conflict. Shusterman has created a world in which retroactive abortion is acceptable. The population has bought into the idea that a child's life doesn't end if his/her body parts are farmed out and donated to other people. This process of harvesting teenage body parts is called "unwinding."  

However, between the ages of thirteen and eighteen, a parent may choose to retroactively "abort" a child . . .
. . . on the condition that the child's life doesn't "technically" end.
The process by which a child is both terminated and yet kept alive is called "unwinding."

Connor, Risa, and many other characters in the book have all been labelled for unwinding, and they don't want that to happen. They know that unwinding is a lie, and they know that they will most certainly not be alive after being unwound. These children that aren't willing to go silently to their deaths try to run away. They are then equivalent to escaped convicts, and they are hunted down by a special branch of law enforcement. This is a central conflict. The kids don't want to be unwound, but the government says that they must be unwound. The kids think they will die, and the society thinks that the kids will live on in pieces. 

"I was never going to amount to much anyway, but now, statistically speaking, there's a better chance that some part of me will go on to greatness somewhere in the world. I'd rather be partly great than entirely useless."

Another central conflict to the story is a person vs. person conflict. This particular conflict type is best illustrated through Connor and Roland. The two characters hate each other, and they are frequently physically violent or very near to it. Once at the Graveyard, their conflict escalates as groups of kids begin supporting either Connor or Roland. 
Finally, the book has a major person vs. self conflict. This conflict type is best seen in Lev. Lev is a tithe.  

Lev was a tithe from the moment he was born. You don't undo thirteen years of brainwashing in two days.

Being a tithe means that Lev's parents always knew that they were going to have Lev unwound. Lev is their 10th child, and they feel that they should donate 1/10 of their children to the world. This means that even before Lev was born, his parents planned to give him up to have his body parts harvested and donated to many other people. 

Lev reluctantly nods, knowing it's true. He was a "true tithe." With five natural siblings, plus one adopted, and three that arrived "by stork," Lev was exactly one-tenth. His parents had always told him that made him all the more special.

The internal, person vs self conflict is that Lev begins to question why he should be the one who has to die.  

"Well . . . I've just been feeling jealous of my brothers and sisters. I keep thinking of how the baseball team is going to miss me. I know it's an honor and a blessing to be a tithe, but I can't stop wondering why it has to be me."

Lev has been raised to believe that being a tithe makes him special and unique; however, as events in the story unfold, Lev begins to doubt everything that he formerly believed about unwinding. By the end of the novel, his attitude has been completely turned around. He's still willing to die, but he's only willing to die in the fight against unwinding. Much of the book focuses on Lev being conflicted and struggling to reconcile his childhood beliefs with what he sees unwinding is really doing to young people.

Describe the lives of the Chinese people during the Cultural Revolution, paying particular attention to women.

During the Cultural Revolution of 1966-1976, Mao tried to silence internal critics, reduce inequalities between social classes, and restore a sense of Communist fervor in Chinese youth. These years were hard for all Chinese people, including women. The Red Guards were tasked with carrying out what was called "mass criticism campaigns" in which they questioned and harassed people who were accused or suspected of carrying out anti-Communist (or capitalist) activities. Red Guards often had a free hand to torture and harass people, and they raped, beat, and tortured women, particularly those seen as "bourgeoisie." Some women were also sent to labor camps and separated from their families as punishment. During much of this time period, universities stopped functioning. It is estimated that anywhere from 500,000 to 7 million Chinese people were killed during the Cultural Revolution, and many people who were deemed "intellectuals" had to serve time in harsh labor camps. 

What is the archaic language of the poem "Huswifery"?

Take note of how different Edward Taylor's language might seem from how we speak and write in the present day, yet we are still able to understand his poems, such as "Huswifery." Taylor spoke and wrote in a time where much transition and transformation was occurring in the English language. Taylor was born and educated in England but traveled to the Massachusetts Bay Colony as a grown man, and already the language in these two places would have been markedly different. England was still experiencing the aftermath of the Great Vowel Shift, but speakers in the Colonies were encountering a much wider variety of native tongues and accents, all of which have had a part in forming the American accent.
In this transitional period, English was transforming from Middle English (whose pronunciation found much more local particularities) to the more highly standardized Modern English. We call this in-between period Early Modern English. This language is really not so archaic at all, but it does demonstrate how much language can change in the space of three or four centuries.
The title, too, demonstrates the shift in language over time. Huswife is a term dating to at least the 13th century, but by the 18th, language had changed to prefer the pronunciation of housewife as having cleaner moral connotations than the older form.
https://public.oed.com/blog/early-modern-english-an-overview/

https://www.etymonline.com/word/housewife

https://www.poetryfoundation.org/poems/46133/huswifery

How does Utnapishtim attain immortality?

Following Enkidu's death, Gilgamesh mourns his friend and decides to journey to the ends of the earth to find Utnapishtim, who was blessed with eternal life from the gods after surviving the "deluge." Gilgamesh persuades Ur-Shanabi to ferry him across the waters of death to meet Utnapishtim, who resides in the land of Dilmun, in the garden of the sun. When Gilgamesh initially meets Utnapishtim, he tells him about Enkidu's friendship and death before he petitions Utnapishtim for the secret to eternal life. Utnapishtim tells Gilgamesh the story of the Great Flood and how he built an ark in preparation for the deluge. Utnapishtim, his family, and many animals survived in the ark during the Great Flood and the god Ea blessed him and his wife with eternal life when the waters subsided. After Utnapishtim explains that everlasting life is only reserved for the gods, he advises Gilgamesh to travel home. Before Gilgamesh leaves, Utnapishtim ends up giving him the solution to eternal life, which is a magic plant that grows at the bottom of the waters of death. Unfortunately, a serpent steals the magic plant from Gilgamesh on his journey back to Uruk and Gilgamesh is forced to accept his mortality by the end of the epic.

According to the Epic of Gilgamesh, Utnapishtim was the only man to escape death and receive immortality from the gods (his wife was also granted immortality). Many years before the events in the story, the gods had sent a flood to punish humanity. Similarly to the story of Noah's ark, the gods told Utnapishtim to build a boat which would preserve both human and animal life. Utnapishtim obeyed, and all who sailed on The Preserver of Life were saved from the flood. Once the waters receded, Utnapishtim made a sacrifice to the gods and then released the animals back into nature to repopulate the earth. The gods rewarded Utnapishtim for his faith and obedience by deifying him and granting him immorality.

What is appeasement policy? Who was appeasing who leading up WWII?

Appeasement policy is using diplomacy to try to avoid a war. It means looking at the situation from the other party's point of view and trying to fix whatever grievance or sore point might lead one's opponent to warfare and destruction. The rationale is: if we simply give the other side what it wants, it will be contented, the problem will be solved, and we can all move on.
Appeasement is most closely associated with the actions of British Prime Minister Chamberlain in the late 1930s as tensions with Germany were building towards another world war. Countries like England and France had suffered greatly in World War I. The death toll had been very high, and Britain, in particular, had exhausted its finances fighting that war. There was worry that the public would rebel against another major war. With one traumatic war only twenty years in the past, Chamberlain feared the effects of another.
Chamberlain wrongly thought that handing an ally, Czechoslovakia, over to Hitler (which was what giving him the Sudetenland effectively did) in 1938 would finally appease Hitler's appetite for territory and avert a war. It is one of the great bloopers of history and surprised even Hitler himself. Obviously, it didn't work.

Analyze and identify the figurative language in "Sonnet 43" by Elizabeth Barrett Browning.

Elizabeth Barrett Browning uses many different aspects of figurative language in "Sonnet 43," outside of the more typically used ones.
First, she uses apostrophe. Apostrophe is where a poet evokes or speaks to someone who is absent, or not present. Here, she opens the poem speaking to an absent person. Readers can assume that the poem is meant to address a love in a reflective way, perhaps reminiscing about their time together and what the future may bring.
Second, Browning uses anaphora. Anaphora is the repetition, at the beginning of a sentence, or in this case a poetic line, for effect. Lines 2, 5, 7, 8, and 9 all begin the same way: "I love thee."
One could also argue that ubi sunt is present in the poem. While ubi sunt typically appears as a series of questions about fate, and Browning only poses one question, the message of a fleeting life is apparent. As the poem progresses, one could justify that Browning speaks of how love changes over the course of one's life. This could be best justified by the final line: "I shall love thee better after death." While the poet does not specify if this death is hers or her lover's, one could argue that the mentioning of death illustrates the passage of life—a characteristic of ubi sunt.
Finally, Browning uses parallelism. Parallelism is used in writing to ensure that symmetry exists within a sentence or poetic line. Lines 7-9 possess parallelism. This is illustrated through the use of the statement made, followed by a comma and an extension to the initial idea presented. The poetic lines are parallel because they possess the same structure.

The metaphorical language used in Elizabeth Barrett Browning’s sonnet, "I love thee to the depth and breadth and height / my soul can reach," seems to refer to love as something physical, a distance that can be reached. It’s as though the speaker’s love feels so tangible and palpable to her that it becomes physical, three-dimensional even. It has mass and substance because it feels so big, and this makes the reality of how it feels to the speaker clearer.
The similes in the sonnet—"I love thee freely, as men strive for right" and "I love thee purely, as they turn from praise"—further describe this most unusual love. The speaker says that she loves her lover in the same way, perhaps for the same reason, as people who strive to do the right thing: it is innate; they cannot help but behave the way they do. They must strive because it is right to do so. This is how the speaker loves. Next, she says that she loves as one who turns from praise. People who strive to do what is right because they feel that is their calling often do not accept praise for their actions. They do what is right for its own sake, not for the awards or accolades it might bring. In fact, they don't want any of these things. So, too, does this speaker love just for the sake of that love, not for any way in which it might benefit her.

In Elizabeth Barrett Browning's "Sonnet 43," identified by literary critics as addressing the poet's husband, Robert Browning, the speaker begins the poem by expressing metaphorically how she seeks to measure or quantify the love she possesses:

I love thee to the depth and breadth and height
My soul can reach

The speaker also uses similes to describe her love to the object of her affection: 

I love thee freely, as men strive for right.
I love thee purely, as they turn from praise.

In addition to similes and metaphors, the speaker uses personification in describing how she loves him: 

To the level of every day's
Most quiet need. . . . 


With the breath,
Smiles, tears, of all my life.

A person, not a life, is capable of breathing, smiling, and shedding tears.
Hyperbole is another form of figurative language, and the poet makes use of it in the many exaggerations of the sonnet such as the similes, metaphors, and personification already noted; additionally, she seems to elevate him to the status of a god when she describes her love for him as replacing or being on par with the passion she felt for God in her "childhood's faith."

Intermediate Algebra, Chapter 3, 3.1, Section 3.1, Problem 2

The graph shows the percentage of Americans who moved in selected years.







a.) If the ordered pair $(x,y)$ represents a point on the graph, what does $x$ represent? What does $y$ represent?

The $x$-coordinates represent the year while the $y$-coordinates represent the percentage of Americans who moved in selected years.

b.) Estimate the percentage of Americans who moved in 2008.

Based from the graph, the estimated percentage of Americans who moved in 2008 was $12 \%$.

c.) Write an ordered pair $(x,y)$ that gives the approximate percentage of Americans who moved in 2008.

$(2008,12)$

d.) What does the ordered pair $(1951,21)$ mean in the context of this graph?

The ordered pair $(1951,21)$ shows that $21 \%$ of Americans moved in the year 1951.

What were the short-term effects of World War II?

In addition to the effects already mentioned, the mass loss of life and the economic devastation during World War II led to food shortages throughout Europe and contributed to a substantial famine in the Soviet Union in 1946–1947. Many people were displaced, and refugees from war zones could be found all across Europe.
The war also led to political instability in Europe. The United States introduced the Truman Doctrine and then presented the European Recovery Program, or the Marshall Plan, to help rebuild Western Europe and dampen the appeal of socialism.
The outcome of the war also led to the emergence of two victors (the United States and the Soviet Union) as superpowers, establishing a world with two major centers of power. In broad historical terms, one might consider the escalating rhetoric between the United States and the Soviet Union in 1946, the creation of the North Atlantic Treaty Organization (NATO) in 1949, the Soviet development of the atomic bomb in the same year, and various other expressions of the antagonism between the two sides as short-term effects of the war. The Cold War would dominate global politics until the fall of communism in the late 1980s to early 1990s.
Japanese defeat led to the US occupation of Japan. The Soviet Union occupied Estonia, Latvia, and Lithuania.
The Holocaust and widespread revulsion to Nazi policies provided an impetus for political support for the establishment of the state of Israel, which officially happened in 1948. This same sentiment, with added fuel from Soviet propaganda efforts to expose American racial inequality, created an urgency for civil rights reforms in the United States.

Some of the short-term effects of World War II are the end of imperial aggression, the end of the Great Depression in the United States, and the division of Germany into four parts.
Italy and Germany surrendered to the allied powers (US, UK, France, and Russia, among others) in 1944. With this, the allied powers focused their attention on Japan. On August 6, 1945, the US dropped the atomic bomb on Hiroshima. Two days later, Russia declared war on Japan. The next day, August 9, 1945, the US dropped a second atomic bomb on Nagasaki. Five days later, Japan unconditionally surrendered to the allied powers. This marked the end of WWII and the end of imperial aggression and territorial expansion; Germany, Italy, and Japan all attempted to grow their empires/nation-states by invading and taking over neighboring lands. One short term impact of WWII was to stop this.
Another short-term effect was the end of the Great Depression in the United States. While other allied powers experienced a short period of inflation as a result of the costly war, the growth of manufacturing industries in the United States led to an economic boom. Shortly after WWII, a growing mass consumer culture erupted in the United States and families were able to move to the suburbs and afford more than they were before.
Another short-term effect of WWII was the division of Germany. Eastern Germany was controlled by the Soviet Union. Western Germany was divided up between the US, UK, and France. Western Germany was slowly transferred back into German control, but Eastern Germany remained part of the Soviet Union for much longer. The city of Berlin, inside East Germany, was also split into parts and controlled by both Germany and the Soviet Union until the fall of the Berlin Wall in the late twentieth century.

Intermediate Algebra, Chapter 3, 3.3, Section 3.3, Problem 36

Determine an equation of the line that satisfies the condition "through $(12,10)$; slope $1$".

(a) Write the equation in standard form.

Use the Point Slope Form of the equation of a line with $(x_1,y_1) = (12,10)$ and $m = 1$


$
\begin{equation}
\begin{aligned}

y - y_1 =& m (x - x_1)
&& \text{Point Slope Form}
\\
y - 10 =& 1 (x - 12)
&& \text{Substitute $x = 12, y = 10$ and $m=1$}
\\
y - 10 =& x - 12
&& \text{Distributive Property}
\\
-x + y =& -12 + 10
&& \text{Subtract each side by $(x-10)$}
\\
-x + y =& -2
&& \text{Standard Form}
\\
\text{or} &
&&
\\
x - y =& 2
&&

\end{aligned}
\end{equation}
$



(b) Write the equation in slope-intercept form.


$
\begin{equation}
\begin{aligned}

-x + y =& -2
&& \text{Standard Form}
\\
y =& x - 2
&& \text{Slope Intercept Form}

\end{aligned}
\end{equation}
$

What is the central idea of the poem "Fire and Ice"?

The central idea of this poem is that regardless of how it happens, humanity is going to destroy itself through its own vices; moreover, this destruction is so inevitable—if we do not change anything—that it is of no use to even get upset about it. The speaker reports that some people say that the world will "end in fire," which he equates with "desire." This could be desire for land, for power, for resources like oil or water, to make another country more like our own: all reasons that we might go to war, employing "fire" with gunpowder and weapons and so forth.
Some people, on the other hand, say that the world will end in "ice," which the speaker equates with "hate." This could be the hatred of people who are unlike ourselves because they are a different race, a different religion, a different ethnicity, and so on: all reasons that we might allow another country or group to suffer through our hate. We might ignore their struggles and allow them to perish, and someday the same could happen to us. "Fire," then, is fast, while "ice" is slow, taking its time, and so the speaker says that he agrees with people who say "fire" will be responsible for our demise. However, he ends the poem with an understatement that underscores its irony: ice, or hate, would more than "suffice" to destroy the world, as it is just as destructive as fire or desire—it just takes longer.

A reader could state that the poem is discussing methods by which the world will end, but I feel that is too limited in scope. The poem is a very short poem, but there is more going on in it than a debate over how the world will end. The speaker admits that he sides with the "fire" side of the argument because he has experienced heated emotions like love and lust, and the speaker feels they have great power to destroy. The speaker also admits that he has experience with quieter and colder killers, like hate. He admits that the cold will work just as well. It is an interesting shift in the poem to go from an opening statement about how the world will end to discussing human emotions. I think it is safe to surmise that the speaker is confident in either fire or ice destroying the world because he has seen and experienced how those hot and cold emotions can destroy human relationships.

One could argue that the poem's central idea is that it's largely a waste of time to speculate on how the world might end. The speaker appears to be suggesting that, whether the world comes to grief through fire or ice, it doesn't really matter. Destruction is destruction; if the world ends through fire or ice then there's absolutely nothing we can do about it, one way or the other. This is just one of those many questions about which we speculate to fill up our free time. Yet the speaker disposes of the question pretty quickly by drawing attention to the equally destructive capabilities of fire and ice and leaves it at that.
Although the speaker doesn't know—or care to know—how the world will end, he does know something about desire. The suggestion here is that we should concentrate on dealing with questions relating to our own conduct and behavior instead of engaging in idle speculation concerning the precise nature of the apocalypse.

Ostensibly, the poem "Fire and Ice" by Robert Frost is about the hypothetical end of the world, with the speaker asserting that it will be destroyed either by fire or by ice. One could argue, though, that the central idea of this poem is that fire and ice are equally destructive, in their own ways.
We can also look at what fire and ice represent within this poem: the speaker says he "holds with those that favor fire" because of "what I've tasted of desire." Fire, then, here represents burning passion; meanwhile, ice is, in his view, also sufficiently destructive to destroy the world, a view he bases on knowing "enough of hate." So, if hate and passion are both extremely destructive forces, we might infer that what seem to be at first polar opposites (fire and ice) are actually far more similar than they are different. It does not matter how a thing is destroyed, it only matters that it is destroyed.

Precalculus, Chapter 8, 8.1, Section 8.1, Problem 70

3x-2y+z=-15
-x+y+2z=-10
x-y-4z=14
A=[[3,-2,1],[-1,1,2],[1,-1,-4]]
b=[[-15],[-10],[14]]
[A|b]=[[3,-2,1,-15],[-1,1,2,-10],[1,-1,-4,14]]
Multiply 2nd Row by 3 and add Row 1
[[3,-2,1,-15],[0,1,7,-45],[1,-1,-4,14]]
Multiply 3rd Row by 3 and subtract it from Row 1
[[3,-2,1,-15],[0,1,7,-45],[0,1,13,-57]]
Subtract Row 2 from Row 3
[[3,-2,1,-15],[0,1,7,-45],[0,0,6,-12]]
Now the equations can be written as,
3x-2y+z=-15 ----equation 1
y+7z=-45 ------ equation 2
6z=-12 ------ equation 3
From equation 3,
z=-12/6=-2
Now substitute back z in equation 2,
y+7(-2)=-45
y-14=-45
y=-45+14
y=-31
Substitute back the value of y and z in equation 1,
3x-2(-31)+(-2)=-15
3x+62-2=-15
3x=-15-60
3x=-75
x=-75/3
x=-25
So the solution is x=-25, y=-31 and z=-2

What was in Anna's letter?

The reader does not know exactly what is in Anna's letter to Sarah.  This is because only Sarah's reply to Anna is shown in the book.  Sarah's letter to Anna does, however, give clues about the first letter.  Sarah responds to several of Anna's questions.
In her letter, Anna asks Sarah if she can braid hair.  Anna's mother had died many years before, and since then no one has been around to braid her hair.  Sarah responds that she is able to braid hair.  Anna also asks Sarah if she can cook stew and bake bread.  Sarah replies, saying that she can indeed do both.  After writing this, Sarah adds that she prefers painting and building bookshelves to baking and cooking.
Anna may have asked Sarah what her favorite colors are.  In Sarah's letter to Anna, she states that her "favorite colors are the colors of the sea, blue and gray and green, depending on the weather" (Sarah, Plain and Tall, Chapter 2).

Can you help me choose an interesting topic and thesis for a sociology paper on Karl Marx's views of religion? My paper needs to take his ideas and attempt to apply them to a particular phenomenon, institution, social relationship, or contemporary controversy. My topic must relate to society, as this is for a sociology course.

Karl Marx largely saw religion as a way that the bourgeois tried to appease the proletariat or working class, as he famously referred to religion as "the opium of the people" in "A Contribution to the Critique of Hegel’s Philosophy of Right" (1843). Marx believed that the upper classes used religion to promise deliverance and happiness in the afterlife that the working class would never receive in life. By calling it "opium," Marx believed that religion provided a temporary and ultimately harmful release from the real problems that the working class faced, and he wrote that "the abolition of religion as the illusory happiness of the people is the demand for their real happiness." In other words, religion provided a happiness or joy that wasn't real, and Marx believed people should fight for real happiness.
There are several sociological concepts today to which you can apply Marx's ideas of religion. For example, drug use (and abuse) is widespread today. Drug overdoses now kill more Americans than car accidents do. People turn to drugs for many reasons, but there is no doubt that the same issues that Marx identified that caused people to seek out religion (suffering and material privation) make people turn to drugs. The states with the greatest numbers of drug overdoses (West Virginia ranks first, followed by New Mexico; see the link below) are among the poorest states. Your thesis could be that people who are suffering from poverty often feel like they have no future and turn to drugs as a way to express and relieve their suffering, as people in Marx's day turned to religion.
White supremacist ideology is another example because it's like a religion (though it's secular). This ideology takes people's minds off their real problems, which are also often caused by poverty and alienation from society, and gives them a convenient target for their anger and isolation. Your thesis could be that white supremacist ideology is similar to religion, as it is an expression of the pain of people who are alienated from society and who relieve this alienation in ways that do not truly help them.
https://247wallst.com/special-report/2016/06/24/10-states-with-the-most-drug-overdoses/3/

Calculus: Early Transcendentals, Chapter 7, 7.4, Section 7.4, Problem 11

int_0^1 2/(2x^2 + 3x + 1) dx
sol:
int_0^1 2/(2x^2 + 3x + 1) dx
= 2* int_0^1 1/(2x^2 + 3x + 1) dx
Now Find the partial fractions of 1/(2x^2 + 3x + 1)
1/(2x^2 + 3x + 1) = 1/((2x+1)(x+1))
= A/(2x+1) + B/(x+1)
= (A(x+1)+B(2x+1))/((2x+1)(x+1))
Now Equating the numerators we get
1=(A(x+1)+B(2x+1))
= Ax+2Bx+A+B
= (A+2B)x+ (A+B)
Equating the co -efficients of x and the constants
(A+2B) =0
=> A=-2B
and
1=A+B
1=-2B+B
1=-B => B=-1 so A=2
Then ,
1/((2x+1)(x+1)) = A/(2x+1) + B/(x+1)
= 2/(2x+1) - 1/(x+1)
Now,
int 1/((2x+1)(x+1)) dx = int [2/(2x+1) - 1/(x+1)] dx
= int 2/(2x+1) dx - int 1/(x+1) dx
= ln(2x+1) - ln(x+1) +c
Now Apply the limits 0 to 1we get
int_0^1 1/((2x+1)(x+1)) dx
= [ln(2x+1) - ln(x+1) +c]_0^1
=[ ln(2+1) - ln(1+1) ]-[ ln(0+1) - ln(0+1) ]
=[ ln(3) - ln(2) ]-[ ln(1) - ln(1) ]
as ln(1) =0 so,
= [ ln(3) - ln(2) ]
so,Now
int_0^1 2/((2x+1)(x+1)) dx = 2 *[ ln(3) - ln(2) ]
=ln(9) - ln(4)
=ln(9/4)
is the solution
:)

How does the relationship shift between Montresor and Fortunato?

Edgar Allen Poe's "The Cask of Amontillado" is all about who has power over who (at least in Montresor's mind, that is). At the beginning of the famous short story, we learn from Montresor, the narrator, that he feels Fortunato has crossed him many times in the past, but recently Fortunato has crossed the line and done something that Montresor cannot forgive.

The thousand injuries of Fortunato I had borne as I best could, but when he ventured upon insult I vowed revenge.

Before the story starts, Fortunato has the upper hand in their relationship being the insulter rather than the insulted, but it is clear that Montresor intends to change that (and he very well does). 
When they first meet up in the story, Montresor makes Fortunato think that they're still on good terms, complimenting him on his knowledge of wine, and never letting a hint drop that he's still seething about the unspecified "insult". As the story moves on, we realize that Montresor's revenge is trapping Fortunato in his catacombs to die. Montresor lets the false niceties fall away, and Fortunato can see his true nature: calculating, cruel, and possibly insane. 
So, their relationship shifts from that of false friendship (which might never have been real friendship in the first place, given how much Montresor hates Fortunato), to that of a revenger who has total power over his victim. 

What is a critical appreciation of the poem "The Echoing Green"?

"The Echoing Green" is from William Blake's 1789 collection of poems called Songs of Innocence. The poem is Romantic in its simple diction, celebration of the simple lives lived close to the natural world, and the depiction of innocent childhood experiences as recalled by an adult speaker.
The Romantic poets made it a point to write in the language of the common person, and Blake does so in this poem. Simple images like "merry bells ring" conjure a village community in words anyone can understand. The simple schema of rhyming couplets gives the poem a sing-song, comforting, nursery rhyme quality.
What the speaker remembers is an idealized springtime pastoral world in the rural England of yesteryear. The thrush and the skylark sing, while "Old John" sits under a tree and watches the children play. Childhood innocence is highlighted as the children play on the green until they are too tired to do so anymore, at which time they are welcomed by their mothers. They are likened to birds in a nest.
Blake captures the natural innocence some children in society experience, but the poem cannot be wholly understand until read in conjunction with Blake's poems in Songs of Experience, such as "The Chimney Sweep," that show that not all children in England experienced this kind of idyllic life.

In this poem from the "Songs of Innocence" section of his eighteenth-century collection Songs of Innocence and Experience, Blake offers a gentle observation of life over the span of a day in a country setting. A spring morning unfolds to reveal children at play on the "echoing green" while their elders watch fondly and remember their own youth.  The poem ends with the close of day and moves indoors, where families gather in their comfortable, loving homes for a peaceful night's rest.
The poem is comprised of three ten-lined stanzas with five end-rhymed couplets in each. The meter is iambic pentameter, creating a traditional, predictable rhythm that echoes the predictable stages of one's life and the stages of a day, which are both observed in the poem.
Blake's diction is simple and accessible; this is not a poem that requires deep analysis to uncover meaning. The imagery he creates appeals to the senses; the sounds he describes include bells, bird songs, and laughter, and the sights are of children at play, white-haired elders who enjoy their antics, the green, an oak tree, and a sunrise and sunset.
Blake's purpose is to recognize the cyclical nature of life and its simpler pleasures of nature, community, and family.

int x(5^(-x^2))dx Find the indefinite integral

Indefinite integral are written in the form of int f(x) dx = F(x) +C
 where: f(x) as the integrand
          F(x) as the anti-derivative function 
          C  as the arbitrary constant known as constant of integration
For the given problem int x(5^(-x^2)) dx has an integrand in a form of exponential function.
 To evaluate this, we may let:
u = -x^2 then   du= -2x dx or (-1/2)(du)= x dx .
Applying u-substitution, we get:
int x(5^(-x^2)) dx =int (5^(-x^2)) * x dx
                            =int (5^(u)) *(-1/2du)
                            =-1/2int (5^(u) du)
The integral part resembles the basic integration formula:
int a^u du = a^u/(ln(a))+C
Applying it to the problem: 
-1/2int (5^(u) du)=-1/2 * 5^(u)/ln(5) +C
Pug-in u =-x^2 , we get the definite integral:
-1/2 * 5^(-x^2)/ln(5) +C
 or
- 5^(-x^2)/(2ln(5)) +C
                      

(4,3) , (8,15) Write a power function y=ax^b whose graph passes through the given points

We are asked to write the equation for a power function whose graph passes through the points (4,3) and (8,15).
We substitute the known values of x and y into the basic equation to get two equations with two unknowns (a and b) and then solve the system for the coefficients.
3=a*4^b, 15=a*8^b
Solving the first equation for a we get:
a=3/(4^b)
Substitute this expression for a in the second equation to get:
15=3/(4^b)*8^b
15=3*(8/4)^b
2^b=5
So b=(ln(5))/(ln(2))~~2.322
Now substitute for b to get a:
a=3/(4^b)=3/(4^((ln(5))/(ln(2))))=3/25=.12
So the model is y=3/25x^((ln(5))/(ln(2)))"or" y~~.12x^2.322  

What happened to John Cunningham’s Stock in Sierra Mills?

John Cunningham's stock in Sierra Mills is stolen and stricken from the books. He is unable to prove that he has any stock in the company.
When the time comes for Cunningham to get the dividends from his stock in Sierra Mills, the money does not arrive. When he writes to the secretary of Sierra Mills to inquire about why the quarterly dividends didn't appear, she says that there's no record of Cunningham owning any Sierra Mills stock.
Cunningham goes to the bank and finds that his safe deposit box is empty; there are no Sierra Mills stock certificates. The Iron Heel took them in order to bankrupt Cunningham and remove any influence he has. It is likely that this stems from his allegiance to socialism, which the Iron Heel wants to stamp out. 
Cunningham takes Sierra Mills to court, but cannot prove that he ever owned stock. As London writes, "He did not control the courts, and the Sierra Mills did."
Eventually, a fake mortgage is foreclosed on and Cunningham loses his home as well.

Why was Enzo alone and locked in the house?

Enzo was alone and locked in the house by accident. Because she was so ill, Eve neglected to think about Enzo's welfare when she left the house with Zoe (her daughter).
According to the text, Eve had awoken the morning of Denny's race with a terrible headache. She had vomited profusely into the sink and complained of pressure against her skull. Panicked at this new development in her illness, Eve had then packed a bag with clothes for herself and Zoe before leaving for her parents' home.
For his part, Enzo understood why Eve forgot all about him. He reasoned that Eve's illness had affected her judgment. To survive, Enzo drank water from the toilet bowl and nibbled on stray scraps of food around the house. Because he could not leave the house, Enzo carefully made sure that he only urinated and defecated on the mat by the back door. After three days and two nights, Denny returned home. Although he was furious when he found Enzo alone, Denny eventually came to realize how ill Eve was.

What hints are there that Lennie will die in Of Mice and Men?

Steinbeck foreshadows Lennie's fate several times throughout the novella. Lennie's inability to understand his own strength, ability to accidentally kill sensitive animals, and tendency to get into serious trouble foreshadows the accidental murder of Curley's wife, which directly leads to Lennie's death. Lennie's incident in Weed particularly foreshadows the fact that he will hurt Curley's wife. In addition to Lennie's checkered past and propensity for accidentally harming small animals, Crooks's comment about nobody's dream ever coming true foreshadows the fact that George and Lennie's fantasy of owning their own estate will not come to fruition. The most prominent example of foreshadowing Lennie's death takes place in chapter 3 when Carlson shoots and kills Candy's lame dog. Candy's helpless, old dog parallels Lennie, who is also vulnerable, weak, and helpless. Carlson shoots Candy's dog in the back of the head to put it out of its misery, which is similar to the way that George shoots Lennie in the back of the head to prevent Curley's mob from brutally murdering him.

For an example of how Steinbeck foreshadows Lennie's death, take a look at chapter 6. In the first paragraph, for example, Steinbeck describes a heron killing a snake that it plucks from the water. Symbolically, the heron and the snake represent George and Lennie—specifically, George's merciful killing of Lennie at the end of the story.
In addition, we can find lots of examples that Lennie will get into serious trouble, trouble which might cost his life. In chapter 1, for instance, George reminds Lennie of what he should do if he gets into trouble. Lennie responds that he should hide in the bush and wait for George to come and get him. This is one example of how Steinbeck hints to the reader that Lennie will get into serious danger.

What quotes show that the mother and daughter are alike in "Two Kinds"?

Jing-mei says that her mother thought she could be "a Chinese Shirley Temple," and they'd watch her movies together as if they were "training films." Jing-mei would watch Shirley dance and sing and pout, and when her new haircut—meant to look like lush Shirley Temple–esque curls—does not work out at all, she says she likes it anyway, "and it made [her] actually look forward to [her] future fame." At first, Jing-mei buys into this idea that she will be famous for something, just like her mother is also hoping and believing. Then, when it comes time for the talent show, after Jing-mei has been taking piano lessons from Mr. Chong (despite the fact that she'd fudged her practices, unbeknownst to the deaf older man), she says, "It was as if I knew, without a doubt, that the prodigy side of me really did exist." Jing-mei also seems to want to show "sulky" Waverly that Jing-mei is wonderful and talented too, just as Jing-mei's mother seems determined to have a more prize-winning daughter than Auntie Lindo.

When the narrator was young, she and her mother shared the belief that she could be famous, and they also shared a desire for it. Jing-mei's mother says, "Of course, you can be a prodigy, too," and Jing-mei echoes this belief with the words "in the beginning I was just as excited as my mother, maybe even more so." Together, they watch old shows on television, studying child stars, like Shirley Temple.
After trying, then abandoning, a few activities, both mother and daughter begin to despair of Jing-mei ever becoming a child prodigy; Jing-mei confesses, "after seeing, once again, my mother's disappointed face, something inside me began to die." They have a shared feeling of letdown, because her fame was something they both wanted.
After having a cry about her situation, Jing-mei studies herself in the mirror and sees that "the girl staring back at me was angry, powerful." In this way, too, mother and daughter are alike. When the narrator is forced to begin piano lessons against her will and rebels when she is ordered to practice, she recalls, "My mother slapped me. 'Who ask you to be genius?' she shouted. 'Only ask you be your best.'" Both mother and daughter are strong-willed and display a temper when thwarted.

I believe this quote shows how Jing-mei and her mother are alike.  

In fact, in the beginning I was just as excited as my mother, maybe even more so. I pictured this prodigy part of me as many different images, and I tried each one on for size.

This quote shows that both mother and daughter desire the fame and uniqueness of the child prodigy concept.  Jing-mei likes the idea of being great at something in order to show off, and her mother likes the idea of having a daughter than she can show off to the world too.  The similarity is pride.  If Jing-mei winds up being a child prodigy, then both ladies will be proud of that fact.  
Another quote that shows a similarity between the two family members is this next quote.  

The girl staring back at me was angry, powerful. She and I were the same. I had new thoughts, willful thoughts - or rather, thoughts filled with lots of won'ts. I won't let her change me, I promised myself. I won't be what I'm not.

This quote shows Jing-mei's stubbornness.  Jing-mei resolves to undermine every single one of her mother's attempts to make her a prodigy.  For every doomed attempt, Jing-mei's mother resolves to find another way to make her daughter successful.  Jing-mei's mother pushes harder and harder to make her daughter great, and Jing-mei pushes back equally hard.  Both ladies are incredibly stubborn, and their attitudes eventually cause a complete break in the relationship. 

Precalculus, Chapter 6, 6.5, Section 6.5, Problem 70

4(1-sqrt3i)^3
Let z=(1-sqrt3i)^3
r=sqrt[(1)^2+(-sqrt3)^2]=sqrt[1+3]=sqrt4=2
theta=arctan(-sqrt3/1)=arctan(-sqrt3)=(5pi)/3
DeMoivre's Theorem
z^n=[r(costheta+isintheta)]^n=r^n[cosntheta+isinntheta]
z^3=[2(cos(5pi)/3+isin(5pi)/3]^3=(2)^3[cos3((5pi)/3)+isin3((5pi)/3)]
z^3=8[cos(5pi)+isin(5pi)
z^3=8[-1+0i]
z^3=-8
4z^3=4(-8)=-32

Identify three characters who are the cause of their own negative or tragic circumstances in Shakespeare's play Romeo and Juliet. Provide supporting evidence and quotations. If possible, provide 3 quotations for each of the 3 characters.

The three characters that I would choose for this question are Tybalt, Romeo, and Mercutio.  All three characters have the same negative/tragic circumstance.  They all die. 
I'll start with Mercutio because he dies first, and I'll provide evidence from Act 3, Scene 1.  This scene begins with Benvolio and Mercutio walking around together in the heat.  Benvolio begs Mercutio to call it a day and head home because he knows that the hot weather brings about bad tempers. 

The day is hot; the Capulets, abroad;
And if we meet we shall not ’scape a brawl,
For now, these hot days, is the mad blood stirring.

Mercutio then gives a great monologue about how Benvolio is the guy that normally fights at the slightest provocation.  

Nay, an there were two such, we should have none shortly, for one would kill the other. Thou, why, thou wilt quarrel with a man that hath a hair more or a hair less in his beard than thou hast. Thou wilt quarrel with a man for cracking nuts, having no other reason but because thou hast hazel eyes.

Those lines strike me as odd every time I read this scene because it is Mercutio that chooses to fight Tybalt.  In fact, I feel that Mercutio does more to goad the fight than Tybalt.  From the moment that Tybalt enters the scene, Mercutio talks to him with open contempt and insults.  Tybalt begins the encounter by nicely saying the equivalent of "hello gentlemen."  


Follow me close, for I will speak to them.
Gentlemen, good e'en. A word with one of you.



But notice Mercutio's response.  

And but one word with one of us? Couple it with
something. Make it a word and a blow.

Mercutio is already goading a powerful adversary into a fight.  Tybalt is hot tempered to begin with, and Mercutio is making it worse.  Romeo finally shows up on the scene and refuses to fight Tybalt.  By this point, Tybalt and Mercutio are both up for a fight.  Mercutio chooses to draw his sword and challenge Tybalt.  


O calm dishonourable, vile submission!

Alla stoccata carries it away. (draws his sword)

Tybalt, you ratcatcher, will you walk?



The end result is Mercutio's death.  
 
Tybalt's death shortly follows, and his death is a result of his actions as well.  Had he not killed Mercutio, Romeo would not have sworn vengeance against him.  


Now, Tybalt, take the “villain” back again
That late thou gavest me, for Mercutio’s soul
Is but a little way above our heads,
Staying for thine to keep him company.
Either thou or I, or both, must go with him.



The other reason that Tybalt is at fault for his own tragic death is the fact that he returned to Romeo.  After killing Mercutio, Tybalt successfully escaped the scene of the crime.  


PETRUCHIO
Away, Tybalt.  Exeunt TYBALT, PETRUCHIO, and the other CAPULETS.


Let's also not forget that much earlier in the play, Tybalt vowed to seek out Romeo and punish him for crashing the Capulet banquet.  


Patience perforce with willful choler meeting
Makes my flesh tremble in their different greeting.
I will withdraw, but this intrusion shall
Now seeming sweet, convert to bitterest gall.



If Tybalt had listened to Lord Capulet and just let the infraction go, he never would have gone looking for Romeo.  If he isn't looking for Romeo, then the entire confrontation that ends with his and Mercutio's deaths never happens. 
 
Finally, let's look at Romeo.  Let's also use Act 3, Scene 1 as a starting place.  Because of Mercutio's death, Romeo feels emasculated.  


O sweet Juliet,
Thy beauty hath made me effeminate
And in my temper softened valor’s steel!



He feels that he has no other option than to bring terror down upon Tybalt.  


This day’s black fate on more days doth depend.
This but begins the woe others must end.



When Tybalt returns to the scene of the crime, Romeo announces his intention to kill him.  Gone is Romeo's aversion to fighting a new family member of his.  Romeo chooses to seek violent revenge.  He chooses to fight Tybalt, and Romeo chooses to kill him.  The result is that Romeo is banished from Verona.  


And for that offence
Immediately we do exile him hence.



Romeo's chosen actions are what cause him to be separated from his love and his wife.  Things go from bad to worse from this point in the play.  Juliet fakes her death, Romeo doesn't realize it's fake, and he chooses to kill himself.