In The Pioneers, what unique role does the vast, unexplored wilderness contribute to the complexity of America in the pioneer days?

In The Pioneers by James Fenimore Cooper, the unexplored wilderness of New York State makes life complicated for both the long-term residents of the wilderness—like the Mohicans—and the residents who recently settled there, who spend their days working the land. They fight with each other over the land, and they fight over how the wilderness should be treated; this conflict includes the interests of John Mohegan, whose Mohican ancestry gives him reason to claim the land, the interests of the agrarian workers who have settled the land, like Billy Kirby, and the interests of the slightly higher class of people represented by Judge Temple, who also feel a sense of ownership over the land.
One relationship that illustrates the complexity of this situation at this time in history is the relationship between Judge Temple and Billy Kirby, who earns money clearing the land. The judge feels a sense of protectiveness over the wilderness, he thanks Providence for the gifts of nature, and wonders if he should have the attitude of a conservationist. Billy Kirby, on the other hand, feels he has the right to profit off the land, and he treats the land as a commodity.
For example, Billy guiltlessly takes elements of the wilderness, like maple sap for syrup, and removes them from the wilderness, taking them to the town and selling them for his own profit. This choice violates nature, according to the judge, and Judge Temple scolds Billy for ravaging the trees for his personal benefit. Billy also abuses the population of bass when fishing for sport, and Judge Temple struggles with the wastefulness of Billy's games. How can Billy squander such a valuable natural resource like fish for fun?
These two competing attitudes toward nature and the bounty of the vast wilderness represent the complexity of America during these pioneer days; after all, in the earliest days of settlement, who gets to decide how to use the land and to what end? The answer is not an easy one, not now and certainly not back then, and the difficulties of these kinds of questions made pioneer days in America a complex time for many.

Geography: How do naturally occurring items become resources?

Naturally occurring items are goods found in nature.  Trees, water, minerals--all of these are naturally occurring.  However, unless someone is there to utilize the items.  Trees become resources when they can be turned into timber for building, fuel for fire, or even tourist attractions which can create a positive interest in one's country.  Water can be used for hydroelectricity, irrigation, or drinking water.  Minerals are useful when people attach artificial values to them such as they do with diamonds or gold or when they serve a useful purpose, like heating homes or fertilizing fields.  These naturally occurring items must be readily accessible and in demand for them to become resources as well.  Until Americans learned how to extract natural gas from shale deposits, no one spoke of this as a resource.  The controversial practice of fracking has given Americans a very valuable resource of natural gas.   

What was IT and what could IT do?

IT is a big disembodied brain. IT can control the minds of all the people on the planet Camazotz. Everyone on the planet is forced into total, synchronized conformity to the will of IT.
IT has captured Meg and Charles Wallace's father and is keeping him imprisoned. When Meg, Calvin, and Charles Wallace appear on the planet, IT tries to gain control of their minds.
We know IT is evil for several reasons. First, the planet is covered in darkness, and Mrs. Whatsit, Mrs. Which, and Mrs. Who are unable to visit it. Second, the children witness a young child making mistakes bouncing a ball. They later see the same young child in Central Central being "retrained" through cruel electric shock therapy to bounce the ball in conformity with everyone else. Third, IT uses lies and deception to try to persuade the children it has their best interests at heart in obliterating their free will.

Comment on the contrasting imagery in the poem Romeo and Juliet. What purpose dose it serve in highlighting the intensity of love?

Romeo and Juliet is not a poem but a full-length play by William Shakespeare. The play is written in two styles, however, prose and verse, and the verse could be seen as poetry since it adheres to a specific poetic meter (iambic pentameter). The most significant opposing imagery occurring in the play is that of light and dark, and a corresponding set of images referring to the sun, moon, and stars also appears.
Juliet is referred to by Romeo using images of sunlight ("It is the east, and Juliet is the sun / arise, fair sun..."), whereas Juliet uses moon imagery when speaking to Romeo ("O, swear not by the moon, th' inconstant moon, that monthly changes in her circled orb"). This is interesting because traditionally in literature the sun is thought to be masculine and the moon is thought to be feminine. This contrast underscores not only the uniqueness of their attraction but also its instability; it is as if the world is turned upside down and the natural order of things is challenged. Since the story became one for the ages, a classic example of romantic enduring love, Shakespeare's imagery was well chosen.
Stars are a frequent motif also (the opening speech by a narrator refers to the "star-cross'd lovers," which means astrology and fate are not in their favor). Juliet muses on Romeo as she looks at the night sky, waiting for him, and says, "when he shall die, take him and cut him out in little stars, so all the world may be in love with night." The emphasis on darkness and night refers to the secrecy of their love but also underscores a sense of opposition: they value the beauty of night over day and find the darkness a welcoming, rather than a frightening, place. It might also serve as a foreshadowing of their deaths.

What plan does Hamlet reveal to the audience once he is alone on stage?

Hamlet gives a lengthy speech at the end of act 2, scene 2 when the significant act of the scene has concluded and he is left alone on stage. In this speech, Hamlet mourns his inability to do anything in defense of his father "upon whose . . . most dear life / A damned defeat was made." He curses himself for a "coward."
Hamlet continues in this vein for some time, but towards the end of his speech he reveals a plan, inspired by the performance of the actors he has just spoken to. He plans to have them put on a performance in front of King Claudius which will be "something like the murder of my father." He will then "observe [Claudius's] looks," stating that if Claudius should "blench" (go white, or otherwise react with obvious shock or disquiet) then Hamlet will "know [his] course." He is sure that Claudius's response to such a performance will cement whether or not Hamlet is right in pursuing a course of vengeance against Claudius for King Hamlet's murder.
The closing couplet of this soliloquy is extremely famous and encapsulates Hamlet's plan:

More relative than this: the play's the thing
Wherein I'll catch the conscience of the king.

In The Grapes of Wrath, why is there an overabundance of references to eyes?

There are certainly lots of references to eyes in the story. Through the eyes of his characters, Steinbeck shows us the experiences of working-class Americans during the Dust Bowl era of the 1930s. 
The eyes in the story speak of human suffering, anxiety, and grief during one of the worst economic depressions of the 20th century. The dust storms caused many tenant farmers to lose their livelihoods and to make the dangerous journey west to look for work.
In Chapter Five, the landowners kick the tenant farmers off the land they've always farmed. Some of the landowners are apologetic about doing this, but others are matter-of-fact about their hard task. This second group of landowners have little sympathy for the plight of their impoverished tenants. Their main concern is their own survival in light of the extreme drought conditions. The text tells us that the "corn-headed children, with wide eyes" watch silently as the landowners talk to their fathers. The wide eyes of the children symbolize the innocence of youth, an innocence that will be destroyed by the hardships ahead.
In Chapter Seventeen, we begin to understand the toll the journey west takes on the migrant farmers. The men's eyes watch the tires and the roads; the men whose minds "had been bound with acres" must now turn their attention to broken gears, dusty roads, gasoline, and the miles ahead. Through the eyes of these men, we see how the working poor have only exchanged one set of worries for another.
In Chapter Seven, the "intent eyes" of used-car salesmen watch the faces of customers' wives to detect signs of "weaknesses." If a customer's wife indicates interest in a car in her expressions, the salesman works hard to get as much money as he can from her husband. The salesmen are predatory businessmen; like the landowners, they have little sympathy for the average working-class American fleeing the devastation of once-thriving farms. Here, Steinbeck uses the eye as a symbol of inhumanity and covetousness. 
In Chapter 19, Steinbeck tells us that the migrant men grow bitter from their continued suffering. While the wealthy farmers in California thrive, the migrant men and their families suffer. Because of the surplus labor, the farmers begin to pay the migrants lower wages for the back-breaking work they do. In this chapter, the "sullen eyes" of the migrant men betray the depth of their suffering and anger. They must watch their children starve, helpless to change the conditions their families live in.
Meanwhile, the farmers also watch

"with eyes to read history and to know the great fact: when property accumulates in too few hands it is taken away. And that companion fact: when a majority of the people are hungry and cold they will take by force what they need. And the little screaming fact that sounds through all history: repression works only to strengthen and knit the repressed."

Here, the eyes take in knowledge, but the spirit is unaffected by the suffering the eyes reveal. There is only concern for one's survival in light of that suffering.
So, in the story, the human eye is used to highlight both the suffering of the working-class (migrants) and the selfishness of the privileged (farmers and used-car salesmen).

What are the character traits of Alan Austen?

Alan Austen is young, naive, and hopelessly in love. He's also quite desperate to solve his problems. Hence his visit to the old man in his little shop to get his hands on some love potion. His love is unrequited and he needs to figure out a way to the get the object of his affections to start paying attention to him. The old man has just what Alan needs.
But Alan is so keen for the love potion to work that he's not really thinking far ahead. Even when the old man tells him how cloying and needy the potion will make his girlfriend, Alan doesn't care. He just hands over his money and eagerly takes possession of this magic elixir.
This is a prime example of Alan's naivety and relative lack of experience with the ways of the world. But the old man's certain that this attitude won't last; that before long Alan, like so many others before him, will be beating a path to his door to get his hands on "the chaser."

In Collier's short story "The Chaser," Alan Austen is described as a nervous, naive, and darkly infatuated boy. The story opens with Austen going up the stairs to meet with the man who, he has been told, can make him a love potion that will win the heart of his beloved, Diana. During the conversation between the two men, Austen shows himself at first to be hesitant but then to grow in confidence. As this dialogue progresses, the reader soon recognizes the dark undertones of the story and of Austen himself. Firstly, by asking for a love potion in the first place, Austen is proving himself to be someone who is content with knowing the love he receives from Diana will not be genuine but rather be a mandated effect of the potion. Thus, the one-sided darkness of the affection is made clear and unsettles the reader.
Also, although the reader sees the danger of the love potion the old man describes, Austen shows no awareness of understanding the true effects that he will see in Diana once he gives her the potion. The old man tells him, "She will want to know all you do . . . All that has happened to you during the day. Every word of it. She will want to know what you are thinking about, why you smile suddenly, why you are looking sad." Through this revelation, the reader becomes aware that the love will not be genuine not only because it is imposed by a potion but also because the "bottled love" is more obsessive and neurotic than true love should be. Yet Austen does not understand this, for he immediately replies to the old man's description, "That is love!"
Unfortunately, it is not love, which Austen will quickly discover once he gives the potion to Diana—to the ruin of them both.

Alan Austen is a young man who is both desperately and passionately in love with a woman who does not love him back. It is fairly clear that he passionately loves this woman, because he knows a great deal of her habits, likes, and dislikes. However, she does not reciprocate his feelings. This is why Alan is a desperate individual. He is desperate enough to have her love that he is willing to drug her. This also shows that Alan has a "never say die" attitude of sorts. He is simply unwilling to give up, and he is willing to think outside of the box and enlist the help a mystical apothecary of a sort. If I am being honest, Alan is also a bit creepy. I understand desperately wanting someone else's affections, but he is willing to chemically change who the woman is in order to have her essentially worship him.

"She will, when she has taken this. She will care intensely. You will be her sole interest in life."
"That is love!" cried Alan.

Alan has a warped view of what a loving relationship looks like. He wants Diana to more or less be a mindless automaton of a woman. He does not care about her feelings as long as her feelings are always her "love" for him.

Precalculus, Chapter 7, 7.2, Section 7.2, Problem 30

EQ1: (x -1)/2+(y+2)/3 =4
EQ2: x-2y=5
To solve using method of substitution, we have to isolate one of the variable.
For this system of equations, it is better that we isolate the x in the second equation.
x-2y=5
x=5+2y
Then, plug-in this to the first equation.
(x-1)/2+(y+2)/3=4
(5+2y-1)/2+(y+2)/3=4
And solve for y.
(2y+4)/2+(y+2)/3=4
To solve this, it is better to eliminate the fractions in our equation. This can be done by multiplying both sides by the LCD. The LCD of the fractions present is 6.
6*((2y+4)/2+(y+2)/3)=4*6
3(2y+4) + 2(y+2)=24
6y+12+2y+4=24
8y+16=24
8y=24-16
8y=8
y=8/8
y=1
Now that the value of y is known, solve for x. Plug-in y=1 to the second equation.
x -2y=5
x-2(1)=5
x-2=5
x=5+2
x=7
Therefore, the solution is (7,1).

What are 11 laboratory tools and their uses?

1. Beaker- used to hold liquid and solid samples while conducting experiments
2. Bunsen Burner or Hot Plate- used as a source of heat during experiments
3. Graduated Cylinder- used to obtain exact measurements in mL of liquid samples
4. Pipette- used to transfer and dispense liquid samples
5. Test Tube- used to hold small amounts of samples 
6. Wash Bottle- used to dispense small amounts of distilled water during experiments
7. Balance- used to calculate mass of a substance in grams
8. Wire Gauze- placed on top of a ring to support a beaker above a flame; allows for uniform heating of the sample in the beaker
9. Ring Stand and Rings- used to hold glassware usually above the bunsen burner
10. Erlenmeyer Flask- similar to a beaker, but contains a smaller mouth opening; used to hold substances and contain reactions
11. Clay Triangle- placed onto a ring and is used to hold and support evaporating dishes, crucibles, and watch glasses

What is the logic of the old man going so far out in the sea?

In The Old Man and the Sea, the old fisherman Santiago becomes obsessed with breaking his unlucky streak. Then he encounters a massive marlin that pulls him very far out from the shore. Out on the sea, far from the safety of his little shack, Santiago experiences the beauty and the horror of the sea and of the world as a whole.
Santiago's excursion far from the sea is more allegorical than realistic. While it's possible that a giant marlin could pull the man out on his boat, it seems fantastical and almost hard to believe. Hemingway's typical style usually follows a firm sense of realism, and so this novella is certainly an exception.
On the other hand, from a character standpoint, there is nothing about the situation that doesn't make sense. Santiago is obsessed with breaking his unlucky streak; he also has a deep appreciation and admiration of the sea, which is shown in his belief that nobody deserves to eat the esteemed marlin. Santiago ventures out to sea because he has nothing else but his love of fishing and his appreciation for the wilderness.

Single Variable Calculus, Chapter 3, 3.5, Section 3.5, Problem 55

a.) Determine the equation of the tangent line to the curve $\displaystyle y= \tan \left( \frac{\pi x^2}{4} \right)$ at the point $(1, 1)$.

Solving for the slope


$
\begin{equation}
\begin{aligned}

y' = m =& \frac{d}{dx} \left[ \tan \left( \frac{\pi x^2}{4} \right) \right]
\\
\\
m =& \sec^2 \left( \frac{\pi x^2}{4} \right) \cdot \frac{d}{dx} \left( \frac{\pi x^2}{4} \right)
\\
\\
m =& \sec ^2 \left( \frac{\pi x^2}{4} \right) \cdot \left( \frac{\pi }{4} \right) \frac{d}{dx} (x^2)
\\
\\
m =& \sec ^ 2 \left( \frac{\pi x^2}{4} \right) \cdot \left( \frac{\pi}{4} \right) (2x)
\\
\\
m =& \sec ^2 \left( \frac{\pi x^2}{4} \right) \cdot \frac{\pi x}{2}
\\
\\
m =& x (5 + x^2) ^{\frac{-1}{2}}
\\
\\
m =& \frac{\displaystyle \pi x \sec ^2 \left( \frac{\pi x^2}{4} \right)}{2}
\\
\\
m =& \frac{\displaystyle \pi 1 \sec ^2 \left( \frac{\pi (1)^2}{4} \right)}{2}
\\
\\
m =& \pi


\end{aligned}
\end{equation}
$



Using the Point Slope Form



$
\begin{equation}
\begin{aligned}

y - y_1 =& m (x - x_1)
\\
\\
y - 1 =& \pi (x - 1)
\\
\\
y - 1 + 1=& \pi (x - 1) + 1
\\
\\
y =& \pi (x - 1) + 1
\qquad \qquad \text{Equation of the tangent line at $(1,1)$}

\end{aligned}
\end{equation}
$


b.) Graph the curve and the tangent line on the same screen.

You are sitting in a boat floating on a very small pond. You take the anchor out of the boat and drop it into the water. Does the water level in the pond rise, fall, or remain the same? Explain your answer.

The water level in the pond will fall slightly. When the anchor is in the boat, the boat displaces enough water so that the buoyant force on it equals the sum of the weight of the boat, your weight, and the weight of the anchor. When you drop the anchor into the water, it displaces just its volume of water (rather than its weight as it did while in the boat.) The total weight of the boat becomes less and the boat displaces less water as a consequence since the anchor is now resting on the bottom of the pond.

Calculus of a Single Variable, Chapter 2, 2.3, Section 2.3, Problem 76

Given: f(x)=(x-4)/(x^2-7)
Find the derivative of the function using the Quotient Rule. Set the derivative equal to zero and solve for the critical x value(s). When the derivative is zero the slope of the tangent line will be horizontal to the graph.
f'(x)=[(x^2-7)(1)-(x-4)(2x)]/(x^2-7)^2=0
(x^2-7-2x^2+8x)=0
-x^2+8x-7=0
x^2-8x+7=0
(x-1)(x-7)=0
x=1,x=7
Plug in the critical values for x into the f(x) equation.
f(x)=(x-4)/(x^2-7)
f(1)=(1-4)/(1^2-7)=-3/-6=1/2
f(7)=(7-4)/(7^2-7)=3/42=1/14
The tangent line will be horizontal to the graph at points (1,1/2) and (7,1/14).

How does William Golding use the conch to depict the descent of the boys into savagery? For example, how does Jack break the rules of the conch?

In Lord of the Flies, the conch is a powerful symbol of civilized society. Readers can track the disintegration of the boys' civilization and their descent into savagery by following the way the conch is treated. 
At first, the conch represents order and following the rules. When Ralph blows the conch, it confers authority on him, and the boys agree to "let him be chief with the trumpet-thing." Jack makes his first challenge against the conch when Piggy scolds the boys for making an inefficient fire. Jack says, "The conch doesn't count on top of the mountain." Ralph asserts his authority, claiming that "where the conch is, that's a meeting." The boys agree, and Jack falls in line, saying, "We're not savages. ... We've got to do the right things."
In chapter 5 when the evening meeting deteriorates around talk of beasts and ghosts, Jack uses the fear to lead the boys away from the meeting. Piggy urges Ralph to use the conch to call the boys back, but Ralph senses that they would not respond. If all the boys outwardly defied the conch, that would be the end of their ordered civilization.
In chapter 6 when Samneric report on seeing the beast on the mountain, Jack becomes openly defiant against the conch:

"Conch! Conch!" shouted Jack, "we don't need the conch anymore. ... It's time some people knew they've got to keep quiet and leave the deciding things to the rest of us."

Jack is advocating a totalitarian type of governance as opposed to Ralph's democratic regime. Ralph silences Jack for speaking without holding the conch, and the boys stay on Ralph's side.
In chapter 8, Jack tries once more to swing the boys to his side by proposing a vote of no confidence toward Ralph. Jack holds the conch, but when he loses the vote, he lays the conch carefully on the grass and goes off by himself. When some of the boys join him, he tells them, "I'm going to get more of the biguns away from the conch and all that." He has rejected the ordered society that the conch represents and wants a society based on his own supremacy. When the boys raid Ralph's camp for Piggy's glasses, Piggy fears they are coming for the conch. But that is because he misunderstands what Jack values. Jack no longer values the type of society the conch represents.
Finally, when Ralph, Piggy, and Samneric confront Jack at Castle Rock, Piggy insists they take the conch. Jack responds with violence, sparring with Ralph with a spear and kidnapping Samneric by force. Then the boys begin to throw rocks and Roger dislodges the boulder, which murders Piggy and shatters the conch. This represents the final descent of the boys into savagery; after that, they deliberately hunt Ralph with the intent to kill him.
Following the role of the conch, particularly the way Jack views it, helps readers track the descent of the boys' civilization from order to savagery. 

Give much information as possible on Marxism from the book "The Dispossessed." Analyze the advantages and disadvantages of the economic basis of Urras and Anarres and the superstructures they produce.

An Overview of Marxism in "The Dispossessed"
Marxism receives a mostly favorable treatment in "The Dispossessed," by author Ursula Le Guin. The author is quoted as saying that the anarchism espoused by Marx is "the most idealistic" among all political theories. This sentiment is echoed throughout "The Dispossessed," which uses Anarres as an example of a society that was founded upon many Marxist principles. Elements of Marxism are also illustrated by contrast in the decadent, vaguely capitalist society of Urras, which loosely corresponds to the United States.
Marxism as a Prospective Future
One of the primary roles of Marxism in "The Dispossessed" is its presentation as a viable mode of living. Despite the fact that Marxism failed to take hold in the 20th century, Le Guin posits through Shevek's observations that Marxism could thrive under the right conditions. While the people of Anarres inhabit a mostly barren desert moon, their Marxist ideals of communal living and shared labor allow them to thrive under harsh conditions. On the other hand, the capitalist ideals of A-Io and the nation of Urras are shown to result in conflict and corruption.
Shared Prosperity
A central doctrine of Marxism is that all who are able should contribute and all should benefit from the spoils of labor. This concept is illustrated in the social system on Anarres, which is indeed "An Ambiguous Utopia." Despite the many flaws presented in the Anarresti way of life, the ultimate message of the story is that individual progress must complement the success of the group. This Marxist ideal is heavily contrasted with the runaway success the wealthy on A-Io have achieved by crushing the poor.
Advantages and Disadvantages of the Urrasti Economy and Superstructures
The nation of Urras has a thriving economy full of innovation, luxury goods, and variety. Because of the freedom of innovation the wealthier members of Urrasti society enjoy due to their privilege and lifestyle, the arts and sciences have flourished. As Marxism predicts, the superstructure created from the Urrasti economy plays a determining role in all aspects of life in the nation. The competition within the nation has led to competition without as well. Urrasti, which serves as a proxy for the United States, is engaged in hostile tensions with Thu, a rival nation that serves as a proxy for the USSR. In this sense, the benefits Urrasti gains from its superstructure are also weaknesses. No matter how much wealth is accumulated, they will always be engaged in competition and there will always be the risk of having it taken away. This fulfills Marx's prediction that a society built on competition will never be at peace and will never work for the good of the group.
Advantages and Disadvantages of the Anarresti Economy and Superstructures
The Anarresti superstructure presents its own challenges and strengths. This superstructure fosters a sense of cooperative ownership and the relinquishment of possession. An example of this superstructure, based significantly on Marxist principles of shared ownership, can be found in the Anarresti language itself. Children learn to refer to their mothers as "the mother," relinquishing ownership even of their closest social contacts. Self-sacrifice is the basis of the Anarresti economy and it is what allows the superstructure to survive.
A Summary of Marxism in "The Dispossessed"
In one particularly emotional scene of the book, Shevek learns that his partner, Takver, has been sent away to work on a solution to the hunger crisis. He uncharacteristically uses singular pronouns to reason that she has gone off "to work against hunger-hers, his and Sadik's hunger." While deeply personal and emotional in nature, this scene is a powerful example of the Anarresti superstructure at play. Shevek comforts himself by reasoning that his partner, with whom he naturally feels a sense of mutual ownership, has gone to work not only on behalf of all of Anarres but for their family as well.
This scene is a powerful summary of the way Marxism is perceived and illustrated throughout "The Dispossessed." It is at this point in the novel that Shevek's break from Anarresti social programming becomes apparent. An Anarrestian who is conforming to the superstructure and the demands of communal living would be comforted by the fact that his partner is helping the collective. There would be no need to personalize the event in such a manner. By showing Shevek's internal struggle with the self-sacrifice necessitated by Marxist ideals as well as contrasting the sacrifices he must make with the gross injustice on Urras, Le Guin proves that she has taken a nuanced approach to the topic. While the author clearly prefers Marxism as the basis for a civilized society under the right conditions, the ideals of Marxism are presented in a practical context which shows their strengths as well as many of their weaknesses.
https://www.depauw.edu/sfs/backissues/15/urbanowicz15art.htm

What are some flashbacks in the story "The Lottery"?

Flashbacks occur when the author or narrator takes the reader back in time to explain certain events connected to the story. Flashbacks play an important role in plot development, and the technique enhances the audience’s understanding of current events in connection to previous situations.
In The Lottery, there aren't any classic examples of flashbacks, but there are moments of recollection that are used to describe the objects and rituals performed during past events. Though there is typically a distinction between a flashback and a recollection, some might regard them as the same thing. The flashbacks are centered on how the lottery changed over time. An instance of flashback occurs when the present black box is described. In the story, the present black box is said to have been constructed using pieces of the first box, which was constructed by founders of the village.
Another instance of flashback occurs when the rituals following the event are described. It is claimed that the official of the lottery was expected to perform a chant as he stood or walked among the people. The flashback also describes a ritual salute, which was used to address each participant during the draw.

How does the Constitution force Americans to compromise?

To be precise, the Constitution does not actually force Americans to compromise.  However, it does make it more likely that they will have to do so.  The Constitution does this because it sets up a system of checks and balances in our government.
Because of the way our Constitution sets up the government, power is divided among various governmental bodies.  Most obviously, power is divided between the House, the Senate, and the Executive Branch, which is led by the President.  In addition, states have some powers that the national government cannot take away from them.  Because of this, Americans are more likely to have to compromise.
Americans are more likely to have to compromise because people with the same ideas will not always control the House, the Senate, the Executive Branch, and the state governments.  Right now, for example, Republicans control the House and the Senate while the President is a Democrat.  In order for any law to be passed, both the Republicans who control Congress and the President must agree.  This means that they are more likely to have to compromise.
In reality, Americans still do not actually have to compromise.  We see this today as the Republicans and the Democrats have had a hard time passing any significant legislation.  They do not want to compromise, so they are willing to simply avoid passing laws.  However, our Constitution does make it more likely that they would compromise.  Our Constitution tells them that they will often have to compromise if they want to make any laws.  By setting up a system in which multiple governmental bodies have powers and in which those bodies can be controlled by different political parties, the Constitution makes it more likely that Americans will have to compromise. 
https://www.huffpost.com/entry/checks-and-balances-the-g_b_4080850

How is Lord Acton's famous quote, "Power tends to corrupt, and absolute power corrupts absolutely,” applicable to George Orwell's Animal Farm?

Lord Acton's belief about the corrupting nature of power can be seen in the political landscape that defines Animal Farm.
One of the reasons why Orwell's novel is so powerful is because it is a study of political power. Whoever is in political control of the farm displays corruption. As the novel opens, Farmer Jones is corrupt. He abuses and exploits the animals because he can. No one is able to challenge his authority. Part of the reason why Old Major's appeal resonates with the animals is because he is right in expressing Farmer Jones's corruption: 

And you hens, how many eggs have you laid in this last year, and how many of those eggs ever hatched into chickens? The rest have all gone to market to bring in money for Jones and his men. And you, Clover, where are those four foals you bore, who should have been the support and pleasure of your old age? Each was sold at a year old—you will never see one of them again.

Jones is corrupt because he has unfettered political power over the farm. He is able to do whatever he likes. He does not display any regard for the animals' feelings. He embodies what Old Major calls "the tyranny of human beings" because he exercises political power without any limitations or checks on his autonomy.
Motivated by Old Major's theory of "Animalism," the animals wage a revolution to overthrow Jones and the humans. After its success, Manor Farm is renamed "Animal Farm." The pigs assume power in the name of all the animals. Over time, though, the pigs, specifically Napoleon and Squealer, begin to display the same trappings of power that Jones displayed. They learn to read and begin to consolidate political control of the farm to maximize their benefits. Squealer uses propaganda and media manipulation to ensure complete deference to "Comrade Napoleon." For his part, Napoleon uses the dogs as his private army. Once he is able to develop political security through force, he exiles Snowball and represses all dissent. Power and control motivate Napoleon. Like Jones, he abuses the animals and bullies them into submission. Like Jones, he takes advantage of the animals' labors because of the strength of his political position. Under Napoleon's leadership, Animal Farm becomes "the tyranny of the pigs."
Both displays of political control show how "power corrupts" and that "absolute power corrupts absolutely." Jones and Napoleon do not exercise power in a shared and collaborative manner. Their display of power is absolute and unchecked. As a result, they embrace corruption because they can. They are able to act outside of the law because they are the sole arbiters of power in their political communities. At the end of the novel, the farm has been renamed again and the animals are unable to differentiate between pigs and humans. This underscores how corruption is a part of the human and pig autocratic displays of power in Animal Farm.

Why does paul not want Miranda to say anything about the dead rabbit?

Miranda and Paul live on a farm, so hunting animals is pretty much a way of life for them (although Miranda only accompanies Paul on his hunt so she can go for a nice walk in the woods). Killing animals is a normal part of living in the country, and Miranda's none too squeamish about it. That said, she only really has a gut instinct for killing snakes, as they're considered dangerous.
During the hunting expedition/walk in the woods, Paul shoots a rabbit. When she gets up close to take a look at her brother's handiwork, Miranda's pleased by what she sees. She watches admiringly as Paul skins the rabbit, and she even allows herself to touch the dead animal's exposed sinews.
But then the atmosphere suddenly changes as the two children realize that the rabbit was pregnant. Miranda's still fascinated; she gently touches the dead babies that look so pretty and peaceful. Paul, however, instructs Miranda not to tell anyone about this. He puts the babies back inside their dead mother's womb and hides them all behind a bush.
Paul's trying to protect his little sister from the harsh realities of life. In effect, he wants her to bury the experience of seeing the dead baby rabbits. He is disturbed by what he's seen and doesn't want Miranda to feel the same way. Ironically, Paul, in not giving the dead rabbit and her babies a proper burial, has treated them in the exact same way that his grandmother treated her late husband's body. But the memory of what Paul and Miranda saw cannot receive its own proper burial, at least not yet—not until they have finally matured and come to a deeper understanding of death's true significance.

In what ways are friendship and trust demonstrated throughout the novel To Kill a Mockingbird?

A great illustration of the themes of trust and friendship can be seen in the episode where Dill runs away from home. Dill's gone AWOL because he's tired of no longer being the center of his mother's universe now that she's remarried. So he runs off to Maycomb, where he seeks sanctuary at the Finch residence. Or, to be more precise, he seeks sanctuary underneath Scout's bed. Scout's pretty shocked to find him there, as one can imagine, but she's glad to see him all the same. Dill's a very good friend of hers, and she'll do whatever she can to help out.
Much to Scout's disgust, however, Jem goes and tells Atticus what's happened. This is a sign of Jem's growing maturity; he knows that Dill needs to go back home as soon as possible and that telling Atticus is the responsible, adult thing to do, but Scout doesn't see it like that. She thinks that Jem has broken the bond of trust that existed between himself and Dill and betrayed their friendship.

In To Kill a Mockingbird, friendship and trust are addressed in several ways, but the tenuous trust and friendship between Arthur “Boo” Radley and the children is the most interesting example.
An unlikely form of friendship in the novel is between the children and Boo Radley. At the beginning of the novel, the children cruelly dehumanize him by making assumptions about him, partly influenced by the intolerance in Maycomb. When Boo begins leaving the children small tokens, he wins them over and dispels their fear.

Boo was our neighbor. He gave us two soap dolls, a broken watch and chain, a pair of good-luck pennies, and our lives. But neighbors give in return. We never put back into the tree what we took out of it: we had given him nothing, and it made me sad.

The children realize that friendship is give and take and they had done nothing but take from Boo. Boo has been injured by a cruel father, and yet he still has a capacity for trust and friendship with the Finch children, despite their initial feelings toward him.
Atticus addresses the issue of trust in the novel when he says,

We're paying the highest tribute you can pay a man. We trust him to do right. It's that simple.

He is pointing out that society functions on the premise that we trust our neighbors, friends and family to do the right thing. Boo Radley trusted his father to care for him and was repaid with evil harm. Yet Boo functions as a trustworthy adult when coming to the children’s aid and saving their lives.

Friendship and trust are explored in the novel through various character's interactions with one another during particularly adverse situations. Miss Maudie displays her friendship and trust by supporting the Finch family before and after the controversial trial of Tom Robinson. She is quick to encourage Jem following the trial and stands up for Atticus' decision to defend Tom during the missionary circle. Jem and Scout's relationship with Dill also demonstrates friendship and trust. They not only play together but also get themselves into several precarious situations. The three children trust each other and stick up for one another whenever threatened with punishment. Jem is quick to deny the fact that they are acting out Boo's life story, and Dill lies to the adults after they raid the Radley's yard.
Other members of Maycomb's community portray the themes of friendship and trust throughout the novel. Sheriff Tate and some locals visit Atticus' home to warn him about the Old Sarum bunch, and Walter Cunningham's friendship with Atticus allows him to see the error in his actions. Boo also seeks to gain the children's friendship by giving them gifts in the knothole of his tree and comes to their defense when they are attacked by Bob Ewell. Harper Lee uses the character's friendship and trust towards one another to illustrate the small town, intimate setting of Maycomb.

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

I will begin to help you answer some of these questions, and then you can finish them.
The portrayal of Walter and Beneatha in A Raisin in the Sun suggests that the children of people who had left the South during the Great Migration struggled to succeed. Some, like Beneatha, put their faith in education, Black pride, and their connection to Africa. Others, like Walter, believed that the best way forward was to achieve economic stability. During this time period, African Americans still faced racism in housing, employment, and other areas in the North.
In "Letter from A Birmingham Jail," Dr. Martin Luther King answers critics who think his actions are "unwise and untimely." His tone is reasonable; he explains the reasons why he is leading the movement and why acting now is necessary to further civil rights for African Americans.
Malcolm X, unlike Martin Luther King, was willing to endorse the use of violence if African Americans did not receive a full recognition of their rights. He saw black nationalism as a means for African Americans to promote their own power and achieve greater political rights.
Audre Lorde, an African American poet and writer, believed poetry was essential to express the desires and hopes of women, particularly African American women. She writes, "[it is] through poetry that we give name to those ideas which are, until the poem, nameless and formless—about to be birthed, but already felt." She felt this art form was necessary to express the creativity, unvoiced thoughts, and dreams of black women, who often could not express them any other way.
During the Black Arts Movement, the "Black Aesthetic" promoted separatism in the arts so that African American people could have their own space to express themselves.
I will allow you to answer this last question, which Alice Walker addressed in In Search of Our Mothers' Gardens (see the link below for more information).

Is "The Celebrated Jumping Frog of Calaveras County" a satire?

Mark Twain's famous short story belongs to (or perhaps even originated) a genre of specifically American satire that survived well into the twentieth century in the form of television comedies such as The Andy Griffith Show and The Beverly Hillbillies.
In the tale of the jumping frog, Mark Twain pokes fun at the folksy, naive attitude of the US frontier class. It's satiric, but in a good-natured way, far removed from the angry, slashing satire typical of Swift and other British and European writers. The colloquialisms of the language are comical, as is the long-windedness of the narration, in which virtually nothing of significance happens except the rather goofy trick that is played upon Jim Smiley and his frog. If there is a moral to the story, it's the basic one that no man is to be trusted. The fact that Smiley is so easily duped is probably meant to illustrate the trusting nature of the American soul in the seemingly uncorrupted backwoods setting.
Admittedly, in this last point, our analysis of the story as a satire is perhaps invalidated. Usually satirists are critical of the object of their satire—in fact, this is the whole purpose of the genre: to hold up to ridicule something considered evil or pernicious. In his folksy style, Mark Twain presents Americans in the way they are expected to be, as innocent rubes.
So another layer of meaning is present—in which the setting and the action are a mild caricature of the way frontiersman are perceived. In this sense, we could even interpret the story as a satire not of rural, western Americans but of those outside observers who would tend to have a stereotyped view of them. But if so, it's a very subtle intention. It's more likely that Mark Twain intended the story as simply a comical anecdote illustrative of life in the New World.

Yes, Mark Twain's "The Celebrating Jumping Frog" is certainly a satire, which (as described by other contributors already) plays heavily on East and Western stereotypes of the United States (in Twain's lifetime), but I would add that the satire runs further, running within the narrative of the Tall Tale being told about Smiley. Here, I would suggest we have a satire of life within the West, and the kinds of diversions that tend to correspond with it. Smiley, as a character, is primarily defined by his obsession with wagers, always gambling about anything and everything, and in this perhaps we can also add that the story satirizes these kinds of vices, especially by conveying just how petty all these wagers ultimately are (because in this story, Smiley has to make wagers just so he'd have something to make a wager about, and he'll take up just about any wager no matter how ludicrous it might be...see his jumping frog for example). I'd suggest Twain's story shines a light on life's banalities, and on the silliness and pettiness which runs through the human condition, and this continues both in the manner through which Wheeler's tall tale plays out (with Smiley cheated by his opponent) as well as in the resolution of the larger story itself, where the tall tale is itself dismissed as a pointless distraction, and the narrator walks out on Wheeler, even as he is starting up in another storytelling digression.

In his short story “The Notorious Jumping Frog of Calaveras County,” the humorist Mark Twain satirizes the tall tale genre and those from the Eastern and the Western parts of America.
An essential element of “The Celebrated Jumping Frog of Calaveras County” is satire. In the narrative, people from the Western and the Eastern parts of America are subjected to ridicule as they are presented in exaggerated forms. The stereotype of the well-educated, cultured, and sophisticated Easterner is held up against the uneducated, gullible, and unworldly Westerner. In the humorous twist of Twain’s narrative, it is the sophisticated Easterner, an irritable snob, who is outdone by the garrulous Westerner, Wheeler. Wheeler speaks in a distinct regional dialect that makes him all the more colorful and unusual. He exaggerates with grave dignity as he elaborates on the talents of Daniel Webster, the frog. For instance, Wheeler describes the talents of Smiley’s frog:

[Simon would] set Dan’l Webster down her on this floor…and sing out, “Flies, Dan’l, flies!” and quicker’n you could wink he’d spring straight up and snake a fly off’n the counter there, and flop down on the floor ag’in as solid as a gob of mud….

In both a funny and satirical twist, the Easterner who comes to Wheeler because he seeks Leonidas W. Smiley is tricked into listening to the tall tale of the frog Daniel Webster. He is fooled by the friend who has sent him to Wheeler, and by Wheeler himself, a seemingly backward man who is really an experienced storyteller whose serious manner tricks even the sophisticated listener.

This 1865 short story by Mark Twain is indeed a social satire. His target in this story were people who subscribed to regional stereotypes in 19th century America.
Easterners were stereotyped as snobby intellectuals with formal education and cultural sophistication. By contrast, Westerners were stereotyped as uneducated, uncivilized, and none too bright.
Twain casts his first-person narrator as an Easterner who is played for a fool by a "friend" who sets him up to become a captive audience for Westerner Simon Wheeler, a long-winded raconteur. Within the tall tale Wheeler spins there is another deception going on between a local and a stranger--thereby humorously deepening the satire.
The sophisticated Easterner proves to be gullible and falls victim to both his friend and the clever and entertaining Simon Wheeler.

Are there any quotes that show Macbeth's self-awareness? If so, could you please include some techniques present in those quotes.

Yes, Macbeth certainly does show self-awareness, even from the beginning of the play. When he first hears the prophecies of the witches—namely that he will be king one day—Macbeth is already aware that he's thinking of killing Duncan and that it's an evil idea. He says in an aside,

Cannot be ill, cannot be good: if ill,Why hath it given me earnest of success,Commencing in a truth? I am thane of Cawdor:If good, why do I yield to that suggestionWhose horrid image doth unfix my hairAnd make my seated heart knock at my ribs,Against the use of nature? (I.iii)

The predictions of the witches, he says, cannot be a bad thing because he benefits by gaining a higher title. He thinks, though, it can't be all good because he's already considering murdering Duncan: "why do I yield to that suggestion / Whose horrid image doth unfix my hair." Macbeth is already aware that he is making a bad decision. He is able to weigh both sides of the issue, as well.
After he commits the murder, Macbeth knows that he will not overcome his guilt or be able to "wash his hands" of his sins. This is what he's referring to when he says "Macbeth doth murder sleep"—he will never sleep easily again because of his guilt. This shows his self-awareness even while his is panicking and upset.

The technical term for such self-awareness is anagnorisis. This is a Greek word used to describe a moment in a work of literature in which a character makes a critical discovery about himself. In the case of Macbeth, there are many such examples. Arguably the most tragic is when Macbeth himself finally breaks free of the Weird Sisters' spell and realizes that they've been playing him all along:

And be these juggling fiends no more believed,
That palter with us in a double sense,
That keep the word of promise to our ear,
And break it to our hope. (Act V, Scene viii).

Macbeth has been made to look like a complete fool by the witches. They prophesied that he would never be defeated by a man born from a woman. But as Macduff informs Macbeth before they face off in mortal combat, he was delivered by Caesarean section and so the prophecy doesn't apply to him. Macbeth's realization, his moment of self-awareness, has come far too late. Macduff is hell-bent on avenging the death of his family, and so Macbeth, no longer under the witches' protection—inasmuch as he ever was—has no choice but to stand and fight for what turns out to be the very last time.

Macbeth demonstrates his self-awareness throughout the play, beginning in Act I, Scene 4, when he says, "Stars, hide your fires; Let not light see my black and deep desires." He recognizes that his ambition to be king by killing Duncan would be an indefensible and immoral act, yet his thoughts drift to that place.
Another quotation that demonstrates Macbeth's self-awareness is found in Act I, Scene 7, when he observes "I have no spur/ To prick the sides of my intent, but only/Vaulting ambition." What Macbeth means is that he has no legitimate reason to commit regicide; Duncan is a fine king with integrity and a loyal following. He admits that the only reason he wants to kill Duncan is because he wants the throne for himself.
Another example is found in Act I, Scene 7, when Lady Macbeth questions her husband's masculinity. He answers her briefly and without apparent heat: "I dare do all that may become a man;/ Who dares do more is none." Here, Macbeth is solid in his self-awareness as a man; he is, after all, a heroic soldier who has just dispatched rebels in the name of Scotland.

Explain how the author uses tension to build up her surprise ending.

Gordimer first builds tension with an opening, from the second paragraph on, that is reminiscent of a Gothic horror story: it is night, and the first-person narrator hears an unexplained creaking sound, as if someone is walking across her floorboards. The narrator also uses imagery that reinforces the sense of danger, such as noting that the neighbors sometimes sleep with guns under their pillows and have barred their windows.
From there, the narrator stresses her vulnerability: her windows are as thin as "rime" and "could shatter like a wineglass." To add to the sense of unease and tension, we learn that a woman was murdered two blocks away.
We learn finally that this creaking sound is a false alarm, simply the result of the house being built on unstable ground, but by this time, we have been introduced to a fearful world.
We then move into a daytime world of anxiety, in which houses are closely guarded and the residents fear riots. Whites are highly fearful of blacks. The family in question adds bars to the windows, a high wall, and an alarm system to their home, but they still do not feel safe. Finally, they install the Dragon's Teeth wall, described thusly:

Placed the length of walls, it consisted of a continuous coil of stiff and shining metal serrated into jagged blades, so that there would be no way of climbing over it and no way through its tunnel without getting entangled in its fangs. There would be no way out, only a struggle getting bloodier and bloodier, a deeper and sharper hooking and tearing of flesh. The wife shuddered to look at it.

The sense of people needing more and more protection builds tension, as does the violent, painful imagery of the jagged blades hooking deeper and deeper into human flesh. With the barbed wire now in place, we wonder if that will finally be enough. It certainly seems the house has been made an armed fortress. What surprises us is that the very barbed wire that is supposed to keep the family safe ends up harming or killing the young son.

First, Gordimer talks about a request that's been made to her to write a children's story. Then she describes waking up to a strange sound. Fearing it might be an intruder, she can not fall asleep. Even after she's confirmed that the noise was her creaking house, she begins a story to help her sleep. Gordimer establishes some tension in this first "frame" story when she describes her fear of a potential intruder in her home. 
Then she goes into the story about the family and their own fears of intruders and crime in neighboring areas. As the story progresses, the family continues to upgrade the security of their home. The family continues to hear about more break-ins and more crime. This stokes their fears and they add to the security of their home: 

But every week there were more reports of intrusion: in broad daylight and the dead of night, in the early hours of the morning, and even in the lovely summer twilight - 

They hear about more intrusions and they respond with more security. The reader might suppose that an intrusion is coming, in spite of the family's proactive work to secure their house. The increased reports of intrusion, coupled with increased security serves to raise the tension. The tragically ironic (surprise) ending is that the "security" coil is what poses the most danger to the little boy. 

What news does Ophelia bring Polonius? How does Polonius misinterpret it, and how does this work to Hamlet’s advantage?

Ophelia tells Polonius that Hamlet burst into her room and started acting crazy. This is a very interesting piece of information for Polonius, as it confirms his suspicions that Hamlet's stark staring mad. What's more, Polonius now thinks he has a neat explanation for Hamlet's unusual behavior: he's fallen head over heels in love with Ophelia.
Wily old Polonius immediately sees an opportunity to exploit what he thinks is Hamlet's amorous feelings. Along with Claudius, he contrives a meeting between the two would-be love birds. As part of the plan, Claudius and Polonius will hide behind a curtain and eavesdrop on their conversation, hoping to find out for sure if Hamlet's lovesickness really does explain why he's been acting so strange lately.
Unfortunately for them—and for poor, innocent Ophelia—nothing goes according to plan. Hamlet realizes that there's something up and turns the situation to his advantage. Instead of proclaiming his undying love for Ophelia, he subjects her to an abusive rant, during which he tells her in no uncertain terms that she should take herself off to a convent to avoid giving birth to sinners like herself. This may not be Hamlet's finest hour, but at least he's turned the tables on Claudius and Polonius, and in doing so has bought himself more time to wreak revenge upon his wicked uncle.

In act II, Ophelia brings her father, Polonius, the news that Hamlet burst into her room looking wild with his clothes messed up. He grabbed her arm and then went away without saying anything.
We as an audience know that Hamlet is wild-eyed and acting crazily around Ophelia because he has just seen his father's ghost. However, Ophelia and Polonius do not know this. (This is dramatic irony: the audience knows what the actors do not.)
Polonius misinterprets Hamlet's action of bursting wildly into Opheila's room as evidence that Hamlet is madly in love with his daughter. He believes that Hamlet is lovesick. This works to Hamlet's advantage because it becomes a believable explanation for his crazy behavior. While Claudius, Gertrude, and Polonius are worried about him being in love with Ophelia, Hamlet can try to discover whether or not Claudius really did murder his father.

Calculus and Its Applications, Chapter 1, 1.2, Section 1.2, Problem 22

Determine the $\displaystyle \lim_{x \to 5} \sqrt{x^2 - 16}$ by using the Limit Principles.
If the limit does not exist, state the fact.


$
\begin{equation}
\begin{aligned}
\lim_{x \to 5} \sqrt{x^2 - 16} &= \sqrt{\lim_{x \to 5} (x^2 - 16)}
&& \text{The limit of a root is the root of the limit}\\
\\
&= \sqrt{\lim_{x \to 5} x^2 - \lim_{x \to 5} 16}
&& \text{The limit of a difference is the difference of the limits}\\
\\
&= \sqrt{\left(\lim_{x \to 5} x \right)^2 - \lim_{x \to 5} 16}
&& \text{The limit of a power is the power of the limit}\\
\\
&= \sqrt{\left(\lim_{x \to 5} x \right)^2 - 16}
&& \text{The limit of a constant is the constant}\\
\\
&= \sqrt{5^2 - 16}
&& \text{Substitute }5\\
\\
&= \sqrt{25 - 16}\\
\\
&= \sqrt{9}\\
\\
&= 3
\end{aligned}
\end{equation}
$

Beginning Algebra With Applications, Chapter 5, 5.3, Section 5.3, Problem 58

Graph $\displaystyle x-3y = 6$ by using the slope and $y$-intercept.

$y$-intercept:


$
\begin{equation}
\begin{aligned}

x-3y =& 6
&& \text{Given equation}
\\
0-3y =& 6
&& \text{To find the $y$-intercept, let } x = 0
\\
-3y =& 6
&& \text{Simplify}
\\
y =& -2
&&

\end{aligned}
\end{equation}
$


The $y$-intercept is $(0,-2)$

Writing the equation in slope form, $y = mx+b$


$
\begin{equation}
\begin{aligned}

-3y =& 6-x
\\
\\
y =& \frac{6-x}{-3}
\\
\\
y =& \frac{1}{3}x- 2

\end{aligned}
\end{equation}
$




$
\begin{equation}
\begin{aligned}

m =& \frac{\text{change in } y}{\text{change in } x}
\\
\\
m =& \frac{1}{3}


\end{aligned}
\end{equation}
$


Beginning at the $y$-intercept, move to the right 3 units and then up 1 unit.







$(3, -1)$ are the coordinates of a second point on the graph.

Draw a line through $(0,-2)$ and $(3, -1)$

Precalculus, Chapter 3, 3.1, Section 3.1, Problem 54

Since you already have the same bases, set the exponents equal to each other.
x^(2)+6=5x
Subtract 5x from both sides
x^(2)-5x+6=0
Factor the quadratic function
(x-2)(x-3)=0
Set each term equal to 0
x-2=0 and x-3=0
Solve each equation for x
x=2 and x=3

What message do the last two lines of "Stopping by Woods on a Snowy Evening" convey? What is the significance of the repetition?

The final two lines of Frost's poem "Stopping by Woods on a Snowy Evening" convey the sheer distance the narrator still has to "go before I sleep." By repeating the line "And miles to go before I sleep," Frost utilizes "and" as an intensifier, with the second line seeming to compound its precedent, emphasizing the sense of distance. We know that the quietude of the poem is only an oasis in the journey of the speaker—on "the darkest evening of the year," pausing only "to see his woods fill up with snow," to the surprise of the horse used only to stopping "with a farmhouse near." The final two lines, then, symbolize the speaker re-embarking upon his original journey, with effort now redoubled after the pause.

For The Kite Runner, prepare responses for each seminar question (minimum of four sentences each with a specific quote from the text). Choose five out of the eight questions to respond to in complete sentences. Key Concepts: Redeem (v) – to free from what distresses or harms Redemption (n) – the act of redeeming Courage (n) – strength to survive fear or danger Circularity (adj) – events/things that occur in a circle or a cycle 1. Discuss the role of violence in the novel. How is violence seen, how does violence shape the plot, and how would the story change if there was not violence? 2. Discuss the idea of forgiveness in the novel. What is forgiveness? Come up with a definition. How is forgiveness seen, and how does it vary (change) amongst characters? 3. Discuss the idea of bravery and courage in the novel. What characters do you consider brave or courageous, and does this concept vary between characters? Who would you consider to be the most courageous character? Why? 4. Discuss how the concept of circularity (cycles) is seen in the novel. Provide specific examples from the text where cycles occur. 5. Discuss the idea of redemption. Is Amir ever able to achieve redemption (be set free) for his actions? Why or why not? 6. Discuss specific examples of quotes that recur throughout the novel. Why does Hosseini use repetition in quotations? Why are those quotes important to the novel? 7. Of all the events that occur, Hosseini chooses to title the novel The Kite Runner. Why would he choose this title and what significance does kite running have in the novel? How has kite running shaped the plot? 8. Did the ending surprise you? How would you change the ending if you could?

You have been asked to choose five of the eight options and write four sentences about each, for a total of 20 sentences. This is a fairly long assignment you have been given, and although our goal here is not to complete your homework for you, we can certainly examine some possible ways to approach a few of these options. Let's look at three here to give you a head start on the assignment. 
1. This option is about violence in the novel. If we think about the role violence plays, which is a significant one, we find that the book would be an entirely different story if the violence were removed. In fact, so much of the novel would be changed that we cannot realistically say it can be removed. Violence occurs between individuals, as in the case of Assef and Hassan. We also see it affect a society as the Taliban takes over Afghanistan, and Hassan is even murdered by the Taliban. In terms of how it shapes the plot, the plot of the story is often advanced due to violence, so taking it out would mean that the motivations of certain people or parts of the story would need to change significantly. For example, if Amir had stepped in and defended Hassan when he was attacked and raped, he would not have had a lifetime of guilt related to the incident, and that would have completely changed the relationship between Amir and Hassan. Violence shapes the characters in this novel.
5. This question asks you if Amir is ever able to achieve redemption. This is interesting because we know early on that Amir not only doesn't protect Hassan from the bully Assef, but in a response to his own guilt over that incident he asks his father to find new servants and then frames Hassan for theft when his father refuses. In short, Amir has made poor choices, feels terrible guilt for them, and then continues to victimize Hassan as a result. That makes it hard for him to achieve redemption. Later, we find that Hassan has died at the hands of the Taliban and Amir, sadly, has not achieved any type of redemption with Hassan prior to this. So, what can he do to make up for the terrible way that he treated and even abandoned Hassan? He decides to track down and adopt Hassan's son, Sohrab. This is a noble thing to do and one could easily argue it is the right thing to do given all that he owed Hassan. While he did not make up for the bad deeds he committed against Hassan, he was able to redeem himself in some way by taking care of Sohrab. What you need to determine is if that act of goodwill is enough to be considered "redemption."
8. This option asks your own opinion of the ending of the book. When Amir learns that Hassan has been killed by the Taliban, this surprises him and makes him feel guilty all over again. In fact, he even tracks down Sohrab, Hassan's son, and adopts him. Perhaps he is saving Sohrab in a way he never saved Hassan. Obviously, if Amir had not fallen out of touch with Hassan and their relationship had continued, things may have been different. Perhaps Amir could have helped Hassan. Consider what might have happened had the two not lost touch. By considering the possible options, you can provide some alternative endings to the novel.

What resources do you use that you could use less of or not at all.

It's likely that you can cut back on your use of many resources. For instance, The Economist reports that the average American uses the paper equivalent of 5.57 forty-foot tall trees each year. By contrast, the average citizen of Ireland uses only 2.21. Different levels of resource use are driven by cultural practices that we can change. Here are some examples.
Trees
Use fewer trees by going "paperless" whenever possible. Recycle and reuse paper, cardboard, and furniture made of wood.
Water
Reduce consumption of water by eliminating wasteful practices (like letting the water run when you are washing dishes, or brushing your teeth). You can also reduce waste usage by taking shorter showers. If you have a yard or garden, and live in an area where dry conditions are common, you can reduce usage by cultivating only drought-resistant plants.
Fossil fuel use in the home
Central air conditioners and heat pumps typically burn more energy during use than any other home appliance. So you can save energy by finding ways to use these devices more sparingly (for example, by insulating your home, and dressing more warmly in winter).
You can also save energy by
turning off electric lights and other devices when not in use
switching from incandescent to fluorescent bulbs
unplugging appliances you use infrequently (because these appliances draw small amounts of electricity even when they are not in use)
drying laundry in the air
replacing energy-wasteful appliances with more efficient models
Fossil fuel used for transportation
You can save energy by walking and riding bikes. When that's not feasible, you can save energy by using public transportation, car pooling, and planning efficient car trips (accomplishing multiple errands with minimal mileage).
Fossil fuel used to make plastic
Avoid buying products with lots of plastic packaging. Use reusable grocery bags.
https://education.seattlepi.com/reduce-use-natural-resources-4106.html

https://homeguides.sfgate.com/description-three-actions-could-reduce-use-natural-resources-78885.html

https://www.economist.com/graphic-detail/2012/04/03/im-a-lumberjack

What is the underlying message of the book "The Silence of the Lambs"?

The Silence of the Lambs is a complex novel with likely more than one underlying message. It clearly explores the nature of evil, and it has much to say about the lengths people will go to to get what they need or want. 
One of the book's subjects explores how law enforcement personnel must sometimes negotiate with criminals and deal with the obstructive actions of other involved parties in order to solve crimes and prevent other crimes from occurring. Clarice Starling, though very intelligent and intuitive, is intellectually outmatched by the brilliant Hannibal Lecter, a psychiatrist and imprisoned serial killer.  In exchange for information that lends insight on the serial killer Buffalo Bill, Clarice must not only endure the manipulations of Lecter but also overcome the duplicity and jealousy of Chilton, Lecter's jailer and the director of the hospital for the criminally insane where Lecter is held. 
Lecter's ultimate escape is the outcome of Chilton's incompetence and obstruction, but the combination of Lecter's clues and Starling's intelligence enable her to save Buffalo Bill's final victim.

Describe Helen Keller's struggle in Cambridge school to prepare for Radcliff college. How did she succeed in her mission?

Helen Keller was fortunate to have a great intellect and desire to learn, but she initially struggled with the paucity of tools available for deaf and blind people to gather and organize data about the world. To prepare herself for Radcliffe College at Harvard, she focused primarily on expanding her vocabulary at an exponential rate. To do so, she learned to move her hands around hundreds of different objects to acquire a haptic understanding of difference that backgrounded her vocabulary. Her understanding of touch metaphors primed her for learning the Braille system, which complemented her experience and object-based vocabulary with a symbolic one suitable for more complex expression. Assisted by various teachers—including her lifelong companion, Anne Sullivan—Keller evolved from understanding the world as largely unintelligible, and even hostile, to being a highly literate, competent, and optimistic woman who treated the conditions of her disability as surmountable problems. It was primarily this shift from a fixed mindset to a growth mindset that qualified her for admission into Radcliffe College.
https://www.perkins.org/history/people/helen-keller

Helen Keller decided she wanted to go college and, therefore, needed more formal education than that provided at home by Miss Sullivan. However, she struggled with her classes at the Cambridge School because the school—and the world in general—was not accustomed to accommodating a special needs student. It was difficult for Keller to get textbooks in braille, so Miss Sullivan had to read all her textbooks and then struggle to summarize their contents into Helen's hand. Most of the teachers could not communicate with Helen through hand language, so Miss Sullivan had to write copious notes and then communicate them to Helen. A few teachers, however, did learn to communicate with Keller directly, such as the German teacher, so that offered some relief.
Keller was able to type out her exams on a typewriter and she passed them. She essentially succeeded in getting through the school due to the willingness of her teachers to work with her, Miss Sullivan's ceaseless efforts, and her own hard work.

Calculus: Early Transcendentals, Chapter 4, 4.3, Section 4.3, Problem 35

Given: f(x)=2+2x^2-x^4
Find the critical values by setting the first derivative equal to zero and solving for the x values.
f'(x)=4x-4x^3=0
4x(1-x^2)=0
x=0,x=-1,x=1
The critical values are x=0, x=-1, x=1.
Part a)
If f'(x)>0 the function is increasing in the interval.
If f'(x)<0 the function is decreasing in the interval.
Select an x value in the interval (- oo ,-1).
Since f'(-2)>0 the function is increasing in the interval (-oo ,-1).
Select an x value in the interval (-1, 0).
Since f'(-1/2)<0 the function is decreasing in the interval (-1, 0).
Select an x value in the interval (0, 1).
Since f'(1/2)> the function is increasing in the interval (0, 1).
Select an x value in the interval (1, oo ).
Since f'(2)<0 the function is decreasing in the interval (1, oo ).
Part b)
Because the function changes direction from increasing to decreasing a local maximum exist at x=-1 and x=1. The local maximum occurs at the points
(-1, 3) and (1, 3).
Because the function changes direction from decreasing to increasing a local minimum exists at x=0. The local minimum occurs at the point (0, 2).
Part c)
Find the critical values of the second derivative.
f''(x)=4-12x^2=0
4(1-3x^2)=0
1=3x^2
x=+-(sqrt(3)/3)=+-.577
If f''(x)>0 the function is concave up.
If f''(x)<0 the function is concave down.
If f"(x)=0 an inflection point exists.
Select an x value in the interval (-oo ,-.577).
Since f''(-1)<0 the function is concave down in the interval (-oo ,-.577).
Select an x value in the interval (-.577, .577).
Since f''(0)>0 the function is concave up in the interval ('.577, .577)
Select an x value in the interval (.577, oo ).
Since f''(1)<0 the function is concave down in the interval (.577, oo ).
Since f''( +- .577)=0 the function will have inflection points at x=+- .577.
The inflection points are at the coordinates (-.577, 2.555) and (.577,2.555).
Part d)

Why does Meg get in trouble at school? How does the principal make matters worse?

In the first chapter of A Wrinkle in Time, we learn that our main character, Meg Murry, is not doing well in school in spite of how smart she is. In the second chapter, which is titled "Mrs. Who," we see Meg in school, tired from the lack of sleep she got the night before. When Meg cannot remember the answer when asked about the imports and exports of Nicaragua, her teacher, Miss Porter, and fellow classmates laugh at her. Meg becomes angry, and the following exchange happens:

"Who cares about the imports and exports of Nicaragua, anyhow?" she muttered.
"If you're going to be rude, Margaret, you may leave the room," the teacher said.
"Okay, I will." Meg flounced out.

Miss Porter tells the principal, Mr. Jenkins, about the incident, and he calls Meg into his office during her study hall. It becomes clear that Mr. Jenkins isn't the most sensitive person when he decides that now is a good time to pry into Meg's home life and have a harsh conversation about her missing father. Meg was already upset earlier, and he makes things much worse by telling her that she should "face facts" about her father. Unlike Meg and her family, Mr. Jenkins believes that Dr. Murry is never going to come back home. For some reason, he thinks that forcing this idea on Meg while simultaneously calling her "antagonistic" and "the most belligerent, uncooperative child in school" will get her to behave the way he wants her to.

What is the suggested theme in “Infant Sorrow” by William Blake?

The overt theme is that of a newborn baby entering the world. Blake evinces the sounds, sights, and movements of that event:

My mother groand [sic]! my father wept. . .
Helpless, naked, piping loud. . .
Struggling in my fathers hands.

This is not a moment of joy, as indicated by the title "Infant Sorrow." The event of birth occurs from the perspective of the newborn, who expresses existential angst over being born:

My mother groand! my father wept. 
 
Into the dangerous world I leapt: 
 
Helpless, naked, piping loud; 
 
Like a fiend hid in a cloud. 

The first sounds he hears are those of pain and weeping, which usually indicate sadness, not happiness. These aural signals suggest danger, but the infant does not shrink from this seemingly unwelcoming world—he leaps into it. There is contrast between the third and fourth lines. Though he is "helpless" and "naked," his voice "[pipes]" loudly, like that of a "fiend." He is fragile, yet also a potentially menacing creature.
 
The second stanza focuses on action and movement:


Struggling in my fathers hands: 
 
Striving against my swaddling bands: 


Bound and weary I thought best 


To sulk upon my mothers breast.

The use of the present participle ("struggling," "striving") gives the infant's experiences a sense of urgency. Moreover, these are actions of resistance. The "swaddling bands" are the blankets in which newborns are wrapped to provide them with comfort, but they make this infant feels "bound." 
 
Ultimately, he decides it is futile to continue to struggle, as he has become "weary." He does not rest against his mother's breast but instead sulks out of resignation and resentment. He is condemned to live in a world that will not bring him the comfort or safety of the womb.

In "The Destructors" by Graham Greene, how does Mr. Thomas's house reflect the character of the postwar era?

The house is a remarkable survivor of the blitz. Although its neighbors have been destroyed by a bomb, somehow this house avoided destruction. It's still standing, even though it leans badly and must be supported by wooden struts. The house also functions as a kind of symbol of the social upheaval going in in postwar Britain. Built by Christopher Wren, it's an architectural masterpiece that, like the rest of the country, is hanging by a thread, a last bit of beauty in an otherwise grim and bombed-out neighborhood. As such, it also becomes the occasion for a kind of class warfare that was also typical of the postwar era. Trevor, the new leader of the gang, comes from an educated family—his dad was an architect "come down in the world." It's Trevor's father that tells him the house was built by Wren, and that distinction makes it a target for Trevor's "anti-Architecture," the artful demolition of the house from the inside with the boys working like "worms inside an apple." In this way, the house and its fate suggest the "rottenness" of postwar Britain, as well as its lost grandeur and prestige; one has to laugh. As the truck driver says to Mr Thomas, who emerges from his outhouse to find his house a pile of rubble, "You got to admit it's funny."

Mr. Thomas's house in "The Destructors" reflects the character of the postwar era in Britain (after World War II) because the house has been shattered by a bomb during the air raids carried out by the Nazis. Greene writes that the house "literally leaned, for it had suffered from the blast of the bomb and the side walls were supported on wooden struts." The neighborhood around it has been destroyed by incendiary bombs, so the house sticks up "like a jagged tooth." Though the house has architectural importance, as it was built by the famous architect Christopher Wren, its owner, Mr. Thomas, does not fix it. Instead, he uses a bathroom in a shed in the garden. This type of frugal living is also characteristic of postwar Britain, which experienced what was called "The Age of Austerity." The government was bankrupt from fighting the war, and people continued to be subject to rationing for many years after the end of the war. 

If my statistical results do not fall within a "normal" curve, does that mean they are wrong? Why?

I assume that you are asking about results that either lie outside a confidence interval, or results during a hypothesis test that lie in the critical region (tail.)
When creating a confidence interval we start with a point estimate for the population parameter we are interested in. For example, if we want to know the average height we might assume that the average from a random sample of sufficient size is a decent point estimate.
Understanding that the point estimate is not likely to exactly match the population parameter, we introduce an error term. This is added to and subtracted from the point estimate to create a confidence interval. The error term includes the standard error of the measurement, as well as a factor that is derived from the confidence level we want to achieve. (The larger the confidence, the larger the interval will be.)
If a secondary test gives results outside this confidence interval, is the result "wrong"? Not necessarily. Suppose the interval was created with a 95% confidence level. Thus we are 95% certain that the population parameter lies within the interval. One out of every twenty samples will have an estimate outside the interval. The true population parameter would lie outside the interval 5% of the time.
If we are doing a hypothesis test, in essence we are creating a confidence interval centered on the reported or accepted value of the parameter. Then we see if our sample statistic lies in that interval. If it does, we assume that the population parameter is as stated. If our sample statistic lies outside the interval (in the critical region), we have evidence to show that the given population parameter is incorrect.
In running a hypothesis test we run the risk of two types of error (assuming the samples are created correctly, etc...) A type I error is when we say that the purported parameter is incorrect, when it is actually correct. We have a lot of control over this type of error, as the probability of this type of error is equal to our confidence level. (I.e. at the 95% confidence level, the chance for a type I error is 5%.)
A type II error occurs when we fail to recognize an incorrect parameter. We can reduce the probability of this error by increasing the sample size and doing additional samples.
So when running a hypothesis test, the true result is not absolutely given. We only have probabilities to work with.
http://mathworld.wolfram.com/ConfidenceInterval.html

http://mathworld.wolfram.com/HypothesisTesting.html

Please provide a detailed summary and historical context for the following primary source. "I Took Final Action in 1903" Theodore Roosevelt https://www.tracy.k12.ca.us/sites/rlee/Shared%20Documents/History%20of%20the%20Americas%20II/US%20Latin%20American%20Relations/Sources/Roosevelt%20Source%20Evaluation.pdf

Roosevelt wrote this document after he failed to be reelected to the Presidency in 1912. In this document, he explains why he believes the construction of the Panama Canal was his most important foreign policy achievement and why it was constitutional, though some argued otherwise at the time. In actuality, Roosevelt supported a revolution in Panama, then part of Colombia, when the Colombians would not agree to the construction of the canal, which the French under de Lesseps had tried but failed to build.
In this document, Roosevelt states that the Colombians had often asked him to protect the isthmus across Panama and that de Lesseps had tried to build the canal but had failed. He writes that the government of Colombia had shown itself to be incapable of controlling the isthmus in the state of Panama and that only the constant intervention of the US had maintained this property under Colombian control. When Panama declared itself independent in 1903, no congress had sat in Colombia since 1898, and it had become a dictatorship.
The US negotiated the Hay-Herran treaty with Colombia to provide the US with a 100-year lease on a strip of land across Panama, but it was not ratified by Colombia. Roosevelt argues that this treaty was overly generous to Colombia. Roosevelt writes that the revolution in 1903 was entirely peaceful and that the U.S. did not aid or abet this revolution. Roosevelt states that both military and civil reasons compelled him to intervene to build the canal, which was of vital importance for American shipping. You can read at the end of his speech how he further justifies the construction of the canal.

How do I analyze an advertisement? I have to analyze, but I don't know which questions to ask. What I should look out for?

Your analysis will depend on the type of advertisement and the type of analysis your teacher wants.  There are many ways to analyze an advertisement, but one way you might want to consider is a rhetorical analysis.
Basically, rhetoric is the art of persuasion.  What are advertisements designed to do?  They are designed to persuade you in some way.  Once you have decided on an advertisement to analyze, you can complete a basic rhetorical analysis pretty easily.
First, ask yourself what the purpose of the advertisement is.  Is is trying to persuade you to buy something? to vote for someone? to donate money?
Once you have discovered the purpose, ask determine who the "speaker" is, or who is trying to persuade you.  Analyse the speaker's "Ethos" or credibility.  Is the speaker believable or not?  Why or why not?
Next, try to determine the targeted audience of the advertisement.  Who is the speaker trying to persuade?  The target audience will shape how the speaker frames his/her argument.
Finally, determine how the speaker tries to persuade the audience.  Does the speaker rely on evidence--facts, statistics, specific examples?  If so, the speaker is using "Logos," or the logical appeal.  Does the speaker rely primarily on getting an emotional reaction from the audience?  In other words, does the speaker try to make the audience feel happy or sad or scared in order to persuade them?  If this is the case, the author is using the "Pathos," or emotional appeal.
In most cases, talented speakers will using a combination of all three appeals-ethos, logos and pathos.  Keep in mind that all of the appeals can be visual and/or verbal/written.  Be sure to cite specific examples from the advertisement which showcase the different appeals.
For further information, you may want to research the "Rhetorical Triangle" or the "Three Rhetorical Appeals."  I hope this helps.

While there are many different kinds of advertisements (print, radio/podcast, television, etc.), many can be analyzed in a similar way.
The first and most basic question you can start with is "What is being sold?" While this may seem obvious at first, you can look far more deeply than you may realize. Perfume commercials, for example, are trying to make money by selling perfume, but the commercials always show gorgeous, glamorous people and settings. This could be interpreted as saying "If you use our perfume, you can be glamorous, too!" 
In a similar vein, you can ask "What is the problem this product is trying to solve?" Is it a legitimate problem? Is the product a legitimate solution? This is extremely subjective, but often produces interesting results. 
Next, very similar to the first question, "How is it being sold?" Are they listing the merits of the product? Are they painting you a picture of how ideal life would be if only you had the product? 
Continuing from #3, "What else does this make me think of?" Advertisements, like books and movies, don't exist in a cultural vacuum. Does this ad allude to another ad, or another piece of media? What sort of trend in advertising is this following? How is this similar to or different from ads for comparable products? 
When thinking through these questions, you'll be able to keep in mind not only the design, format, and medium of the advertisement, but the larger cultural values and mores at play. 

While this question may seem intimidating, if you focus on the following advertisement elements, you should have an easier time.
Elements of advertisement:
Who is the company/group?
What are they advertising?
Who is the intended audience?
What advertising techniques (flashy, pulls at emotional strings, etc) are used? 
What is the design of the ad?
What is the mood of the ad?
Once, you have answered the first questions, you can move on to a category/type specific analysis. In the advertising category, there is Radio, Podcast, Television, or the Internet. Each of these subcategories will use specific techniques that you can discuss.
Radio, Podcast, Television, or Internet Specific Advertisement Categories:
In the Radio and Podcast advertisement category, consider:
Is there a hook? In other words, does the ad catch your attention and how or how not?
Does the sound volume increase when the ad begins? If so, what impact does that have on you as a listener?
Is there music or other accompanying sounds that draw you into the speaker’s voice?
What is the speaker's voice like? Is it jarring, pleasant or excited?
What is used to entice the listener? For example, are there unique adjectives that make the product enticing?
In the Television category, consider:
What visual elements are used to draw you into the advertisement?
Does the advertisement move quickly from scene to scene or does it focus on one image? What impact does the pace of the images have on you?
Does it attempt to produce a specific emotion in the viewer? For example, is it an image of a starving child that produces empathy?
In the Internet category, consider:
Is it a pop-up ad? If so, what were you doing when the pop-up occurred? Then, who do you think is the intended audience of the ad?
What visual elements are used?
Color
Font
Size of font
High or low resolution of images
Did you see the ad through a social media website? If so, why is social media a good place to advertise in?
Overall, when you look at or listen to the advertisement, take notes on the experience you have with the content. Once you have taken notes, reflect on “how” the company was able to produce that experience for you. Then, you can discuss the advertisements use of sound, imagery, or pace.
I hope this was helpful and good luck!
 
 

Firstly, there are different types of advertisements: print, radio and television commercials, and Internet ads, which may still be images or commercials similar to what one would see on television.
In the case of a radio advertisement, the focus is on the message:
What does the announcer tell us about the product or service?
What adjectives are used to describe it?
What tone of voice does the announcer use? For example, you may have noticed that announcers who are promoting retail sales tend to speak loudly and excitedly. Those who are selling an insurance service will speak more calmly and in a softer tone. 
Is the speaker male or female? Why might the advertiser have chosen a male or female speaker for this particular product?
What kind of music (if any) is playing in the background? What sound effects (if any) are used?
In the case of a print ad or still image, the focus is on the image and the brief message that accompanies it:
What kind of font does the advertiser use? Why? What is the size of the font?
How does the image draw attention to the quality of the product? For example, a recent Heinz ad creates a bottle of ketchup out of a tower of sliced tomatoes. The message below reads, "No one grows ketchup like Heinz." Heinz is clearly emphasizing the freshness of its product and its use of all-natural ingredients. It does not matter if this is true or not, it is what they want you to believe.
Many print ads use models or celebrities. In these cases, think about why they may have chosen that particular person. To whom might they be marketing this product? How does this particular person appeal to that demographic?
In the case of a TV commercial or other moving image, the focus is on the narrative:
Who are the characters in the commercial? You may have noticed that in commercials for household cleaning products, the main character—sometimes the only character—is a middle-aged woman, usually white, who is doing housework. Very often, advertisers reinforce our social prejudices.
Once again, when a celebrity is used, why have they chosen this celebrity? On which aspect of the person's fame is the advertiser capitalizing?
If there is music in the ad, what kind of music is it? Is it a famous song? Why might they have chosen this song?
What is the slogan and how do they provide it to the viewer? Is it merely spoken or is it displayed?
Who, if anyone, narrates the commercial? Is it a male or a female voice? What tone does the person use? What is the pace of his or her speech?
Is this a commercial that emphasizes diversity? How might that relate to the promotion of this product?
If the characters in the commercial are of a particular age group, race, or gender, why might the advertisers have cast in this way?
There are other things to explore, but this should help you get started.

int dx / sqrt(1-(x+1)^2) 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, the integrand f(x) =1/sqrt(1 -(x+1)^2)  we apply
u-substitution by letting u =(x+1)  and du = 1 dx or du= dx .
int (dx)/sqrt(1 -(x+1)^2) = int (du)/sqrt(1 -u^2)
 
int (du)/sqrt(1 -u^2)   resembles the basic integration formula for inverse sine function: int (dx)/sqrt(1-x^2)=arcsin(x) +C .
By applying the formula, we get:
int (du)/sqrt(1 -u^2) =arcsin(u) +C
Then to express it in terms of x, we substitute u=(x+1) :
arcsin(u) +C =arcsin(x+1) +C
 

How are minerals connected to the Big Bang?

Minerals are connected to the Big Bang in the same way you and (almost) everything else is. To understand this connection, we simply need to understand what the Big Bang theory is.The Big Bang theory is a cosmological model of the universe. It is a theory that tries to describe our universe in its early ages, and this includes an answer to some very interesting questions: how matter came into existence, how atoms came together, how stars formed, and so on. Since the universe seems to be around 14 billion years old, it is very hard to test any model like the Big Bang. The best we can do is look at how our universe looks today and guess how it looked in the past.Now a mineral is a "thing" made out of atoms that follows some criteria—the atoms must be ordered in an atomic arrangement, they must be formed by natural processes, they must be a solid at some certain temperature and pressure, and so on. For our discussion, the most important aspect of a mineral is that it is made of atoms (or molecules), and the Big Bang is a model that gives an explanation of how atoms came into existence!So the physical connection between the Big Bang theory and minerals is very trivial. Almost everything that exists can be connected to the Big Bang. Minerals are a little bit more interesting because, due to their very basic structure, you can find them almost everywhere in the universe. You can find them in asteroids, nebulae, planets, and so on. Thanks to their large presence, the study of minerals can give us information about how matter around the universe evolved, contributing to our understanding of the so-called Big Bang theory.
https://en.wikipedia.org/wiki/Big_Bang

https://en.wikipedia.org/wiki/Mineral

Minerals are connected to the Big Bang both directly, in a physical sense, as well as metaphorically, as an analogy to understand how solid matter "crystalized" out of pure energy over time.
The direct connection between minerals and the Big Bang Theory relies on the understanding that minerals are specific arrangements and compositions of specific types of solid matter--elements, compounds and mixtures--and the Big Bang Theory explains is where all matter in the universe originated--a long, slow cooling of pure energy that expanded from a singularity in space-time.
Metaphorically, minerals can help us understand what the Big Bang Theory describes, especially as the moniker (name) "Big Bang" is a poor description of what the Theory actually states. The Big Bang has also been referred to as the "Slow Freeze" -- rather than a bright, loud "Bang", there was actually no light, and no matter to carry sound waves, for the first several hundred "years" after the big bang (remember, our idea of a year is based on earth's journey around the sun, and neither of those objects existed at the time of the big bang). As the universe expanded, creating time and space as it grew, the extreme energy of the singularity slowed down, forming quarks and gluons, then protons and neutrons and finally atoms -- mostly Hydrogen gas. Over billions of years, through a variety of chemical processes such as nuclear fusion in stars and supernova explosions, all of the elements were formed, and as they slow down and cool off (Kinetic Molecular Theory explains that relationship), they "crystalize" into metals, ice, and minerals.
Therefore, the big bang theory explains the origins of the atoms and molecules which make up minerals today, but the big bang theory itself also explains a sort of "crystalization" of the universe in a process similar to the formation of minerals on earth.
This first reference has a good description of an attempt to study the universe as geologists study a crystal: https://phys.org/news/2012-08-big-theory-chill.html
https://sciencing.com/how-minerals-formed-4619330.html
https://www.smithsonianmag.com/science-nature/life-and-rocks-may-have-co-evolved-on-earth-180957807/
http://www.medicaldaily.com/big-bang-was-actually-big-freeze-say-scientists-242129
https://www.space.com/17217-big-bang-phase-change-theory.html

Should we have different types of homicide?

The criminal justice system distinguishes between various types of homicide. Although all types of homicide involve one person killing another person, criminal law divides such killings into two categories, murder and manslaughter, with murder involving "malice aforethought"—that is, a deliberate plan in advance of the act of killing someone.
There are strong arguments for making some distinctions among types of homicide. The most obvious is the distinction between deliberate and accidental homicide. For example, if someone is driving on an icy road under the speed limit, skids on a patch of black ice, and accidentally hits a pedestrian on the sidewalk, someone has indeed died, but the driver had no intention of killing the person and is probably utterly horrified by the course of events. In fact, the act may not be considered a crime.
The next type of involuntary manslaughter is more problematic. Imagine that a driver was under the influence of drugs or alcohol, or was driving substantially over the speed limit, and accidentally hit a pedestrian. In such a case, there is an element of negligence, but the perpetrator may be struggling with substance abuse issues or simply young, thoughtless, and impulsive. While the act is definitely criminal, there is a major difference between this and someone, for example, who deliberately kills during the course of an armed robbery or a rape. One major difference is the possibility of the person being rehabilitated through substance abuse and metal health treatment. That being said, the high recidivism rates for impaired drivers suggest that strong sanctions may be needed.
Obviously, there are a wide range of possible scenarios in which homicide may occur. Society's response to such homicides should be based on evidence concerning the possibility of rehabilitation. A serial killer or gang member who has deliberately killed many people and perhaps committed other criminal acts is unlikely to change and needs to be incarcerated for the protection of society. Someone with a substance abuse or mental health problem who commits involuntary manslaughter may be a person who can be rehabilitated and become a productive member of society with appropriate monitoring and support mechanisms. Therefore it makes sense to treat these types of crimes differently.

Precalculus, Chapter 1, 1.3, Section 1.3, Problem 52

Determine an equation for the line with a slope $-2$ and $y$-intercept $-2$. Express your answer using the general form or the slope intercept form of the equation of a line, which ever you prefer.

Using the slope-intercept form, $y = mx + b$, where $m$ is the slope and $b$ is the $y$-intercept.


$
\begin{equation}
\begin{aligned}

y =& -2x + (-2)
&& \text{Substitute } m = -2 \text{ and } b = -2
\\
y =& -2x-2
&& \text{Slope Intercept Form}
\\
\text{or} &
&&
\\
2x + y =& -2
&& \text{General Form}


\end{aligned}
\end{equation}
$

Intermediate Algebra, Chapter 2, 2.1, Section 2.1, Problem 54

Evaluate the equation $\displaystyle \frac{x}{5} - \frac{x}{4} = 1$ and check your solution.


$
\begin{equation}
\begin{aligned}

\frac{x}{5} - \frac{x}{4} =& 1
&& \text{Given equation}
\\
\\
20 \left( \frac{x}{5} - \frac{x}{4} \right) =& 1(20)
&& \text{Multiply each side by } 20
\\
\\
4x - 5x =& 20
&& \text{Distributive property}
\\
\\
-x =& 20
&& \text{Combine like terms}
\\
\\
x =& -20
&& \text{Divide both sides by $-1$}


\end{aligned}
\end{equation}
$


Checking:


$
\begin{equation}
\begin{aligned}

\frac{-20}{5} - \left( \frac{-20}{4} \right) =& 1
&& \text{Let } x = -20
\\
\\
-4 + 5 =& 1
&& \text{Simplify}
\\
\\
1 =& 1
&& \text{True}

\end{aligned}
\end{equation}
$

What is the theme of Ray Bradbury's story "The Skeleton"?

If you reconsider the basic outlines of the plot, I think you will start to detect the theme of self-destructive obsession and fear of mortality that runs through Bradbury's story "The Skeleton."
Mr. Harris becomes obsessed with his skeleton, a symbol of death in cultures throughout the world. He regards his skeleton as separate from his true self, and it horrifies him:

"It's vulgar, it's terrible, it's frightening. Skeletons are horrors; they clink and tinkle and rattle in old castles, hung from oaken beams…"

Mr. Harris can't or won't internalize the reassurances of his wife and other people who lack his obsession. He eventually comes to believe that his skeleton is trying to kill him. He thinks it wants to free itself from Mr. Harris's flesh and Mr. Harris's control.
So Mr. Harris entrusts himself to a mysterious and self-proclaimed "bone specialist" -- a sinister little man who helped encourage Mr. Harris's obsession in the first place -- and this man responds by feeding on Mr. Harris's bones.
When Mr. Harris's wife comes home, she discovers her husband lying on the floor -- a human "jellyfish."
Did Mr. Harris get what he wanted? Obviously, existence without a skeleton is far more horrifying than existence with a skeleton -- even if you associate skeletons with death and gothic horror tales. If you strip away the surface details, and look at the underlying conflicts, you see a man who destroys himself because he can't reconcile himself to his vulnerable, animal, biological nature. If he had seen reason, and come to terms with the fact that bones are essential, he could have saved himself from ruin. But he was too much in the grip of his fear and horror, driven by his revulsion towards skeletons as terrifying, repulsive reminders of death and decay.
You can develop your own articulation of this theme by looking over the people Mr. Harris interacts with. Why don't other characters share Mr. Harris's obsession? His wife is clearly aware of the biological frailties of the human body. Note his conversations with her, and the fact that she works, or volunteers for, the Red Cross. Mr. Harris regards the fat man as someone who has successfully asserted control over his skeleton. What advice does the fat man give Mr. Harris, and how might Mr. Harris have benefited from it?
Remember that Bradbury could have made other choices, e.g., he could have given Mrs. Harris a different occupation. If you ask yourself why Bradbury made the choices he did, you will find more evidence to help you develop your own account of the theme.