Before the action of the play begins, what have Betty Parris and her friends been doing?

On the night before the play begins, Betty Parris and her cousin, Abigail Williams, as well as some other local girls, went dancing in the forest with Reverend Parris's Barbadian slave, Tituba.  Apparently, Mrs. Putnam sent her daughter, Ruth, to Tituba to ask the slave to conjure the spirits of her dead babies in order to figure out who might have been responsible for their deaths.  Mrs. Putnam's terrible luck -- seven out of eight of her children died shortly after birth -- has led her to believe that one or more of her midwives must be a witch, and she is desperate to learn of some reason for her children's deaths.  In addition, Abigail also drank a charm to kill Elizabeth Proctor, the wife of Abigail's former lover, and one of the girls danced naked.

What cognitive systems underlie thinking and decision making? What evidence supports the existence of these systems?

Underlying decision making are three types of reasoning: deductive reasoning, inductive reasoning and abductive reasoning. These forms of reasoning can sometimes be affected by emotion and bias, as well. 
Deductive Reasoning
This type of reasoning involves working intellectually from a general rule or premise to a specific application of this rule, and from there to a logical conclusion about the specific application. Deductive reasoning is often arranged in a syllogism that moves from a general statement to a particular one that logically follows.
A simple example of this can be made if someone were planning a trip:

Temperatures in southern Italy are very warm in the summer.Marge is planning to travel there when she finishes college in the summer.Therefore, she is packing light clothing for her trip.

Inductive Reasoning
This type of reasoning moves a specific idea to a logical conclusion about its application. Such reasoning begins with an idea that is later generalized as it is applied to other similar concepts. After details that have been observed are gathered together, a person can draw a generalization that stems logically from these details, thus using inductive reasoning.
While inductive reasoning may not always lead to the soundly logical conclusion, it often generates observations that allow creative ideas to develop that lead to new discoveries.
Abductive Reasoning
Abductive reasoning typically begins with an incomplete set of observations and proceeds to the likeliest possible explanation for the set. Abductive reasoning yields the kind of daily decision-making that does its best with the information at hand, which often is incomplete.
This is a flawed reasoning in comparison to deductive and inductive reasoning. For, it starts with a set of observations that are not complete, but enough that a person can move to a possible explanation for this set. 
https://en.wikibooks.org/wiki/Cognitive_Psychology_and_Cognitive_Neuroscience/Reasoning_and_Decision_Making

https://www.butte.edu/departments/cas/tipsheets/thinking/reasoning.html

What might be a good thesis in which to write an essay based on the personal characters of Emilia and Desdemona?

Emilia is generally considered to be a foil for Desdemona in this play, where their differing characters contrast and illuminate each other. Emilia is older, wiser, and cynical about men and their desires. Their conversation about fidelity in Act IV, Scene III is particularly illuminating. Desdemona, young and naive, does not believe "there be women who do abuse their husbands" by being unfaithful to them and insists that Emilia herself would not; Emilia scoffs and describes infidelity as "a small vice." Elsewhere in the play, Iago suggests that Emilia has been unfaithful to him with Othello. Emilia seems very aware of the lowly way in which women are regarded in Venetian society and declares that it is a husband's fault "if wives do fall." Ultimately, it is Emilia who unmasks Iago as the villain he is and who comes to Desdemona's rescue, albeit too late, when Othello has smothered her.
A thesis for the two of them might, then, focus on the question of why these two women characters are written together in the play. Does Emilia's cynicism help us to appreciate Desdemona's youth, naiveté, and innocence? Could Desdemona have avoided her fate if she had been more like Emilia, believing that Othello wanted nothing more from her than sex, rather than trusting in his love? What about the fact that, in the end, both the cynical wife and the idealistic wife is killed by her own husband—perhaps this illustrates the powerlessness of women in the society of the play, whatever their personal natures.

What are three topics addressed by The Night Circus, and what theme do they portray?

I believe that the question wants three motifs/symbols/etc. that illustrate a single theme.  That's definitely doable with The Night Circus.  The book is a visual banquet, and it's loaded with themes.  
Three topics that the book addresses are power, magical reality, and eternity.  All three of those topics are used for various events during the book, but all three of them do help illustrate the book's theme of true love.   
Celia Bowen and Marco Alisdair are both apprentice magicians who are supposed to battle each other to the death.  Fortunately, they fall in love with each other and find a way to both survive despite the rules of the magical bet placed between Alexander and Hector Bowen. 
Both Celia and Marco have the power to destroy each other.  However, instead of using their magic for death, they use their magical powers to bring surreal fantasy images into reality.  They do this as a form of courtship.  Celia and Marco both use the confines of the circus in order to dazzle and delight each other.  As long as both characters are alive and take care of the circus, the night circus will continue.  In other words, as long as the two of them remain in love, they will not age.  Their relationship is eternal. 
At the end of the book, Celia and Marco find a way to continue being in love forever outside of the circus.  Marco, Celia, and their actions illustrate the theme of love and some common beliefs about love.  Beliefs like the following which come from the culture studies course that I teach.
True love is the height of existence
True love is eternal
True love is a powerful and unstoppable force
There is only a single "one and only"
Love transcends all boundaries
Love survives all problems
Love is mysterious

What are the poetic devices used in the poem "Caged Bird"?

The "free bird" of the first stanza that "leaps" and "floats" and "dips" in the sun's rays and "dares to claim the sky" is a metaphor for white people, with their racial privilege that allows them to feel so entitled and free. A metaphor compares two unalike things, where one is said to be another; it does not have literal meaning, only figurative. Because these birds are anthropomorphic (given human traits, ambitions, and emotions), we would not necessarily read them as symbols (with both literal and figurative meanings). The free birds are not confined by their race, and they enjoy all the benefits that are conferred by such privilege. The "caged bird" of the second and third stanzas is a metaphor for persons of color. Rather than enjoying the same freedoms and opportunities as the free birds, they are held in a "narrow cage" with "clipped" wings and "tied" feet; they are only able to "sing of freedom" but not actually enjoy it. The "dreams" of the caged bird are personified, given the ability to die and be buried in a "grave" on which the bird stands. The trees are likewise personified as "sighing."

In the poem "Caged Bird," Maya Angelou uses many poetic devices, including anthropomorphism and metaphor. Anthropomorphism is when an animal, an inanimate object, or any other non-human entity is given human characteristics or emotions. The most notable example of anthropomorphism in this poem is Angelou's choice of pronouns for the birds. She uses "he/his" pronouns instead of the typical "it/its," a subtle tactic that often creates a more relatable character for readers. A metaphor is a figure of speech that, for rhetorical effect, directly refers to one thing by mentioning another. The entire poem is a metaphor for the differences between the lived experiences of white Americans and African Americans. The free bird is a metaphor for white Americans, who are free to live and move throughout the world as they please, while the caged bird represents the systemic oppression and imprisonment faced by African Americans within the United States.

In "Caged Bird," Maya Angelou uses several poetic devices including alliteration, imagery, and symbolism. Alliteration, the repetition of consonant sounds, is used for emphasis on phrasing. An example from the poem includes “his shadow shouts on a nightmare scream”.
Imagery is used throughout Angelou’s work. Imagery is the author’s use of words to create a sensory experience for the reader. For example, “the caged bird sings with a fearful trill” helps us almost hear the unpleasant sound of the bird’s cry. Another example from the poem is “and the trade winds soft through the sighing trees” provides a more pleasant auditory experience for the reader.
Symbolism is an object or event in a poem that represents something beyond itself. Symbolism is the most powerful poetic device used in “Caged Bird.” Angelou’s contrast of the “free bird” and the “caged bird” represents humans who are “free” as opposed to “caged” in some way. The “caged” individuals may be held back by beliefs or fears or even others who are holding them back or enslaving them in some way. Angelou portrays the “free bird” as one who has the confidence to “claim the sky." In contract, the “caged bird” is associated with “the grave of dreams” and “a nightmare scream”. Alliteration, imagery, and symbolism are all used by Angelou to create this classic poem.

Precalculus, Chapter 1, 1.2, Section 1.2, Problem 38

Plot the point $(-3,0)$ then plot the point that is symmetric to it with respect to (a) the $x$-axis; (b) the $y$-axis; (c) the origin

a. The $x$-axis

If the point $(-x,y)$ is reflected over the $x$-axis, then the image is the point $(-x,-y)$. So

$(-3,0) \to (-3,0)$







The point has no symmetry over the $x$-axis because $y$-coordinate is .

b. The $y$-axis

If the point $(-x,y)$ is reflected over the $y$-axis, then the image is the point $(x,y)$. So

$(-3,0) \to (3,0)$







c. The origin

If the point $(-x,y)$ is reflected over the origin then the image is the point $(x,-y)$. So

$(-3,0) \to (3,0)$

What are conflicts that Stella and Blanche deal with in A Streetcar Named Desire?

Stella and Blanche deal with a great many conflicts throughout the story.  I'll break the conflicts up by character, and then I'll further break them down into internal and external conflicts.  
I'll start with Stella Kowalski.  I believe that Stella's main internal conflict is her struggle with knowing that her sister, Blanche, doesn't approve of her life, residence, relationship with Stanley, etc.  She feels beholden to both her sister and her husband, but Stanley and Blanche are on complete opposite ends of a spectrum.  For most of the play, Stella fervently supports and protects her sister.  

"You didn't know Blanche as a girl. Nobody, nobody, was tender and trusting as she was. But people like you abused her, and forced her to change."

That's why Stella's decision to stick with Stanley at the end of the play is so shocking.  She had to have struggled with the possibility that Stanley did indeed rape Blanche.  She has an inner struggle of how to believe something like that and continue to live with him.  
I believe that Stella's main external conflict is with her husband.  He's an abusive husband, and she has physical and emotional wounds because of it.  
As for Blanche, I feel that everything about her is conflicted.  She struggles with knowing that her family's property was foreclosed on because of her financial situation.  She struggles with the loss of her husband.  She feels that she is partly to blame for his suicide because she discovered and chastised him for his homosexuality. Blanche also struggles with her grip on reality, and she is eventually committed to a mental asylum.
Blanche's external conflicts mainly deal with her relationship with Stanley.  The two simply do not get along.  The conflict eventually ends up with Stanley raping Blanche.  

What do you think would have happened had the Anti-Federalists, rather than the Federalists, prevailed in the ratification process of the Constitution? What kind of government would they have shaped? How would that government have dealt with the difficult issues facing the new republic—slavery, concerns about mob rule, and continuing hostility in the international community?

Federalists believed in the establishment of a strong central government, and the US Constitution was devised as a way of achieving this goal. Anti-Federalists, on the other hand, feared that this would enable the kind of tyranny from which Americans had freed themselves in their war against the British. They favored a looser, more decentralized system of government in which ultimate sovereignty remained with the individual states. Had they prevailed, the United States would've been a very different country indeed. That's not to say that the existing constitutional arrangement, the Articles of Confederation, would've been retained in their entirety, but the underlying principles on which they were based certainly would have.
Legal and political sovereignty would still have resided with the states under the anti-Federalists. In relation to slavery, this would have meant no attempt being made by the limited federal government to interfere in slavery and its expansion. The issue of slavery, like all important matters, would be left to the states to decide.
Federalists were anxious to control what they saw as outbreaks of mob rule. Indeed, one such outbreak, Shay's Rebellion, was one of the main factors that led to the convening of the Constitutional Convention. Any major act of public disturbance or lawlessness could only be dealt with by the relevant state. If they chose not to do so, for whatever reason, then the federal government could do little or nothing. This is precisely what happened in the case of Shay's Rebellion. So it was felt necessary by Federalist delegates at Philadelphia to establish a central government with a police power capable of getting a grip on domestic disorder.
To the anti-Federalists, this once again smacked of tyranny. The United States had been founded on the basis of armed rebellion against a centralized government. The people sometimes needed to resort to direct action in order to stand up for their liberties as American citizens. The war may be over, they believed, but the principles on which it had been fought were still as relevant as ever, and must be protected. Whatever the value of such principles in theory, in practice it's difficult to see how an anti-Federalist system of government would have been able to stop the spread of serious public disorder from one state to another, thereby endangering the safety of the Republic as a whole.
In relation of foreign affairs, the anti-Federalists might have found it a little hard going without the existence of a strong central government. Under the Articles of Confederation, it was virtually impossible to formulate a distinct American foreign policy. The United States would need to gain the approval of all states before any treaty with a foreign state could be ratified, and this was a tall order indeed. The radically decentralized system of government favored by the anti-Federalists would've made it impossible for the United States to speak with one voice on the international stage.
The American economy would've been a whole lot different under the anti-Federalists too. They tended to represent agrarian interests, especially in the South. They deeply resented the close relationship that the Federalists had developed with commercial and banking elites, which were perceived by anti-Federalists as a threat to the economic interests of farmers and other landowners. As well as general concerns over too great a concentration of power at the federal level, this helps to explain why anti-Federalists were so implacably hostile to the establishment of a National Bank. Theirs was the Jeffersonian ideal of a republican democracy based upon a wise, disinterested class of landowners acting selflessly for the good of the country. Had their vision prevailed, the United States would not have developed along the lines of a modern, industrialized economy.

Calculus of a Single Variable, Chapter 8, 8.4, Section 8.4, Problem 28

Recall that indefinite integral follows the formula: int f(x) dx = F(x) +C
where: f(x) as the integrand
F(x) as the anti-derivative function
C as the arbitrary constant known as constant of integration
For the given problem int 1/(xsqrt(9x^2+1)) dx , it resembles one of the formula from integration table. We may apply the integral formula for rational function with roots as:
int dx/(xsqrt(x^2+a^2))= -1/aln((a+sqrt(x^2+a^2))/x)+C .
For easier comparison, we apply u-substitution by letting: u^2 =9x^2 or (3x)^2 then u = 3x or u/3 =x .
Note: The corresponding value of a^2=1 or 1^2 then a=1 .
For the derivative of u , we get: du = 3 dx or (du)/3= dx .
Plug-in the values on the integral problem, we get:
int 1/(xsqrt(9x^2+1)) dx =int 1/((u/3)sqrt(u^2+1)) *(du)/3
=int 3/(usqrt(u^2+1)) *(du)/3
=int (du)/(usqrt(u^2+1))
Applying the aforementioned integral formula where a^2=1 and a=1 , we get:
int (du)/(usqrt(u^2+1)) =-1/1ln((1+sqrt(u^2+1))/u)+C
=-ln((1+sqrt(u^2+1))/u)+C
=ln(((1+sqrt(u^2+1))/u)^-1) + C
=ln(u/(1+sqrt(u^2+1))) + C
Plug-in u^2 =9x^2 and u =3x and we get the indefinite integral as:
int 1/(xsqrt(9x^2+1)) dx=ln((3x)/(1+sqrt(9x^2+1)))+C

What confuses Scout about Miss Gates' view of Hitler in Chapter 26 of Harper Lee's To Kill a Mockingbird?

In Chapter 26, Scout is confused about Miss Gates' lack of consistency: while she claims to despise Hitler's horrific abuse of the Jews, she welcomes extremely biased treatment of the black people in her own community.
In the schoolroom, Miss Gates is a respected authority figure. When she cautions her students against the same type of prejudice Hitler entertains, they take her words to heart. To her students, Miss Gates is a trusted source of wisdom and the very epitome of honor. It is not surprising, then, that Scout becomes confused when she hears her teacher railing against the supposed arrogance of black people. According to Miss Gates, "it’s time somebody taught ’em a lesson, they were gettin‘ way above themselves, an’ the next thing they think they can do is marry us."
Scout is so shocked by what she overhears that she brings her concerns to Jem. However, Jem is still too traumatized about the recent events surrounding the trial and Tom Robinson's death to adequately address Scout's concerns.
Basically, what confuses Scout about Miss Gates' view of Hitler is that her teacher doesn't see a connection between Hitler's type of prejudice with that of her own. For her own part, Scout doesn't understand how her teacher can rationalize her own ugly attitudes. Also, very likely, Scout finds it difficult to accept that an upstanding teacher can harbor such an obviously wrong perspective about others. To Miss Gates, white people are justified in their concerns; Hitler's prejudice, on the other hand, has more of a diabolical quality to it and must be disavowed at all costs. Miss Gates doesn't realize the inherent hypocrisy in her contradictory attitudes.

What are some connections from the Manhatten Project to Lord of the Flies?

The Manhattan Project refers to the attempt to design and create an atomic weapon; the result of this experiment became the bombs dropped on Hiroshima and Nagasaki during World War II, which effectively forced Japan to surrender to the United States. Lord of the Flies is a novel by William Golding, published in 1954, a few years after the war ended. The action takes place during an unnamed war. The boys are in a plane that crashes over the Pacific and they are marooned on an island and forced to figure out how to survive.
The situation could be said to be metaphorical, symbolizing the state of the world in which the specter of nuclear annihilation has been unleashed. The remaining survivors of a nuclear war would be forced to figure out how to build shelter and find food, as well as rebuild a society, and this is the very situation that faces the boys in Golding's novel. Their situation breaks down over arguments about who is in charge and what their goals and activities should be. Golding paints a picture of bleak humanity in which aggression and brutality seem to win out over justice and compassion. In this way it is a commentary upon the decision to use destructive nuclear weapons to win war as an inhumane and ultimately humanity-destroying solution.

Where in the play is Henry V at conflict with himself?

Henry V is a man who, upon ascending to the throne, has vowed to change from the feckless young man we saw in Henry IV, Parts 1 & 2. He is intent upon being "no tyrant, but a Christian king," with the result that we see him engaged in conflict with himself at various points in the play. In the opening scene, for example, he questions whether it is actually appropriate for him to claim France—"May I with right and conscience make this claim?" The Archbishop of Canterbury assures Henry that he has an excellent claim based on his lineage, but Henry remains unsure. He points out that he "fear[s] the main intendment of the Scot," given that the Scots frequently attacked the "unfurnish'd kingdom" of his great-grandfather when he dedicated his forces to France. As he struggles to be a good king, Henry must weigh numerous options and select the best, which is often not obvious to him.
It sometimes seems that Henry is not sure how to balance being a Christian with being a king; the French king notes at the end of the play, at the marriage of Henry and Kate, that "Christian-like accord" between the two countries should necessarily mean an end to war, the implication being that war is un-Christian. It is also notable that the Dauphin, in sending Henry a "treasure" of tennis balls, succeeds in stirring Henry because he thinks he is behaving like the boy we saw in the previous plays—"You savour too much of your youth." Henry's ire is aroused largely because of a desire to prove that he is no longer that boy.

And we understand him well,How he comes o'er us with our wilder days,Not measuring what use we made of them.

Henry is saying that he has grown beyond what the Dauphin thinks of him and has learned to be good: he says he will "put forth / my rightful hand in a well-hallow'd cause" and "be like a king and show my sail of greatness." The irony is, of course, that if Henry had really grown beyond his foolish youth, he would not have been so provoked by the jest of a gift. This is a tension in Henry which motivates him throughout the play: he needs to prove himself as a king, and to prove wrong others' opinions of him, but he is not always sure exactly how to do so.

Calculus: Early Transcendentals, Chapter 3, 3.6, Section 3.6, Problem 20

H(z)=lnsqrt((a^2-z^2)/(a^2+z^2))
Differentiating both sides with respect to z, we get
H'(z)=(1/sqrt((a^2-z^2)/(a^2+z^2))) d/dzsqrt((a^2-z^2)/(a^2+z^2))
H'(z)=sqrt((a^2+z^2)/(a^2-z^2)) ((sqrt(a^2+z^2)d/dzsqrt(a^2-z^2)-sqrt(a^2-z^2)d/dzsqrt(a^2+z^2))/(a^2+z^2))
H'(z)=sqrt((a^2+z^2)/(a^2-z^2)) ((sqrt(a^2+z^2)(1/2)(a^2-z^2)^(-1/2)(-2z)-sqrt(a^2-z^2)(1/2)(a^2+z^2)^(-1/2)(2z))/(a^2+z^2))
H'(z)=sqrt((a^2+z^2)/(a^2-z^2))((-zsqrt((a^2+z^2)/(a^2-z^2))-zsqrt((a^2-z^2)/(a^2+z^2)))/(a^2+z^2))
H'(z)=(((-z(a^2+z^2))/(a^2-z^2))-z)/(a^2+z^2)
H'(z)=(-z(a^2+z^2)-z(a^2-z^2))/((a^2-z^2)(a^2+z^2))
H'(z)=(-z(a^2+z^2+a^2-z^2))/(a^4-z^4)
H'(z)=(-2a^2z)/(a^4-z^4)

int x/(16x^4-1) dx Use partial fractions to find the indefinite integral

int x/(16x^4-1)dx
To solve using partial fraction method, the denominator of the integrand should be factored.
x/(16x^4-1)=x/((2x-1)(2x+1)(4x^2+1))
Take note that if the factors in the denominator are linear, each factor has a partial fraction in the form A/(ax+b) .
If the factors are in quadratic form, each factor has a partial fraction in the form (Ax+B)/(ax^2+bx+c) .
So expressing the integrand as sum of fractions, it becomes:
x/((2x-1)(2x+1)(4x^2+1))=A/(2x-1)+B/(2x+1)+(Cx+D)/(4x^2+1)
To determine the values of A, B, C and D, multiply both sides by the LCD of the fractions present.
(2x-1)(2x+1)(4x^2+1)*x/((2x-1)(2x+1)(4x^2+1))=(A/(2x-1)+B/(2x+1)+(Cx+D)/(4x^2+1)) *(2x-1)(2x+1)(4x^2+1)
x= A(2x+1)(4x^2+1) + B(2x-1)(4x^2+1)+ (Cx+D)(2x-1)(2x+1)
Then, assign values to x in which either 2x-1,  2x+1, or4x^2+1 will become zero.
So plug-in x=1/2 to get the value of A.
1/2=A(2(1/2)+1)(4(1/2)^2+1)+B(2(1/2)-1)(4(1/2)^2 + 1) + (C(1/2)+D)(2(1/2)-1)(2(1/2)+1)
1/2=A(4) + B(0)+(C(1/2)+D)(0)
1/2=4A
1/8=A
Plug-in x=-1/2 to get the value of B.
-1/2=A(2(-1/2)+1)(4(-1/2)^2+1) + B(2(-1/2)-1)(4(-1/2)^2+1) + (C(-1/2)+D)(2(-1/2)-1)(2(-1/2)+1)
-1/2=A(0)+B(-4) +(C(-1/2)+D)(0)
-1/2=-4B
1/8=B
To solve for D, plug-in the values of A and B. Also, plug-in x=0.
0=1/8(2(0)+1)(4(0)^2+1) + 1/8(2(0)-1)(4(0)^2+1) + (C(0)+D)(2(0)-1)(2(0)+1)
0=1/8 - 1/8 -D
0=D
To solve for C, plug-in the values of A, B and D. Also, assign any value to x. Let it be x=1.
1=1/8(2(1)+1)(4(1)^2+1) +1/8(2(1) -1)(4(1)^2+1) + (C(1) + 0)(2(1) -1)(2(1)+1)
1=15/8+5/8+C(3)
1=10/4+3C
-3/2=3C
-1/2=C
So the partial fraction decomposition of the integrand is:
int x/(16x^4-1)dx
=int(x/((2x-1)(2x+1)(4x^2+1)))dx
=int (1/(8(2x-1)) + 1/(8(2x+1)) - x/(2(4x^2+1)) )dx
Then, express it as three integrals.
=int 1/(8(2x-1))dx + int 1/(8(2x+1))dx - int x/(2(4x^2+1)) dx
=1/8int 1/(2x-1)dx + 1/8int 1/(2x+1)dx - 1/2int x/(4x^2+1) dx
To take the integral of each, apply substitution method.
For the first integral, let the substitution be:

u=2x-1
du=2dx
(du)/2=dx

For the second integral, let the substitution be:

v = 2x+1
dv=2dx
(dv)/2=dx

And for the third integral, let the substitution be:

w=4x^2+1
dw=8xdx
(dw)/8=xdx

So the three integrals become:
= 1/8 int 1/u * (du)/2 + 1/8 int 1/v *(dv)/2 -1/2 int 1/w * (dw)/8
=1/16 int 1/u du + 1/16 int 1/v dv - 1/16 int 1/w dx
Then, apply the formula int 1/x dx = ln|x| + C .
=1/16 ln|u| + 1/16 ln|v| - 1/16ln|w|+C
And substitute back u = 2x - 1 , v = 2x + 1 and w = 4x^2+1 .
= 1/16ln|2x-1| + 1/16ln|2x+1| -1/16|ln4x^2+1|+C
 
Therefore, int x/(16x^4-1)dx=1/16ln|2x-1| + 1/16ln|2x+1| -1/16|ln4x^2+1|+C .

Why did people move west in the 1840s and the 1850s?

The short answer: The Manifest Destiny. Americans believe that they had the God given right to expand and conquer the land from sea to shining sea, from coast to coast.
This idea of the Manifest Destiny was fueled by the Gold Rush in California in the 1940s. But there were also settlement trails, like the famous (via game playing) Oregon Trail. People are eager to explore and settle new land. Promise of riches and gold enticed people to risk the dangerous journey. This is where we see boomtowns in the West, towns they grow at a rapid rate due to a high influx of people. They are often correlated with finding minerals in the land, such as silver, copper, and lead.
This desire for land was also fueled by the sectionalism debate regarding slavery. The Missouri Compromise (1920) established where slavery could and couldn't be in the United States. Slave states were south of the 36 compromise line, and Free states were north. See the attached map for more detail. As the demand for cotton grew, so did the demand for slavery. Before the Civil War, cotton accounted for over 50% of the nation's exports. Slavery was moving west below the line, but we were running out of land. Land west of Louisiana belonged to Mexico. This demand for land was one of the causes of the Mexican-American War (1946-9148). As a result of this war, the United States acquired land including New Mexico, Arizona, and Texas (which is also a very interesting story).
Westward expansion continued after the time period in question. Contributing factors include the Homestead Act of 1962, the devastation of the South during the Civil War and Reconstruction, the impact of Black Codes and the resulting Exoduster, and the continued influence of the Manifest Destiny.

The western expansion of the 1840s and 1850s is often discussed in the same breath as the Gold Rush, but, in fact, there were many other settlers who had already begun moving west before the Gold Rush began. In 1841, the first wagon trails began to move along the Oregon Trail into the West, the beginning of many similar journeys made by those who had heard tell of the cheap land and opportunities in the West for people to make something of themselves, free from the confinement and expense of the growing cities on the Eastern seaboard. While the Oregon Trail was long and dangerous, and many died of sickness and conflict with Native Americans along the way, stories continued to be told of the opportunities the unsettled West offered.
It was indeed the discovery of gold, however, which turned the steady trickle of westward settlers into a deluge. Gold was found in California in 1848; tens of thousands of would-be miners had arrived in California by the following year. These men were known as forty-niners, and many of them did make a fortune from gold. This sparked the root of the American Dream: any man, people came to think, could make his fortune if he would only put in the work. The miners soon sent for their wives and children, settled and intermarried, and the mining settlements became towns of some significance. By 1850, California had been set up with a governor as a state of the Union (it had to reach a population of 60,000 to do this, so a publicity campaign had helped encourage westward expansion until this point was reached).
Westward expansion continued well into the 1860s and 70s, after the Homestead Act was established to offer 160 acres of land in the West to anyone willing to work it for five years. Meanwhile, the establishment and spread of the railroads meant that the journey west was no longer the terrifying prospect it had once been when it had to be made by wagon trail. However, it was the Gold Rush which truly turned westward expansion into the dream of fortune and opportunity which continued to drive movement in that direction for decades afterwards.
https://www.bbc.co.uk/bitesize/subjects/zj26n39

Should it be illegal for tourists to climb Uluru in Australia?

Uluru, located  in the Uluru-Kata Tjutu National Park of Australia, was given back to the Anangu people by the government of Australia, and the Anangu people leased it to Australia for 99 years, allowing tourists to visit the park and rock. Climbing Uluru, as well as preventing tourists from climbing Uluru, poses multiple ethical and cultural problems. First, the climb has "great spiritual significance" to the Anangu because they celebrate the Mala "hare wallaby" people as creation beings who walked the sacred climb since creation (McClintock, "Climbing the Rock," ABC News). For this reason, tourists are dissuaded from making the sacred climb.Secondly, 30 people have died climbing Uluru in the past few decades. These deaths are particularly disturbing to the Anangu who believe people should "take responsibility for their [own] actions" (McClintock). Since Uluru is the responsibility of the Anangu, they feel responsible for these deaths, which is very distressing for them.However, making Uluru completely illegal to climb poses cultural problems. Since the Anangu believe people should be responsible for their own actions, they believe people should choose for themselves what is right or wrong. Therefore, hanging a sign on Uluru saying it's wrong, or illegal, to climb the rock contradicts the culture of the Anangu. According to some views, such as Thomas Jefferson's Utilitarian view, it is ethical to create laws to protect both safety and happiness. While it would be ethical to create a law to protect the safety of tourists, it would be unethical to create such a law if doing so infringes on the culture and, therefore the happiness, of the people most affected by the law, the Anangu.

Where are Tamara and Herman married?

Tamara and Herman are married in Warsaw. In the story, Tamara is Herman's first wife.
Both Herman and Tamara come from wealthy homes. Tamara's father, Reb Shachnah Luria is a lumber dealer and the co-owner of a glass business. Meanwhile, Herman is the only child of Reb Shmuel Leib Broder, a wealthy man who owns several homes in Tzivkev.
During Herman's youth, his father hired a rabbi to instruct him in matters concerning the Jewish religion. Herman's father also hired a Polish tutor to educate Herman in secular subjects. Both Herman's parents had high hopes for their son. Reb Shmuel had wanted his only son to become a modern rabbi, while his wife wanted Herman to become a doctor.
In the end, Herman disappointed both parents. After he passed his matriculation exams at nineteen, he went to Warsaw. There, he enrolled in the school of philosophy at the university. Shortly after, against the wishes of his parents, Herman married Tamara in Warsaw. Tamara was a student of biology at Wszechnica. The marriage was not a happy one, as Herman had never intended to marry.

What makes Jonathan decide to return to the Breakfast Flock after it has cast him out?

In this enchanting and insightful short story, Jonathan Seagull is an inspiration; he is the one seagull who wants to achieve perfection in flight. When he reaches terminal velocity at two hundred fourteen miles per hour, he is ecstatic. However, he is soon ostracized by the rest of his flock and condemned to exile by the Council Flock.
Eventually, Jonathan is taken to the great seagull beyond, where he is able to further hone his ability to soar. He is happy there for a time, but he soon decides that he must return to the Breakfast Flock. As an enduring believer in ultimate flight, Jonathan is also an instructor at heart. He yearns to share all the knowledge he has gleaned with other seagulls who want to excel in flight and to be immersed in the truths that he cherishes. This is the main reason Jonathan wants to return to the flock, despite his outcast status.
Because passing on his knowledge is an act of love, Jonathan is compelled to seek out other outcasts once he returns. As time progresses, he is able to train other outcasts and eventually, they themselves are able to become instructors. Thus, Jonathan Seagull's desire of passing on his knowledge is fulfilled.
 

Single Variable Calculus, Chapter 7, Review Exercises, Section Review Exercises, Problem 98

Evaluate $\displaystyle \int \frac{\cos (\ln x)}{x} dx$


$
\begin{equation}
\begin{aligned}

\text{If we let } u =& \ln x, \text{ then}
\\
\\
du =& \frac{dx}{x}

\end{aligned}
\end{equation}
$


So,


$
\begin{equation}
\begin{aligned}

\int \frac{\cos (\ln x)}{x} dx =& \int \cos u du
\\
\\
=& \sin u + c
\\
\\
=& \sin (\ln x) + c


\end{aligned}
\end{equation}
$

what was the significant in vietnam's declaration of independence

The first line in the document repeats verbatim the most famous sentence in America's Declaration of Independence: "all men are created equal." The document then goes on to describe how the French had exploited the people of Vietnam for decades. This is also similar to America's Declaration of Independence in that Jefferson lays out a list of wrongdoings committed by the British government and thus makes the case for independence. The last segment of Vietnam's Declaration of Independence states that the country is already free and independent by virtue of defeating both the Japanese in WWII and the French colonization efforts. This piece of the document has echoes of Thomas Paine's Common Sense in that Vietnam's Declaration of Independence states that independence is already a reality and this document makes it official to the world.
Another item of note about the document: this declaration was a speech by Ho Chi Minh, the founder of North Vietnam and a beloved anti-colonialist figure in Vietnamese history. Ho Chi Minh saw himself as what could be equated to the George Washington of Vietnam.
http://historymatters.gmu.edu/d/5139/

What is the imagery in "Sonnet 129"?

"Sonnet 129" takes a rather pessimistic approach to sex and lust. In the poem, the "spirit" which drives man's "lust" is described vividly as "perjured, murderous, bloody," like a criminal whose behavior is driven by madness. Indeed, lust is "savage, extreme, rude, cruel," and absolutely not something that should be trusted. The use of language conjures images of a bestial creature within man and separate from him.
Lust is something that is "hunted" "past reason," until such time as the hunter has achieved his goal, after which he despises his own lust (and, possibly, the object of his lust) as if he has been offered "bait / On purpose laid to make the taker mad." So, after man has expended his lust and regained his reason, he comes to despise whatever caused him to lose his reason in the first place, imagining it as some kind of poison laid out in an appealing way for him to consume.
The concluding couplet aptly summarizes the problem of lust: men know that "this hell" is what will result from pursuing sex, as after they have partaken in it, they "despise" it and themselves, feeling "shame." However, they do not have the wits to shun the "heaven" (love, courtship, sex itself) which will lead them into this misery.

Discuss the relationship between Macbeth and Banquo.

Macbeth and Banquo have a very dynamic relationship. In the beginning of the tragedy, Macbeth and Banquo are old friends bonded through their shared time serving as generals and fighting alongside each other for their king, Duncan. Both of the men are also the only ones to see the three witches and receive a prophecy. Macbeth's is as follows, "All hail, Macbeth! Hail to thee, thane of Glamis!/All hail Macbeth, hail to thee, thane of Cawdor!/All hail, Macbeth, thou shalt be king hereafter!" Banquo's is such: "Lesser than Macbeth, and greater./Not so happy, yet much happier./Thou shalt get kings, though thou be none." This is a shared experience that, in theory, should bring the men closer together. However, as Macbeth begins his descent into madness and obsession with the witches' predictions, their relationship takes a turn.
After killing Duncan in the pursuit for kingship and gaining the crown, Macbeth realizes that not only is Banquo is the only other person who heard the witches' predictions, but that their prediction for Banquo states that he shall not be king, but his sons will be. This is a major kink in Macbeth's plans. Macbeth is concerned that Banquo and his son, Fleance, will conspire together in order to take the throne from Macbeth. In his panic, Macbeth does the only thing he thinks will solve this problem-- kill his now ex-best friend and scare away his son. With Banquo murdered, Macbeth loses his only true friend, as this puts a pretty large damper on Macbeth and Banquo's relationship.
In his guilt over both murders he has now been a part of, at a great dinner with all of the other nobleman, Macbeth sees Banquo's ghost. Even in death, Banquo is serving as a reminder of the wrong doings Macbeth has committed in his greed and ambitious behaviors. Even after death, the two men's relationship continues to change. Now, rather than a friend or a direct threat, Banquo serves as Macbeth's conscious. He is present to remind Macbeth that what he is doing is a sin and he will be punished if he continues down this path.

Quote Source:
http://www.shakespeare-online.com/plays/macbeth_1_3.html

Initially, the relationship between the two men is perfectly amicable. They are friends and fellow nobleman, loyal servants of their king, Duncan. Yet as the play progresses, things turn sour, with each man gradually perceiving the other as a threat, albeit for different reasons. It all starts to go wrong after the witches' prophecy, which predicts not only that Macbeth will be king but also that Banquo's sons will also one day ascend the throne. Though both Macbeth and Banquo are disturbed by the prophecy, Macbeth takes it much more seriously. It exerts a dangerous hold upon his imagination, making him insanely ambitious. As such, Banquo is no longer a friend or a colleague but a rival—a very dangerous rival at that, a threat to be removed.
Once Macbeth has become ensconced upon the throne, Banquo's days are effectively numbered. Macbeth is no longer prepared to listen to advice, whether it's from Lady Macbeth, Banquo, or anyone else. Banquo, for his part, suspects that Macbeth had something to do with Duncan's murder; this makes him even more of a threat. Unlike Macbeth, Banquo understands all too well the dangers of messing around with the forces of darkness. Yet it is precisely those very forces to which Macbeth has succumbed in his seemingly insatiable lust for power. There can, therefore, be no reconciliation between the two former friends, and by the time of Banquo's murder they are sworn enemies.

Do you think that the speaker has been successful in immortalizing his love in the words of Sonnet 18? To what extent is this only a poetic device?

The speaker is successful in immortalizing his beloved. Part of this success is showing how his beloved is more "lovely" than a summer's day. Summer is too erratic, whereas his beloved is more temperate. Summer has "rough winds," is "too hot," or it's "lease hath all too short a date." Here, "temperate" means mild. And in the context of being eternal, temperate also means unchanging. Summer only lasts three months, while his beloved's "eternal summer shall not fade." So, how can his beloved's beauty and/or essence be immortal?
Since his beloved cannot literally survive death, nor can he be young and beautiful forever, the speaker intends to find another way to immortalize him. This immortalization has more to do with the overall effect of the poem itself than it does with the metaphors and comparisons between the summer and his beloved. The poem itself is what the speaker intends to immortalize. As an immortal tribute, the poem then gives immortal status to his beloved. The final two lines express this:

So long as men can breathe or eyes can see,
So long lives this, and this gives life to thee.

If the poem is immortal, so is his beloved. So, it is about poetic devices, but in a broader sense, it is about writing itself.

How did Madame Loisel's new life change her appearance and manner?

With Madame Forestier's sparkling diamonds adorning her pretty neck, Mathilde Loisel feels like a star. She's always thought herself so much better than her lowly petit bourgeois existence would suggest; but now, she feels like a princess as she becomes the center of attention at the Education Ministry ball. Heads turn; she's by far the most beautiful woman there, and all men's eyes are upon her. No less a VIP than the Minister himself notices Mathilde, and all the cabinet officials want to dance with her. She is truly the belle of the ball and the toast of high society. Isn't it amazing what a diamond necklace can do?
Madame Loisel feels that she's now become what she always really was: a lady of the aristocracy. Only, she isn't really. Just as her aristocratic pretensions are fake, so too are the diamonds which so cruelly fan the flames of her delusions of grandeur.
When she subsequently loses the necklace, Madame Loisel is devastated. But somehow she and her husband must pay for a replacement, however much it costs. So they take out huge loans with a number of different creditors, even though they know full well they won't be able to pay them back for many years to come.
After laying down 36,000 francs for a replacement necklace, the Loisels are humiliatingly forced into a drastic change in their lifestyle. They dismiss their maid; they move into a poky little garret; they have no choice but to work their fingers to the bone just to make ends meet. And this goes on for ten long, miserable years. Mathilde and her husband now know what it's like to be very poor.
And this is what's so ironic. In wearing the necklace, Mathilde thought she would rise above her straightened circumstances, to become the princess she always thought she was. Yet now, when Madame Forestier catches up with her after all this time, the physical signs of a decade of grinding poverty are visibly etched all over Mathilde's drawn, haggard features. Instead of going up in the world, Madame Loisel has come crashing down to the very bottom. Although she may have developed all the strength and hardy roughness of the impoverished Parisienne, her new life is still a far cry, not just from her fantasies of gracious living, but also from the simple but perfectly comfortable lifestyle she enjoyed before that fateful night at the Education Ministry ball.

What is Gatsby's American Dream?

Gatsby may be able to amass great wealth, but this wealth does not garner him the change in status for which he was hoping. His American Dream isn't just about getting rich but about changing stations, so to speak; he wants to rise to Daisy's social level. However, he purchases a home in West Egg, the "less fashionable" of the two vaguely egg-shaped land formations on Long Island, rather than East Egg, where all the most elite people with old money live. People with old money inherited it rather than having had to work for it, and this makes it superior to new money, which is earned. Nick describes Daisy as belonging to a "rather distinguished secret society to which she and Tom belonged." Gatsby, however, never seems to realize this. He wears a pink suit and drives a flashy car and lives in a somewhat gaudy house and throws parties that include vulgar and shady people. He's obviously rich, but he's also obviously not from "polite" society. He doesn't see that he is over-the-top, that he simply does not fit in with people like the Buchanans and he never will.

The American Dream is the idea that an individual from humble beginnings can earn financial freedom and advance their social class through hard work and dedication. Jay Gatsby earns the typical American Dream by entering the bootlegging business and amassing wealth through illegal means. Despite growing up in a working class family, Gatsby earns enough money to buy a beautiful mansion located on Long Island's West Egg. Despite his seemingly unlimited material possessions, Gatsby's energy is focused toward Daisy Buchanan. Jay Gatsby's American Dream involves a healthy marriage with Daisy Buchanan, which is something he cannot achieve. Gatsby's motivation for becoming extremely wealthy revolves around the possibility of one day getting married to Daisy. Unlike Gatsby, Daisy hails from a traditionally wealthy family and would not agree to marry a man of Gatsby's original social status. Gatsby eventually achieves his dream of becoming wealthy and prestigious throughout New York, only to have his hopes destroyed once Tom exposes him as a bootlegger. Daisy decides to remain in her unhealthy relationship with Tom because she does not feel secure with Gatsby. Gatsby's American Dream is unattainable because Daisy is a superficial, hollow individual, who predominantly cares about money.

Single Variable Calculus, Chapter 7, 7.8, Section 7.8, Problem 16

Determine the $\displaystyle \lim_{x \to \infty} \frac{x + x^2}{1 - 2x^2}$. Use L'Hospital's Rule where appropriate. Use some Elementary method if posible. If L'Hospitals Rule doesn't apply. Explain why.

$\displaystyle \lim_{x \to \infty} \frac{x + x^2}{1 - 2x^2} = \frac{\infty + \infty^2}{1-2(\infty)^2} = - \frac{\infty}{\infty} \text{ Indeterminate}$

Thus, by Applying L'Hospital's Rule,
$\displaystyle \lim_{x \to \infty} \frac{x+x^2}{1-2x^2} = \lim_{x \to \infty} \frac{1+2x}{1-4x}$
We will still get an indeterminate form if we evaluate the limit we obtained. Again,
By applying L'Hospital's Rule.

$
\begin{equation}
\begin{aligned}
\lim_{x \to \infty} \frac{1+2x}{1-4x} &= \lim_{x \to \infty} \frac{2}{-4}\\
\\
&= \frac{2}{-4}\\
\\
&= -\frac{1}{2}
\end{aligned}
\end{equation}
$

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

Given to solve ,
lim_(x->oo) cosx/x
by applying the squeeze theorem we can solve the limits
and it is as follows,
as we know the boundaries of the cos(x) as
-1<=cos(x)<=1
now dividing the above expression with x , we get
-1/x<=cos(x)/x<=1/x
now applying the limits of x-> oo for the above expression, we get
lim_(x->oo) (-1/x)<=lim_(x->oo) cos(x)/x<=lim_(x->oo) (1/x)
now upon x-> oo we get
lim_(x->oo) (-1/x) =(-1/oo) =0
and
lim_(x->oo) (1/x) = (1/oo)=0
so,
lim_(x->oo) (-1/x)<=lim_(x->oo) cos(x)/x<=lim_(x->oo) (1/x)
=>0<=lim_(x->oo) cos(x)/x<=0
=>lim_(x->oo) cos(x)/x =0

Why does the speaker let the fish go?

In Elizabeth Bishop's famous poem "The Fish," the speaker spends most of the poem describing what she sees as she looks at the fish, and the poem ends, of course, with the speaker letting the fish go. 
Early in the poem, the speaker notes that the fish "didn't fight. / He hadn't fought at all" (5-6). This seems a bit unusual, but then the speaker goes on to record other details and observations about the fish's appearance. The fish is described as "venerable," with "skin . . . / like ancient wallpaper" (8, 10-11). The word venerable, paired with "homely" is an interesting choice on Bishop's part. To venerate something is to respect it, usually due to its age or wisdom. Homely is a less positive word, making the fish seem ordinary and not beautiful. However, it could also mean that the fish is at home or comfortable in that place.
The fish is "speckled" and "infested," which seems to further indicate that the fish is quite ugly and nothing to really be admired; however, his age is reiterated here and later in the poem. The speaker starts to imagine the make-up of the fish's body, the inside textures of the fish, in a way that is revelatory to the speaker. The speaker doesn't get much reaction when she looks into the fish's eyes, but she "admired his sullen face" (45). Here, the turning point of the poem seems to occur: the speaker notices the hooks of other fisherman in the fish's mouth. She writes, 

and then I saw
that from his lower lip
—if you could call it a lip—
grim, wet, and weapon-like
hung five old pieces of fish-line,
or four and a wire leader,
with the swivel still attached,
with all their five big hooks
grown firmly in his mouth. (47-55)

It is the speaker's observation that he has been hooked at least four other times and either thrown back or fought his way free, that seems to lead the speaker to her decision to let him go. The speaker goes on to describe the old hooks as "Like medals with their ribbons / frayed and wavering" (61-62). Here the speaker seems to interpret the hooks as trophies to the fish, that he has won over the fishermen who have tried to capture him before. As the speaker continued to look intently at the fish, "victory filled up / the little rented boat" (66-67). It is unclear whether the speaker is referring to the victory she interprets the fish to feel because of its past triumphs or the speaker's sense of victory at having caught a fish that had escaped several times before. The speaker gets excited looking at the colors in the water and then decides to throw the fish back into the water. 
Bishop's poem is ambiguous in the sense that we don't know exactly why the speaker made the decision she did. However, it's possible that multiple meanings can exist at once. It could be that the speaker feels the fish belongs in that water, that he is sort of the old, wise ruler of that environment. It is possible that she feels sympathy and has connected on a level with the fish that does not allow her to kill or eat it. It also could be that she feels having caught and held the fish for the time she did was enough "victory" for her, and she is satisfied with the experience even if she doesn't take her figurative trophy home with her. 

4. Compare the British and American colonies’ strategy for the Revolutionary War.

The Revolutionary War was based on territorial control between the different groups. Control of larger territories provided access to resources essential for the war efforts and bolstered the troops' morale.
Britain initially focused on a containment strategy aimed at ensuring the conflict remained confined in Massachusetts. However, the colonists responded by laying siege to British positions, as was the case in the Siege of Boston. The developments forced Britain to abandon the containment strategy and retreat.
After facing defeat in Boston, Britain made plans to conquer New York, which they did in 1776. They used the area as their base of operations to isolate New England, which harbored most of the revolutionary activities. The idea was to conquer New England and then proceed to crush the revolution in the south. However, the plan failed, leading to the devastating loss at Saratoga.
The colonists avoided a conventional war with the British, focusing more on guerrilla warfare to tire out their opponents. Failure by the British to apply conventional strategies and challenges in accessing supplies forced them to engage the colonists in their kind of warfare. In this regard, the colonists had the upper hand and "home field advantage" over the British troops.
http://www.digitalhistory.uh.edu/disp_textbook.cfm?smtid=2&psid=3219

https://historyofmassachusetts.org/revolutionary-war-strategies/

https://www.ushistory.org/us/11a.asp

What is energy conservation?

Physics is full of "conservation" laws. There is a law of conservation of mass and a law for the conservation of momentum. The law of conservation of energy works the same way. In simple terms, the law of conservation of energy states that energy cannot be created or destroyed. To be a bit more specific, the law of conservation of energy is referring to the energy within a "closed system." In reality, a closed system is a bit left up to the person doing the calculations. The closed system is the group of objects that are interacting with one another and exchanging energy. In other words, the energy of a closed system will never be lost. It can change from energy type to energy type, but the total energy being exchanged remains the same.
I like to use a roller coaster when I teach this concept to students. Let's simplify and say that the closed system that is the roller coaster is the track, the cars (with wheels), and the air immediately surrounding the roller coaster. When the roller coaster is at the top of the tallest hill, the coaster's potential energy is at its maximum. That potential energy will then be converted to kinetic energy as the coaster goes down the hill. Ideally, all of the potential energy of the hill is turned into kinetic energy of speed. If the hill gave the coaster 1,000 J of potential energy, the coaster should have 1,000 J of kinetic energy at the bottom of the hill. The total energy of the system was conserved. None of the energy was lost, and the coaster didn't end with more energy than it started with.
Some savvy students like to point out that the coaster's 2nd hill should be able to be as tall as the first hill if all of the energy was conserved and converted to kinetic energy of moving a set of coaster cars. Unfortunately, that isn't possible. The reason for that is because not all of the initial potential energy was converted into "useful" energy. Friction exists within the system as does some vibration. The friction causes a conversion of energy from potential to thermal energy. The thermal seems to be "created," but it is result of an energy conversion. Vibrations will cause sound, and sound energy is a result. The thermal energy and sound energy are not useful forms of energy for roller coaster speedy fun, but the energy does get included into the closed system. The initial potential energy might be 1,000 J, and some of that will be used to create sound, heat, and coaster speed. It's helpful to write it out as an equation to see the conservation. It might look something like the following equation.
1,000 J potential energy = 850 J kinetic energy + 100 J thermal energy + 50 J sound energy
http://www.nyu.edu/classes/tuckerman/adv.chem/lectures/lecture_2/node4.html

https://energyeducation.ca/encyclopedia/Law_of_conservation_of_energy

In " There Will Come Soft Rains", what does the radioactive glow represent, mean and indicate?

In Bradbury's short story "There Will Comes Soft Rains," he writes that the destroyed city gives off a radioactive glow at night that can be seen for miles. The significance of the radioactive glow indicates that the story is set in a post-apocalyptic world, where civilization has been destroyed by nuclear weapons. One of the main themes of the short story examines the relationship between humanity and technology and also reveals the dual nature of technology. The nuclear blast not only destroyed the entire city but has also eliminated the natural environment and all life forms. Therefore, the radioactive glow symbolizes the destructive power of technology, the ignorance of humanity, and also represents the toxic atmosphere of the post-apocalyptic world. In the wake of a nuclear explosion, only artificial life remains and is eventually destroyed by the natural elements.

"There Will Come Soft Rains" by Ray Bradbury is a post-apocalyptic story focusing on the aftermath of a nuclear war in which all human life has been destroyed. The radioactive glow is evidence that the world being described exists in the aftermath of a nuclear holocaust and that all living beings have died. Thus the main function of the glow is that it is a very concise and efficient way of signalling to the reader the background situation of the story.
Next, radioactivity kills organic life but not machines, although machinery can be disrupted by the electromagnetic pulses associated with nuclear explosions. Thus the glow suggests that we are now in a world inhospitable to organic life forms. Thus it emphasizes that our technology is capable of eliminating humanity. The outdoors, normally pictured in literature as a wholesome scene of pastoral innocence, has become a toxic wasteland, not glowing under a benign sun but with a form of energy that is toxic to humanity. 

Discuss the class structure present in "Lay of the Were-Wolf" and if there are any gender influences on that structure. Are men treated differently from women? If so, in what way?

Marie de France's lais, including "The Lay of the Were-Wolf" are stories about courtly love and court interactions; therefore, by their very nature they explore the behaviors and relationships of upper-class people. The main characters are a lord and lady, a king, and a second lord.
The first lord is a "bisclavret" or "werewolf," and when he confesses to his wife that his second identity as a wolf is the reason he is missing for days at a time. She outwardly supports him but plans to betray him behind his back. The lady starts up a relationship with another lord who had previously written love letters to her. In courtly love conventions, lords could express such sentiments to married ladies as a form of appreciation, though nothing was expected to happen as a result (so as not to disturb the sanctity of the lord and lady's marriage).
The lady plans with her new lord to steal her husband's clothes when he transforms to a wolf so that he cannot change back to a human. Thus, she is able to claim her husband has disappeared and marry the new lord. Meanwhile, the wolf comes across the king and his men in the woods, and the king recognizes something noble about him and takes him in. Later, he is able to reveal his true self and is rewarded by the king. Again, all of the interactions here are between nobility.
In terms of gender, the lady is the character who is probably depicted as the most conniving and is punished the most harshly, when her nose is bitten off. The whole scheme is credited to her and she is considered the bad influence even though the lord is the one who first approached her through the love notes.

Marie de France's "Lay of the Werewolf," a courtly romance, focuses on upper-class people: aristocrats and royalty. The story presents us with a baron, a lady, a knight, and a king as the main characters. These characters are primarily identified by their social roles. Lower-class people are invisible in this story. When the king has a banquet, he invites to it "his great vassals and barons." He also invites his huntsmen or "lords of the venery," but these are clearly high-status people. The king shows his power and his favor through the pomp and "show" of a great feast. There is a clear hierarchy: the other guests at the feast are the king's subordinates, who have been summoned to be with him.
Only the werewolf would be potentially outside of this feudal class structure. But in this case, since the werewolf Bisclavret is actually a baron, he behaves within the confines of the courtly system, presenting himself as a gentle vassal of the king by putting his paw on the king's stirrup and offering his loyalty. This is what saves Bisclavret and, in the end, allows him to be vindicated, for the king takes an interest in this gentleman-like wolf servant.
The story shows men having more agency than the sole woman character, the lady. She notices that her husband goes away mysteriously for periods while she is stuck at home. She can only find out why he goes off by coaxing the story out of him; his love for her is her only leverage. When he tells her his story—which is that he goes off as a werewolf and can only regain human form by putting his clothes back on—she must again work through a man, her beloved knight. He, not she, is the one who steals the baron's clothes. The story shows us a female character who, though near the top of her social hierarchy, must depend on a male to act for her. 
 
https://frielingretc.files.wordpress.com/2013/10/the-lay-of-the-were-wolf-clear-2.pdf

Why are winters cold?

Winters are cold for two main reasons.  Both of these reasons come about because of the fact that the Earth tilts on its axis.  When the Earth tilts, sun comes to hit one of its hemispheres more directly and the other less directly.  The hemisphere which the sun hits less directly gets colder.
The first reason has to do with the length of the day.  As the Earth tilts, the sun “moves” farther towards the equator.  When this happens, days at higher latitudes get shorter and shorter in terms of how long the sun is above the horizon.  Because the sun spends less and less time above the horizon, it has a much shorter time during which it can heat the atmosphere.
When the Earth tilts on its axis, the angle at which the sun’s rays hit Earth also changes.  During the summer, the sun’s rays hit the Earth at an angle that is close to 90 degrees.  This means that the light points (more or less) straight down at the Earth.  The light does not have to pass through much of the atmosphere before it hits Earth and it does not spread out over very much of the Earth.  By contrast, in the winter, the sun’s light hits Earth at a very oblique angle.  It has to go through much of the atmosphere before hitting the surface, robbing it of some of its energy.  In addition, the light spreads out over a larger surface area, bringing less energy to any particular area.
These factors combine to create a situation in which a particular hemisphere of the Earth gets colder when it is winter in that hemisphere.
 
http://www.planet-science.com/categories/over-11s/natural-world/2012/11/why-is-winter-cold.aspx

https://www.loc.gov/everyday-mysteries/item/why-is-it-hot-in-summer-and-cold-in-winter/

In chemistry, give examples of structures that are polar at one end and nonpolar at the other end.

In chemistry, molecules can be polar or nonpolar. Which of these they are depends on the overall structure that their component chemical bonds (between the atoms present in the molecule) form. Polar molecules, water being a notable example, have positive and negative 'ends' so that when molecules of that substance are physically close the molecules weakly attract each other much like polar magnets would. 
Some chemicals, formed of component molecules, can have a polar end and nonpolar end. For example, soap, when agitated in water, forms chemical structures called micelles that have polar heads and nonpolar tails. The polar heads are water-loving (hydrophilic) and face outward towards the water environment, whereas the nonpolar tails are water - hating (hydrophobic) and huddle inward away from the water. Any greasy fats (lipids) that are in the water get shrouded by the micelles. This is because the fats are also hydrophobic so can escape from the water by joining the nonpolar lining of the micelles and being protected by the polar outer of those micelles. This is how greasy things are cleaned in water using soap (surfactants).
A similar chemical structure to soap micelles, with polar heads and nonpolar tails, can be found in the human body. Cell membranes have hydrophilic phosphate polar heads and hydrophobic lipid nonpolar tails. Nonpolar chemicals like oxygen and CO2 pass through the membrane easily. Larger polar chemicals can only enter and exit by the cell gates. This allows the body to control cell inputs and outputs.
http://jan.ucc.nau.edu/lrm22/lessons/polar_nonpolar/polar_nonpolar.html

Precalculus, Chapter 1, 1.2, Section 1.2, Problem 24

Determine the intercepts and graph equation $y = -x^2 + 1$ by plotting points. Be sure to label the intercepts.

$x$-intercept:


$
\begin{equation}
\begin{aligned}

y =& -x^2 + 1
&& \text{Given equation}
\\
0 =& -x^2 + 1
&& \text{To find the $x$-intercept, we let } y = 0
\\
x^2 =& 1
&&
\\
x =& \pm 1
&&

\end{aligned}
\end{equation}
$


The $x$-intercept is $(1,0)$ and $(-1,0)$

$y$-intercept:


$
\begin{equation}
\begin{aligned}

y =& -x^2 + 1
&& \text{Given equation}
\\
y =& -(0)^2 + 1
&& \text{To find the $y$-intercept, we let } x = 0
\\
y =& 1
&&

\end{aligned}
\end{equation}
$


The $y$-intercept is $(0,1)$

Single Variable Calculus, Chapter 3, 3.5, Section 3.5, Problem 30

Determine the derivative of the function $\displaystyle G(y) = \left(\frac{y^2}{y+1}\right)^5$


$
\begin{equation}
\begin{aligned}
G'(y) &= \frac{d}{dy} \left(\frac{y^2}{y+1}\right)^5\\
\\
G'(y) &= 5 \left( \frac{y^2}{y+1} \right)^4 \frac{d}{dy} \left( \frac{y^2}{y+1}\right)\\
\\
G'(y) &= 5\left(\frac{y^2}{y+1}\right)^4 \left[ \frac{(y+1)\frac{d}{dy}(y^2) - (y^2) \frac{d}{dy} (y+1)}{(y+1)^2}\right]\\
\\
G'(y) &= 5\left(\frac{y^2}{y+1}\right)^4 \left[ \frac{(y+1)(2y)-(y^2)(1)}{(y+1)^2}\right]\\
\\
G'(y) &= 5\left(\frac{y^2}{y+1}\right)^4 \left[\frac{2y^2+2y-y^2}{(y+1)^2} \right]\\
\\
G'(y) &= 5\left(\frac{y^2}{y+1}\right)^4 \left[ \frac{y^2 + 2y }{(y+1)^2}\right]\\
\\
G'(y) &= \frac{5(y^2)^4(y^2+2y)}{(y+1)^4(y+1)^2}\\
\\
G'(y) &= \frac{5(y^8)(y^2+2y)}{(y+1)^6}\\
\\
G'(y) &= \frac{5y^{10}+ 10y^9}{(y+1)^6}

\end{aligned}
\end{equation}
$

College Algebra, Chapter 3, 3.4, Section 3.4, Problem 24

The graph represents the population $P$ in a small industrial city from 1950 to 2000. The variable $x$ represents the number of years since 1950.

"Please refer to the graph in the book"

a.) What was the average rate of change of $P$ between $x = 20$ and $x = 40$?


$
\begin{equation}
\begin{aligned}

\text{average rate of change } =& \frac{f(b) - f(a)}{b - a}
&& \text{Model}
\\
\\
\text{average rate of change } =& \frac{f(40) - f(20)}{40 - 20}
&& \text{Substitute } a = 20 \text{ and } b = 40
\\
\\
\text{average rate of change } =& \frac{40 - 40}{20}
&& \text{Simplify}
\\
\\
\text{average rate of change } =& \frac{0}{20}
&& \text{Simplify}
\\
\\
\text{average rate of change } =& 0
&& \text{Answer}

\end{aligned}
\end{equation}
$


b.) Interpret the value of the average rate of change that you found in part (a).

There is no average rate of change of the population between 1970 to 1990.

What did the young lady tell Framton about the open window?

The young lady Vera tells Framton a scary shaggy-dog story. She tells him that, three years ago, her aunt's husband and her two young brothers went out for a day's shooting. While out on the moors, all three men became trapped in a deep, treacherous bog, from which they never escaped. To this day, their bodies have never been discovered.
Yet Vera gives the impression that her aunt is still in denial, deeply traumatized by her loss. She seems to think that one day all the men will return home with the little brown spaniel that was lost with them. In the past, whenever they came home from a day's hunting, the men would always walk through the large French window that opens on to the lawn. And so Vera's aunt always leaves open the French window every evening until dusk, hoping against hope that they'll walk through it some day. Vera also claims—with a perfectly straight face—that she gets a creepy feeling that the men will indeed return at any moment.

What's the most convincing evidence that Brigid O'Shaughnessy killed Miles Archer?

He did.

Sam Spade does not have much concrete evidence that Brigid O'Shaughnessy killed Spade's partner Miles Archer. He puts her under extreme emotional and time pressure, while the police are on their way to his apartment, to break down and confess to him by explaining his reasons for suspecting her. He makes her believe that if she tells him the true facts he will continue to protect her from the authorities. She is extremely young and inexperienced. In her initial interview with Spade, she tells him she is five years older than her mythical seventeen-year-old missing sister. She relied on Floyd Thursby for protection before, and now she is relying on Sam Spade, another tough, worldly man. If she doesn't break down and confess to him, he will turn her over to the police when they arrive. They haven't made a thorough investigation of the crime scene at Burritt Street because they assumed Miles Archer was killed by Floyd Thursby, who was killed a short time later on Geary Street in front of his hotel. If the police learn that Thursby was actually killed by Wilmer Cook, they will go back to Burritt Street and ask questions all over the densely populated neighborhood of apartment buildings and hotels. They are sure to find people who saw a young woman resembling Brigid O'Shaughnessy coming out of the blind alley onto Bush Street right after a shot had been fired.
Brigid doesn't know anyone in San Francisco except Spade. She has no money to hire a lawyer. Joel Cairo, Wilmer Cook, Caspar Gutman's daughter Rhea, Caspar Gutman (whom Brigid believes is still alive), and Sam Spade could all testify that Brigid has a bad character and that she had been Floyd Thursby's mistress. The Maltese falcon could serve as evidence against her because it would represent her motive for hiring Spade and Archer to tail Thursby and either frighten him into leaving San Francisco or else into trying to kill whichever partner was tailing him. She would be under heavy pressure from the police and the D.A. to confess her guilt and would probably be offered a plea bargain and get off with twenty years in prison rather than hanging. 
Sam Spade surveyed the crime scene at Burritt Street right after being told over the phone that his partner had been shot there. He tells Brigid why he knows she is guilty of murdering Archer.

Miles hadn't many brains, but, Christ! he had too many years' experience as a detective to be caught like that by the man he was shadowing. Up a blind alley with his gun tucked away on his hip and his overcoat buttoned? Not a chance. . . But he'd have gone up there with you, angel, if he was sure nobody else was up there. You were his client, so he would have had no reason for not dropping the shadow on your say-so, and if you caught up with him and asked him to go up there he'd've gone. He was just dumb enough for that. He'd've looked you up and down and licked his lips and gone grinning from ear to ear—and then you could've stood as close to him as you liked in the dark and put a hole through him with the gun you had got from Thursby that evening.

The best, most convincing concrete evidence to indicate that Brigid O'Shaughnessy killed Miles Archer is that she employed him to tail her paramour Floyd Thursby; that she has a bad character; that she stole the Maltese falcon from General Kemidov and then stole it from Caspar Gutman, who had employed her to steal it for him; that she is the only one who could have had access to Floyd Thursby's Webley-Fosbery automatic revolver; and, finally, that she confessed to Sam Spade because he made her think they were both in danger of hanging and she thought she could trust him.

"Will you stop it?" he demanded in a low, impatient voice. "This isn't the spot for the schoolgirl-act. Listen to me. The pair of us are sitting under the gallows." He took hold of her wrists and made her stand up straight in front of him. "Talk!"
"I—I—How did you know he—licked his lips and looked—?"

Single Variable Calculus, Chapter 3, 3.3, Section 3.3, Problem 52

a.) $\displaystyle y = \frac{x}{(1 + x^2)}$ is a curve called Serpentine. Find the equation of the tangent line to this curve at $P ( 3, 0.3)$

Required:

Equation of the tangent line to the curve at $P(3,0.3)$

Solution:

Let $y' = m$ (slope)


$
\begin{equation}
\begin{aligned}

\qquad y' = m =& \frac{\displaystyle (1 + x^2) \frac{d}{dx} (x) - \left[ (x) \frac{d}{dx} (1 + x^2) \right]}{(1 + x^2)^2}
&&
\\
\\
\qquad y' = m =& \frac{(1 + x^2) (1) - (x)(2x)}{(1 + x^2)^2}
&&
\\
\\
\qquad y' = m =& \frac{1 + x^2 - 2x^2}{(1 + x^2)^2}
&&
\\
\\
\qquad m =& \frac{1 - x^2}{(1 + x^2)^2}
&& \text{Substitute the value of $x$ which is $3$}
\\
\\
\qquad m =& \frac{1 - (3)^2}{[ 1 + (3)^2]^2}
&& \text{Simplify the equation}
\\
\\
\qquad m =& \frac{-8}{100}
&& \text{Reduce to lowest term}
\\
\\
\qquad m =& \frac{-2}{25}
&&


\end{aligned}
\end{equation}
$


Solving for the equation of the tangent line:


$
\begin{equation}
\begin{aligned}

\qquad y - y_1 =& m(x - x_1)
&& \text{Substitute the value of the slope $(m)$ and the given point}
\\
\\
\qquad y - 0.3 =& \frac{-2}{25} (x - 3)
&& \text{Multiply $\large \frac{-2}{25}$ the equation}
\\
\\
\qquad y - 0.3 =& \frac{-2x + 6}{25}
&& \text{Add $0.3$ to each sides}
\\
\\
\qquad y =& \frac{-2x + 6}{25} + 0.3
&& \text{Get the LCD}
\\
\\
\qquad y =& \frac{-2x + 6 + 7.5}{25}
&& \text{Combine like terms}
\\
\\
\qquad y =& \frac{-2x + 13.5}{25} \text{ or } -0.08x + 0.54
&& \text{Equation of the tangent line to the curve at $P (3, 0.3)$}


\end{aligned}
\end{equation}
$


b.) Graph the curve and the tangent line on part (a).

Was Stalin a true hero?

The answer to this question depends largely on your definition of what a hero is.  By my definition, Stalin is most definitely not a hero.
It would be possible to say that Stalin was a true hero if you define a hero simply as someone who accomplishes notable things.  Stalin certainly accomplished some important things.  He was the ruler/dictator of the Soviet Union for over 20 years.  During that time, he led the country through World War II, in which it did much of the work of defeating Nazi Germany.  He forced the country to industrialize, taking it from a backwards economy to one that could at least compete with the US in terms of military power.  Under his rule, the Soviet Union became one of the two most powerful countries in the world.  This is notable, so if you think that a person can become a hero just by doing notable things, Stalin was a true hero.
However, in my mind, a hero is not just someone who accomplishes notable things.  Instead, a hero has to be in some way noble and has to be morally admirable.  We have to be able to look at a hero and say “I would want to have those qualities.”  A hero also has to work for goals that we can applaud.  If we look at things in this way, it is hard to call Stalin a true hero.  It is true that he was driven and determined, and it is true that those are good qualities.  However he was also extremely vicious, ruthless, and selfish.  He killed or imprisoned millions of people simply for disagreeing with him or for being, in his mind, a threat to his power.  He implemented policies that caused millions more to die of starvation.  He had no compunctions about condemning people to death (either through execution or through overwork/starvation) in order to achieve the goals that he had set. 
A hero (in my view) has to be someone who has good moral qualities and who pursues worthy goals in good ways.  If we define a hero in this way, Stalin was not a hero.
https://www.history.com/topics/russia/joseph-stalin

Why is precision of language so important to the people of Jonas's society?

Language "precision," as it is called, is another tool used by the society of The Giver to control the community and keep them content and safe by desensitizing them.
In his essay "Politics and the English Language," George Orwell writes,

Now, it is clear that the decline of a language must ultimately have political and economic causes....(http://www.orwell.ru/library/essays/politics/english/e_polit/)

In this passage and further in the essay, Orwell writes of the power of language. Certainly, language is is a tool for powerful governments; indeed, it is a type of thought control. Continuing some of Orwell's ideas from this essay, he writes, "If thought corrupts language, language can also corrupt thought." This is the very concept behind the invention of Newspeak in Orwell's 1984.Similarly, in the society of The Giver, language is used to control and corrupt thought. In order to control any intense emotion, which could cause negative results, the society has people discuss their feelings, but only with "precision"; that is, they are restricted to approved words that can be used in the community. Many of them are mere euphemisms, words which are rather innocuous and will neither stir deep emotion in the speaker nor excite it in the listener. By requiring people to use these euphemisms, the thoughts and emotions of the citizenry can better be controlled, as well as modified.
In Chapter 1, for instance, as he rides his bicycle home, Jonas worries over his word choice for the evening ritual in which the members of his family share their feelings about the events of the day. Later, after one of Jonas's family expresses feelings, the others commiserate and offer their words of comfort or support. But, these words really are all too sanguine to be genuine or comforting. In fact, Jonas finds that he must "sift through his complicated emotions" to find the soft words demanded by his society. When he does this, he is left unsatisfied. For instance, as Jonas nears home, he contemplates the upcoming Ceremony of Twelve in which he will receive his Assignment for his life:

...he realized that frightened was the wrong word to capture his feelings about the momentous ceremony.....It was too strong an adjective.

Even though he is eager, excited, and rather nervous about the ceremony, Jonas knows that he must not express all these feelings. So, instead, he decides upon the more euphemistic adjective apprehensive and uses it to describe his feelings about the forthcoming December ceremony. His father merely tells him, "I'm glad that you told us of your feelings."
This sedated conversation of the family keeps a certain calmness in the home, but it also makes for a desensitized and empty life. Nevertheless, this desensitized life is desired by the community because it is safer for the members of the society as they are less likely to disobey the rules or conflict with one another or the authorities than if they expressed powerfully their emotions.The society of Lowry's novel is created by those who want to eliminate all the conflicts, pain, and griefs to the safe keeping of one person, who alone bares the burdens of these human agonies and emotions. While this one person, who is called the Giver, carries memories and bears the burden of pain and deep emotion, the others opt for sameness over individuality and safety over freedom. And, language is one tool used to maintain this structure.
http://www.orwell.ru/library/essays/politics/english/e_polit/

What are the differences between seed cones and pollen cones?

The proper name for seed cone is megastrobilus (plural form is megastrobili), but it is also known as a female cone. The proper name for pollen cone is microstrobilus, but it is also known as a male cone.
Pollen cones tend to be located on the lower branches. They survive just long enough to release pollen. Since they wither, there is little evidence of their existence after pollination. They also tend to display less structural variation than seed cones among different species.
When people imagine conifer cones, they are most likely thinking of seed cones. Seed cones are both larger and longer lived than pollen cones. After pollination, megastrobilus scales will both harden and darken. They are the ones you find on the ground around conifers. Due to their structural variation, they are often used to identify different species.
http://www.pinetum.org/Lovett/pinecones.htm

https://dnr.wi.gov/wnrmag/html/stories/1996/dec96/cones.htm

Why is the city of Ember underground?

The titular city of Ember is a vast underground city meant to serve as a last resort to ensure the survival of humanity in the event of a catastrophic or even apocalyptic event. The city, however, is not a permanent solution and was only built to sustain the remnants of humanity for roughly two centuries. The central conflict of the story revolves around the dwindling supply of food and decay of the hydroelectric apparatus that powers the city, as the inhabitants have passed the 200 year mark. The nature of the city is completely lost upon the primary characters of the novel, who until the very end of the story not only are unaware of the apocalyptic and dystopian nature of their society, but don't even realize that they are underground. Due to a lack of education of young persons in Ember, as well as some misfortune and ineptitude on the part of the leaders of the city, memory of the nature of the world was almost completely erased over the course of just a few generations.

The city of Ember is underground as a precautionary measure. In the book, we don't learn why the city is underground until the last chapters.
Long ago, the people who lived aboveground decided that Ember would be the only way to guarantee the continuation of the human race in the event of a catastrophe. The people believed that the underground city of humans would be humans' last resort to repopulate the earth.
The people aboveground arrived at this unconventional solution after realizing that the human race faced extinction from some unexplained catastrophe. According to the notebook that Lina and Doon find, the first humans to populate Ember were old people and babies. Each elderly couple was "matched" with two babies. In all, Ember began with two hundred humans. The babies were raised with little knowledge of the world aboveground.
By the time the babies reached adulthood, they were bereft of their elderly caregivers. The new adults then married and had children: this was how Ember flourished for more than two hundred years. So, the city of Ember is underground as a precautionary measure; it is an attempt at preserving the human race after the destruction of civilization.

How do I write a rough draft for a literary analytical essay about the short story "A Rose for Emily" by William Faulkner?

You might begin by identifying a theme of the story, and that theme can go into your thesis statement. For example, Emily Grierson has trouble letting go of the past. When Emily tries to live as though the past were the present, she ends up completely alienating herself from other people and engaging in behaviors that are unsafe and, frankly, gross. In trying to hang on to her beautiful past, Emily Grierson actually becomes something disgusting: she hoards dead bodies and actually looks like a dead body herself. The narrator compares her to someone who has drowned: it is as though she has become pale and bloated after laying in water for a long time.
Her respectability fades when she begins to age and it becomes clear that she will not marry. It fades more when the townspeople identify her house as the source of the terrible smell (that turns out to be Homer Barron's body). It fades even more when she crustily refuses to pay taxes and refers the town's new officials, for proof, to the long-dead sheriff. It nearly disappears, we might imagine, when officials find Homer's dead body in her bed, with her hair on the pillow next to his. Therefore, we can infer that, when someone cannot let go of the past, there is no way for them to have a satisfying or productive present or future.
You might use this theme, or another like it, to form an analytical argument about the story in your thesis statement. Then, each of your body paragraphs can outline one reason that you know this theme to be true, using textual examples.

x = 1/3(y^2 + 2)^(3/2) , 0

Arc length (L) of the function x=h(y) on the interval [c,d] is given by the formula,
 L=int_c^dsqrt(1+(dx/dy)^2)dy , if x=h(y) and c <=  y <=  d,
x=1/3(y^2+2)^(3/2)
dx/dy=1/3(3/2)(y^2+2)^(3/2-1)(2y)
dx/dy=y(y^2+2)^(1/2)
Plug in the above derivative in the arc length formula,
L=int_0^4sqrt(1+(y(y^2+2)^(1/2))^2)dy
L=int_0^4sqrt(1+y^2(y^2+2))dy
L=int_0^4sqrt(1+y^4+2y^2)dy
L=int_0^4sqrt((y^2+1)^2)dy
L=int_0^4(y^2+1)dy
L=[y^3/3+y]_0^4
L=[4^3/3+4]-[0^3/3+0]
L=[64/3+4]
L=[(64+12)/3]
L=76/3
Arc length of the function over the given interval is 76/3
 

What does Miss Maudie mean by "sometimes the Bible in one hand of one man is worse than a whiskey bottle in the hand of-oh your father?"

Miss Maudie means that it is the person using a substance that matters, not the substance itself. The Bible, usually seen as a positive moral force, can become a force for evil in the wrong hands. Likewise, whiskey, often seen as evil force driving people to drunkenness, won't be as damaging if consumed by an ethical man like Atticus.
This points to Atticus as the moral center of the book. A good part of Scout's education during the novel is in her learning that her father is an exemplary human being, a man of character guided by conscience. Here we learn that we don't know what might go on behind closed doors at the Radleys, nor how their private behavior might differ from their public behavior. As Miss Maudie says:

"The things that happen to people we never really know. What happens in houses behind closed doors, what secrets—”

When Scout defends Atticus by saying he treats her and Jem the same way whether they are in the house or in the yard, Miss Maudie agrees. This consistency shows that Atticus is a man of integrity.

Miss Maudie means that the Bible can be harmful when someone uses its content for evil. Even though the Bible is meant to inspire hope and love in modern Christian theology, people can twist its words in a negative way and use it to justify negative actions. Alcohol, on the other hand, was often seen as a negative; but it is all about the person using it, Miss Maudie says.
Miss Maudie is explaining to Scout what she knows about the Radley family. Scout is curious about Arthur "Boo" Radley, a shut-in who Scout, Jem, and Dill wonder about all summer. Miss Maudie knew him as a child and explains that his family was very religious. They belonged to a type of Baptist group that Miss Maudie calls "foot-washing Baptists." They believed that every type of pleasure was sinful. 
Miss Maudie tells Scout:

"Wasn’t talking about your father," she said. "What I meant was, if Atticus Finch drank until he was drunk he wouldn’t be as hard as some men are at their best. There are just some kind of men who—who’re so busy worrying about the next world they’ve never learned to live in this one, and you can look down the street and see the results."

In this way, she is explaining how Boo Radley's father twisted the Bible's messages and made his home a sad one.

Explain the relevance of Book IV of the Aeneid to the overall structure of the heroic quest and the epic.

Book 4 of the Aeneid is the test of resolve for the classic hero, Aeneas. In every heroic story, there is a period of time where their true motivations and devotion to the cause are tested, such as when Luke Skywalker leaves Yoda's tutelage on Dagobah to rescue his friends in spite of the consequences of departure from his duty.
In the Aeneid, Aeneas falls in love with Dido, and his attention and devotion are diverted towards her instead of his task of building the new city. The Gods remind him of the importance of his journey, and he eventually comes to his senses and returns to the task at hand, regardless of how upsetting it is to leave Dido. In doing so, he proves to be a true hero, putting the fate of his people and the will of the Gods above his own personal desires.

In Book IV, Aeneas falls in love with Dido, the queen of Carthage. The two engage in a passionate love affair which culminates in Dido wanting to make Aeneas her consort. However, Aeneas chooses to leave Dido and continue his quest to found a new home for his people.
This narrative development is significant in The Aeneid for many reasons. Firstly, it shows that Aeneas is vulnerable and not made of stone. He can fall in love and be tempted to stray from his duty. Secondly, it makes Aeneas seem more selfless and heroic when he does give up romance for duty to his people. Lastly, it highlights one of the epic's major themes: the individual giving up his own selfish interests for the sake of something greater.
In most epics, the hero must make sacrifices in order to fulfill his or her personal quest. This is part of transcending one's own desires to do something greater. Aeneas does this, though Dido does not. Dido's fate—killing herself out of grief and effectively abandoning her people by leaving them without a ruler—is meant as a contrast to Aeneas's.
So in the end, Book IV is a vital stage in Aeneas's heroic journey, a place to show he is willing to do the right thing in putting aside his own interests for the sake of a noble cause.

Book 4 is pivotal to the book's thematic structure. Aeneas's quest is a heroic one; he has been charged with the sacred duty of founding a new city, a city that will one day become Rome. Like any future Roman hero, Aeneas understands the supreme importance of bringing honor to his ancestors and descendants. Founding the city of Rome will redound to the glory of his family name forever. It is imperative, then, for Aeneas to hold firm to his quest, not to allow anything to distract him from performing his vital role in this grand divine plan.
The events of book 4 represent a real test to Aeneas's overriding sense of duty. He falls head over heels in love with Dido, losing sight of his sole purpose in life. For her part, Dido also neglects her duties as Queen of Carthage, allowing her city to go to wrack and ruin. The gods are worried; it seems that Aeneas is putting his heart before his duty. So Jupiter dispatches Mercury, the winged messenger, to remind Aeneas of his destiny and to tell him that he must leave for Italy.
Aeneas loves Dido dearly, but he has to be strong; he has to display the kind of noble manliness expected of Roman heroes. He must put aside all personal feelings and carry on with his heroic quest. And he does. Aeneas has passed a difficult test; and now he has also learned that in founding a new civilization, especially one sanctioned by the gods, the individual is of relatively little importance. That applies to Aeneas every bit as much as to Dido.

Why did Dill run away from home

In chapter 14, Dill runs away from Meridian, sneaks into the Finch household, and hides underneath Scout's bed. After Scout and Jem get into a fight, Scout accidentally steps on Dill's body, and he comes out from underneath her bed. Jem immediately tells Atticus, who informs Dill's aunt that he is at their home and allows Dill to spend the night. That night, Dill climbs into Scout's bed and explains to her why he decided to run away. Dill tells Scout that his parents are relatively nice, loving people but do not spend quality time with him. According to Dill, his parents let him play alone while they go into other rooms to read. Despite the fact that they buy him new toys, Dill's parents rarely play with him, and he feels like he is not needed. Dill tells Scout,

That wasn’t it, he—they just wasn’t interested in me (Lee, 144).

Dill's parents contrast greatly with Atticus's as a parent, and the audience feels sympathy for Dill after listening to his reasons for running away.

Why do you think Wordsworth compared the solitary reaper's song to that of the nightingale and cuckoo bird?

Often, as you have probably already guessed, birds are symbolic of other things in literature; similarly, many flowers have their own accompanying forms of symbolism and so do trees!  In literature, nightingales can be representative of some connection between love and death, or a mixture of love and loss, sadness and joy.  Perhaps Wordsworth compares the maiden's voice to that of a nightingale because the melancholy nature of the melody she sings conjures up images of lost love or even of a lover who has died.  This possibility seems even more likely when paired with the fact that the young woman is reaping, an activity often symbolically connected with the passage of time and of our own mortality (think about images of the Grim Reaper—he is, essentially, death).  
The cuckoo, on the other hand, is a bird often associated with infidelity and even selfishness because the female cuckoo lays eggs in other birds' nests.  Perhaps, then, the speaker might imagine that the song is about a young man or woman who fell in love with someone who was not faithful to them and that ended the relationship (leading to the love and loss associated with the nightingale).  Alternatively, maybe the person in the song was unfaithful and now regrets their choices because their lover has left them.

In the poem of the same name, Wordsworth is wandering in the Scottish highlands when he comes across a woman, the solitary reaper, singing and reaping grain all alone. Her beautiful song fills the air and the poet is transfixed. He likens her music to that of the nightingale and cuckoo because both birds have distinctive voices. The nightingale in particular is often noted for its song. Further, Wordworth and other Romantic poets placed a very high value on nature and also tried to show the worth of common people. By comparing the song of this ordinary, laboring woman to the sound of natural creatures, the narrator pays her a high compliment: she sings as well as a bird. This elevates the common worker. Often in poems, the laborer was depicted as a clown or a clod, someone rough and uncouth. By describing this woman as a sublime element of nature, the poet elevates her status.

What part did Diana, Betsy, and Brigid play in Lyddie's life?

Diana, Betsy, and Brigid all play important roles in Lyddie's life.  
Diana is really the first to welcome Lyddie to being a factory girl.  Diana takes Lyddie under her wing and teaches Lyddie how to operate within the very busy factory.  Diana is also the woman who first treats Lyddie's injury on the factory floor.  Additionally, Diana secures Lyddie access to a doctor.  Lastly, Diana is the woman that really encourages Lyddie to sign the petition. 
Betsy's main role is that she turns Lyddie toward the importance of education and learning.  Betsy first does this by reading Oliver Twist to Lyddie.  Eventually Lyddie learns that Betsy is working in the factory to put herself through college.  The possibility of that for Lyddie had never really crossed her mind until she met Betsy.  
Lyddie does not like Brigid at first.  Lyddie is forced to help her learn how to work in the factory.  That causes Lyddie's production to fall a bit, and Lyddie isn't happy about that.  Eventually, Lyddie becomes Brigid's protector in the same way that Diana was Lyddie's protector.  Near the end of the book, Lyddie helps Brigid escape from Mr. Marsden's sexual advances.  The incident leads to Lyddie being fired. 

sum_(n=1)^oo 1/(2n+3)^3 Confirm that the Integral Test can be applied to the series. Then use the Integral Test to determine the convergence or divergence of the series.

sum_(n=1)^oo1/(2n+3)^3
For the integral test, if f is positive, continuous and decreasing for x>=1 and a_n=f(n) , then sum_(n=1)^ooa_n and int_1^oof(x)dx either both converge or diverge.
Now, f(x)=1/(2x+3)^3
Now function is positive and continuous.
Let's determine whether f(x) is decreasing, by finding its derivative f'(x)
f(x)=(2x+3)^(-3)
f'(x)=-3(2x+3)^(-3-1)d/dx(2x+3)
f'(x)=-3(2x+3)^(-4)(2)
f'(x)=-6/(2x+3)^4
f'(x)<0 , so the function is decreasing
Because f(x) satisfies the conditions for the integral test, we can apply integral test.
int_1^oo1/(2x+3)^3dx
=[1/2(2x+3)^(-3+1)/(-3+1)]_1^oo
=[1/-4(1/(2x+3)^2)]_1^oo
=-1/4[1/(2*oo+3)^2-1/(2*1+3)^2]
=-1/4[0-1/5^2]
=-1/4(-1/25)
=1/100
So f(x) converges.
Therefore, sum_(n=1)^oo1/(2n+3)^2 converges.

Slim states, “I seen the guys that go around on the ranches alone. That ain’t no good. They don’t know how to have fun. After a long time they get mean” Why do you think the men get mean being alone?

This quote actually comes from George, but Slim agrees with the idea that men who travel alone "get mean." The reason that men like this become mean and nasty is simple: they are so consumed by loneliness and isolation that when they do make a human connection, they often vent the frustrations that are caused by this extreme loneliness.
We see lots of examples of this in the novel. Take Crooks, for instance, who delights in torturing Lennie by telling him that George might not come back from town. Crooks does not really mean to be so hurtful towards Lennie. What's happened is that he has become bitter as a result of years of isolation because of the color of his skin.
Similarly, Curley's wife also gets mean and nasty with Crooks in Chapter Four:

Well, you keep your place then, Nigger. I could get you strung up on a tree so easy it ain't even funny."

Again, Curley's wife is not nasty by nature. Instead, she has become mean and nasty because she is so fed up with her loneliness and isolation. Remember that not only is she the only woman on the ranch, she is actively ignored by Curley and the others. This has created feelings of isolation and powerlessness which she takes out on Crooks as soon as she gets the chance.
What Steinbeck is showing us, then, is that isolation and loneliness can bring out the very worst human characteristics. It is for this reason that we need friendship in our lives, as demonstrated through the characters of George and Lennie.

What protection does Jones evoke against spells & ghosts

After resigning his position as "emperor," Brutus Jones attempts to make good his escape through the forest. His life is in serious danger as there's rebellion in the air. The natives are restless due to Jones's rampant greed and corruption. Jones keeps up a facade of bravado, insisting that he'll shoot himself with a silver bullet should the marauding "natives" get too close. Yet despite this reckless display of defiance, Jones is absolutely terrified at what might happen. It doesn't help when Smithers, the white English trader, spooks him with talks of ghosts and heathen spells. In his mounting desperation, Jones tries to convince Smithers—and himself—that his good standing as a member of the Baptist Church will be enough to protect him from the natives' black magic, from their "heathen tricks" as he calls them. If his "subjects" should attack him, then he warns that they will end up in Hell for their sins.

What is a short summary of the poem "Five Ways to Kill a Man" by Edwin Brock?

"Five ways to kill a man", describes different ways man has used from ancient times till twentieth century,to kill other human beings. It mocks at the dehumanisation of man.
The first stanza talks about crucifixion of Jesus Christ it included complicated method to torture and kill him. A crowd walked up the Golgotha hill and forced Christ to carry the wooden cross on his back. 
St. Peter the leader of his disciples refused thrice to know him. The cock crowed to remind Peter of Christ's prediction that he would deny him.
They nailed him onto the cross and pulled the cross up erect.After that Jesus was asked to remove his cloak leaving him semi clad.They tortured him in various ways and he asked for water,he was provided with a sponge soaked  in vinegar.
Eventually Christ died and then they divided his clothes among themselves.
the second stanza describes war fought for the sake of crown and honour in the medeival age.
it refers to the Wars of Roses (1455-1485)a series of dynastic wars fought between the House of Lancaster and House of York for the throne of England.They fought with bows and arrows, wearing an armour known as metal cage and riding of white horses.
The third stanza describes first world war and the use of gas warfare. In 1915 the British used gas cylinders to attack German front lines. The wind direction changed and the gas came back to poison the British soldiers. The poet also refers to use of trench warfare , bombs , mud blackened boots , plague of mice. He also talks about the dozen songs of war chants used to boast the morale of soldiers to make them proud of their act of killing the enemies.
The fourth stanza describes advent of aeroplanes and atomic warfare. 
This warfare required an aeroplane to fly above the victims head without even knowing them or seeing them. The poet refers to the bombings of Hiroshima and Nagasaki of Japan by USA during the second World War.
The poet says this required "an ocean to seperate you" referring to the cultural and geographical gap between US and Japan;" two systems of government" referring to the difference in adminstrative system of the two countries;'a nation's scientists' and "several factories" to produce the lethal weapon like atom bomb. All this deadly acts were executed by the orders of a psychopath, probably Harry S. Truman, the then president of USA who authorised atomic bombing on Japan.
the poet then says "land that no one needs for several years", a reference to the regions of Hiroshima and Nagasaki,which were totally devastated due to the effects of radiations.
In the last stanza the poet devised a far more simpler and direct method than the four methods he described in the above four stanzas, to leave the victim in the middle  of the twentieth century in the miserable condition of the post effects of the second world war which included poverty, hunger ,malnutrition, dieseases,religious intolerances; In such conditions man was being inflicted with with pain everyday in order to survive and in doing so, he would die a slow but painful death.
Each stanza of the poem deals with one method of killing and each one further creates a distance between the killler and the victim, till in the last stanza there remains neither the killer nor the victim only a living Death. 

"Five Ways to Kill a Man" is a fairly straightforward poem in terms of what events are taking place.  
The first stanza opens with a bold statement about there being "many cumbersome ways to kill a man."  It then continues to tell about the crucifixion of Christ.  The stanza coldly states what few tools and elements are needed to crucify a person.  

To do this properly you require a crowd of peoplewearing sandals, a cock that crows, a cloakto dissect, a sponge, some vinegar and oneman to hammer the nails home.

Stanza two moves forward in time about one thousand years.  It talks about medieval knights battling each other in suits of armor.  It talks about how swords and arrows are designed to penetrate that armor.  The end of the second stanza also includes a bit of narration on the need for royalty to celebrate the violence being done at their command.  
Stanzas three and four are about World War I and II.  Stanza three focuses on how toxic gasses killed thousands of men in the trenches.  Stanza four is about the dropping of the atomic bombs on Japan.  There appears to be an insult directed at the US president for dropping the bombs.  The poem says that in order to drop the bomb, a "psychopath" is needed.  This stanza also ends by stating that the effects of the bombs lasted a lot longer than a day or two.  

                                         All you thenrequire is an ocean to separate you, twosystems of government, a nation's scientists,several factories, a psychopath andland that no-one needs for several years.

The fifth stanza states that all of the previous methods for killing a man are "cumbersome."  It states that the easiest way to kill a man is to just leave him somewhere in the twentieth century.  The narrator is calling reader attention to the increasing violence that has been happening throughout history.  In addition to that, the narrator is showing readers how mankind's technology has allowed us to kill in easier and easier ways from farther and farther away.  No longer do we need to stand next to the man we are killing and drive nails through his hands. We simply need to drop a bomb thousands of miles away with the push of a button and watch thousands of people die via live video feed.