Why is Gretel surprised when she looks out the window?

In chapter 4 of The Boy in the Striped Pajamas, Gretel gets the opportunity to look out of Bruno's window, and the view is very confusing to her. The reason Gretel is so confused is because she has never seen a sight like the one she views out of the window. Gretel sees a community made up of only males, living in squalor in one-floor huts in an area with no greenery. She struggles with her lack of understanding, stating at one point, "I don't understand. . . . Who would build such a nasty-looking place?"
Gretel and Bruno have grown up in a fairly affluent lifestyle. They live in a large house, the family employs a cook and a maid, and the children attend a good school. They are not used to being around a community where people are struggling like the ones outside the window. But Gretel is uncomfortable with this lack of understanding and feels a need to explain what she is seeing. The author states, "She was twelve years old and considered to be one of the brightest girls in her class, so she squeezed her lips together and narrowed her eyes and forced her brain to understand what she was looking at." While Gretel is confused by what she sees because it is so unknown to her, she still wants to understand it.

In chapter 3, Bruno laments about their new home at Out-With and mentions to Gretel that the children he saw do not look happy. Gretel is initially confused and ends up following her brother to his room, where there is a window that overlooks the concentration camp. At the beginning of chapter 4, Gretel follows Bruno into his room and is surprised to see numerous people of various ages behind the fence. Both Gretel and Bruno are confused at what they witness and Gretel asks where the females are located. Gretel then tells her brother that she thinks they have moved to the countryside because there are no buildings that resemble a town or the city of Berlin. However, Bruno challenges her assumption by asking Gretel why there are no animals in the countryside. Both Bruno and his sister have no clue that they have moved to the largest concentration camp under German control and the people they are looking at through the window are Jewish prisoners.

Describe x^3 - 2 x^2 -14 x +40 as product of linear factors.

Hey there!
There are multiple methods to factor polynomials and get there linear factors. One method that will give you the real and rational roots is to use the rational root theorem. This states that all the possible rational roots of a polynomial can be found by taking the factors of constant term and dividing it by the factors of the leading coefficient.
In your example the constant is 40 and the leading coefficient is 1 , so all the possible rational roots are all the factors of 40/1 or just 40 .
+-1,+-2,+-4,+-5,+-8,+-10,+-20,+-40
we can test these roots by trial and error using synthetic division and find that x=-4
is a root. Now we can divide out x-(-4) or x+4.
Our polynomial now becomes:
(x+4)(x^2-6x+10).


We can now use the quadratic formula on the remaining polynomial, which will yield the two remaining roots of 3+-i.
giving us our completely factored polynomial: (x+4)(x-3-i)(x-3+i).

Hello!
To factor a polynomial it is useful to find its roots. If a polynomial P(x) has a root a, then it may be expressed as P(x) = (x - a)Q(x), where Q(x) is a polynomial of the degree one less than the degree of P(x).
Let's try to find an integer root of our P(x) = x^3 - 2x^2 - 14x + 40. It must be a divisor of the constant term, 40. Trial and error gives us a root x_1 = -4:
(-4)^3 - 2*(-4)^2 - 14*(-4) + 40 = -64 - 32 + 56 + 40 = 0.
Therefore we can divide P(x) by (x+4):
x^3 - 2x^2 - 14x + 40 =x^2(x+4) - 4x^2 - 2x^2 - 14x + 40 =x^2(x+4) - 6x^2 - 14x + 40 =
= x^2(x+4) - 6x(x+4) + 24x - 14x + 40 =x^2(x+4) - 6x(x+4) + 10x + 40 =
= x^2(x+4) - 6x(x+4) + 10(x + 4) = (x^2 - 6x + 10)(x + 4).
The polynomial Q(x) =x^2 - 6x + 10 has no real roots because its discriminant is negative: (-6)^2-4*10=-4lt0. Its complex roots are 3+-i. So we cannot make it a product of linear factors under real numbers,
x^3 - 2x^2 - 14x + 40 =(x^2 - 6x + 10)(x + 4).
Under complex numbers we have the answer,
x^3 - 2x^2 - 14x + 40 =(x-3-i)(x-3+i)(x + 4).

Single Variable Calculus, Chapter 3, Review Exercises, Section Review Exercises, Problem 52

a.) Suppose that $f(x) = 4x - \tan x$, $\displaystyle \frac{-\pi}{2} < x < \frac{\pi}{2}$. Find $f'$ and $f''$

$
\begin{equation}
\begin{aligned}
f'(x) &= 4 \frac{d}{dx} (x) - \frac{d}{dx} (\tan x)\\
\\
f'(x) &= 4 - \sec ^2 x\\
\\
f''(x) &= \frac{d}{dx} (4) - \frac{d}{dx} (\sec^2 x)\\
\\
f''(x) &= \frac{d}{dx} (4) - \frac{d}{dx} (\sec x)^2\\
\\
f''(x) &= 0 -2 (\sec x) \frac{d}{dx} (\sec x)\\
\\
f''(x) &= - 2 \sec x \sec x \tan x \\
\\
f''(x) &= -2 \sec^2 x \tan x
\end{aligned}
\end{equation}
$


b.) Graph $f$, $f'$, and $f''$

Why is what happens to the boy unexpected in "Once Upon a Time?"

In the beginning of the overall story, Gordimer explains how she's been asked to write a children's story. Initially, she does not want to. Then, she describes waking up to a strange noise. At first, she fears an intruder is breaking into her home. Her fear stems from racial and political conflicts in the waning years of the apartheid in South Africa. (The story was published in 1989.) However, she realizes the noise is her house creaking over top of an underground mine. Given that this introduction or "frame" story ends with the elimination of fear, we might suspect that the subsequent "story within a story" (about the family) will have a "happily ever after" ending. 
In the "story within a story," there is a family whose fear of crime and potential intruders causes them to increase the security of their home. This fear feeds upon itself and they continue reinforcing their home until it is more like the design of a prison. Given all of these precautions, one might think that the family will be completely safe and will "live happily ever after." However, their last addition of a jagged security coil ends up becoming a real danger. One of the brutal ironies of this story is that the little boy had been inspired by a fairy tale and tried to get through the coil: 

Next day he pretended to be the Prince who braves the terrible thicket of thorns to enter the palace and kiss the Sleeping Beauty back to life. 

Fairy tales usually have happy endings. The family takes drastic measures to make themselves safe in their home, which is why it is unexpected or even ironic that the little boy comes to harm because of those very measures and in defiance of the typical fairy tale ending.

Single Variable Calculus, Chapter 3, 3.3, Section 3.3, Problem 69

If $g$ is a differentiable function, find an express for the derivative of each of the following functions.

$
\begin{equation}
\begin{aligned}
\text{a.) } y &= xg(x) && \text{b.) } y = \frac{x}{g(x)}\\
\text{c.) } y &= \frac{g(x)}{x}
\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}
\text{a.) } y &= xg(x)\\
\\
y'&= x g'(x) + g(x) \frac{d}{dx} (x)\\
\\
y'&= x g'(x) + g(x) (1)\\
\\
y'&= x g'(x) + g(x)
\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}
\text{b.) } y &= \frac{x}{g(x)}\\
\\
y'&= \frac{g(x) \frac{d}{dx}(x) - g'(x)}{[g(x)]^2}\\
\\
y'&= \frac{g(x)(1) - x g'(x)}{[g(x)]^2}\\
\\
y'&= \frac{g(x) - xg'(x)}{[g(x)]^2}
\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}
\text{c.) } y &= \frac{g(x)}{x}\\
\\
y'&= \frac{xg'(x) - g(x) \frac{d}{dx}(x)}{x^2}\\
\\
y'&= \frac{xg'(x) - g(x) (1) }{x^2}\\
\\
y'&= \frac{xg'(x) - g(x)}{x^2}
\end{aligned}
\end{equation}
$

Beginning Algebra With Applications, Chapter 7, 7.2, Section 7.2, Problem 88

Simplify $\displaystyle 9x^3 (3x^2 y)^2 - x(x^3 y)^2$


$
\begin{equation}
\begin{aligned}

9x^3 (3x^2 y)^2 - x(x^3 y)^2 =& 9x^3 (3)^2 x^4 y^2 - x \left( x^6 y^2 \right)
&& \text{Multiply each exponent in $3x^2 y$ and in $x^3 y$ by the exponent outside the parentheses}
\\
\\
=& (9x^3) \left( 9x^4 y^2 \right) - x \left( x^6 y^2 \right)
&& \text{Simplify } (3)^2
\\
\\
=& (9 \cdot 9) \left( x^3 \cdot x^4 \right) y^2 - (x \cdot x^6) y^2
&& \text{Use Properties of Multiplication to rearrange and group factors}
\\
\\
=& 81x^7 y^2 - x^7 y^2
&& \text{Multiply variables with the same base by adding the exponents}
\\
\\
=& 80 x^7 y^2
&&

\end{aligned}
\end{equation}
$

Describe Miss Maudie Atkinson. Is she similar to other women in Maycomb? What do the children think of her?

Miss Maudie Atkinson is one of the Finches' neighbors and an old family friend. She is one of the more individual characters in Maycomb, being very much a free spirit who likes to do her own thing. She certainly doesn't fit the traditional mold of a refined Southern lady, especially not by Aunt Alexandra's elevated standards. An avid gardener, she spends a lot of time wearing overalls, making Scout feel like she is a kindred spirit. Another thing that sets Miss Maudie apart from most other women in Maycomb—indeed, most other people there—is her lack of prejudice and racial bigotry. This is another positive character trait that endears her to Scout and Jem.
Maudie stands out among the adults of Maycomb as being very friendly towards the Finch children. Her lack of conventionality means that she has a natural empathy with Scout and Jem; she understands them in a way that no one else does. The children are, therefore, naturally drawn towards her.

Why do Pam and Ned have such a hard time finding housing?

There are a number of reasons. For one thing, they're both drug addicts. Pam has made efforts in the past to stay off drugs, but without success. The couple's drug addictions have landed them in hot water with the law. They've both served time in prison for drug-related crimes, and this also counts against them as they search for a new place. As well as a lengthy rap sheet between them, Pam and Ned have also racked up an extensive list of evictions. Such a bad record indicates to future landlords that they're untrustworthy and can't be relied upon to pay the rent. In fact, they're evicted from Tobin's trailer park because they owe him around $3,000 in unpaid rent.
The biggest challenge that Pam and Ned face in finding a place to stay, however, is that they have children. So many landlords just don't want to know as soon as they discover that the couple has kids. Children tend to cause wear and tear on a property, so landlords are often reluctant to rent out to families with kids. Pam has two children with Ned, two from a previous relationship, and another baby on the way. This makes it all the more difficult for them to find somewhere to live.

A nonrelativistic electron is confined to a length of 500 pm on the x-axis. What is the kinetic energy of the electron if its speed is equal to the minimum uncertainty possible in its speed? h = 6.626 * 10^(-34) J * s, m_(el) = 9.11 * 10^-31 kg, 1 eV = 1.60 * 10^(-19) J). I got both .15 eV and 1.5 eV and I dunno if correct. Choices are A) 1.5 eV B) .015 eV C) 150 eV D) 15 eV E) .15 eV Wordz from old buddy previous test said "The minimum kinetic energy of the electron is closest to" not this minimum uncertainty stuff. old answer was .15 eV.

No actually 1.5 eV is correct I asked my professor but how do you get that then?

Hello!
Again, we have a deal with the uncertainty principle for a position and a momentum. Mathematically it is expressed as
Delta p*Delta x gt= h/(4 pi),
where Delta p = m*Delta v is an uncertainty in a momentum and Delta x is the uncertainty in a position.
Also we know that the kinetic energy of an electron is equal to (m_(el) v^2)/2, and it is given that the speed is the same as the minimum uncertainty of a speed. So the kinetic energy is equal to
E_k = (m_(el) v^2)/2 =(m_(el) (Delta v)^2)/2 = m_(el)/2 * (h/(4 pi) * 1/(m_(el)*Delta x))^2 =1/2 (h/(4 pi))^2 1/(m_(el)*(Delta x)^2).
All values are given, and we can compute the result in Joules (note that p means pico- means 10^(-12) ):
E_k = 1/2*(1.055*10^(-34))^2/(9.11*10^(-31)*25*10^(-20)) = (1.055)^2/(2*9.11*25)*10^(-17) approx 0.00244*10^(-17) (J).
To convert this to eV we have to divide by eV value:
E_k =0.00244*10^(-17) / (1.60*10^(-19)) = 0.00244*10^2/1.60 approx0.153 (eV).
So your hypothesis is correct, the answer is about 0.15 eV, E.

In "Fences" how is the father-son relationship depicted? How does Troy's relationship with his father compare to and shape his relationship with his son? Why do you think the play includes Lyons as well as Cory?

"Fences" is part of August Wilson's "century cycle." All of Wilson's plays deal with black life in a particular decade of the 20th-century. "Fences" examines black life in the post-World War II 1950s—1957 to be exact—and moves into the early 1960s, on the eve of the United States's intervention in Vietnam. After Troy dies, we see that Cory has entered the Marines.
The relationship between Troy and Cory is defined partly by Troy's envy of his son's opportunities and also by the fact that Troy does not know how to be a loving father. Instead, he only knows how to fulfill his paternal obligations ("I put food in your mouth and clothes on your back"), which is still more than his father, an abusive sharecropper, offered him.
The obvious of tension between Troy and Cory is that the latter demonstrates talent in football. Troy, in his youth, had also demonstrated talent for a sport: baseball. However, his ambitions were spoiled by racism. Cory, it seems, has an opportunity to pursue his ambition, but Troy's inability to let go of the past, coupled with his envy, discourages him from supporting his son. 
The title of the play is a double metaphor. "Fences" alludes to the ways in which people limit their lives, both due to circumstances out of their control (e.g., racism) and, in the case of Rose, out of love for someone else and the sense that love requires great personal sacrifice. Troy is working on the building of the fence throughout the play and does not finish it until the end of his life, around the same time that he has his final confrontation with Cory, who decides to leave home and assert his manhood by joining the Marines. Similarly, Troy left home after his confrontation with his father more than fifty years before.
Troy asserted his manhood by leaving the farm on which his family worked and to move to Mobile, Alabama, then to Pittsburgh. Northern segregation coerced him into a life of crime, which landed him in prison after Lyons was born. In his own way, Troy wants to fulfill his obligations to Cory in ways in which he was not able to fulfill his paternal obligations to Lyons. Thus, the other meaning of "fences" could also be the almost never-ending job of building and mending (as we do with fences) our relationships with those whom we love.
 
 

Did the duke kill the duchess?

Robert Browning's dramatic poem "His Last Duchess" leaves little doubt that its narrator, a duke of palpably tyrannical and possessive temperament, murdered his young wife himself or had her slain by servants. Her crime: a joyous and spontaneous nature that took pleasure, as any young woman might, in the myriad diversions of social life. Although the duke's fierce jealousy is aroused by the fact that

she liked whate'er
She looked on, and her looks went everywhere.


he seems most incensed that she's no more impressed by the gift of his noble lineage in marriage than by the simple yet tangible gifts of other men. The haughtiness of this self-styled esthete won't permit him to even attempt to 'correct' supposed defects of hers that "disgust me."


and if she let
Herself be lessoned so, nor plainly set
Her wits to yours, forsooth, and made excuse--
E'en than would be some stooping; and I choose
Never to stoop.


Browning suggests the madness that lies beneath the duke's controlled surface in his belief that his wife treated him no differently from other men and implies his desire for a total monopoly of her attention.


Oh, sir, she smiled, no doubt,
Whene'er I passed her; but who passed without
Much the same smile? This grew; I gave commands;
Then all smiles stopped together. There she stands
As if alive.


With her death, the duke is in complete control of the image of his wife. No other man can view her likeness without his permission. Yet, he seems more than a bit concerned that the emissary of the wealthy count, whose daughter and dowry he hopes to gain, might be able to grasp the terrible truth in the evocative painting of Fra Pandolf.

The duke did not kill the duchess himself, but he had her killed. He tells the envoy who has come to arrange another marriage that

I gave commands;
Then all smiles stopped together. There she stands
As if alive.


The smiles stopping altogether indicates that due to the duke's commands, the duchess was killed. We know from his account that she was not the type of person to stop smiling while alive: she had a natural exuberance and love of life and people. Certainly, too, she cannot be alive if he is trying to remarry.

The duke, as he states in his dramatic monologue, simply couldn't bear that the duchess was kind and attentive to people other than himself. He prefers her as the static art object she is in the portrait rather than as the living person she was, a young woman he could never quite control.

That would certainly appear to be the case. The count is going to marry his daughter off to the duke and has sent an emissary to negotiate the impending nuptials. The duke shows the emissary a picture of his late wife, the duchess. As he discusses the painting, the full extent of the duke's loathing for his late wife becomes disturbingly clear. One of the things the duke hated about his wife was the way that she was so easily pleased, shamelessly flirting with every man who set eyes on her:

She had A heart—how shall I say?—too soon made glad, Too easily impressed; she liked whate’er She looked on, and her looks went everywhere. Sir, ’twas all one! My favour at her breast, The dropping of the daylight in the West, The bough of cherries some officious fool Broke in the orchard for her, the white mule She rode with round the terrace—all and each Would draw from her alike the approving speech

An even worse offense, in the duke's eyes, is the fact that his late wife seemed to place trivial gifts from other men on the same level as the ancient noble title he'd graciously bestowed upon her by marriage:

Somehow—I know not how—as if she ranked My gift of a nine-hundred-years-old name With anybody’s gift.

The duchess flashed her sweet smile indiscriminately in all directions. But that all changed for good when the duke put his foot down and started giving her orders. Then she stopped smiling altogether. The rather frightening implication is that the duke was somehow responsible for the duchess's death. What's even more chilling about the duke's rant against the last duchess is that we're not even sure if any of her behavior was real or imagined. It's difficult to shake off the sense that this was all in the duke's mind— that in his unhinged, jealous state he mistook his wife's pleasant demeanor with other men as evidence of serial infidelity.
https://www.poetryfoundation.org/poems/43768/my-last-duchess

In Mary Shelley's Frankenstein, what are Henry Clerval's strengths and weaknesses?

Victor Frankenstein describes his best friend, Henry Clerval, as a "boy of singular talent and fancy."  He wrote a fairy tale at the tender age of nine, and he read voraciously.  He would compose plays with various popular characters from his favorite stories for Victor, Elizabeth, and himself to act out.  In other words, Henry's strengths were his imagination, his writing ability, and his ability to truthfully depict human lives in his own creative works.  He also, as a young man, nurses Victor back to health when Victor becomes very ill after the creation of his monster.  Henry was nurturing and gentle and kind.
In terms of his weaknesses, he is, perhaps, too trusting.  He does not question his friend's integrity or intentions even when there is reason to do so; he only goes along with whatever Victor seems to need or want.  Had he questioned Victor about his real motives in wanting to delay his marriage to Elizabeth, it is possible that Victor would have revealed to him that he'd created a monster and was now tasked with making its mate.  Henry might have been able to protect himself or even distance himself from Victor (though it seems unlikely that he would).  It is difficult to find a real weakness in Henry himself as it seems that his biggest mistake was his choice of friend. 

What are the figures of speech used in the poem "Anthem for Doomed Youth" by Wilfred Owen?

There are lots of figures of speech in the second stanza of "Anthem for Doomed Youth," most of which draw on a motif of light and darkness. For example, in the opening line, "What candles may be held to speed them all?", the "candles" are symbolic of remembrance. The rhetorical question implies that these soldiers will not be remembered adequately for their sacrifices.
In the next line, the speaker says that "in their eyes / Shall shine the holy glimmers of good-byes." The light in the eyes of the soldiers here might be symbolic of the hope with which they set out for war. The fact that the light only "glimmers" suggests that it is a weak, faint hope. The adjective "holy" to describe the "glimmers" of light alludes to the purity and innocence of the boys setting out for war.
In the following line, the speaker says that "the pallor of girls' brows shall be their pall." A pall is a piece of cloth draped over a coffin at a funeral. The metaphor describing the "pallor of girls' brows" as the soldiers' pall implies the deaths of the soldiers will be marked by the sickness of the girls they leave behind.
The concluding line of the poem, "And each slow dusk a drawing-down of blinds," uses symbolism and imagery to emphasize the number of deaths consequent of war. The dusk is a time of the day when light is fading to be replaced by darkness. Dusk is thus usually symbolic of death or dying. This image of darkness is then compounded by the image of the "drawing-down of blinds." The impression of darkness alludes to the lives of the soldiers being extinguished. And these deaths are as inevitable as is the setting of the sun.

Some of the figures of speech employed by this poem include simile, personification, and alliteration. In the first line, the speaker asks, "What passing-bells for these who die as cattle?" He compares the young men who die in war to cattle, via simile, in order to emphasize the way they seem to be slaughtered, thoughtlessly, and by the thousands. A simile is a comparison of two unalike things using the word like or as.
In the next few lines, the guns are personified as feeling a "monstrous anger" and the rifles are "stuttering" while they "patter out their hasty orisons"; orisons are prayers, and so these lines personify the rifles by stating that they can pray. Personification is when something nonhuman is granted human characteristics. Later in this stanza, the "wailing shells" are personified as "choirs" that possess a "voice of mourning."
Alliteration is the repetition of the initial consonant sound in words, and it is often used to mimic or enhance the words' actual meaning. In the third line, the phrase "rifles' rapid rattle" is an example of alliteration. We can read the repeated "r" sound as echoing the sound guns make when fired over and over.

What is the syntactic function of the noun phrases above in their respective clauses (see text)? a) The media is one of the most powerful weapons in this society (line 1) In this sentence, we deal with only one main clause where The media function as the subject. b) The most important thing is to decide what the purpose of the interview is for you. (line 14) c) If another colleague is better than you on television and radio, then push him or her forward. d) You should insist on meeting the other people involved before the discussion starts e) at least try to find a quiet place with a plain background.

 Syntax refers to the arrangement of different parts of speech according to a set of rules about patterns and order. That is, in English syntactical function refers to the grammatical constructions of words and their arrangement in a sentence. For, as a syntactic language, English makes use of this system of ordering words (especially nouns) to indicate relationships that convey meaning. (Other languages sometimes change the spelling of nouns in order to convey meaning or case, a process called declension.)
 
Here is the syntactic function of the following noun phrases given above: 
(a) (This one has been completed as described above.)
(b) The most important thing is to decide what the purpose of the interview is for you.
This sentence is also a simple sentence composed of one main clause. The syntactic function of the words in bold is that of the subject of the sentence. The noun thing is the simple subject, and "The most important" modify this subject. [The=an article, most=adverb of degree which qualifies important, and important = an adjective]
(c)  If another colleague is better than you on television and radio, then push him or her forward. 
This is a complex sentence (an independent clause and a subordinate clause=a complex sentence). another colleague functions as the subject of the subordinate clause which begins with the subordinating conjunction if. [another=adjective, colleague=noun]
(d)  You should insist on meeting the other people involved before the discussion starts.
Since "the other people involved" is all in bold together, the implication here is that "involved" is attached to people as a past participle acting as a limiting adjective for this noun. The words in bold are part of a participial phrase:"meeting the other people involved." Therefore, the syntactical function of the words in bold are as the object of a participle. (meeting the other people involved = a participial phrase.)  As verbals, participles can take objects. [http://grammar.about.com/od/pq/g/partphraseterm.htm}
(Note: Qualifying the type of sentence is a little tricky because traditionalists may argue that this sentence is elliptical because who are is understood, not stated, after the word people and, therefore, begins a subordinate clause. So, according to this argument, the sentence can be read as a complex sentence, rather than a simple sentence with only one main clause as it appears to be when read with "involved" as past participle used as an adjective.) 
https://literarydevices.net/syntax/

https://www.thefreedictionary.com/Syntactic+structure

https://www.thoughtco.com/what-is-a-participial-phrase-1691588

How does Giles Corey get killed?

Giles Corey is pressed to death because he would not enter a plea in court. Elizabeth Proctor tells her husband, John, in act four that Giles knew he'd be convicted if he allowed the court to proceed (which it cannot if he refuses to respond to the charges against him). If the court proceeded, he knew he'd be convicted of witchcraft, and then his property would go up for public auction. By keeping quiet, he allowed his farm to be inherited by his sons. The court decided to "press" him in an attempt to get him to enter a plea. Elizabeth says,

Great stones they lay upon his chest until he plead aye or nay. They say he give them but two words. "More weight," he says. And died.

Although the details of Giles Corey's real life are somewhat different than the way Miller presents them in the play, his death is recorded here with some accuracy. He was, in fact, pressed to death for refusing to enter a plea in court, and pressing was absolutely a legal method for the court to use in such a situation. He would have been stripped of clothes and laid in a kind of shallow trough in the ground, a heavy wooden board placed atop him, and then large stones would be piled on top of it. The goal was to force him to enter a plea, though he never would. Giles even cursed the sheriff before he died, and many believe that the curse actually did work, as that sheriff (and a great many others since then) died of mysterious heart-related causes.

In act 3, Giles Corey interrupts the court proceedings by claiming that he has evidence that Thomas Putnam is influencing his daughter to falsely accuse citizens of witchcraft in order to buy the land of the accused after it has been foreclosed. When Deputy Governor Danforth asks Giles Corey to identify the man who overheard Thomas Putnam speaking to his daughter about George Jacobs, Giles refuses and is charged with contempt of court. Giles Corey is then arrested and thrown in prison after challenging the corrupt court.
In act 4, Elizabeth Proctor visits her husband in prison and tells him about Giles Corey's fate. When Elizabeth tells John that Giles is dead, he initially assumes that Giles was hanged. However, Elizabeth tells her husband that great stones were placed on Giles Corey's chest until he was crushed to death. Giles refused to answer or admit to witchcraft, so that his sons would inherit his land. Elizabeth tells John that Giles's last words were "More weight" (Miller, 135).

Glencoe Algebra 2, Chapter 2, 2.3, Section 2.3, Problem 58

In order to find y and x intercepts, we first need to know does they mean...

What is x intercept ?

It can be represented as point of a line intercepting x axis, if any point is to intercept x axis it's vertical position(y) has to be 0.

What is y intercept ?

if any point is to intercept y axis it's horizontal position(x) needs be 0.

We can determine x intercept by setting y = 0


and y intercept by setting x = 0.

so, for the line -2x+5y=20


1) Y intercept (x = 0) is

-2(0) +5y =20

=> 5y= 20

=> y=4




2) x intercept (y = 0) is

-2x+5(0) =20
=> -2x= 20

=> x = -10


so x= -10 ,y =4 are the intercepts and is plotted with a dot in the graph below

Calculus: Early Transcendentals, Chapter 4, 4.3, Section 4.3, Problem 36

g(x)=200+8x^3+x^4
differentiating,
g'(x)=24x^2+4x^3
g'(x)=4x^2(x+6)
Now let us find our critical numbers by setting g'(x)=0
4x^2(x+6)=0
solving above , x=0 and x=-6
Now let us check sign of g'(x) at test values in the intervals (-oo ,-6) , (-6,0) and (0,oo )
f'(-7)=4(-7)^2(-7+6)=-196
f'(-1)=4(-1)^2(-1+6)=20
f'(1)=4(1)^2(1+6)=28
Since f'(-7) is negative , function is decreasing in the interval (-oo ,-6)
f'(-1) is positive so function is increasing in the interval (-6,0)
f'(1) is positive so function is increasing in the interval (0,oo )
Since f'(-7) is negative and f'(-1) is positive , therefore Local minimum is at x=-6 . Local minima can be found by plugging in x=-6 in the function.
f(-6)=200+8(-6)^3+x^4=-232
Local minimum=-232 at x=-6
Now to find the intervals of concavity and inflection points,
g''(x)=4(x^2+(x+6)(2x))
g''(x)=4(x^2+2x^2+12x)
g''(x)=4(3x^2+12x)
g''(x)=12x(x+4)
set g''(x)=0
x=0 , x=-4
Now let us check the concavity in the intervals (-oo ,-4) , (-4,0) and (0,oo ) by plugging test values in g''(x).
g''(-5)=12(-5)(-5+4)=60
g''(-2)=12(-2)(-2+4)=-48
g''(1)=12(1)(1+4)=60
Since g''(-5) is positive , function is concave up in the interval (-oo ,-4)
g''(-2) is negative , so the function is concave down in the interval (-4,0)
g''(1) is positive , so the function is concave up in the interval (0,oo )
Since the concavity is changing so x=0 and x=-4 are the inflection points.

y = 3/2 x^(2/3) , [1, 8] Find the arc length of the graph of the function over the indicated interval.

Arc length (L) of the function y=f(x) on the interval [a,b] is given by the formula,
 L=int_a^bsqrt(1+(dy/dx)^2) dx, if y=f(x) and  a <=  x <=  b,
Now let's differentiate the function,
y=3/2x^(2/3)
dy/dx=3/2(2/3)x^(2/3-1)
dy/dx=1/x^(1/3)
Now let's plug the derivative in the arc length formula,
L=int_1^8sqrt(1+(1/x^(1/3))^2)dx
L=int_1^8sqrt(1+1/x^(2/3))dx
L=int_1^8sqrt((x^(2/3)+1)/x^(2/3))dx
L=int_1^8(1/x^(1/3))sqrt(x^(2/3)+1)dx
 Now let's evaluate first the indefinite integral by using integral substitution,
Let t=x^(2/3)+1
dt=2/3x^(2/3-1)dx
dt/dx=2/(3x^(1/3))
dx/x^(1/3)=3/2dt
intsqrt(x^(2/3)+1)(1/x^(1/3))dx=int3/2sqrt(t)dt
=3/2(t^(1/2+1)/(1/2+1))
=3/2(t^(3/2)/(3/2))
=t^(3/2)
=(x^(2/3)+1)^(3/2)
L=[(x^(2/3)+1)^(3/2)]_1^8
L=[(8^(2/3)+1)^(3/2)]-[(1^(2/3)+1)^(3/2)]
L=[5^(3/2)]-[2^(3/2)]
L=11.18033989-2.828427125
L=8.351912763
Arc length (L) of the function over the given interval is ~~8.352
 

Calculus of a Single Variable, Chapter 2, 2.4, Section 2.4, Problem 72

Hello!
y(x) = (1/x) + sqrt(cos(x)) .
cos(x) must be >=0 and cos(x) < 0 for pigtxgtpi/2 (at the right neighborhood of pi/2 ). So there can be only the left derivative.
Check that y(pi/2) = 2/pi :cos(pi/2) = 0 and y(pi/2) = 2/pi + 0 = 2/pi .
Next, find the derivative of y:y'(x) = -(1/x^2) + (1/2)*(cos(x))^(-1/2)*(-sin(x)) .
For x-gtpi/2-0
y'(x) ->-oo
(1/x^2 is finite, sin(x) is finite and (cos(x))^(-1/2)-gt+oo )
and therefore the tangent line is vertical, its equation is x=pi/2 .
The graph is here: https://www.desmos.com/calculator/4owqqw7egh

Why is "I Have a Dream" considered the defining moment of the American civil rights movement?

The timing, content, setting, and legacy of Dr. King's iconic speech mark its delivery as a defining moment of the American Civil Rights Movement.
Dr. King gave the speech at the foot of the Lincoln Memorial in America's capital in August of 1963 during the March on Washington for Jobs and Freedom. A quarter of a million people gathered for a nonviolent protest of social conditions for African Americans, and the setting was symbolic. President Abraham Lincoln had signed the Emancipation Proclamation one hundred years earlier.
Dr. King's thesis was that the promise of the Emancipation Proclamation had not been fulfilled, because African Americans had still not received their full rights as American citizens.
Less than a year later, President John F. Kennedy proposed the Civil Rights Act, which banned discrimination based on race, color, religion, national origin, or gender. Dr. King's speech paved the way for moving that legislation along. The law was designed to end manipulation of voting requirements that kept African Americans from the polls and to desegregate motels, hotels, schools, and so on. It also outlawed discrimination against African American job seekers.

What are some quotes that illustrate jealousy in The Merchant of Venice?

There's a very good quotation about jealousy in act 3, scene 2. Bassanio is about to open the lead casket as part of the Three Caskets test set by Portia's father. According to the rules of the test, whoever chooses the correct casket will take Portia's hand in marriage. Bassanio—with a little prompting, it must be said, from Portia—has chosen the correct box, the lead one. Portia's heart is positively overflowing with a mixture of love and relief. Bassanio's made the right choice and will soon be hers forever more.
So strong is the love that Portia feels for Bassanio at that moment that all her doubts and worries, all her feelings of jealousy have been suddenly driven away:

How all the other passions fleet to air, As doubtful thoughts, and rash-embraced despair, And shuddering fear, and green-eyed jealousy! (Emphasis added)

There's often a fine line between love and jealousy. But as Portia shows in the above quotation, it is only true love that can vanquish the green-eyed monster.

What are the major themes of The White Castle?

The overriding theme of The White Castle is the fundamental unity of humanity, one that transcends (what for Pamuk are) the artificial differences of race, color, culture, and class that human beings put between themselves as barriers. This theme is established in the book's central relationship between Hoja and the anonymous narrator. Not only do they physically resemble one another, they even come to anticipate each other's thoughts and concerns. 
The book's central theme is that of identity. Hoja and the narrator's respective identities are so fluid and so changeable that they imperceptibly merge into one. At various points, it no longer becomes possible to speak of two separate individuals. As we reach the end of the story, Hoja and the narrator exchange clothes and go their separate ways. In doing so, they put on the mantle of each other's outward identities: Hoja as a Venetian slave and the narrator as Hoja, Ottoman court astrologer.
The nature of power is another major theme. Initially, the narrator is a slave, and Hoja is unequivocally the master. However, as the story progresses, their dynamic shifts back and forth rapidly. What Pamuk is trying to do here is get us to see that power does not reside in the identities imposed upon us by society, it comes from within, from the common humanity that each and every one of us shares.
The ultimate ease with which the two men exchange identities forces us to question the dominant Western conception of the self. Since Descartes revolutionized philosophy in the 17th century, the self has tended to be construed as isolated, set against a world of nature, objects, and other selves, which makes it becomes difficult to establish any kind of meaningful connection. Here the problem is dissolved. We are all one. The self, as conceived by Descartes, is simply another artificial construct of the human mind, one used to keep us apart and forever in conflict.
Finally, Pamuk explores the theme of the often tense relationship between East and West in modern day Turkey. Constantinople (present day Istanbul) is the ideal location in which to do this, as it straddles the continents of Europe and Asia. Pamuk, as a European from an overwhelmingly Asian country, embodies the paradox which lies at the heart of Turkish national identity. As an ardent secularist, Pamuk identifies with the Venetian slave to a considerable extent. His capture at the hands of a stagnant, corrupt empire, riddled with obscurantism and superstition, ably symbolizes the present day plight of the secular Turkish intellectual.

1.What objections did George Herbert Mead have to behaviorism? 2.How did he propose studying these internal attitudes? 3.Regarding Mead's concept of the "act," does Mead give priority to the social aspect of the act or the psychological aspect of the act?

1. What objections did Mead have to behaviorism?
George Herbert Mead objected to the behaviorist theories of John Watson, who held that only observable behavior could be studied. Watson held that environmental factors determined behavior; therefore, it was impossible to study mental experiences. Mead, however, held that the inner experiences of people should be considered, too.
2. How did Mead propose studying these internal attitudes?
Mead held that such factors as inner experience, consciousness, and mental imagery were contributors to human behavior. Therefore, he developed the notion of "significant others," people who are meaningful and whose judgments are important to the developing individual. For, children first shape their behavior according to norms modeled by significant others. After they reach adulthood, guidelines are made on their own. Mead contended that the mind could be included in the study of social behavior because the individual responds in behavior to stimuli provided by "significant others."
3. Regarding Mead's concept of the "act," does Mead give priority to the social aspect of the act or the psychological aspect of the act?
Mead intended to study the social aspect of behavior since he examined the psychological aspect only as stimulus for actions and socialization.
Mead held that the mind should be included in the study of social behavior because the individual responds to stimuli provided by "significant others." For Mead, thinking is only explained by its relationship to behavioral traits.

What is one important lesson Ponyboy learns during the novel? Why do you believe this is important?

Ponyboy learns a lot of life lessons in this short novel, so feel free to pick one that resonates with you and explain why that is so. Personally, I feel that learning that the Greasers and Socs have more in common than he once thought is the most important thing that Ponyboy learns. Cherry introduces him to this concept by telling him that things are "rough all over." Ponyboy admits that he believes her, but he truly learns it as events in the novel unfold. By the end of the novel, Ponyboy is able to understand what Cherry meant by saying that Greasers and Socs aren't that different. They each have struggles. By the end of chapter 7, Ponyboy is not even willing to call Randy a Soc. Ponyboy says that Randy is just another guy.

"What'd he want?" Two-Bit asked. "What'd Mr. Super-Soc have to say?"
"He ain't a Soc," I said, "he's just a guy. He just wanted to talk."

How does the author develop the idea of freedom of choice in The Other Wes Moore?

The author develops the idea that the freedom of choice is real but it's affected by external factors that a person might not have control over. This can change the entire trajectory of a person's life.
Wes Moore grew up a few blocks away from the other Wes Moore. They had very different lives, however. The author had a life that supported his ambitions and helped him find success; the other Wes Moore didn't have the same support and ended up in prison.
Both men are the result of their choices. However, the other Wes Moore wasn't a person who always mad bad decisions. At one point, he opted to go to Job Corps in the hope that he'd be able to find a good job. When that didn't pan out, he turned to crime.
The author, on the other hand, had less of a concern about his future. He knew he'd have support. Even if things didn't work out, it was less likely that he'd turn to crime because of his background. He had the freedom of choice—like the author—but it was less likely that he was going to have a successful outcome because he didn't have the same variety of choices and support.

The idea of freedom of choice is presented in the book in a complex, subtle way. Although the other Wes Moore grew up in a rough neighborhood, living in poverty and without any parental guidance, he still had freedom of choice, albeit severely restricted. No one forced him to lead a life of crime, to get involved with selling drugs on the mean streets of Baltimore. And no one forced him to get involved in the events leading up to the murder of a police officer. The other Wes Moore may not have had many choices in life, but he still had them.
By the same token, the author's more privileged background didn't prevent him from making bad choices himself. When he winds up at military school, instead of seeing the experience as a great opportunity to change his life, he doesn't take it in the least bit seriously. He fails to get with the program and tries to go AWOL four times. Yet thankfully for him, he makes the crucial decision to stay at military school and knuckle down to some serious work. In other words, unlike the other Wes Moore, he redeemed his bad choices in life with a good one.

One of the author's main points is that the other Wes Moore did not have a great deal of freedom in the choices he made. The other Wes Moore was raised in an environment in which drug dealing was perhaps the clearest and easiest way to make money, and the other Wes Moore did not have access to educational and other opportunities that could have paved the way for a different life for him. 
The author makes the point that chance or luck plays a critical role in determining the paths of African American men in this society. The author was fortunate to have a mother and grandparents who supported him and who helped him get on a better path by emphasizing education and by helping him make good choices, even when he faltered (for example, when the author did not do well in private school, his mother sent him to a military school). The other Wes Moore, through no fault of his own, did not have access to these types of chances, and his freedom of choice was limited. 

Precalculus, Chapter 5, 5.5, Section 5.5, Problem 9

cos(2x)-cos(x)=0 , 0<=x<=2pi
using the identity cos(2x)=2cos^2(x)-1
cos(2x)-cos(x)=0
2cos^2(x)-1-cos(x)=0
Let cos(x)=y,
2y^2-y-1=0
solving using the quadratic formula,
y=(1+-sqrt((-1)^2-4*2(-1)))/(2*2)
y=(1+-sqrt(9))/4=(1+-3)/4=1,-1/2
:. cos(x)=1, cos(x)=-1/2
cos(x)=-1/2
General solutions are,
x=(2pi)/3+2pin, x=(4pi)/3+2pin
Solutions for the range 0<=x<=2pi are,
x=(2pi)/3 , x=(4pi)/3
cos(x)=1
General solutions are,
x=0+2pin
solutions for the range 0<=x<=2pi are,
x=0 , x=2pi
combine all the solutions ,
x=0, x=2pi , x=(2pi)/3 , x=(4pi)/3

How is gender inequality played out in the home?

The Second Shift describes the problems created by expectations placed on women who work full-time but also take on the bulk of the household duties. According to the book, once more women began to enter the workplace so that the family could have two incomes and better meet the increasing financial demands of daily life, "the second shift" emerged.
When men were the primary breadwinners and women were stay-at-home mothers, the women were responsible for the upkeep of the home; women performed childcare duties and also maintained the home by cooking and cleaning. Men would work full-time, come home, and be tended to by their wives. When more women began working full-time, however, the roles at home did not adjust accordingly. Therefore, women were performing a "second shift" of work when they returned home from their full-time jobs. They were working all day, then coming home to care for children, cook dinner, and perform other household tasks. The studies found that men were not contributing much, while women were stressed out and exhausted by their double duties. The Second Shift also argues that women are more often found multitasking, so they also perform proportionally more work than men in the home.
It is possible that today the divide is not quite as large as it used to be between men's and women's duties in the home. Younger parents may now be dividing work more equally, and it is somewhat more common now for men to split childcare duties with their wives. We would need updated studies to see how much the problem has developed in the decades since The Second Shift was first published.

Single Variable Calculus, Chapter 6, 6.2, Section 6.2, Problem 28

Find the value generated by rotating $\mathscr{R}_3$ about $OC$


If you rotate $\mathscr{R}_3$ about $OC$, by using horizontal strip, you will form a circular washer with outer radius $\sqrt[3]{y}$ and inner radius $y^2$. Thus, the cross sectional area can be computed by substracting the area of the outer circle to the inner circle. $A_{\text{washer}} = A_{\text{outer}} - A_{\text{inner}} = \pi (\sqrt[3]{y})^2 - \pi (y^2)^2$. Therefore, the value is...


$
\begin{equation}
\begin{aligned}
V &= \int^1_0 \pi \left[ (\sqrt[3]{y})^2 - (y^2)^2 \right] dy\\
\\
V &= \pi \left[ \frac{y^{\frac{5}{3}}}{\frac{5}{3}} - \frac{y^5}{5} \right]^1_0\\
\\
V &= \frac{2\pi}{5} \text{cubic units}
\end{aligned}
\end{equation}
$

College Algebra, Chapter 2, Review Exercises, Section Review Exercises, Problem 10

Find an equation of the circle that contains the points $P(2,3)$ and $Q(-1,8)$ and has the midpoint of the segment $PQ$ as its center
Recall that the general equation for the circle with center $(h,k)$ and radius $r$ is...
$(x - h)^2 + (y - k)^2 = r^2$

To get the center, we use midpoint formula...

$
\begin{equation}
\begin{aligned}
m_{PQ}, \quad x &= \frac{2-1}{2} = \frac{1}{2}\\
\\
y &= \frac{3+8}{2} = \frac{11}{2}
\end{aligned}
\end{equation}
$

Therefore, $\displaystyle \left( \frac{1}{2}, \frac{11}{2} \right)$
Thus, $\displaystyle \left( x - \frac{1}{2} \right)^2 + \left( y - \frac{11}{2} \right)^2 = r^2$
Since the circle pass through $P(2,3)$

$
\begin{equation}
\begin{aligned}
\left( 2 - \frac{1}{2} \right)^2 + \left( 3 - \frac{11}{2} \right)^2 &= r^2\\
\\
\left( \frac{3}{2} \right)^2 + \left( \frac{-5}{2} \right)^2 &= r^2\\
\\
r^2 &= \frac{17}{2} = 8.5
\end{aligned}
\end{equation}
$

Thus, the equation of the circle is...
$\displaystyle \left( x - \frac{1}{2} \right)^2 + \left( y - \frac{11}{2} \right)^2 = \frac{17}{2}$

Should the governor have more power? What additional powers should the governor have? How would you give them to him or her?

Just as the federal government is split into three branches, state government is divided into a judicial branch, legislative branch, and executive branch. The legislative branch passes laws, the judicial branch interprets laws, and the executive branch carries out laws. At the state level, the governor represents the executive branch and is responsible for carrying out laws.
The governor's responsibilities include signing laws passed by the state legislature, serving as commander in chief of the state's military forces (if they have any), convening the state legislature for special purposes, delivering an annual State of the State address (similar to the President's State of the Union Address), providing the state legislature with a recommended annual budget for their approval, granting pardons to state prisoners, and declaring special elections to fill vacant positions in state government. 
The question asks what powers you would give the governor in addition to those that they already have. This would mean taking powers that are otherwise granted to the state legislature and judiciary or the federal government and giving them to the governor. It requires you to first consider whether you think that the governor currently has enough power. If you believe that the governor should have additional powers, you then must consider what those would be. 
If you feel that the governor should have greater power to interpret the law, then you would remove power that is currently vested in the judiciary and give it to the governor. If you feel that the governor should have greater law making power, you would take power from the legislature and give it to the executive. 
My suggestion is to look at your specific state and see what specific powers are vested in the judiciary and legislature (specifically those belonging to the state house of representatives and state senate individually) before answering the question. At that point, you will have a better idea which specific responsibilities other branches of government have that you feel should be given to the governor.

What are some inventions and works by Leonardo Da Vinci that impacted humankind and society?

When we use the term "Renaissance Man" today, we still first think of Leonardo da Vinci as the epitome of the moniker, though he lived over 500 years ago.
Da Vinci created new techniques in painting, particularly sfumato, the smoky quality present in many of his works which depicted a receding background. However, he also envisioned many ideas in science and technology long before the tools and scientific theories were available to bring his visions to fruition.
In his sketchbooks, there are plans for the following inventions: the helicopter, the parachute, the armored car, the giant crossbow, the triple-barrel cannon, a more accurate clock, a self-propelled cart (the first robot), early scuba gear, and a revolving bridge designed to help armies escape from and foil the forces pursuing them.
Da Vinci is not credited with inventing many of these things. He is credited, instead, with thinking of them first. For example, the first helicopter did not take flight until 1939. 
We are mainly impacted by da Vinci's ideas about classical beauty. His drawing Vitruvian Man depicts the ideal proportions of the male body. We are also inspired by the voracity of his interests and the wide breadth of his ideas.

What is a detailed analysis of Elizabeth Jennings' poem "Reminiscence" in terms of summary, language, tone, imagery, and themes?

Summary
The poem describes the author’s childhood and the character of her love. The last wasn’t complicated but more gentle as if she “weave a web”. This feeling is compared with her adult world in which the author becomes “subtle” and “fretting at the thought”. This means the author looks for some sense of things, including love. The adult world becomes “stony staff” which also means that the concept of love is more complicated. For the author, childhood had less clarity but was full of new senses and unexpectedness.
Language
The author uses simple language but comparing her adult world and childhood implements bright imagery. For instance, epithets like “cloudless and gentle” describe the feeling of childhood love while adulthood is more like “shapeless stony”. This way the author appeals to our senses.
Theme
Generally, this poem is a lyrical comparison of two worlds of a child and an adult. Both are still in one person who remembers and misses someone she was. She’s tired of being too “subtle” and thinking of serious things instead of sensing the world around her.
Tone
The whole poem is full of the author’s yearning and reminiscence of her childhood.
Imagery
The metaphor “web to weave” stands out among other figures of speech and refers to the easiness and levity of being a child. Another adulthood metaphor “shapeless stony stuff” contrasts the gentleness of immaturity. The diversity of life is realized via “glittering landscape” metaphor.

As the title indicates, in this poem, Jennings remembers her childhood. She contrasts her childhood state of mind with her adult state. As a child she lived without analyzing her world too deeply and that was a happier state for her. Then she did not "fret at thought" (in other words, worry) or try to figure everything out: she simply lived and did not try to "whittle a pattern" (make sense of everything). Adult thinking causes her anxiety, making her sometimes "numb with fear." She looks back nostalgically and with longing to the time when she "would find the day/Long as I wished its length or web to weave."
The theme of this poem is the longing for and idealizing of the simpler days of childhood. While normally we think it is good to become more clear, analytical, and sophisticated in our thinking, she prefers a time when her mind was not so "clear," when she simply sensed and existed more than thought. Thinking is a burden to her: she is "confused" now that she has "grown too subtle."
The tone of the poem is gentle and lyrical, while the imagery contrasts the soft images of her child's mind with the hard images of her adult mind. Her child self was "happy" and could be loved in a way that was "cloudless and gentle." The day was like "web," a soft, delicate object.
Her adult mind is described with harder images: it is trying to "whittle ... stony stuff." Her mind's "landscape" is now "glittering." The word glittering conjures hard objects like stones or gems that can cut and hurt.  

In Shakespeare's Macbeth, what is "nose-painting"?

The short answer to this question is that we don't actually know for certain what Shakespeare meant by this term, a colloquialism whose meaning has not survived. However, we can certainly speculate as to what it indicates, based on context. The Porter says that drink "especially provoke[s] . . . nose-painting, sleep and urine." Some scholars have suggested that "nose-painting" simply refers to the reddening of the nose which occurs alongside a generally flushed face when one has drunk too much, but this does not explain why the Porter then goes on to discuss "lechery."
He comments to Macbeth that drink "provokes the desire, but it takes away the performance"—that is, alcohol makes people want to copulate but also makes it difficult for them to do so. The positioning of this discussion strongly suggests that "lechery" has been mentioned in his original list of the things drink provokes; thus, we could assume that "nose-painting" signifies lechery and is sexual slang. There are a few other places in Shakespeare's works where "nose" seems to have a sexual connotation (Othello says to Cassio, whom he believes to be sleeping with his wife, "I see that nose of yours, but not the dog I shall throw it to," for example). So we may infer that, if "nose" means "penis," "nose-painting" is a slang term for copulation. (Compare other slang terms involving the insertion of a pen into an inkwell, for example. You can probably think of several modern slang terms which are similar.)

In Act 2, Scene 3 of Macbeth, on the second page, the Porter says that drinking provokes "nose-painting, sleep and urine." While we know what the last two things are, it is a little more unclear what the term "nose-painting" refers to. While many people assume that it means the turning red of your nose when you drink, other sources point to the real meaning being a little more bawdy than that.
Shakespeare uses many euphemisms to refer to sexual acts, and this might be no exception. If we look at the context surrounding the quote, we get a clue as to what it might signify: "Lechery, sir, it provokes and unprovokes; it provokes the desire, but it takes away the performance... makes him stand to and not stand to." If we take this to mean that he is using these phrases as a metaphor for sexual behavior, such as the desire to perform and not to perform and the ability to "stand to" (achieve an erection), then we might assume that painting one's nose could refer to some sort of sexual act. 
Furthermore, the term "lechery" is used, and this is a strong indicator of a sexual reference. Lechery is defined as excessive sexual desire, or lustfulness. This seems to suggest that although the drunk person in question has the desire to engage in sexual activity, he will be unable to "get it up," so to speak, and will thus be unable to perform sexually. 

What are Gar's emotions toward his departure?

Gar is excited to go to Philadelphia but also nervous about what it means for his future and disappointed by the reactions of those around him.
Philadelphia offers a host of options to Gar—it offers the chance of a better life. The life he had in Ireland offered nothing but dead ends. However, he isn't quite ready to put it or his family there behind him. He loves them despite the troubles he's experienced. However, it's clear that he's trying to make himself excited for his journey and to convince those around him that he's ready to go.
One problem is that he doesn't yet know what life in Philadelphia will be like. This gives him a sense of uneasiness as he dreams of a somewhat blank future. He believes that things have the potential to be better—but it's a scary unknown.
The other thing holding him back from only feeling happiness is that he'll have to leave the people he loves, like his father. S.B. doesn't seem outwardly upset about Gar leaving, which hurts him. However, it's clear that his father is going to miss him greatly once he leaves for Philadelphia.

Gar has mixed emotions about his departure as demonstrated by both Gar Public and Gar Private. In the opening scene, Gar is optimistic about his departure to Philadelphia the following day and fantasizes about the opportunities that await him there. His ambitions and desire for a better life can no longer be contained by the monotony and hopelessness of Ballybeg. To him, his father and the group of friends symbolize the type of life that he seeks to escape from.
However, Gar expresses his disappointment on several occasions due to the fact nobody shows concern about his departure. He is particularly pained by his father’s lack of concern. In fact, during a conversation with his father, he pleads in his thoughts for his father to say one unpredictable thing that would cause him to stay in Ballybeg. Gar also expresses to Madge his reservations about leaving. It is therefore clear that, even though Gar looks forward to leaving for Philadelphia, he also has concerns about whether or not life would turn out for the best.

What is the difference between the Leeuwenhoek microscope and the Hooke microscope?

Robert Hooke did research that contributed to the Cell Theory. He actually coined the term "cell" in his book "Micrographia", which was based on observations of cork. The dead plant cells looked like cells that monks lived in--rectangular boxes.
In the late 1600's he worked with a light microscope that he helped to design. It contained an eyepiece, a barrel, a focusing screw, an objective, a specimen holder and was accompanied by a light source from an oil lamp. This lamp gave off light which passed through a flask filled with water to help illuminate specimens he was observing. 
Anton van Leeuwenhoek designed his own simple microscopes which were capable of between 70x and 250X magnification. He designed his own lenses which were of an excellent quality. Although not technically a scientist, he extensively studied the microscopic world and kept excellent records of his observations. His microscopes were considered to be superior to all other models of the time period.
The advent of the microscope changed the way the world was viewed at the time in terms of its living inhabitants. It opened up a new world invisible to the naked eye.
The links I have provided have pictures and details regarding each microscope.
http://www.history-of-the-microscope.org/history-of-the-microscope-who-invented-the-microscope.php

http://www.history-of-the-microscope.org/robert-hooke-microscope-history-micrographia.php

How was the Catholic Church corrupt in this period of the Renaissance?

Leaders of the Catholic Church during the Renaissance era certainly engaged in corrupt behaviors and acts. High ranking leaders of the church lived lavish lifestyles while they preached the holiness of a humble and modest life. Affairs, adultery, and pedophilic behaviors by church leaders were all too common.
One of the most notable examples of the Catholic Church during the Renaissance era was in their selling of indulgences. Indulgences were pieces of paper that church leaders would sell as an erasure of one's sins. The more indulgences one bought, the more one's soul was in good moral standing with God. Church leaders directly profited from selling indulgences. This corruption created a dynamic in which people with wealth were told they had more access to spiritual purity, and subsequently, Heaven, than poor people.
The Catholic Church was so powerful that it was essentially the law of the land is some areas of Western Europe in the 16th century. Anyone who defied the teachings of the church through presenting a different narrative were subject to be burnt at the stake.

The Catholic Church was quite corrupt in the Middle Ages and early Renaissance. Many popes looked at growing personally wealthy and powerful from their holy office and they did not speak much about spiritual matters. Priests and nuns who took orders of celibacy were sometimes promiscuous. There were even well-documented cases of popes having illegitimate children. In many towns the clergy were the most literate people, but some priests did not even know how to read, and they too looked to gain riches and power from their positions. While much of the clergy stayed true to its religious mission, there were enough members who didn't to provide satirists with plenty of material.
The Decameron takes place during the plague and it is a collection of tales told by young people who are leaving for the countryside in order to avoid the sickness. Since the Church was still the most important institution in Europe at the time, many of the tales in the book humorously describe the abuses of the Church.

College Algebra, Chapter 4, 4.2, Section 4.2, Problem 38

Factor the polynomial $P(x) = x^4 - 2x^3 + 8x - 16$ and use the factored form to find the zeros. Then sketch the graph.
Since the function has an even degree of 4 and a positive leading coefficient, its end behaviour is $y \rightarrow \infty \text{ as } x \rightarrow -\infty \text{ and } y \rightarrow \infty \text{ as } x \rightarrow \infty$. To find the $x$ intercepts (or zeros), we set $y = 0$.


$
\begin{equation}
\begin{aligned}
0 &= x^4 - 2x^3 + 8x - 16\\
\\
0 &= x^4 - 2x^3 + (8x - 16) && \text{Group terms}\\
\\
0 &= x^3(x-2)+8(x-2) && \text{Factor out } x -2\\
\\
0 &= (x^3+8)(x-2) && \text{Factor out } x^3 + 8
\end{aligned}
\end{equation}
$



By zero product property, we have
$x^3 + 8 = 0$ and $x - 2 = 0$

Thus, the $x$-intercept are $x = -2$ and $x = 2$

In what ways did the Eastern Empire change from the Western Empire?

I will assume the question concerns the Roman Empire.
The Roman Empire grew vast and became harder to manage from Rome. This forced Emperor Diocletian to divide the Empire into two manageable territories, the Eastern and Western Roman Empires. The Western Empire maintained the administration center in Rome, while the Eastern Empire established Byzantium/Constantinople as its administrative center. However, after the dissolution of the Greater Roman Empire, the Eastern Empire developed its own character. The Eastern Empire adopted Greek over the traditionally established Latin. Christianity was established as the Empire's official religion and other religious practices including the traditional Roman pagan practices were declared illegal. The Eastern Empire also sought to ban Iconoclasm (worship of religious icons and imagery). The situation caused the continued rift between the Western and Eastern Empires religiously and politically.
https://www.ancient.eu/Western_Roman_Empire/

https://www.britannica.com/place/Byzantine-Empire

Calculus of a Single Variable, Chapter 2, 2.2, Section 2.2, Problem 67

The tangent line must touch a point on the f(x) function.
Set both equations equal to each other.
kx^3 = x+1
Take the derivative of f(x) to find another relationship with k and x. The k is a constant, so do not eliminate it!
f(x)= kx^3
f'(x)= 3kx^2
Set this equal to the slope of the tangent line given, 1.
1= 3kx^2
Solve for k, since this is easier than solving for x.
k = 1/(3x^2)
Substitute the k back into the first equation.
(1/(3x^2))x^3 = x+1
x/3 = x+1
Multiply three on both sides.
x= 3x+3
-2x =3
x= -3/2
Re-substitute the x back to the first equation to solve for k.
k(-3/2)^3 = -3/2+1
k(-27/8) = -1/2
k=1/2 * 8/27 = 4/27

Calculus: Early Transcendentals, Chapter 4, 4.3, Section 4.3, Problem 15

You need to determine where the function increases or decreases, hence, you need to verify where f'(x)>0 or f'(x)<0.
You need to determine derivative of the function:
f'(x) = 2e^(2x) - e^(-x)
Putting f'(x) = 0, yields:
2e^(2x) - e^(-x) = 0
2e^(2x) - 1/(e^x) = 0 => 2e^(3x) - 1 = 0 => e^(3x) = 1/2 => e^x = root(3)(1/2)
x = ln root(3)(1/2)
Hence, the function decreases for x in (-oo, ln root(3)(1/2)) and the function increases for x in ( ln root(3)(1/2), oo) .
b)You need to remember that the function reaches it's extrema for x, such as f'(x) = 0.
The function reaches it's minimum point at x = ln root(3)(1/2).
c) The function is concave up for f''(x)>0 and concave down for f''(x)<0.
Evaluating f''(x) yields:
f''(x) = 4e^(2x) + e^(-x)
4e^(2x) + e^(-x) = 0=> 4e^(2x) + 1/(e^x) = 0 => 4e^(3x) + 1 = 0
e^x = root(3)(-1/4) = -root(3)(1/4) impossible since e^x>0 for all x in R.
Hence, the function has no inflection points and it is concave up for x in R , since f''(x) = 4e^(2x) + e^(-x) > 0 for all x in R .

College Algebra, Chapter 9, 9.2, Section 9.2, Problem 56

Determine the product of the numbers $10^{\frac{1}{10}}, 10^{\frac{2}{10}}, 10^{\frac{3}{10}}, 10^{\frac{4}{10}},....., 10^{\frac{19}{10}}$

By Laws of Exponent, we have

$10^{\frac{1}{10} + \frac{2}{10} + \frac{3}{10}, \frac{4}{10} + ..... + \frac{19}{10}}$

To solve for the sum, we use both formulas of partial sums of the arithmetic sequence; solve for $n$, where $\displaystyle d = \frac{2}{10} -\frac{1}{10} = \frac{1}{10}$


$
\begin{equation}
\begin{aligned}

\frac{n}{2} \left[ 2a + (n - 1) d \right] =& n \left( \frac{a + a_n}{2} \right)
&&
\\
\\
2a + (n - 1)d =& a + a_n
&& \text{Multiply both sides by } \frac{2}{n}
\\
\\
(n - 1)d =& a_n - a
&& \text{Combine like terms}
\\
\\
n - 1 =& \frac{a_n - a}{d}
&& \text{Divide by } d
\\
\\
n =& \frac{a_n - a}{d} + 1
&& \text{Add } 1
\\
\\
n =& \frac{\displaystyle \frac{19}{10} - \frac{1}{10}}{ \displaystyle \frac{1}{10}} + 1
&&
\\
\\
n =& \frac{\displaystyle \frac{18}{\cancel{10}}}{\displaystyle \frac{1}{\cancel{10}}} + 1
&&
\\
\\
n =& 19
&&

\end{aligned}
\end{equation}
$


Now we solve the partial sum,


$
\begin{equation}
\begin{aligned}

S_{19} =& 19 \left( \frac{\displaystyle \frac{1}{10} + \frac{19}{10}}{2} \right)
\\
\\
S_{19} =& 19(1)
\\
\\
S_{19} =& 19


\end{aligned}
\end{equation}
$


So the product is

$10^{\frac{1}{10} + \frac{2}{10} + \frac{3}{10} + \frac{4}{10} + ..... + \frac{19}{10}} = 10^{19}$

How do the soliloquies in Hamlet create atmosphere?

Hamlet is a dark play with a mood of foreboding and death hovering in the air. The play opens on a foggy night with rumors of war and the frightening appearance of a ghost. Hamlet's seven soliloquies, which often deal with thoughts of suicide or death, reinforce the dark tone of the play, as well as the tone of deep introspection. This is not simply a revenge play, but a play that thinks deeply about the implications of revenge and death. Hamlet's soliloquies are key to getting us as an audience to slow down, stop, and think about what is going in Denmark's court. They also provide the audience with crucial information about why Hamlet is or is not taking action and offer insights into Hamlet's brooding.
For example, in the "to be or not to be" soliloquy, Hamlet makes clear how distressed he is about the situation the ghost has put him in—so much so that he wishes he were dead rather than having to face that his uncle might have killed his father. But the soliloquy also informs us of Hamlet's religious sensibilities: he fears what might happen to him after death were he to commit suicide. This helps us understand why he doesn't kill Claudius when he sees him as his prayers in Act III, scene 3: as Hamlet explains in this soliloquy, he doesn't want Claudius to die in a state of grace and go to heaven while his father haunts the earth as a ghost:

Now might I do it pat now he is praying,And now I'll do it, and so he goes to heaven.

Hamlet's soliloquy about not killing Claudius is also somewhat ironic, for we as an audience know that Claudius, though seemingly at his prayers, can't repent of his crimes and wouldn't have died in grace.
Hamlet's soliloquy about confronting his mother In Act III, scene 2, gives us crucial information. He says:

'Tis now the very witching time of night,When churchyards yawn, and hell itself breathes outContagion to this world...Soft! now to my mother...Let me be cruel, not unnatural;I will speak daggers to her, but use none

He tells us, his audience, that he will not try to kill her—he will only speak daggers, meaning speak sharply, but not use one. This too is ironic, because she could have benefitted from that information, which she doesn't have—she does think Hamlet is planning to kill her, which is why she cries out, leading to Polonius's death. However, the soliloquy is also important in continuing the mood of darkness and foreboding that permeates the play: Hamlet speaks of a "witching time of night," of "hell" and of "contagion." The mood shows the tenor of Hamlet's thoughts.

Beginning Algebra With Applications, Chapter 5, 5.4, Section 5.4, Problem 72

The table below shows the median weekly salary of a union member for various years.

$\begin{array}{|c|c|}
\hline\\
\text{Year} & \text{Weekly Salary} \\
& \text{(in dollars)} \\
\hline\\
2000 & 696 \\
\hline\\
2001 & 718 \\
\hline\\
2002 & 740 \\
\hline\\
2003 & 760 \\
\hline\\
2004 & 781 \\
\hline
\end{array} $

a. Determine the equation of the line between (2000, 696) and (2004, 781).

We let $(x_1, y_1) = (2000,696)$ and $(x_2, y_2) = (2004, 781)$

Using the slope of the line,


$
\begin{equation}
\begin{aligned}

m =& \frac{y_2 - y_1}{x_2 - x_1}
\\
\\
m =& \frac{781-696}{2004-2000}
\\
\\
m =& \frac{85}{4}

\end{aligned}
\end{equation}
$


Using the Point Slope Formula, where $\displaystyle m = \frac{85}{4}$ and $(x_1, y_1) = (2000,696)$


$
\begin{equation}
\begin{aligned}

y - y_1 =& m(x - x_1)
&&
\\
\\
y-696 =& \frac{85}{4} (x-2000)
&& \text{Substitute } m = \frac{85}{4} \text{ and } (x_1, y_1) = (2000,696)
\\
\\
y - 696 =& \frac{85}{4}x - 500
&& \text{Apply Distributive Property}
\\
\\
y =& \frac{85}{4}x - 500 + 696
&& \text{Simplify}
\\
\\
y =& \frac{85}{4}x + 196
&&

\end{aligned}
\end{equation}
$


b. What was the average annual rate of change in the median weekly salary for a union employee between 2000 and 2004?


$
\begin{equation}
\begin{aligned}

\text{average rate of change} =& \frac{\text{weekly salary from 2004 - weekly salary from 2000}}{2004-2000}
\\
\\
=& \frac{781-696}{2004-2000}
\\
\\
=& \frac{85}{4}
\\
\\
=& 21.25

\end{aligned}
\end{equation}
$


The average annual rate of change in the median weekly salary for a union employee between 2000 and 2004 is $\$ 21.25$.

c. Suppose the trend shown by the equation in part a were to continue, what would be the median weekly salary of a union worker in 2012?

Since the rate of change is linear, the slope is the same for any points. So we let $(x_1, y_1) = (2000, 696)$ and $(x_2, y_2) = (2012,n)$, $\displaystyle m = \frac{85}{4}$, then


$
\begin{equation}
\begin{aligned}

\frac{85}{4} =& \frac{n-696}{2012-2000}
&&
\\
\\
\frac{85}{4} =& \frac{n-696}{12}
&& \text{Multiply both sides by } 12
\\
\\
255 =& n-696
&& \text{Add } 696
\\
\\
n =& 951
&&

\end{aligned}
\end{equation}
$


The median weekly salary of a union worker in 2012 is $\$ 951$.

Why does Clarisse like to stay up all night walking and watch the sunrise?

Clarisse is very different from most of the people in her society, as is the rest of her family. She doesn't like to be joined night and day to technology, even though that is what is considered normal behavior in this dystopia. Instead, she enjoys experiencing nature for itself, in its reality, rather than by watching it on a screen. She tells Montag that it's important to walk in nature so that you can experience it slowly and fully. She says:

"I sometimes think drivers don't know what grass is, or flowers, because they never see them slowly," she said. "If you showed a driver a green blur, Oh yes! he'd say, that's grass!"

Clarisse represents the old-fashioned world of people living close to nature and actually talking to each other, a world that the novel mourns as lost. Clarisse and her family talk and laugh together. Clarisse does old-fashioned things:

Once he [Montag] saw her shaking a walnut tree, once he saw her sitting on the lawn knitting a blue sweater, three or four times he found a bouquet of late flowers on his porch, or a handful of chestnuts in a little sack, or some autumn leaves neatly pinned to a sheet of white paper and thumbtacked to his door.

Because of his encounters with Clarisse, something begins to awaken inside Montag's soul. His buried dissatisfaction with his existence begins to come to life.

What effect did Depth Charges have on WW1 and how did they change warfare?

The depth charge was invented in 1916 by British naval engineer Herbert Taylor.  His "hydrostatic pistol" could be launched out of a ship and detonated at a predetermined depth, hence the name "depth charge."  Herbert designed this weapon to combat the U-boat menace against British shipping.  The depth charge was designed to cause submarines to leak and force them to surface, where they could be shot or rammed by surface vessels.  During WWI, depth charges are credited with destroying twenty submarines.  Germany utilized 390 submarines during WWI.  
The depth charge was a defensive counter against submarines who did not have to surface in order to sink ships.  By the end of the war, Americans developed ways to launch depth charges farther from ships thus placing them closer to their targets.  Depth charge technology improved and more submarines were destroyed due to depth charges than by mines in WWII.  Submarines in WWII were also built sturdier in order to better withstand attack.  
https://graphics.wsj.com/100-legacies-from-world-war-1/

I have an interview assignment for my class that includes preparation of an analytical memo, research about the interviewee, and an agenda.

If I understand the student's assignment, and with reference to the attached document, he is required to analyze and comment upon an interview from the perspective of the individual being interviewed. The first question on the questionnaire asks, "What are your frank reactions to the manner in which the student initiated the interview?" From this, it can be inferred that the student posting this question is required to assess the conduct of a fellow student who is  assigned to interview another individual. It can further be surmised that the student's assignment exists within the context of an academic course designed to educate students in how to conduct interviews, as well, perhaps, on how to respond to interview requests made of the student. Finally, it can be suggested that the assignment involves the preparation and execution of public surveys in which the object of the interview is to identify public attitudes on a given topic, such as politics.
Before interviewing respondents, it is imperative that the individual(s) asking questions be very clear and concise as to the purpose of the questions and the uses to which the information gleaned from interviews will be used. Additionally, it is important that the interviewer (vice, interviewee) appear and act professionally and objectively. Inappropriate apparel or a physical appearance considered outside the norms of contemporary society (whatever that may be in the age of body piercings and tattoos) may dissuade some categories of prospective respondents from being interviewed, and may also skew the categories of respondents willing to accede to being questioned. That may be advantageous depending upon the nature of the exercise, but it may also be disadvantageous if the goal is to identify a broad spectrum of opinions. Hence, the "manner in which the student initiated the interview" is an important indicator of the professionalism of that student.
Any student or professional introducing him- or herself to prospective respondents must be cognizant of his or her body language, including facial expressions and hand gestures that could, rightly or wrongly, be interpreted as solicitous of a particular point of view. And, most individuals would, in this context, place a high value on the interviewer's ability to maintain eye contact and to exude a certain level of enthusiasm for the exercise.
The third question on the attached document--"what is your reaction to the student's organization of the interview as a whole"--and the follow-up question ("Did the questions elicit information that you feel is important?") are very important. Respondents should not walk away from the interview thinking, "gee, he/she should have asked me my thoughts on _______," or "the questions were too involved for such simplistic answers as the interview allowed." Unfortunately, many public opinion surveys lack objectivity; the questions are designed to elicit a certain response that can be exploited for the benefit of the organization soliciting information.
Questionnaires and/or interviews are designed with a specific purpose in mind. That purpose could be something as benign as identifying what types of restaurants are most popular or what consumers most look for when choosing a restaurant, type of automobile, or laptop computer. The purpose could also, however, be a little more nefarious, such as attempting to influence public perceptions of the success or failure of a particular public policy advanced by elected officials. The interviewee, ideally, is sensitive to such attempts at manipulation. Too often, unfortunately, the interviewee is unaware of the context in which certain questions are being asked, or is aware but hopes to influence to outcome him- or herself.
The agenda behind an interview or series of interviews should be clear. Absent the requisite level of clarity, the interviewee should beware. Whether the interviewer is forthcoming, or appears ignorant of the purposes of the interview, can determine the receptivity of the prospective respondents. That, however, all comes back to the issue of professionalism mentioned above. Whether the student's assignment involves the perspective of the interviewer or of the interviewee, the integrity of the interview process must be preserved. Otherwise, the entire exercise is morally fraudulent.

McDougal Littell Algebra 2, Chapter 3, 3.2, Section 3.2, Problem 45

1. Make one of the equations equal either x or y, this way you can use substitution to solve the question.
Since the first equation given is simpler, I changed x-y=17 into y=-17=x
2. Now, since we have an equation that equals y, we can substitute that value into the other given equation:
1/2 x-3(-17+x)=1, Now we only have to solve for the x's! X ends up equaling 20!
3. Once we get a numerical value for x, 20, we can plug 20 into the x spot of either equation in order to find y. Y ends up equaling 3.
4. The Completed Result?
X=20
y=3

How are people in the community interdependent in the book The Giver?

In Jonas's highly structured, organized community, the Committee of Elders make every significant decision regarding how society functions by regulating the citizens' relationships, occupations, and family structure. In Jonas's society, each citizen is given a specific occupation that they must excel at in order for the community to function smoothly. From birth, the citizens are taught to rely on their neighbors and children must wear jackets with buttons in the back to nurture interdependence until they turn eight years old. In a society where individualism does not exist, the citizens view themselves as simply a part of the greater community.
The Speaker makes sure that each citizen is obeying the laws of the community and the Committee of Elders assigns all twelve-year-old children occupations. The highly organized, austere society is relatively small in order to avoid overpopulation and requires that each citizen contribute in some way, shape, or form to the community. If a citizen does not excel at their assignment or breaks the rules three times, they risk being released from the community.

What major role does Scout play to calm Mr. Cunningham and help Atticus?

In Chapter 15, Atticus stations himself outside the jailhouse to guard Tom Robinson, his client accused of and about to stand trial for rape. While outside the jailhouse, a group of men confronts Atticus and tries to persuade him to let them by, ostensibly so they can cause the prisoner (Tom Robinson) physical harm. Unbeknownst to them all, Atticus' two children and their friend Dill are spying on them nearby, and Atticus' daughter, Scout, bursts onto the scene. Scout informs the reader that "I sought once more for a familiar face, and at the center of the semi-circle I found one. 'Hey, Mr. Cunningham" (Lee 175). 
By singling out an individual from the mob formed outside the jailhouse, Scout accomplishes several things. First, she reminds them that they are known individuals in the town, and in this way reminds them they are accountable for their actions as individuals. She also mentions Mr. Cunningham's son, which, coupled with her own childishness, serves to remind the crowd that they are threatening a fellow father and family-man (Atticus). Finally, before Scout intervened, the mob viewed Atticus as an enemy and obstacle to the goal of maiming Tom Robinson. Once Scout appears, they once again view him primarily as Atticus Finch, father of two, and fellow neighbor: a man they consider one of their own. 
These revelations disquiet the mob, and make them question their intended actions. In short, Scout inadvertently shames the men. She makes them feel poorly and shy away from their original decision to commit violence, both by reminding them of Atticus' role in their own lives, and inserting her childhood innocence into what was about to be a dark, violent scene. It is enough to derail their plans, and lead by Cunningham's polite response to Scout's chatter, they do not move forward with their attack. As Atticus later puts it, "you children last night made Walter Cunningham stand in my shoes for a minute. That was enough" (Lee 180).

In chapter 15, the Old Sarum bunch surrounds Atticus outside of the Maycomb jailhouse in an attempt to lynch Tom Robinson. While the men are circled around Atticus, Jem and Scout (accompanied by Dill) are secretly watching their father speak to the mob from across the street. However, Scout cannot contain her curiosity and runs out into the middle of the group, which surprises Atticus and the Old Sarum bunch. When Scout enters the group of men, she recognizes Mr. Cunningham and attempts to strike up a conversation. Scout mentions that she goes to school with Walter Jr. and brings up Mr. Cunningham's legal entailments. Despite his numerous attempts to ignore Scout, Mr. Cunningham begins to view the precarious situation from Atticus's perspective and finally acknowledges Scout. Shortly after speaking to Scout, Mr. Cunningham tells the Old Sarum bunch to leave the scene. Scout's presence made Mr. Cunningham aware of his actions and allowed him to sympathize with Atticus, who was in a difficult position.

How did Renaissance inventions affect the world?

One Renaissance invention was the printing press. This made books more affordable, and more people learned to read because of this invention. Books began to appear in the languages of the masses—English, French, and German among others—and this led to the growth of nationalism  Movable type also made books easier to mass produce, and this also helped to make books more affordable.
Another Renaissance invention was the violin, a mainstay in classical music and in American folk music (where it is known as the fiddle). While Leonardo da Vinci had prototypes and designs for such inventions as scuba gear, parachutes, and armored cars, these were not widely manufactured or used during the Renaissance period. The printing press, movable type, and the violin are three inventions that would have been used by the people who lived during that era, and therefore affected the world.  
https://theculturetrip.com/europe/italy/articles/inventions-of-the-renaissance/

State the theme of the story as you see it. Support your conclusion by considering the setting, symbols, and the ending.

We might glean several themes from this story. However, one of my personal favorites is that goodness has nothing to do with one's social class; in fact, the existence of social classes can actually victimize some individuals, corrupting them to become "bad" even if they were once good.
The grandmother has a fairly superficial idea of what goodness is.  She seems to believe that her status as "a lady" confers goodness in and of itself; in addition, while she focuses on what is, to her, proof of one's goodness—qualities like having good manners—she lies to her son, manipulates almost everyone in the story, and uses horribly racist and pejorative language to describe African Americans.  Although the grandmother believes that she is uniquely qualified to be "good" because of her status, we see that this woman is elitist, racist, and hypocritical at best.  We might read the grandmother's clothing—her fancy hat, gloves, and dress—as symbolic of her social class and her own belief in her moral superiority.
In the end, we see that the Misfit did not start out with criminal intentions.  He was wrongly accused and convicted of his father's murder, and this—being blamed for something he did not do—ironically put him on the path of criminal behavior.  It seems that people found it easy to blame him as a result of his social class.  However, it is clear that he did not want to kill this family; he only felt that he had to because the grandmother recognized him.  He even tries to comfort her when her son speaks harshly to her.  While he is hardly a "good man" by most people's standards, he is not evil. We can see that there was once, if there is not now, a shred of goodness in him.  He was, in fact, victimized by society—by people just like the grandmother—and this caused him to become the misfit he is now.

What did Kennedy, Johnson, and Nixon have in common, and what set them apart from each other?

What all three presidents have most in common is the Vietnam War. Due to his idealization in public memory, many people often forget that it was John F. Kennedy who initiated the United States' role in Vietnam. Kennedy believed in the domino theory, which would later be touted by President Richard Nixon's secretary of state, Henry Kissinger—that is, the notion that the success of Communism in one part of the world would lead to other nations falling to Communism. The only solution to what presented a problem for the capitalist West was to eliminate Communism wherever it took root in order to dissuade other nations from adopting Communist rule. This interest in disrupting Communism explains Kennedy's disastrous Bay of Pigs invasion, which was an attempt to overthrow Fidel Castro in Cuba.
Kennedy may have been sympathetic with the civil rights effort (James Baldwin, for instance, was a guest at the Kennedy White House). However, he was slow to act. He regarded himself mainly as a foreign policy president and did not make any move to deal with civil rights until 1963, close to the time of his assassination.
President Lyndon Johnson is actually responsible for the passage of the most important civil rights legislation, including the Civil Rights Act of 1964 and the Voting Rights Act of 1965, overriding the Southern Coalition—a group of powerful incumbent Southern senators—to pass both laws. While signing the legislation, Johnson famously noted that the Democratic Party would lose the South forever. He was right; the South became solidly Republican as a result. Kennedy, while running for president, was still able to court the Southern states and the Dixiecrats despite their skepticism toward his Catholic faith.
Under President Johnson, the United States officially entered the Vietnam War in 1964 after the Gulf of Tonkin incident. Supposedly, the North Vietnamese fired on a United States naval ship, prompting aggressions. This has never been confirmed, however. Johnson was determined to win the war, which was becoming increasingly unpopular with his party. It is for this reason that Johnson did not seek the presidential nomination in 1968, which ended up going to Hubert Humphrey.
Humphrey lost the 1968 election to Richard Nixon. The latter's authoritarian image appealed to "the silent majority": white, middle-aged voters, particularly in suburban areas, who worried about how violent radicalism and the unrest in major cities would impact their lives. Nixon escalated the Vietnam War, rather senselessly, by carpet-bombing Cambodia. Some historians believe that this act prompted hostility against the West, thereby making it easier for the Khmer Rouge to come to power.
Under its leader, Pol Pot, the Khmer Rouge unleashed violence that resulted in the genocide of an entire generation. The massacres of "the educated class" did not end until 1977, after an invasion by the Vietnamese army put an end to the Khmer Rouge's rule.
One could argue that all three presidents, despite their differences in ideologies and political affiliations, were very ambitious and sought to institute regime changes in parts of the world that they barely understood.
https://www.britannica.com/event/Vietnam-War/The-U-S-role-grows

Kennedy, Johnson, and Nixon were all presidents during the Vietnam era in American history.  All three presidents had strong civil rights records and helped end segregation.  
Kennedy and Johnson were both Democrats whereas Nixon was a Republican.  Johnson was a long-time senator before he was picked as Kennedy's vice-president.  Nixon was vice-president under Eisenhower and lost the 1960 election to Kennedy before he won the White House in 1968.  Kennedy won the 1960 election before he was assassinated in 1963.  Kennedy also had the shortest political record of the three, having served just one term in the Senate.  Nixon resigned in 1973 during the Watergate scandal.  Kennedy is best known for his role during Bay of Pigs fiasco and the Cuban Missile Crisis in which he opened up better relations with the Soviet Union.  Johnson is best known for his role in escalating the Vietnam War.  Internationally, Nixon is best known for bringing about a closer American relationship with China.  

What is the Judiciary Act of 1789 and how did it affect the the states?

The Judiciary Act of 1789 was a landmark piece of legislation in American history that established the federal judiciary, most notably the Supreme Court, and the position of Attorney General. The act was an expression of the Federalist desire to have a strong, centralized system of government capable of meeting the challenges faced by the new nation. Opponents of Washington's judicial reforms believed that ultimate sovereignty should reside with the states, their legislatures, and their courts. A system of federal courts was something they regarded as a possible instrument of tyranny.
As regards the states, the Judiciary Act gave the newly formed Supreme Court jurisdiction over cases in which a state was a party unless the case was between the state and its own citizens, the state and citizens of another state, or the state and aliens, in which cases the Supreme Court would have original, but not exclusive, jurisdiction.
The most controversial provision of the act, section 25, also related to state sovereignty. The Supreme Court was given jurisdiction in cases in which the highest court of a state had ruled a federal law to be invalid, had upheld a state law that had been challenged as violating the Constitution, or had ruled against a right claimed under the Constitution, a federal law, or a treaty.
To opponents of the Judiciary Act, this represented an unwarranted intrusion into what they believed to be the exclusive rights of the states. But if this provision had not been made, then there is no way that the federal judiciary would've been able to function properly. Unless the new federal judiciary had substantial jurisdiction over state courts, then the states could ride roughshod over any federal law they disliked, using their courts to challenge the power and legitimacy of the federal authorities.
https://avalon.law.yale.edu/18th_century/judiciary_act.asp

https://www.uscourts.gov/about-federal-courts/educational-resources/annual-observances/anniversary-federal-court-system

When they want me to show evidence of the theme and then they want me to link that evidence. What are they looking for?

The poem is narrated by a man who loved a girl who died young. Thus, the poem's main theme is love. Depending on one's reading of the poem, one could interpret the narrator's devotion to Annabel Lee, even in death, as romantic, or as morbid and unhealthy.
In the first stanza, the narrator gives us an idealized and insular portrait of his romance with Annabel Lee:

It was many and many a year ago,
In a kingdom by the sea,
That a maiden there lived whom you may know
By the name of Annabel Lee;
And this maiden she lived with no other thought
Than to love and be loved by me.

I would focus on the last two lines: "no other thought / Than to love and be loved by me." This gives the impression of something obsessive between the two. However, because we only have the narrator's version of events, we do not know if this love obsession was mutual. Thus, obsession is another theme and you can use portions of the poem to explore that as well.

The narrator is in a struggle—in his own mind—between supernatural forces who have deprived him of Annabel Lee out of presumed jealousy, and elements of the natural world that remind him of her. The theme of obsession is repeated in the final stanza:


For the moon never beams, without bringing me dreams
Of the beautiful Annabel Lee;
And the stars never rise, but I feel the bright eyes
Of the beautiful Annabel Lee;
And so, all the night-tide, I lie down by the side
Of my darling—my darling—my life and my bride,
In her sepulchre there by the sea—
In her tomb by the sounding sea.
https://www.poetryfoundation.org/poems/44885/annabel-lee

In The Great Gatsby, does Gatsby accomplish his dreams, and, if so, how did he do it?

In my opinion Jay Gatsby didn't achieve his dreams. 
You would think that he had made all his dreams come true. Rising from a farm boy to an overnight man of means. Jay Gatsby, the man with the big house, ridiculous amounts of money, and flashy parties, really wasn't interested in any of it. He's invested his dreams, goals, practically framing his life around the notion that maybe some day, he and Daisy would be together.
           "He hadn't once ceased looking at Daisy, and I think he revalued everything in his house according to the measure of response it drew from her well-loved eyes. Sometimes, too, he stared around at his possessions in a dazed way, as though in her actual and astounding presence none of it was any longer real. Once he nearly toppled down a flight of stairs."
No, he didn't obtain his true objective. To have Daisy, and sadly we see at the end of the story, that the only true closeness he could feel with is love, is the green light separating the two.
           "he stretched out his arms toward the dark water in a curious way, and, far as I was from him, I could have sworn he was trembling. Involuntarily I glanced seaward—and distinguished nothing except a single green light, minute and far away, that might have been the end of a dock. When I looked once more for Gatsby he had vanished, and I was alone again in the unquiet darkness."

In my opinion, Jay Gatsby in F. Scott Fitzgerald's novel The Great Gatsby did not accomplish his dreams. 
Gatsby's dream was to be married to Daisy and, more expansively, to be worthy of Daisy's love. To achieve that end, he set about making his fortune. He did achieve his fortune, but, as you can see from reading the novel, the parties and the money did not make him happy.
He met Daisy five years earlier at her home in Kentucky. He was about to go off to war as an officer in the army. Daisy's family was wealthy, and her mother pressured her to find a good marriage. Daisy was forbidden to go to New York to see Gatsby as he went off to war.
It was Gatsby's own insecurities and humble beginnings that made him feel he was not worthy of her. After the war ended, he did everything he could to become worthy of her. In the meantime, Daisy met and married Tom. Tom was a very wealthy man when he married Daisy. He came from "old money," which meant his success was generational. His family was established and well-known for their success. Gatsby, after he earned his fortune, was what was called "new money," and the old money types scorned the newly rich as beneath them.  
Gatsby built a grand castle of a house across the bay from Daisy's house. He throws parties every weekend and asks around to see if anyone knows Daisy. Finally, he finds out that Jordan Baker knows her and that Nick is her cousin. He asks Nick to invite Daisy to tea so he can be reunited with her. Prior to their meeting, he invents a story about his past to tell Nick Carraway. This invention is for the purpose of being considered worthy of Daisy. He understands how "new money" people are perceived, so he invents a story to show that he is not one of them. 

"I am the son of some wealthy people in the Middle West all dead now. I was brought up in America but educated at Oxford, because all my ancestors have been educated there for many years. It is a family tradition." He looked at me sideways and I knew why Jordan Baker had believed he was lying. He hurried the phrase "educated at Oxford," or swallowed it, or choked on it, as though it had bothered him before.

After Gatsby's relationship with Daisy begins to blossom again, he reveals his dream to Nick. He has amassed all of his wealth, bought a house overlooking Daisy's, thrown parties every weekend, and invented the story of his past all for this purpose. The dream is found in the quote below: 

He wanted nothing less of Daisy than that she should go to Tom and say: "I never loved you." After she had obliterated four years with that sentence they could decide upon the more practical measures to be taken. One of them was that, after she was free, they were to go back to Louisville and be married from her house just as if it were five years ago. 

Gatsby wants to simply erase the five years in which he was separated from Daisy. Nick tells him that the past cannot be repeated. Gatsby replies "Can't repeat the past? Why of course you can." The problem is that Daisy does love Gatsby, but she cannot deny that she loved Tom, too. She had a child with Tom, and she does have some happy memories of him. Daisy is willing to let Tom go, but she is not willing to say what Gatsby wants her to say—she is not willing to erase the five years. 
Following Daisy's denial of Gatsby's dream, the accident in which Myrtle is killed happens, and Daisy and Tom cling together, leaving Gatsby shut out of her life once again. Nick says they were careless people, Daisy and Tom. Gatsby is murdered in the end by Myrtle's husband, and his dream is never realized.