Clarify the farcical elements of The Second Shepherds' Play and how they relate to the more serious nature of the play.

"The Second Shepherds' Play" is known for its slapstick humor and serious depiction of the nativity. One example of the farcical elements in the play is when the shepherds make several unsuccessful attempts to locate the Christ child, only to discover a sheep in his cradle. These humorous elements actually comprise more of the play than its serious nature, but they serve the purpose of providing contrast. With this contrast, "The Second Shepherd's Play" uses the familiar literary technique of getting the reader to let his or her guard down with humor so the play can deliver a brief yet strong message that seems all the more important in comparison.
Alternating moments of brevity and seriousness is a common literary device that is used to great effect in this play. The medieval setting gives this play a naturally somber air that is then undercut by the regular use of slapstick humor. Even the characters continue this theme. The second shepherd's wife is used as a humorous character and a social commentary on the way that marriage changes people. The three shepherds themselves engage in silly behavior, such as singing while they travel. Mak, the sheep thief, is another strong example of farcical humor in the play as he tricks the shepherds into feeling sorry for him only to steal one of their sheep while they are sleeping.
The farcical elements in "The Second Shepherds' Play" serve the purpose of highlighting its serious message, which is the nativity story itself. By using humor to lead up to the central story, the writer increases reader engagement and sets the stage for contrast.

Calculus of a Single Variable, Chapter 8, 8.7, Section 8.7, Problem 35

Given to solve,
lim_(x->oo) e^x/(x^4)
as x->oo then the e^x/(x^4) =oo/oo form
so upon applying the L 'Hopital rule we get the solution as follows,
as for the general equation it is as follows
lim_(x->a) f(x)/g(x) is = 0/0 or (+-oo)/(+-oo) then by using the L'Hopital Rule we get the solution with the below form.
lim_(x->a) (f'(x))/(g'(x))

so , now evaluating
lim_(x->oo) (e^x)/(x^4)
= lim_(x->oo) ((e^x)')/((x^4)')
= lim_(x->oo) ((e^x))/((4x^3))
again ((e^x))/((4x^3)) is of the form oo/oo so , we can apply again L'Hopital Rule .
=lim_(x->oo) ((e^x)')/((4x^3)')
=lim_(x->oo) ((e^x))/(((4*3)x^2))
=lim_(x->oo) ((e^x))/((12x^2))
again ((e^x))/((12x^2)) is of the form oo/oo so , we can apply again L'Hopital Rule . =lim_(x->oo) ((e^x)')/((12x^2)')
=lim_(x->oo) ((e^x))/(((12*2)x))
= lim_(x->oo) ((e^x))/(((24)x))
again ((e^x))/(((24)x)) is of the form oo/oo so , we can apply again L'Hopital Rule .
= lim_(x->oo) ((e^x)')/(((24)x)')
=lim_(x->oo) ((e^x))/(24)
on plugging the valuex= oo , we get
=((e^(oo)))/(24)
=oo

How did the space and arms races impact society/population?

Following World War II, the United States and the Soviet Union became enemies for various reasons (see the reference for specifics and views from both sides of the conflict). This led to the "Cold War," which was a very scary time. 
The arms race was part of the Cold War. The US had developed the atomic bomb during World War II and had used it on Japan. The Soviet Union recognized that this was a very dangerous weapon and went to all lengths to develop their own. Soon, the US was developing more powerful weapons and the Soviet Union followed suit. This race led to the Mutual Assured Destruction doctrine (the apt acronym is "MAD"), where it was alleged that peace could be maintained if both sides knew that they and their enemies would both be destroyed. 
The space race was also part of this. When the Soviet Union launched a satellite in 1955, the US recognized that this could potentially become a new weapon. This eventually led to the race to the moon, which the US won in 1969. 
The arms race was distressing for many Americans. In the early days, the US government hid the fact of radiation effects and launched the famous "duck and cover" campaign where school children were instructed to get under their desks in the event of nuclear war. Later, public fallout shelters were created and the signs for them (see file) became a common sight. People even created bunkers and fallout shelters in their basements or back yards. 
The response to the space race was more positive as the US cheered their "team" onto victory. President Kennedy made a speech setting the goal of landing a man on the moon in the next decade and after Kennedy's assassination, President Johnson carried on that commitment. NASA embarked upon this ambitious goal by creating a series of missions that taught them what they needed to know in order to put a human being on the moon. Even though the space race was also about weapons, it was also about meeting a challenge and it was a less fearful experience than the arms race. 
The space race was abandoned after awhile and the Soviet Union disintegrated, ending the Cold War. The world switched from battles between giants to the David and Goliath of terrorism, where small groups of people learned how to disrupt the workings of large countries. MAD did not lead to peace, although the International Space Station brings nations together to work on science. 
https://en.wikipedia.org/wiki/Mutual_assured_destruction

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

What is the stress pattern of Macbeth's soliloquy in act 2, scene 1?

The speech, as favoritethings's answer states, is in iambic pentameter, with only a few alterations to the meter. These alterations begin entirely conventional, not the kind of unusual alterations that Shakespeare often uses to suggest a stirred-up state of mind. As the speech continues, however, things get more irregular.
The first irregularity is early on:

a DAGger OF THE MIND, a FALSE, creATion

This line has 11 syllables, with the 11th unemphasized. This is known as a feminine ending. It's very common in Shakespeare and should not be taken as an indication of anything unusual, unless a speech uses a series of them in a row, which this one does not. There is another feminine ending at "senses."
The next irregularity is a more unusual, a short line, only 6 syllables:

as THIS which NOW i DRAW

[da DUM da DUM is missing here]
This short pause may give a moment for Macbeth to contemplatively draw his dagger without speaking.
Another very conventional type of irregularity in meter is called an "initial trochee," where the first two syllables of a line are emphasized, "DUM-da," instead of "da-DUM":

NATure seems DEAD, and WICKed DREAMS aBuse

Because the word nature is emphasized on the first syllable, the line starts with a trochee instead of an iamb. This is a very conventional irregularity and not to be over-interpreted.
Right after this, though, things get more interesting. We have the line:

The curtained sleep. Witchcraft celebrates.

One might initially scan this as follows:

the CURtained SLEEP. witchCRAFT celEbrates

However, there are only 9 syllables here, and "witchcraft" and "celebrates" are both mis-emphasized. What is going here is that there's a missing syllable at the middle of the line. This is called a broken-backed line and is scanned as follows:

the CURtained SLEEP [da] WITCHcraft CELeBRATES

This makes it a regular line. Broken-backed lines are very unusual and suggest something strange is happening with the character. It's up to you to interpret why this happens at this exact moment, though!
The rest of the speech is regular, with the exception of one feminine ending on "murder." If anything, it's surprising how regular Macbeth's meter is, given the complexity of his emotions at this moment. What do you make of that? Why do you think the more unusual irregularities come at the moments in which they do?

There are a few lines that are not regular, strictly speaking, but the soliloquy itself is, for the most part, comprised of speech in blank verse: unrhymed iambic pentameter.  This means that each line has five feet, each foot consisting of two syllables: one unstressed (or unaccented) syllable followed by one stressed (or accented) syllable.  I will try to show the stresses by capitalizing stressed syllables in the words of the quotation below.  The end of each foot is marked off by a slash.

I HAVE / thee NOT / and YET / I SEE / thee STILL. /Art THOU / not, FAtal / VIsion / SENsi / ble (EM syllable)To FEE / ling AS / to SIGHT? / Or ART / thou BUT /A DAG / ger OF / the MIND, / a FALSE / CreA / tion (EM syllable)ProCEE / ding FROM / the HEAT / OpPRESS / ed BRAIN? /

I've used the phrase "EM syllable" to indicate that two lines end with an extrametrical syllable: an additional unstressed (or unaccented) syllable at the very end of the line.  It does seem to make sense, however, that this soliloquy would have so many lines that are irregular (like the lines with the extrametrical syllables) because Macbeth's state of mind is disturbed.  He is actually hallucinating the murder weapon here, and so his speech seems to be a bit confused, just as his thoughts are.

What is the underlying meaning of Foucault's Pendulum?

The chief underlying meaning of "Foucault's Pendulum" is the relatedness of seemingly unrelated ideas. Casaubon's research begins as a casual interest in seemingly separate secret organizations, such as the Knights Templar, which spirals into an obsession when he unravels one thread only to discover that it is woven into a larger tapestry than any historian or archaeologist has yet to imagine. As Casaubon progresses further in his research, the connectedness he observes becomes more overt. A subtle theme of the work is whether or not this connectedness is an element of objective reality or rather inspired by Casaubon's own obsession.
Other characters, from Casaubon's colleague, Jacopo Belbo, to his largely atheistic girlfriend, Lia, raise the question of Casaubon's perceived connections in subtle ways throughout the story. While Casaubon becomes prone to observing connections between ancient societies and rituals, Lia remains grounded in objective reality, providing a much-needed counterweight of rationalism.
The theme of connectedness reaches its zenith when Casaubon and his colleagues discover a formula woven throughout human history. The realization of a connectedness beyond his ability to imagine sends editor Diotallevi into isolation and the brink of madness, draining his very life force. The connectedness uncovered by Diotallevi, Casaubon and Belbo begins to take on a cosmic nature. While Diotallevi loses himself to his obsession, Casaubon takes a more playful attitude towards their discovery. In this way, "Focault's Pendulum" examines the theme of interconnected truth through the very different perspectives of its three major characters. To Diotallevi, the connectedness itself takes on godlike qualities, while to Casaubon and Lisa it remains a fascinating yet detached concept to study.

How does research and development help to improve efficiency of resource allocation?

Research and development departments have various goals depending on the organization.  However, there are two general goals of every R&D facility.  The first is to generate new products or improvements for the organization to sell in the marketplace.  This is generally deemed the development side.  The second goal is to determine what products are desired, how to meet customer demand and anticipating trends.  The second part is the research portion of the department.  Although there appears to be two separate missions, the interaction between the two is seamless and should be seen as one unit.
R&D departments can greatly influence resource allocation efficiency through trend prediction and technology investment.  Trend prediction relies on R&D to understand upcoming changes to the marketplace which will affect the organizations bottom line.  For example, print newspapers have dwindled dramatically over the last few decades with the rise of the internet.  News organization that did not invest in an online edition simply failed to survive the consumer driven change in the marketplace.  Instead of allocating resources to beat reporters, it may have been more efficient to invest in an online presence.
Technology investment focuses resource allocation on the most efficient means of producing a new or improved product for the marketplace.  When there are multiple competing projects R&D should be able to analyze the cost benefit of each by calculating the production cost, time delay and launch projections.  This allows the company to focus resources on projects with an expected return versus the "long shot" project.
https://research.iu.edu/about/research-units/index.html

https://smallbusiness.chron.com/strategic-management-allocate-resources-11682.html

https://www.nordp.org/index.php%3Foption%3Dcom_content%26view%3Darticle%26catid%3D19%253Adefault%26id%3D29%253Awhat-is-research-development%253F%26Itemid%3D106

Single Variable Calculus, Chapter 2, 2.5, Section 2.5, Problem 40

Check if $F$ is a continuous function of $r$ for the gravitational force $
\displaystyle
F(r) = \left\{
\begin{array}{c}
\frac{GMr}{R^3} & \text{ if } & r < R\\
\frac{GM}{r^2} & \text{ if } & r \geq R
\end{array}
\right.
\quad
$
exerted by the earth on a unit mass at a distance $r$ from the center of the planet.


Where $M$ is the mass of the earth, $R$ is its radius and $G$ is the gravitational constant.

Based from the definition of continuity,
The function is continuous of at a number if and only if the left and right hand limits of the function at the same number is equal. So,



$
\begin{equation}
\begin{aligned}

\lim \limits_{r \to R^-} \frac{GMr}{R^3} &= \lim \limits_{r \to R^+} \frac{GM}{R^2}\\
\frac{GM\cancel{(R)}}{R^{\cancel{3}}} & = \frac{GM}{(R)^2}\\
\frac{GM}{R^2} &= \frac{GM}{R^2}

\end{aligned}
\end{equation}
$


Therefore,
$F$ is a continuous function of $r$.

What is the electoral college and how does it work?

The Electoral College is the actual system by which the President of the United States is elected. The President is not actually elected directly by the voters; rather, there are 538 electors, chosen to represent each state based on the number of Representatives and Senators that state has in Congress. This system was defined by the Constitution, and created primarily because it offered a compromise between electing the President by the legislature as in a parliamentary system, and electing the President directly. Many of the Founding Fathers were uncomfortable with the idea of giving the people that much direct power, and wanted there to be some sort of filtering mechanism; but others felt that allowing the legislature to elect the President would give them too much power, so a compromise was struck.Each state can choose how their electors will cast votes for the President. Most states are "winner-takes-all", meaning that whoever wins the popular vote in that state will win all the electors of that state. However, a few states allocate their electors proportionally. Strictly speaking, the Constitution always allows electors to change their minds and vote for a candidate other than the one they pledged to based on the state's rules (called a "faithless elector"), but this rarely happens, and it is actually illegal in many states. Because of this convoluted system, voters are not represented equally across the United States. By the way electors are allocated, voters in small states such as Delaware and Wyoming and voters in "swing states" such as Ohio and Florida that regularly switch which party they vote for have substantially more influence on the election than voters in large, non-swing states such as California and Texas. Many people consider that unfair and undemocratic. But removing this system would require a Constitutional Amendment, which is unlikely to happen any time soon.
https://www.archives.gov/electoral-college/about

What has the Sea of Faith done in the poet's age? What is the only sound that he hears? What was the sound the sand made?

The Sea of Faith is in retreat. Arnold hears its "melancholy, long, withdrawing roar" as the ebbing tide recedes over the shingle beach. The world of Victorian religious certainty is going out with the tide, yet still it lets out a proud, final roar, at once defiant and sad. Although it is still possible to hear the "grating roar" of the pebbles as the waves pull back, there is no doubt that high tide—the assertive, confident Christian faith of mid-Victorian Britain—has begun an irreversible retreat.
In the midst of all this epoch-ending melancholy and confusion, there is still a place for love. And to their love, Arnold and his new bride must be true, building a life for themselves among the darkened ruins of a slowly dying age. 

int sin(theta)sin(3theta) d theta Find the indefinite integral

Indefinite integrals are written in the form of int f(x) dx = F(x) +C
 where: f(x) as the integrand
           F(x) as the anti-derivative function 
           C  as the arbitrary constant known as constant of integration
For the given problem int sin(theta)sin(3theta) d theta  or  int sin(3theta)sin(theta) d theta   has a integrand in a form of trigonometric function. To evaluate this, we apply the identity:
sin(A)sin(B) =[-cos(A+B) +cos(A-B)]/2
The integral becomes:
intsin(3theta)sin(theta)d theta= int[-cos(3theta+theta) + cos(3theta -theta)]/2 d theta
 Apply the basic properties of integration: int c*f(x) dx= c int f(x) dx .
int[-cos(3theta+theta) + cos(3theta -theta)]/2 d theta= 1/2int[-cos(3theta+theta) + cos(3theta -theta)] d theta
 Apply the basic integration property: int (u+v) dx = int (u) dx + int (v) dx .
1/2 *[int -cos(3theta+theta)d theta+cos(3theta -theta)d theta]
Then apply u-substitution to be able to apply integration formula for cosine function: int cos(u) du= sin(u) +C .
For the integral: int -cos(3theta+theta)d theta , we let u =3theta +theta =4theta then du= 4 d theta or (du)/4 =d theta .
int -cos(3theta+theta)d theta=int -cos(4theta)d theta
                                 =int -cos(u) *(du)/4
                                = -1/4 int cos(u)du
                                = -1/4 sin(u) +C
Plug-in u =4theta on -1/4 sin(u) +C , we get:
int -cos(3theta+theta)d theta= -1/4 sin(4theta) +C
 For the integral: intcos(3theta -theta)d theta , we let u =3theta -theta =2theta then du= 2 d theta or (du)/2 =d theta .
intcos(3theta -theta)d theta = intcos(2theta) d theta
                              =intcos(u) *(du)/2
                              = 1/2 int cos(u)du
                              = 1/2 sin(u) +C
Plug-in u =2 theta on 1/2 sin(u) +C , we get:
intcos(3theta -theta)d theta =1/2 sin(2theta) +C
Combining the results, we get the indefinite integral as:
intsin(theta)sin(3theta)d theta = 1/2*[ -1/4 sin(4theta) +1/2 sin(2theta)] +C
or  - 1/8 sin(4theta) +1/4 sin(2theta) +C

In "Odalie Misses Mass," what does Kate Chopin say about southerners using ironic criticism?

In "Odalie Misses Mass," the main character, Odalie, is a young white girl who goes to visit her an older black woman named Aunt Pinky. At first, Odalie says and does many things that could be conceived of as critical of Aunt Pinky. Odalie intends to only stop for a minute at the old woman's house to "show herself." As Odalie displays her church outfit and turns about "like a mechanical dummy," Aunt Pinky laughs. As Chopin writes, "Aunt Pinky beamed and chuckled; Odalie hardly expected her to be able to do more." Odalie is content at first to merely display herself to Aunt Pinky, and then she expects one of Aunt Pinky's relatives to come to watch the older woman. When Odalie learns that a relative of Aunt Pinky's named Pug isn't present, "Odalie's plump cheeks fairly quivered with indignation and she stamped her foot." Later, when Odalie orders a black boy named Baptiste to call his mother to sit with Aunt Pinky, he says his mother has gone to church. Odalie responds, "w'at's taken you all darkies with yo' 'church' to-day?"
At first glance, Odalie seems dismissive of Aunt Pinky and superficial in her appreciation of the older woman. Odalie also seems contemptuous of the black people around her, as she doesn't appreciate that they have gone to church on Assumption, just as she wanted to. However, this criticism on the part of Odalie is ironic, as she truly loves Miss Pinky and brings her water in a gourd. She then sits by Aunt Pinky as her older friend slips into reveries from days gone by. Chopin writes, "Odalie had grown accustomed to these flights of fancy on the part of her old friend; she liked to humor her." Odalie comforts Aunt Pinky and falls asleep on her knee as Aunt Pinky dies. In the end, she is there to comfort Aunt Pinky as the older woman dies. Therefore, the criticisms that Odalie, a white southern girl, initially directs at Aunt Pinky are ironic in that she truly loves the older woman. Odalie cloaks her love for Aunt Pinky in these criticisms, and perhaps Chopin's message is that despite generalized racism, white individuals did develop real affection for the black people around them; the presentation of this affection in the midst of a racist society often created irony. 

"Good sir, why do you start, and seem to fear / Things that do sound so fair?" What does Macbeth's initial reaction to the witches' prophecy suggest, in act one scene 3?

The witches greet Macbeth as Thane of Glamis, which he knows he is, but also as Thane of Cawdor and King of Scotland, two titles he does not hold. In this quote, Banquo asks Macbeth why he acts startled and seems afraid of the prophecy. Macbeth's reaction would suggest that the witches are expressing his innermost thoughts and desires—the wild ambitions, especially to be king, that he reveals to nobody. He would be startled and afraid because he would wonder how these weird creatures could so precisely know his innermost, buried dreams and wishes. He would also be afraid because of his realization that his ambitions are so potent and alive to him that any encouragement might inspire him to take steps that he would later regret.
Yet for all his fears, Macbeth shows his palpable thirst to know more, saying to the witches, right before they disappear, that they should stay and explain how he could possibly become Thane of Cawdor or King:

Stay, you imperfect speakers, tell me more.
By Sinel’s death I know I am thane of Glamis.
But how of Cawdor? The thane of Cawdor lives,
A prosperous gentleman, and to be king
Stands not within the prospect of belief . . .

Describe the causes, events, and consequences of Shays' rebellion from the perspective of someone who will become an Anti-Federalist. Use specific arguments that will be brought up in the discussion of the ratification of the Constitution.

Shays' Rebellion occurred in central and western Massachusetts in 1786 and 1787. The farmers in these areas were upset that they were losing their farms and being put in jail because they couldn’t pay their debts. In Massachusetts, the government didn’t forgive the debts or print more money to help the farmers who were struggling to pay their debts. The farmers felt that high taxes and a lack of helpful actions by the government caused them to lose their farms. As a result, they rebelled.
The people who rebelled forced the courts to close, which delayed any foreclosures from occurring. They also freed people who had been jailed because they hadn't pay their debts. The rebellion picked up steam when Daniel Shays led the rebels. The governor of Massachusetts formed a militia that took on the rebels. The resistance crumbled, and Shays' Rebellion ended.
The Antifederalists were opposed to the ratification of the Constitution. They believed the federal government would be too strong and would abuse its powers. They felt that the causes of Shays' Rebellion were examples of their fears. They felt the federal government would tax the people too much and wouldn’t respond to the needs of the people. They believed this new government would be similar to the one from which they fought to be free in the Revolutionary War. The Antifederalists could use Shays' Rebellion as an example of what would be wrong with the new government created by the Constitution.
https://www.ushistory.org/us/15a.asp

Why did Jimmy/Snowman not believe people when they told him the ducks on his boots were only like pictures and "had no feelings"?

Jimmy/Snowman did not believe the people because he was only five or six years old at the time. A young child's conception of reality differs greatly from that of an adult.
In Chapter 2, we learn that Snowman's earliest memories stem from when he was only five or six years old. At the time, Snowman was known as Jimmy. Accordingly, Jimmy owned red rubber boots with a smiling duck's face on each toe.
Snowman remembers that he had been fascinated by a bonfire then. After watching the fire for a time, Jimmy (Snowman) had walked through a pan of disinfectant in his boots. He remembers that he was warned to walk carefully and to refrain from splashing. The disinfectant was poisonous, and the adults cautioned Jimmy about splashing it on himself.
However, Snowman remembers that he was more worried about the ducks on his boots. Being a very young child, he did not believe that the poisonous disinfectant would not hurt the ducks on his boots.

Calculus of a Single Variable, Chapter 3, 3.4, Section 3.4, Problem 15

Given: f(x)=x^3-6x^2+12x
Find the critical values for x by setting the second derivative of the function equal to zero and solving for the x value(s).
f'(x)=3x^2-12x+12
f''(x)=6x-12=0
6x=12
x=2
The critical value for the second derivative is x=2.
If f''(x)>0, the curve is concave up in the interval.
If f''(x)<0, the curve is concave down in the interval.
Choose a value for x that is less than 2.
f''(0)=-12 Since f''(0)<0 the graph is concave down in the interval (-oo, 2).
Choose a value for x that is greater that 2.
f''(3)=6 Since f''(3)>0 the graph is concave up in the interval (2, oo).

In what ways and to what effect does Mulk Raj Anand use irony and juxtaposition in his short story "Lullaby"?

In the short story "Lullaby," Mulk Raj Anand juxtaposes Phalini's singing against the sounds of the jute machine. The machine sounds highlight the oppressing monotony in Phalini's life. On a deeper level, the repetitive industrial sounds represent a life of entrenched bondage for women like Phalini.
No matter what life brings, Phalini must be at her station feeding the jute machine. Her baby is sick, but there is no one to help her. As she sings to soothe the feverish baby, the machine sounds accompany her pleading, soulful melody.

The engine chuk-chuked; the leather belt khupp-khupped; the bolts jig-jigged; the plugs tik-tikked; the whole floor shook like the hard wooden seat of a railway train.

Above the sounds of the machines, the dominant voices of other women threaten to drown out Phalini's singing. The women are "sharp-tongued" and will tolerate no other songs in their midst. There is a certain irony in this. Despite their shared gender, Phalini's colleagues remain detached from the suffering mother. Phalini earns no sympathy from them for her sick baby. In this atmosphere of mechanized drudgery, the only valued traits appear to be resilience, strength, and competence.
There is a further irony as the story progresses. We learn that Phalini's lover does not know he has a son. Phalini is still married, so that means she can never reveal the truth about her son's paternal heritage to anyone. Phalini suffers alone. Meanwhile, her lover remains free to enjoy life as he desires. He is unencumbered by Phalini's burdens.
In the factory, life is an unrelenting struggle for Phalini. With a sick baby, the challenges increase. As long as Phalini sings to soothe her baby, she must breathe in fumes of jute fluff with every breath she takes. She cannot cover her mouth or nose with a rag because her voice is her baby's only comfort.
Meanwhile, the machine sounds continue without ceasing. The sounds mean that women like Phalini will be able to earn a living. However, they also mean the end of good health. In the story, we learn that Phalini has pawned her nose ring because she can no longer bear the thought of it adorning her sunken face. The irony of the machines is that they both provide and destroy. Interestingly, the machine sounds are described as "dithyrambic" by Anand. These sounds are juxtaposed against the baby's weak cries. A dithyramb was originally an ode to Dionysus (the god of wine, ritual madness, and spiritual ecstasy).
So, the machine sounds are intensely hypnotic, lulling Phalini into an emotional stupor. She does not realize that the "thick, sickly, tasteless air" will soon kill her baby.
The baby's name, Suraj Mukhi, is also ironic. In Sanskrit, "suraj" refers to the sun. The name points to the celestial realms and can also mean that one is "born of the gods." Meanwhile, "mukhi" has Hindu origins (cloud), which points to the heavens. Despite such an auspicious name, Suraj Mukhi's life is short and filled with unbearable suffering.

For my Romeo and Juliet project I need a poem relating to the theme of "parents and children." What are some poems from notable poets I can use?

Great question! The first poem that comes to mind for me is Philip Larkin's "This Be The Verse," which is an extremely well-known poem about the relationship between parents and children. This poem takes the cynical view that parents "fill you with the faults they had / and add some extra, just for you." This can be related to Romeo and Juliet in that the parents in the play are passing on their own difficulties to their children, who must now cope with inherited tension. The parents in Larkin's poem, too, have inherited their problems in their turn. We can relate this to the ongoing feud between the Capulets and the Montagues, which affects the lives of Romeo and Juliet through no fault of their own.
There's also Stephen Spender's "My Parents." In this poem, the speaker's parents seek to protect him "from children who were rough." They impose their own view of the world upon their child, out of a desire to protect him, and ultimately the child is created in the image of its parents. The problem is that this makes it difficult for the child to fit in with those whom the parents have deemed inadmissible to their social circles, again something we could relate to this play.

What are the next two gifts that the children find in the tree? Explain what you think may be the possible significance of each.

In To Kill a Mockingbird, the mysterious Boo Radley leaves gifts for Scout and Jem in the tree near his house. As the novel progresses, the two siblings discover a wide range of gifts, including two pieces of gum, a purple velvet box containing Indian-head pennies, some twine, an entire pack of chewing gum, a medal, and a pocket-watch.
While it's difficult to determine any personal significance behind these items in regard to Boo Radley himself, it certainly seems as though each item is a prized possession of the childlike Boo, who selflessly aims to pass on his mementos to the children.
From a literary standpoint, each item serves a metaphorical and plot-supporting purpose as well. The first stick of gum serves as a method to show the children's distrustful curiosity in regards to the gifts. Jem suggests the gum is likely to be poisoned, but Scout hesitantly takes and chews the gum. The Indian-head pennies hint at Boo's age, for pennies pressed with that head stopped being pressed in 1909.
The pack of chewing gum shows how the children have come to trust these gifts, for they have no hesitation in chewing each stick. Lastly, the medal and pocket-watch show the significance and value of the gifts offered by Boo. While the first gifts seem to be generally worthless, Boo finally gives the children something sentimental (his spelling medal) and something literally valuable (an expensive pocket watch).
https://www.jmbullion.com/coin-info/cents/indian-head-pennies/

What does Desdemona think of Iago (II.1.112-181)?

In act 2, scene 1, Iago proceeds to criticize his wife before going on a rant about the negative qualities he believes to be found in all women. After Iago reveals his sexist opinions by ridiculing the entire female gender, Desdemona calls him a "slanderer" in line 119. When Desdemona petitions Iago to say something nice about her, Iago responds cleverly before once again criticizing females for using sex to manipulate men. Despite Iago's ignorant comments and prejudice against women, Desdemona continues to question his perception regarding various types of women, only to be astonished and appalled by his repeated offensive, sexists responses. After Iago tells Desdemona that the perfect woman could only "suckle fools and chronicle small beer," Desdemona responds by telling Cassio that Iago is a "profane and liberal counselor." Overall, Desdemona views Iago as an offensive, sexist man who does not respect women and is very rude.

Line 119 is a good start to figuring out what Desdemona thinks about Iago. She bluntly calls him a slanderer. She does not even waste time saying it with flowery language either. She just accuses him of spreading lies about a person with the specific intention of ruining his/her reputation. In this case, it is Emilia's reputation.

Oh, fie upon thee, slanderer!

Then, in line 158, she tells Iago that he is ignorant about women and their overall intelligence. Then, a bit later, Desdemona says that he is a horribly disrespectful and "profane" individual that should not be listened to. She directs much of her thoughts and advice about Iago to his wife. Desdemona is not wrong either. Audiences that know this play know that he is a horrible person, but even first-time readers and audiences cannot help but know that Iago deserves to be hated because of all of his racist and sexist comments about women in this scene.

In "The Possibility of Evil" by Shirley Jackson, is Miss Strangeworth's name ironic?

I don't think Miss Strangeworth's name is intended to be ironic. Rather, it seems intended to characterize her as a strange woman who has a lot of dignity and high moral standards. I can't help feeling that the author's choice of the name was a mistake. For one thing, it doesn't sound like anybody's real name, does it? Besides that, it forewarns the reader that this old lady is a little bit crazy, doesn't it? The reader shouldn't be forewarned but surprised when the nice little old lady sits down and begins writing her poison-pen letters. In my humble opinion, a simple name would have been better because it would not have made Miss Strangeworth stand out among the other townspeople.
William Faulkner chose the fairly simple name of Emily Grierson for the main character in his short story "A Rose for Emily" because he didn't want to dilute the shock that comes at the end when the reader, along with the townspeople, learns that this apparently normal and conservative old woman has been doing something really insane.

What else accounts for Britain's great transformation, other than access to coal?

Britain had a thriving international trade and there was a huge demand for English manufactured goods, such as metal tools, in the British colonies in North America and the Caribbean. There was a lot of shipbuilding; the British navy was the strongest in the world. In the middle of the 18th century, the British East India Company conquered Bengal, which at that time was the most populous and wealthy part of India. Colonial officials benefited from control over Bengal finances and taxation and brought the enormous wealth that accumulated in India back to England. They used some of these resources to invest in new industrial enterprises. As the population grew more rapidly after 1750, and rural migrants moved to the cities, British industrial manufacturers had a large supply of cheap labor.
Britain and Scotland had a well-developed culture of experimental science and technology with origins going back to the late medieval and Renaissance period. The Baconian ideal of experimental inductive science inspired the creation of the Royal Society, whose members included Newton and other key figures of the Scientific Revolution. Science and technology were better integrated in Britain than in many other countries. This favorable environment facilitated the adoption of industrial inventions beginning in the middle of the 18th century. Scientists, mechanics, and technologically savvy businessmen formed informal or formal clubs and associations, and these came to play a large role in promoting technological innovation. The most famous of them was the Lunar Society of Birmingham, which counted among its members the chemist Joseph Priestly; James Watt, the inventor of the steam engine; and Josiah Wedgwood, the producer of affordable porcelain dishes.
In the 18th century, Britain started to produce large quantities of cotton textiles. India had played a prominent role in global textile production since the Roman period, but British industrialists asked the British government to prohibit the import of many Indian textiles. In the early 19th century, British colonialists working in India imported large quantities of British factory-made textiles into India, thereby destroying the livelihood of millions of Indian weavers. By enforcing numerous restrictions on colonial industries and bringing British goods into their colonies duty free, the 18th and 19th century British colonial authorities actively promoted their country’s emerging role as “the workshop of the world.”

What are some important details about Francis Cabot Lowell and Lucretia Mott? How were these figures involved in reform?

Born on the eve of the American Revolution in 1775, Francis Cabot Lowell is credited with bringing textile mills to the United States. On a trip to England when he was in his 30s, he toured textile mills and decided to bring this technology to the U.S.
In 1813, he founded the Boston Manufacturing Company with other investors. He and his partners used the British power loom but introduced improvements in its functioning, and they also sold shares in their company. In Waltham, Massachusetts, Lowell built a mill that would become the model for other mills by incorporating several different forms of mechanization that turned cotton into cloth. Formerly, this process had been largely done by hand in different locations--not in one building.
Lowell also began employing farm girls from New England in his mills in a system that in some ways tried to replicate the ideals of the cult of domesticity. Even though the mill girls were living far from home, they at first lived in chaperoned boarding houses. Lowell also afforded them the opportunity to attend religious and educational events.
After he died in 1817, the city of Lowell, Massachusetts, an industrial town, was named after him. The Lowell system, as the factory system that Lowell devised was called, was later replicated in factories in New England and then in the Midwest and South. Though Lowell himself was not a figure in the reform movement, his employment of farm girls in his mills, while controversial to many at the time, provided women a source of employment and degree of freedom that they would not otherwise have enjoyed (though it should be noted that he paid women less than men).
Lucretia Mott was a pioneering figure in women's rights. She was a Quaker born in 1793 in Nantucket, and she originally became involved in the abolitionist movement. Along with others, she founded the Philadelphia Female Anti-Slavery Society, and she went to London in 1840 to attend the World Anti-Slavery Convention. However, she and other women, including fellow future women's rights leader Elizabeth Cady Stanton, were turned away from the meeting because they were women.
Determined to fight for women's rights because of this humiliating event, Mott, Stanton and others organized the First Women's Rights Convention, which was held in Seneca Falls, New York, in 1848. This convention produced the Declaration of Sentiments, modeled on the Declaration of Independence, to advocate for women's rights. Mott continued to be active in the abolitionist movement and women's rights, and she was a member of the American Equal Rights Association that advocated for women's rights and those of African-Americans. 
 
http://www.pbs.org/wgbh/theymadeamerica/whomade/lowell_hi.html

https://www.gilderlehrman.org/user/login?destination=node/82232

Calculus of a Single Variable, Chapter 5, 5.5, Section 5.5, Problem 50

g(t) = log_2 (t^2+7)^3
Before taking the derivative of the function, apply the logarithm rule log_b (a^m)= m*log_b(a) . So the function becomes:
g(t) = 3log_2(t^2+7)
Take note that the derivative formula of logarithm is d/dx[log_b (u)] = 1/(ln(b)*u)*(du)/dx .
So g'(t) will be:
g'(t) = d/dt [3log_2 (t^2+7)]
g'(t) = 3d/dt [log_2 (t^2+7)]
g'(t) =3 * 1/(ln(2) * (t^2+7)) * d/dt(t^2+7)
g'(t) = 3 * 1/(ln(2) * (t^2+7)) * 2t
g'(t) = (3*2t)/(ln(2) * (t^2+7))
g'(t) = (6t)/((t^2+7)ln(2))

Therefore, the derivative of the function is g'(t) = (6t)/((t^2+7)ln(2)) .

What are examples of dramatic and situational irony in "The Daydreams of a Drunk Woman" by Clarice Lispector?

There are definitely examples of situational irony in the story. In The Daydreams of a Drunk Woman, Maria Quitera is a bored housewife who despises her life.
Because of her inner discontent, Maria is hypercritical of her husband. Her constant focus on her unhappiness causes her judgment to become increasingly flawed as the days go by, but she's unaware of her danger. At the beginning of the story, she addresses herself "coquettishly with her hand on her hip." Her solipsism escapes her notice. Maria is too busy dreaming about a better life with a more sophisticated man at her side to recognize the danger of her apathy. When her husband reaches over to kiss her before he leaves for work, Maria rebuffs him angrily and accuses him of pawing her like an "old tomcat."
Her husband firmly proclaims that she's "ill," and the reader is similarly aware that Maria's self-absorption is enervating and destructive. Maria doesn't seem aware her constant focus on her misery is self-defeating; this is an example of dramatic irony, where the reader knows something about a main character that the character seems oblivious to.
When Maria accompanies her husband to a tavern at the invitation of a wealthy businessman, she ends up getting drunk. Her inebriation clouds her judgment, but again, she's oblivious to the results of her actions. Here, we have a bit of situational irony. This is when a character's actions result in a completely different outcome than he/ she expected. Instead of appearing sophisticated and elegant, Maria essentially makes an embarrassing spectacle of herself at the tavern. While she believes she can preserve her self-respect in the face of her intoxication, we know this isn't the case.
Maria becomes so drunk she can barely stand; her husband (who she despises and who she thinks looks foolish in his suit) must physically support her. Maria is determined to prove she's no "provincial ninny," but her lack of self-control obliterates any semblance of elegance and refinement in her. Her judgment of other people becomes more crass and disparaging as she becomes more inebriated. She imagines another female patron is "flat-chested," a "pious ninny," and one of a number of "shameless sluts" and that she's "nothing more than a fishwife trying to pass herself off as a duchess."
The irony is that Maria is inwardly criticizing the other woman for something she's guilty of herself. Maria wants her husband's client to be attracted to her, and she thinks that, by appearing sophisticated, she's capable of attracting a better man into her life. She's not actually very confident in her ability to do so, though. This causes her to drink copiously in a social setting to mask her inadequacies. Her actions only make matters worse; instead of appearing elegant and refined, she embarrasses herself. Sadly, she only recognizes this the next day when she reminisces about the previous evening. That's situational irony: when events don't turn out the way a character imagines they will.

When her husband's friend saw her so plump and pretty he had immediately felt respect for her. And when she started to get embarrassed she did not know which way to look. Such misery! What was one to do? Seated on the edge of the bed, blinking in resignation.

What were the two goals of the Declaration of Independence?

The first goal of the Declaration of Independence was to outline the legitimate complaints of the colonists against Parliament. Keep in mind that many in the colonies still saw a compromise as possible between the colonies and Britain. Several people were worried that independence would lead to unintended consequences such as a domestic tyranny or foreign takeover. Jefferson outlined the abuses against Parliament and even stated that the people had a right to abolish the government when it did not protect life, liberty and the pursuit of happiness. Jefferson even states that the decision to overthrow the government should not be taken lightly. By doing this he makes the colonists appear quite reasonable. Jefferson hoped that this document might push some colonists into supporting the independence movement.
The second goal was to state what the ideals of the new government would be if and when the colonists succeeded in gaining their independence. It is easy to forget that the colonists did not know how the revolution would end. Jefferson stated the lofty goals that government existed by consent of the governed and that the people should have the rights of life, liberty, and the pursuit of happiness. This was an ideal government, as in the colonies at the time everyone did not enjoy these rights as slavery still existed.

The main goal of the Declaration of Independence was to persuade reluctant colonists that there was no longer any hope of compromise with Britain and that it was therefore necessary for America to proclaim its independence. It may seem strange to us in the present day, but a large number of colonists genuinely believed that some kind of amicable settlement with the British could still be reached. The declaration, with its extensive list of grievances against King George III, aimed to disabuse them of their increasingly unrealistic hopes.
An additional goal was the establishment of the primary function of government as the securing of inalienable rights such as "life, liberty, and the pursuit of happiness." Many Americans felt that their ancient liberties under the unwritten British constitution had been systematically violated. It was therefore important that the principles on which government should be based were clearly articulated and written down for all to see.

Based on Chapter 5, "The Young and the Ruthless," in the textbook The Will to Kill: Making Sense of Senseless Murder, how can I use specific criteria from the lesson to explain a plan to reduce youth violence?

Chapter 5 explores the prevalence of youth homicides but also addresses the reasons for the decline in youth crime in the 1990s. The authors also connect juvenile crimes to the influence of drugs and gangs as well as the accessibility of guns. Interestingly, the authors raise the question of whether media-glorified violence is a contributing factor to homicidal tendencies among juveniles. Perhaps most importantly, the authors also provide examples of programs that are designed to combat and prevent juvenile violence.
From what I can see of the posted lesson above, William Bratton greatly stresses the importance of cooperative efforts between the mayor of New York City and the police department. Since Chapter 5 also stresses the importance of community efforts to combat juvenile crime (and the necessity of continuing vigilance in this area), your best approach would be to lay out a plan that incorporates these factors.
In fact, you may be interested in tailoring your plan according to how some of America's major cities (Chicago, Boston, Detroit, NYC) have come together to address the prevalence of juvenile homicides. To date, these cities have come up with a plan that focuses on four concept areas:
1) Prevention programming: This includes family and community-centered mentoring efforts as well as extracurricular activities for at-risk teens.
2) Intervention programming: This specifically addresses at-risk juveniles and youth who have already participated in gang-related activity. Intervention programming incorporates social services, health treatments, and educational activities.
3) Law Enforcement efforts: Police increase vigilance and efforts towards the most violent and serious cases of juvenile crime.
4) Re-entry programs: These programs help youth offenders after incarceration periods and are focused on education (high school and college) as well as job training.
Here's the link for the National Forum on Youth Violence Prevention's strategic planning efforts. Another link you might be interested in addresses how America's largest cities are utilizing coordinated and multi-sector approaches to combat juvenile homicides. One of these cities is Baltimore.
In 2014, the city of Baltimore worked with faith-based organizations, law enforcement, and interested community members to address the high rate of juvenile crimes in the city. The city introduced several important programs that are still in use today. Some of them are:
1) Emergency Room Violence Interruption Program: This program is a collaboration between medical professionals and the Baltimore City Health Department. It trains doctors to refer the youth they treat to appropriate city programs.
2) Youth Health and Wellness: This program focuses on the well-being of youth from the cradle to age 18. In your plan, you may consider emphasizing media violence (something the authors of the book do). For example, psychologists have concluded in recent years that media violence only affects teens who are already immersed in aggressive environments. Specifics of your plan can address how you will use community organizations and social programs to address domestic violence. For example, the city of Chicago has utilized cognitive behavioral therapy / social emotional learning initiatives to help young people develop social-emotional skills.
3) Baltimore Police Chaplaincy Program: This program incorporates the efforts of law enforcement and faith-based counselors/religious leaders.
4) United States Attorney's Office Project Safe Neighborhoods: You may be able to combine the above programs with one like this, where federal, state, and local officials work together to address the immediate consequences of gang-related gun crimes.
5) Youth Job Training Program, Mayor’s Office of Employment Development (MOED): You may decide to combine a program like this with one such as the Baltimore City Temporary Cash Assistance Employment and Training Program.
Based on the book and the criteria you reference, you're looking at designing a plan that incorporates community, federal, state, and law enforcement efforts to fight or reduce youth violence.

How is Piggy civilized in the novel Lord of the Flies?

Piggy is the novel's most civilized character and is Ralph's biggest supporter throughout the story. Although Piggy is regarded as physically inferior by the other boys, he is by far the most intelligent boy on the island. He is the first to identify the conch and fiercely defends its power when Jack begins to disregard the rules during the assemblies. The conch is a symbol of civility throughout the novel that Piggy protects and honors. Piggy also continually reminds Ralph about the importance of maintaining a signal fire. Similar to the conch, the signal fire is also a symbol of civilization, hope, and rescue. Piggy is in favor of a democratic, egalitarian society where even the littluns have a say during the assemblies. He believes that the boys should work together to accomplish various tasks and continually chastises those who act like "savages." Piggy understands that without rules, regulations, and structure he will not survive because he is not as physically strong as the others. Creating and maintaining a structured society where people respect each other and act civilly is Piggy's only hope to remain alive on the island. Unfortunately, Piggy is killed by a massive boulder that Roger hurls at him. Piggy's death and the broken conch both symbolize the utter destruction of civility on the island.

What are some themes of "Hillbilly Elegy: A Memoir of a Family and Culture in Crisis" from Chapters 1-8?

In the first half of the book, J.D. Vance relates what life was like growing up in a white, poverty-stricken working class environment. Two main themes from Chapters 1-8 are how unrelenting poverty contributes to domestic instability and how a lack of personal will/agency leads to systemic dysfunction within a community.
Vance spends the first half of the book describing how he grew up in the Midwest. His Scots-Irish family moved from Jackson, Kentucky to Middletown, Ohio, before his teens. Vance relates how he learned to navigate various father figures with cynical ease during his childhood years.
He describes without apology the white, Appalachian working-class lifestyle and how the "hillbillies" cherished their own brand of justice (what is termed the "honor culture"). For example, Vance relates how his Uncle Pet almost killed a man for what he considered an insult to his mother. At the time, no one criticized Uncle Pet's literal interpretation of Big Red's words--honor was a sacred thing in the hillbilly community. Vance remembers another incident of hillbilly justice when a suspected rapist was found "facedown in a local lake with sixteen bullet wounds in his back."
Despite his pride in his hillbilly heritage, Vance is unflinchingly honest about the problems his community faces: "...the hardest truths about hill people are the ones they must tell about themselves." The hillbilly insistence on extrajudicial justice may well be a matter of honor; however, this tendency to resolve problems with violence negates thoughtful analysis when the situation calls for it. Vance maintains that avoidance of the real issues promotes psychological resilience, but it also masks dysfunction. Papaw and Mamaw fought with their fists, but violence solved very little in their relationship.
He notes that many of the hillbilly communities in Appalachia are riddled by a prescription drug addiction epidemic, failing schools, moral degeneracy, and chronic dependency on government assistance. So, one of the main themes in the first half of the book is the lack of personal will to fix the systemic dysfunction that keeps everyone in poverty. Vance openly admits that this "learned helplessness" frustrates him.
He relates how a friend quits his job because of his hatred of waking up early. Later, this same friend takes to Facebook to detail his woes and to blame the loss of his job on the Obama economy. Vance also notes a similar situation when nineteen-year-old Bob gets fired from his job for being chronically late. After he is fired, Bob approaches the manager and yells, "How could you do this to me? Don't you know I've got a pregnant girlfriend?" Vance concludes that this inability to take full responsibility for one's actions is largely responsible for the continued dysfunction in the hillbilly community.
This theme of "learned helplessness" coincides with the theme of domestic instability under the burden of unrelenting poverty. Vance notes that violence and alcohol addiction dogged his childhood years. Mamaw and Papaw often engaged in fisticuffs, and Papaw cheated on Mamaw. Later, Vance's own mother became a drug addict, and this led to Vance being placed under Mamaw's custody.
The cycle of drug/alcohol abuse, violence, and poverty became a crushing burden, and Vance soon found himself at a crossroads. Would he continue the cycle or would he break from it? With help from his no-nonsense Mamaw, Vince managed to break free. Vance later served four years as a Marine and graduated from Yale Law School. The main reason he wrote the book was to show that the "story of economic insecurity is, at best, incomplete." I would argue that the main theme of the book is encapsulated in Vance's own words.

I want people to know what it feels like to nearly give up on yourself and why you might do it. I want people to understand what happens in the lives of the poor and the psychological impact that spiritual and material poverty have on their children.
https://www.newyorker.com/culture/cultural-comment/the-lives-of-poor-white-people

What happened when Poseidon caught Odysseus?

Your question asks what happens when Poseidon "catches" Odysseus, so I think you must be wondering about why Poseidon punishes Odysseus and what that punishment entails. I will explain both of these situations, and I hope that this response answers your question.
In The Odyssey, which is the tale of Odysseus's long journey home to Ithaca from the Trojan War, Odysseus and his men encounter Polyphemus, a giant Cyclops who happens to be the son of Poseidon. To escape being eaten by Polyphemus, Odysseus tricks the Cyclops and then blinds him, which makes Polyphemus very upset. Once Odysseus is safely back on his boat, he shouts his name back to the Cyclops, bragging about his victory and unwisely identifying himself. This is a terrible idea because Polyphemus tells his father, Poseidon, the god of the sea, and Poseidon avenges his son, striking back at Odysseus, causing violent storms that make the sea journey home very difficult for Odysseus and his men.

College Algebra, Chapter 5, 5.3, Section 5.3, Problem 46

Combine the expression $\displaystyle \log 12 + \frac{1}{2} \log 7 - \log 2$, using the Laws of Logarithm


$
\begin{equation}
\begin{aligned}

\log 12 + \frac{1}{2} \log 7 - \log 2 =& \log 12 + \log 7^{\frac{1}{2}} - \log 2
&& \text{Law of Logarithm } \log_a (A^C) = C \log_a A
\\
\\
\log 12 + \frac{1}{2} \log 7 - \log 2 =& \log \left( 12 \sqrt{7} \right) - \log 2
&& \text{Law of Logarithm } \log_a (AB) = \log_a A + \log_a B
\\
\\
\log 12 + \frac{1}{2} \log 7 - \log 2 =& \log \left( \frac{12 \sqrt{7}}{2} \right)
&& \text{Law of Logarithm } \log_a \left( \frac{A}{B} \right) = \log_a A - \log_a B
\\
\\
\log 12 + \frac{1}{2} \log 7 - \log 2 =& \log \left( 6 \sqrt{7} \right)
&& \text{Reduce to lowest term}

\end{aligned}
\end{equation}
$

Why is it important that Williams doesn't die in The Hunt For Red October?

For most readers, keeping Williams alive is important because he is one of the "good guys."  Williams and Ramius are both shot by Loginov, who is trying to destroy the Red October.  We want Williams to survive for the simple reason that we see no reason for him to die.  Williams is also important to the plot, and he needs to stay alive in order to help Jack Ryan and Ramius fake the destruction of the Red October, so that the United States can secretly bring it back to study. The reason that Williams is so important to Jack's mission is the fact that Jack Ryan doesn't speak Russian.  Williams does, and many of the crew and officers of the Red October do not speak any English.  Williams needs to stay alive so that Ryan has a way of communicating his needs with various crew members.  Williams is also a security blanket for Ryan.  Since Williams understands Russian, the Russian crew isn't able to say anything subversive that goes against what Ryan wants to happen. 

"Excuse me, Commander," Kamarov said. "Do you speak Russian?"
"Sorry, Lieutenant Williams here does, but I do not. A group of Russian-speaking officers was supposed to be here in my place, but their helicopter crashed at sea last night." Williams translated this. Four of the officers had no knowledge of English.  

In "Lord of the Flies", how does Jack feel about the rules the boys create? What is their plan to get rescued?

Initially, Jack is in favor of the rules, and when Ralph elaborates on how they will use the conch to take turns speaking, Jack says,

We'll have rules!...Lots of rules! Then when anyone breaks 'em (Golding, 25).

Despite Jack's initial enthusiasm, it is implied that he is more interested in punishing individuals who break the rules than he is in following them. As the novel progresses, Jack gradually begins to break the rules by continually interrupting boys that are speaking while holding the conch. Jack then encourages Samneric to leave the signal fire so they can hunt and continually neglects the duties agreed upon during the assemblies. At the end of chapter 5, Jack begins to argue with Ralph regarding the rules, and Jack says,

Bollocks to the rules! (Golding, 70).

Towards the end of the novel, Jack becomes a complete savage and starts his own tribe at the far end of the island. Jack emphatically tells Ralph that the conch does not count at his end of the island, which demonstrates his lack of civility and respect for rules in general.
Initially, Ralph's plan to get rescued is to create and maintain a signal fire on the top of the mountain for passing ships to see. Unfortunately, the boys begin to descend into savagery and neglect the signal fire. After the signal fire goes out, the boys fear that the beast inhabits the top of the mountain and they are forced to make a signal fire on the lower platform, which eventually also goes out.

Jack supposedly supports the rules at first; when the boys first suggest having rules, such as the conch giving its holder the sole privilege to speak, Jack responds enthusiastically, saying they'll have "lots and lots of rules", and gleefully promising punishment to anyone who breaks them. This is a foreshadowing of his future rule by force. Later, when we look back on Jack's behavior at this point in the development of the tribe and its social relationships, it seems like Jack's true interest in having "lots and lots" of rules, was to provide more opportunities for people to break them, and therefore to be punished.
Jack, ironically, is the first and most frequent breaker of the rules, particularly the rule of the conch, and he often invents exceptions to the rules that benefit him, such as claiming the conch doesn't apply on the mountain. It only takes a few chapters before Jack completely reverses his position;

“The rules!” shouted Ralph. “You’re breaking the rules!”
“Who cares?”
Ralph summoned his wits. “Because the rules are the only thing we’ve got!”
But Jack was shouting against him. “Bollocks to the rules!"

So, regardless of his early enthusiasm, Jack doesn't really invest any meaning in the rules, particularly if they get in his way. An important aspect of the rules that prevented Jack from respecting them was the fact that he was never actually punished for breaking them.
The rescue plan, established by Ralph during the boys' first assembly in Chapter 2, is to make themselves more obvious to any passing ships by starting a fire on the mountain, so the smoke will be more visible, and signal to anyone who can see it that there are people on the island. 
 

In chapters 19–21 of The Shakespeare Stealer, how is Shakespeare seen through Widge’s eyes?

Shakespeare is exacting during rehearsals but disconnected and melancholy at other times.
One thing Widge mentions is practicing while Shakespeare and Mr. Phillips watch and criticize the performance. It doesn't seem like they're being unfair; rather, it seems like they're trying to create a better performance. It's clear that when Shakespeare is watching the play, he's paying enough attention to notice how the actors are performing their parts and working to improve the play.
However, outside rehearsals, Shakespeare is a self-contained person who seems sad to Widge. He walks by Widge, Sander, Julian, and Nick without noticing them. They decide they don't want to interrupt him because he might be working out issues in the play. However, Julian also speculates that he could be heartbroken over a woman; Sander says that, no, he's married with children.
The boys debate over whether it's a love affair, the memory of his son who died, or simply depression.

In these chapters, we get a glimpse of how Widge views Shakespeare.
Widge comments on Shakespeare's proverbial gloominess in chapter 20. He is surprised that the Bard fails to notice the boys, despite walking past them. To Widge, Shakespeare is a mysterious figure. Meanwhile, Julian slyly suggests that Shakespeare's persistent despondency is actually caused by a thwarted love affair.
Sander counters by saying that Shakespeare is currently married and has two daughters. This prompts Julian to retort that being married has never prevented any man from indulging in an extramarital liaison. As for Widge, he concludes that Shakespeare merely has a melancholic disposition. He then explains to the other boys that everyone is ruled by one of the four "humors." Widge suggests that Nick is choleric, while Julian is sanguine in temperament.
In Widge's eyes, Shakespeare's sustained melancholy is the result of a biological disposition toward that temperament.

What is Benito Mussolini’s view of man and his role in fascist society?

Mussolini's fascism rejected the liberal importance placed on the individual. In fascism, the individual was subordinated to the state. Mussolini used the image of the "fasces" or a tightly bound bundle of sticks, to argue that the state was stronger when all people in it were tightly knit together and completely obedient to the state's dictates. He understood the state to have a "will and a personality" stronger than that of any individual person. As he put it:

the [individual person] is deprived of all useless and possibly harmful freedom, but retains what is essential; the deciding power in this question cannot be the individual, but the State alone . . .

Fascism also rejected pacifism and believed that the struggles and sacrifices of warfare brought out and developed what was strongest and most noble in the human spirit. In fascist society, the role of both men and women was to prepare for war, the men as soldiers and the women as the mothers of soldiers. Related to this was empire building: individuals within the state needed to prepare for the conquest and control of weaker areas. Only in this way would the state remain "vital" and strong.
Fascism was based on hierarchy and looking to the past to find an idealized vision of a national ethnicity to which the current decadent period of history could aspire. Not everyone would be part of the fascist nation (Jews, for example, were excluded) and certainly all people would not be treated as political equals, an idea Mussolini called "absurd." Under the theory of the survival of the fittest, those deemed the strongest would have special privileges—but always with the caveat of the individual person as subordinate to the needs of the state.

Select an author from The Literary 100 list and give a brief (100-200 word) statement about the author's overall importance. I chose Edgar Allen Poe, but feel free to pick anyone you like.

The work of John Milton represents the ultimate synthesis of the two foundational elements of Western culture: Greco-Roman civilization and Christianity. It is in his sublimely skillful fusion of such disparate elements that Milton's true greatness lies.
In his timeless works, Milton tapped into the rich seam of pagan literature to give life to his Christian moral vision. In writing his magnum opus Paradise Lost he consciously set out to emulate the epic visions of Homer and Virgil, not just in their massive scale, but also in the acuteness of their deep understanding of human nature. Milton takes us on a journey through biblical Paradise, but as with Dante in the Divine Comedy, it was Virgil who led him to the gates.
In his work Samson Agonistes, Milton takes the well-known story of Samson from the Old Testament and turns it into a Greek tragedy, complete with brutal violence, bloodshed, and a chorus. Milton does full justice to the Scripture and to the Greeks while subtly changing both. Once again, he achieves a truly remarkable synthesis, combining a thundering Christian morality with the catharsis of Greek tragedy to create something new that transcends both elements.
Milton's work lives on in each new generation, rising as it does from humanity's very deepest roots.
https://www.dartmouth.edu/~milton/reading_room/pl/intro/text.shtml

What are Scout's and Jem's tones toward Calpurina when asking her about her use of English in her community?

In chapter 12 of To Kill A Mockingbird Scout and Jem accompany Calpurnia to church one Sunday. The entire congregation, like Calpurnia, is African American. Both children notice that Calpurnia speaks differently to members of her church than she does when she is at the Finch residence. Calpurnia explains that she taught her son Zeebo to read using Blackstone's Commentaries, an eighteenth century English law book:

“That’s why you don’t talk like the rest of ‘em,” said Jem.
“The rest of who?”
“Rest of the colored folks. Cal, but you talked like they did in church”

Jem's tone is one of curiosity. He picks up straight away on the fact that Calpurnia speaks differently in church than she does at home. But he still doesn't know the whole story. There is a reason why Calpurnia changes her way of speaking depending on whom she is talking to, as Scout soon finds out:

“Cal,” I asked, “why do you talk n——rtalk to the—to your folks when you know it’s not right?”

Scout's tone, like Jem's, is curious, but she is also being presumptuous in assuming that there is a "right" way of talking. Scout thinks that if you know how to talk in the "proper" way, then there is no excuse for speaking in the kind of dialect used by African Americans.
Scout's tone might also be said to be a little arrogant as she automatically assumes that Calpurnia does not have a life or identity of her own outside the Finch household.
Calpurnia explains that people at church would think she was putting on airs and graces if she talked like she did at home. Yes, she knows better, but sometimes it's best not to let on, otherwise people might think you're trying to make yourself feel superior to them.
This brief episode in the story provides us with another insight into the various hierarchies that exist in Maycomb—different races, different classes, even different ways of speaking that keep people apart.

In comparing Sarah Kemble Knight's The Journal of Madame Knight with The Account of Mary Rowlandson and Other Indian Captivity Narratives, use three quotes to demonstrate a preference for one or the other writer. The choice of writer is irrelevant, as long as you use three quotes to prove your stand.

If you choose to write about The Journal of Madame Knight, you might want to mention that Sarah Kemble Knight's writing is lively and personable. While describing the travails she encounters getting around colonial New England, she narrates her travels with a keen sense of description and a wry sense of humor.
For example, in the following passage, she describes crossing a river in Rhode Island:

"The Post got a Ladd and Cannoo to carry me to tother side, and hee rid thro’ and Led my hors. The Cannoo was very small and shallow, so that when we were in she seem’d redy to take in water, which greatly terrified mee, and caused me to be very circumspect, sitting with my hands fast on each side, my eyes stedy, not daring so much as to lodg my tongue a hair’s breadth more on one side of my mouth then tother, nor so much as think on Lott’s wife, for a wry thought would have oversett our wherey:"

In this passage, she conveys her predicament with humor, as she says that even moving her tongue might cause the canoe to tip over. She also says that even thinking about Lott's wife (a Biblical story) would have upset her canoe, which is obviously humorous because a thought cannot upset a boat.
Another quote you could use to demonstrate your preference for Knight describes how, later, in looking at the moon above the countryside, she is moved and writes a poem:

"But being got to the Top, was there amply recompenced with the friendly Appearance of the Kind Conductress of the night, Just then Advancing above the Horisontall Line. The Raptures wch the Sight of that fair Planett produced in mee, caused mee, for the Moment, to forgett my present wearyness and past toils; and Inspir’d me for most of the remaining way with very divirting tho’ts, some of which, with the other Occurances of the day, I reserved to note down when I should come to my Stage. My tho’ts on the sight of the moon were to this purpose:
Fair Cynthia, all the Homage that I may Unto a Creature, unto thee I pay/In Lonesome woods to meet so kind a guide,/To Mee’s more worth than all the world beside."

The moon, which she refers to as the "Kind Conductress of the night," causes her to forget her weariness in traveling. She is moved to write down her thoughts about the moon, which she also refers to as Cynthia, using an allusion to the Greek goddess of the moon. This type of poetic writing has a unique voice and conveys Knight's personality and style.
One approach you could consider for your third example would be to use a quote from The Account of Mary Rowlandson and Other Indian Captivity Narratives to demonstrate why you prefer Knight. While Mary Rowlandson's narrative is filled with the excitement of conveying an attack by Native Americans, you might find it has a wooden quality. For example, even when Native Americans are attacking her house, her account has a stilted quality to it:




"We had six stout dogs belonging to our garrison, but none of them would stir, though another time, if any Indian had come to the door, they were ready to fly upon him and tear him down. The Lord hereby would make us the more acknowledge His hand, and to see that our help is always in Him. But out we must go, the fire increasing, and coming along behind us, roaring, and the Indians gaping before us with their guns, spears, and hatchets to devour us."

Rowlandson's narrative also has a religious overlay, so she attributes what happens to divine intervention. She narrates a very dramatic episode with an economy of words, and the writing does not provide the reader with access to her innermost thoughts and feelings the way that Knight's writing does.

If I had to compare and contrast Willy Loman from Death of a Salesman and Hamlet from Shakespeare, what would be their main similarities and differences?

Both Willy Loman and Hamlet are tragic and melancholic figures, but there is an important difference between the two: unlike Loman, Hamlet does not try to evade responsibility for his actions.
To forget his dismal failures, Loman tries to cocoon himself inside a strange, alternate reality. For his part, Hamlet simply accepts that the act of revenge will demand an unswerving commitment from him. True, Hamlet understands his dark destiny (and simultaneously loathes it). Yet, he understands that he must pursue a certain course of action if he is to avenge his father's death properly. On the other hand, Loman tries to evade personal responsibility for his actions, choosing instead to blame others for his failures and present unhappiness.
Let us first discuss Hamlet in act 5, scene 2:

Not a whit. We defy augury. There’s a special providence in the fall of a sparrow. If it be now, ’tis not to come. If it be not to come, it will be now. If it be not now, yet it will come—the readiness is all. Since no man of aught he leaves knows, what is ’t to leave betimes? Let be.

Here, Hamlet's words indicate that he believes in facing dangers with courage. For his part, Horatio urges prudence, but Hamlet is undeterred (despite his reservations). Prior to his fight with Laertes, we learn that Hamlet doctored the papers, so it is Rosencrantz and Guildenstern who go to their deaths. Here, we see Hamlet's decisiveness at play; he does not shrink from action when it is needed. Hamlet's decision to duel Laertes is also fortuitous because his subsequent wounding by Laertes provokes a confession. Before dying, Laertes reveals that Claudius was behind the plot to kill Hamlet.
Although he is dying, Hamlet seizes the poisoned sword and stabs Claudius. He even makes the king drink from the poisoned chalice (the same one Gertrude drank from). Claudius dies, but Hamlet's victory is a Pyrrhic one. Despite his fate, however, Hamlet remains resolutely in control of his mental faculties to the end, even designating Fortinbras as the next king of Denmark. Despite the fact that certain characters in the play have decried Hamlet's supposed "madness," the latter displays a surprising lucidity during the last moments of his death.
Hamlet's behavior is in contrast to that of Willy Loman's in Death of a Salesman. In fact, Loman never matches Hamlet's dynamism and thirst for action. To protect himself from pain, Loman relies on an alternative reality that allows him to forget his failures. He has an affair and deludes himself into thinking that his sons are interested in starting a business. To keep up appearances, Loman continues to take out loans from his friend, Charley. Here, you may be able to provide your own perspectives about Loman's behavior as well.
Although Loman is unhappy that he is not a successful salesman, he does almost nothing tangible to change his present situation. Although Hamlet and Loman are tragic characters, there is an important difference between the two. While Hamlet chooses to face the grimness of reality head on, Loman endeavors to hide from it. Loman's passivity is in direct contrast to Hamlet's ultimately aggressive approach to life's challenges.

Calculus: Early Transcendentals, Chapter 4, 4.6, Section 4.6, Problem 29

We can factor the function to get f(x)=\sqrt{x^2(x^2+c)}=|x|\sqrt{x^2+c}. There are several cases.

When c=0 , the domain is all real numbers, and the function becomes the simple quadratic f(x)=x^2 . This has a minimum at x=0 , and no inflection points, since the function is concave up for all real numbers.
The graph is given by

When c>0 , the function is more complicated. The domain is still all real numbers, but now the derivative is found to be (by using the original, unfactored function):
f'(x)=\frac{1}{2}(x^4+cx^2)^{-1/2}(4x^3+2cx) factor numerator and denominator
=\frac{x(2x^2+c)}{|x|\sqrt{x^2+c}} replace |x| with its definition
=\frac{2x^2+c}{\sqrt{x^2+c}}
The graph has a minimum at x=0 which we can see from the original function since it vanishes there and must be positive everywhere else.
The second derivative is f''(x)=+-\frac{x(2x^2+3c)}{(x^2+c)^{3/2}} . A sample graph is given by

When c=-k<0 , we can carry out exactly the same computations as in the positive case, except that now there are x-intercepts at x=+-\sqrt k . But the domain is only when the argument is positive, which means that x<=-k and x>=k .
The first derivative is f'(x)=\frac{2x^2-k}{\sqrt{x^2-k}} , which indicates the minimums at the x-intercepts.
Finally, the second derivative is f''(x)=+-\frac{x(2x^2-3k)}{(x^2-k)^{3/2}} which has inflection points at x=+-\sqrt{{3k}/2} .

Where Helen Keller's family lived, there were no resources for the blind and the deaf. Where did Helen's parents take her to see a famous eye doctor?

Helen reveals these details in Chapter 3 of The Story of My Life. Her mother had read Charles Dickens’ book American Notes. She had absorbed the author’s description of a visit to the Perkins Institution in Boston, where he met a blind and deaf woman named Laura Bridgman. Unfortunately, Samuel Gridley Howe, who had been the head of Perkins when Laura Bridgman was there, had since died. But Helen’s parents knew that specialized help was indeed possible. When she was about six years old, they took Helen to see Dr. Chisholm in Baltimore. He recommended Alexander Graham Bell in Washington, D.C. Bell in turn told them to write a letter to Mr. Anagnos at the Perkins Institution. By the summer of 1886, Anagnos said a teacher had been found. He would send Anne Mansfield Sullivan to Helen’s house in March 1887. The Kellers had finally tapped into the right assistive network.

What is the main conflict in Trouble by Gary Schmidt?

Stating the main conflict of this book is a bit difficult. Schmidt intricately weaves a few major conflicts throughout Trouble, and I believe different readers will see a different main conflict.  
One central conflict is definitely a man vs. nature conflict. Henry and the other three climbers struggle to climb Katahdin. As with all mountain climbing, it's dangerous. The group is risking their lives, so I would be remiss to think this part of the story is not a central conflict.  
There is conflict within the group, too. Henry wants to do the climb alone, but his best friend won't let him. Chay Chouan also wants to climb with the group. He is the guy who was supposedly driving the car that killed Henry's brother. Lastly, Henry's little sister wants to join the group. If you've grown up with younger siblings, you know there's conflict when they always want to "tag along."  
Internally, Henry struggles to come to terms with the real person his brother was. Henry idolized his older brother Franklin, but Henry learns Franklin wasn't all that wonderful to other people.  
There are other conflicts present throughout the book too, and a central theme of the book focuses on the book's title—Trouble. Trouble and conflict can't be avoided. The key to living well is appropriately managing and dealing with trouble.

What is the most important part of the Declaration of Independence?

Of all of Jefferson's rhetorical techniques in the Declaration of Independence, perhaps the most important and persuasive inclusion is the litany of abuses of King George III of England.  
Jefferson structures a long run of parallelism with the repeated phrase "He has..." to enumerate very specifically what the king has done to hurt the colonies as well as the things he has not done to help them, ranging from denying the passage of laws that would be helpful to the colonies to stirring up domestic troubles in the colonies and inciting Native Americans to kill colonists without regard to the traditional rules of engagement.  This recitation of abuses offers a strong piece of inductive reasoning and a convincing rationale for separation.
Jefferson follows the litany of King George III's abuses with a statement that the colonies have tried repeatedly and in vain to resolve their differences with England in "the most humble terms."

What is the house of worship for Judaism?

In Judaism a house of worship is called a synagogue. The word itself is of Greek origin, and means "assembly.'" In Hebrew, a synagogue is known as either a "bet kenesset"(house of assembly) or "bet tefila" (house of prayer). Synagogues are among the oldest known places of religious worship, first established several thousand years ago. As well as being places for prayer, synagogues are also regularly used for religious reading and study. They can also serve as focal points for the local Jewish community, providing facilities such as catering halls, libraries, and day care centers.
Whatever function a synagogue serves, its most sacred spot is the Torah Ark, a cabinet in which the scrolls of the Torah, the Jewish book of scripture, are kept. The Torah Ark replicates the Ark of the Covenant, which held the tablets given to Moses by God, and on which were inscribed the Ten Commandments.

Single Variable Calculus, Chapter 5, 5.4, Section 5.4, Problem 60

Find the amount of $H_2 O$ that flows from the tank during the first 10min. Suppose that the $H_2 O$ flows from the bottom of a storage tank at a rate of $r(t) = 200 - 4t$ $\displaystyle \frac{\text{liters}}{\text{min}}$, where $0 \leq t \leq 50$.
Using Net Change Theorem


$
\begin{equation}
\begin{aligned}
\int^b_a r(t) dt &= \int^{10}_0 (200 -4t) dt\\
\\
\int^b_a r(t) dt &= \left[ 200t - 2t^2 \right]^{10}_0\\
\\
\int^b_a r(t) dt &= 200(10) - 2(10)^2 - \left[ 200(0) - 2(0)^2 \right]\\
\\
\int^b_a r(t) dt &= 2000 - 200 - 0\\
\\
\int^b_a r(t) dt &= 1800 \text{ liters}

\end{aligned}
\end{equation}
$


This means that during the first 10 mins. the amount of water that flows inside the tank is 1800 liters.

Foreshadowing is a literary device that gives readers a hint about the events to come. Malala says, "I'd had a strange, gnawing feeling that something bad was gong to happen." What does this foreshadow?

Malala's words foreshadow the terrible events of the following day. One night she starts wondering about death and what it's really like. She prays to Allah and asks him what happens when you die and how you would feel. The very next day Malala comes frighteningly close to receiving an answer to those questions.
The following morning, Malala is sitting on board the school bus with other pupils and some teachers. After traveling a short distance, the bus is stopped by a couple of young men in white robes. They board the bus and ask where Malala is. The men are from the Taliban; they know of Malala's reputation as an impassioned advocate for the education of women and girls. The Taliban are fiercely hostile to any kind of female education. They want to confine women and girls to home and the marketplace. The man who asks for Malala by name suddenly opens fire, shooting her in the head, neck, and shoulder. Two of her friends are also injured in the attack. Thankfully, all the girls survive, but they come dangerously close to being murdered, and all because they want to get an education.

Single Variable Calculus, Chapter 4, 4.3, Section 4.3, Problem 34

Suppose that $f(x) = x^5 - 2x^3 + x$

a.) Determine the intervals of increase or decrease.

If $f(x) = x^5 - 2x^3 + x$ then,


$
\begin{equation}
\begin{aligned}

f'(x) =& 5x^4 - 6x^2 + 1
\\
\\
f''(x) =& 20x^3 - 12x

\end{aligned}
\end{equation}
$


To find the critical numbers, we set $f'(x) = 0$, so..


$
\begin{equation}
\begin{aligned}


f'(x) = 0 =& 5x^4 - 6x^2 + 1
\\
\\
0 =& 5x^4 - 6x^2 + 1
\\
\\
0 =& (5x^2 - 1)(x^2 - 1)

\end{aligned}
\end{equation}
$


The critical numbers are at

$
\begin{array}{ccc}
\displaystyle x = \pm \sqrt{\frac{1}{5}} & \text{and} & x = \pm \sqrt{1} \\
\displaystyle x = \pm \frac{1}{\sqrt{5}} & \text{and} & x = \pm 1
\end{array}
$

Hence, we can divide the interval of $f$ by:

$
\begin{array}{|c|c|c|}
\hline\\
\text{Interval} & f'(x) & f \\
\hline\\
x < -1 & + & \text{increasing on} (- \infty, -1) \\
\hline\\
-1 < x < \frac{-1}{\sqrt{5}} & - & \text{decreasing on} \left( - 1, \frac{-1}{\sqrt{5}} \right) \\
\hline\\
\frac{-1}{\sqrt{5}} < x < \frac{1}{\sqrt{5}} & + & \text{increasing on} \left( \frac{-1}{\sqrt{5}} , \frac{1}{\sqrt{5}}\right) \\
\hline\\
\frac{1}{\sqrt{5}} < x < 1 & - & \text{decreasing on} \left( \frac{1}{\sqrt{5}}, 1 \right) \\
\hline\\
x > 1 & + & \text{increasing on} (1, \infty)\\
\hline
\end{array}
$

These data obtained by substituting any values of $x$ to $f'(x)$ within the specified interval. Check its sign, if it's positive, it means that the curve is increasing on that interval. On the other hand, if the sign is negative, it means that the curve is decreasing on that interval.


b.) Find the local maximum and minimum values.

We will use Second Derivative Test to evaluate $f''(x)$ at these critical numbers:


$
\begin{equation}
\begin{aligned}

& \text{So when $x = 1$,}
&& \text{when $x = -1$,} \\
\\
\\
& f''(1) = 20(1)^3 - 12(1)
&& f''(-1) = 20(-1)^3 - 12 (-1)\\
\\
\\
& f''(1) = 8
&& f''(-1) = -8

\end{aligned}
\end{equation}
$





$
\begin{equation}
\begin{aligned}

\text{when } x =& \frac{1}{\sqrt{5}},
&& \text{when } x = \frac{-1}{\sqrt{5}}
\\
\\
f'' \left( \frac{1}{\sqrt{5}} \right) =& 20 \left( \frac{1}{\sqrt{5}} \right)^3 - 12 \left( \frac{1}{\sqrt{5}} \right)
&& f'' \left( \frac{-1}{\sqrt{5}} \right) = \frac{8 \sqrt{5}}{5}


\end{aligned}
\end{equation}
$


Since $f'(1)$ and $\displaystyle f'\left( \frac{-1}{\sqrt{5}} \right) = 0, f''(1)$ and $\displaystyle f''\left( \frac{-1}{\sqrt{5}} \right) > 0$ are local minimums. On the other hand, since $f(-1)$ and $\displaystyle f' \left( \frac{1}{\sqrt{5}} \right) = 0, f''(-1)$ and $\displaystyle f''\left( \frac{1}{\sqrt{5}} \right) < 0, f(-1) = 0$ and $\displaystyle f\left( \frac{1}{\sqrt{5}} \right) = 0.2862$ are local maximums.

c.) Find the intervals of concavity and the inflection points.

We set $f''(x) = 0$, to determine the inflection points..


$
\begin{equation}
\begin{aligned}

f''(x) = 0 =& 20x^3 - 12x
\\
\\
0 =& 20x ^3 - 12x
\\
\\
0 =& 4x (5x^2 - 3)
\\
\\
x =& 0 \text{ and } 5x^2 - 3 = 0

\end{aligned}
\end{equation}
$


Therefore, the inflection points are $x = 0$ and $\displaystyle x = \pm \sqrt{\frac{3}{5}}$.

Let's divide the interval to determine the concavity..

$
\begin{array}{|c|c|c|}
\hline\\
\text{Interval} & f''(x) & \text{Concavity} \\
\hline\\
\displaystyle x < - \sqrt{\frac{3}{5}} & - & \text{Downward} \\
\hline\\
\displaystyle - \sqrt{\frac{3}{5}} < x < 0 & + & \text{Upward} \\
\hline\\
\displaystyle 0 < x < \sqrt{\frac{3}{5}} & - & \text{Downward} \\
\hline\\
\displaystyle x > \sqrt{\frac{3}{5}} & + & \text{Upward}\\
\hline
\end{array}
$

These values are obtained by evaluating $f''(x)$ within the specified interval. The concavity is upward when the sign of $f''(x)$ is positive. On the other hand, the concavity is downward when the sign of $f''(x)$ is negative.


d.) Using the values obtained, illustrate the graph of $f$.

Single Variable Calculus, Chapter 3, Review Exercises, Section Review Exercises, Problem 42

Suppose that $g(\theta) = \theta \sin \theta$, find $g''\left(\frac{\pi}{6}\right)$


$
\begin{equation}
\begin{aligned}
g'(\theta) &= \frac{d}{d \theta} ( \theta \sin \theta )\\
\\
g'(\theta) &= (\theta) \frac{d}{d\theta} (\sin \theta) + (\sin \theta) \frac{d}{d\theta}(\theta)\\
\\
g'(\theta) &= (\theta) (\cos \theta) + (\sin \theta) (1)\\
\\
g'(\theta) &= \theta \cos \theta + \sin \theta\\
\\
g''(\theta) &= \frac{d}{d \theta} ( \theta \cos \theta ) + \frac{d}{d \theta} (\sin \theta)\\
\\
g''(\theta) &= \left[ (\theta) \frac{d}{d\theta} (\cos \theta) + (\cos \theta) \frac{d}{d\theta}(\theta) \right] + \cos \theta\\
\\
g''(\theta) &= (\theta)(-\sin \theta) + (\cos \theta) (1) + \cos \theta\\
\\
g''(\theta) &= - \theta \sin \theta + \cos \theta + \cos \theta\\
\\
g''(\theta) &= - \theta \sin \theta + 2 \cos \theta\\
\\
g''\left(\frac{\pi}{6}\right) &= 2 \cos \theta - \theta \sin \theta\\
\\
g''\left(\frac{\pi}{6}\right) &= 2 \cos \frac{\pi}{6} - \left(\frac{\pi}{6}\right)\left(\sin\frac{\pi}{6}\right)\\
\\
g''\left(\frac{\pi}{6}\right) &= (\cancel{2}) \left(\frac{\sqrt{3}}{\cancel{2}}\right) - \left(\frac{\pi}{6}\right) \left(\frac{1}{2}\right)\\
\\
g''\left(\frac{\pi}{6}\right) &= \sqrt{3} - \frac{\pi}{12} \qquad \text{or} \qquad g''\left(\frac{\pi}{6}\right) = 1.47025142
\end{aligned}
\end{equation}
$

What is a contrast of the reactions of mother, father, and son to the paw with the progression of the narrative of "The Monkey's Paw"?

The Whites are a content family of father, mother, and adult son who live in the countryside. But, a visit from a friend changes their lives forever.
Before Sergeant Major Morris shows the monkey's paw to the Whites, they all three lean forward eagerly; however, Mrs. White is repulsed by its appearance. Herbert takes it and examines the paw, then his father reaches for it, and after examining it, he places it on a table. 
As the last one to own this talisman, the sergeant major explains that he has had his three wishes and tosses it into the fireplace of the Whites. Swiftly, Mr. White snatches it off the fire, and he refuses to be rid of it as the soldier suggests. When he asks how to make a wish, the soldier instructs him, but warns him of the consequences. Mrs. White says jokingly, 

"Sounds like the Arabian Nights....Don't you think you might wish for four pairs of hands for me?"

Mr. White draws the talisman from his pocket, and all three family members laugh. But, the sergeant major is alarmed, grabs the arm of Mr. White and reiterates, "Wish for something sensible."
Mr. White replaces the paw in his pocket and the guest and the Whites eat dinner. Afterwards, their guest tells them more tales of his adventures in India. When he departs, Herbert cynically says that if the tale of the monkey's paw is anything like the others of the soldier, "we shan't make much of it." Then, he pretends to be horrified after Mr. White said his friend begged him to throw it away. He adds flippantly,

"Why, we're going to be rich, and famous and happy. Wish to be emperor, Father, to begin with; then you can't be bossed around."

His mother, having been so teased, chases Herbert around the table. Pulling the paw out of his pocket, Mr. White says that he does not know what to wish for. Herbert suggests that he wish for the amount that the Whites owe on their mortgage: "Wish for two hundred pounds, then; that'll just do it."Somewhat ashamed of his credulity, Mr. White holds up the paw and makes this wish. There is a quick sound of piano keys struck; the father suddenly utters "a shuddering cry" and tells his wife and son that the paw moved and twisted in his hand. 
Herbert is unimpressed. He says that he does not see the money, and placing the paw on the table, he adds, "and I bet I never shall." Mrs. White is more anxious, and she tries to calm her husband, telling him it must have been his imagination that the paw moved. When the wind blows harder outdoors, Mr. White becomes nervous at the sound of a door banging upstairs. In fact, "[A] silence depressing settled upon all three." After the parents go upstairs to bed, Herbert grasps the monkey's paw; he shivers slightly, releases the paw and wipes his hand upon his coat. Then, he, too, goes upstairs to his room, disturbed by what has just happened.
But, the next morning Herbert laughs at his fears of the previous night. Even the atmosphere of the rooms seems improved from the night before. Mr. White, on the other hand, yet shows some discomfort; he recalls that Morris said that things happen that might just be attributed to coincidence. But, Herbert jokes about the money that will soon arrive, and Mrs. White laughs as she follows him to the door. At the end of the day, Mr. White returns to his fixation on how the paw moved while Mrs. White watches a man outside who pauses at their gate, then walks past it. After doing this three more times, he resolutely opens the gate and knocks on their door.
The Whites are informed that Herbert has been killed at work. The parents are given a check for compensation: £ 200, the amount for which Mr. White wished the night before. Horrified at the turn of events and the coincidence of the amount of the check, as well as devastated by the death of their only child, Mr. White faints as his wife shrieks.
Now, their lives are ruined; the Whites have buried their son and are alone. As the days pass, one evening Mrs. White realizes that they have two wishes left, and she demands that her husband wish for Herbert to be returned to them. Fearfully, Mr. White wishes, and collapses in a chair. After hours, there is a sound at their front door; "It's Herbert," his wife screams, running to open it. But, hearing some horrific sounds outside, the husband realizes that they forgot to wish that Herbert would be restored to life as he was before the accident, so he rushes for the paw and desperately makes his third wish. The horrible noises and rattling of a chain stop.

Were the Reform Movements of the 1840s successful ?

The answer here depends on which specific reform movements you are interested in, the country to which you are referring, and what you mean by successful. There were reform movements in this period in both Britain and the United States. Some were geared towards widening the right to vote in the direction of universal suffrage. Others were focused on other aspects of election reform. In Britain, many rotten and pocket boroughs had been eliminated in the 1832 Reform Bill but cities were still under-represented and rural areas over-represented.
In the United States, many different reform movements aimed towards improving quality of life. Two notable ones were the abolitionist movement which aimed to abolish slavery and the temperance movement which aimed to reduce or eliminate the consumption of alcohol. Activists were also concerned with animal rights, human rights, labor conditions, treatment of minorities, and other measures affecting the poor and destitute. 
Many of the goals of the reformers in both countries were eventually completely or partly achieved. Both nations have universal suffrage, slavery has been abolished, labor laws have been amended, and many laws exist forbidding human and animal abuse of the kinds that were prevalent in the nineteenth century. While not all of the goals of these reform movements have been completely attained, they should be judged successful in so far as they did lead to many positive social changes. 

int xsin^2x dx Find the indefinite integral

To solve the indefinite integral, we follow int f(x) dx = F(x) +C
where:
f(x) as the integrand function
F(x) as the antiderivative of f(x)
C as the constant of integration.
For the given integral problem: int x sin^2(x) dx, we may apply integration by parts: int u *dv = uv - int v *du .
We may let:
u = x  then du =1 dx or dx
dv= sin^2(x) dx then v = x/2 - sin(2x)/4
Note: From the table of integrals, we have int sin^2(ax) dx = x/2 - sin(2ax)/(4a) . We apply this on v =int dv =intsin^2(x) dx  where a =1 .
Applying the formula for integration by parts, we have:
int x sin^2(x) dx= x*(x/2 - sin(2x)/4 ) - int (x/2 - sin(2x)/4 ) dx
                              =x^2/2 - (xsin(2x))/4 - int (x/2 - sin(2x)/4 ) dx
For the integral:  int (x/2 - sin(2x)/4 ) dx , we may apply the basic integration property: : int (u-v) dx = int (u) dx - int (v) dx .
 
int (x/2 - sin(2x)/4 ) dx =int (x/2) dx -int sin(2x)/4 ) dx
                                    = 1/2 int x dx - 1/4 int sin(2x) dx .
 
Apply the Power rule for integration:
int x^n dx = x^(n+1)/(n+1) +c 
1/2 int x dx = 1/2*x^(1+1)/(1+1)
                  = 1/2* x^2/2
                  = x^2/4
Apply the basic integration formula for sine function: int sin(u) du = -cos(u) +C .
Let: u =2x then du = 2 dx or (du)/2 = dx .
1/4 int sin(2x) dx = 1/4 int sin(u) * (du)/2
                              = 1/4 *1/2 int sin(u) du
                              = 1/8 (-cos(u))
                               = -cos(u)/8
Plug-in u = 2x on -cos(u)/8 , we get: 1/4 int sin(2x) dx =-cos(2x)/8 .
Combining the results, we get:
int (x/2 - sin(2x)/4 ) dx =x^2/4 - (-cos(2x)/8) +C
                                      =x^2/4+ cos(2x)/8 +C
Then, the complete indefinite integral will be:
int x sin^2(x) dx=x^2/2 - (xsin(2x))/4 - int (x/2 - sin(2x)/4 ) dx
                               =x^2/2 - (xsin(2x))/4 -(x^2/4+ cos(2x)/8) +C
                               =x^2/2 - (xsin(2x))/4 - x^2/4 - cos(2x)/8 +C
                               = (x^2)/4- (xsin(2x))/4- cos(2x)/8 +C 

Why does Pip refuse to take any more of Magwitch's money?

When Magwitch returns to England and reveals himself as Pip's benefactor, Pip is completely at a loss for how to respond. His decision to not take anymore of Magwitch's money results from a combination of shame, fear, and possibly a bit of prudishness.

Consider that, at this point in the novel, Pip is confronting the fact that everything he thought was true about his life, his expectations, and his newly created identity is untrue. Miss Havisham did not choose him to receive a great fortune; he is not destined to marry Estella, the love of his life; and his finances are not nearly as stable as he had previously thought. Money from Magwitch is drastically different from money from Miss Havisham. Pip views the money as connected to a criminal past, and he tells Herbert in chapter 41 that he is afraid of the debt he now owes to a dangerous man. Pip is perhaps afraid that he is now under the control of a convict. Additionally, the money is not associated with the glamorous life of Estella, Satis House, and the British upper class but rather associated with the most traumatic event of Pip's childhood and the very world Pip has decided to abandon.

This is largely because, by this point in the novel, Pip has become a snob. Now wealthy and well-educated, Pip is ashamed to be connected to anyone who isn't. We have already seen him, for instance, attempting to dissociate himself from Joe, which he later admits was a cruel and selfish thing to do. Given that Joe raised him (and is simply working-class, rather than a convict), it's hardly surprising that Pip reacts negatively to Magwitch. Although Magwitch claims to have earned his fortune honestly, Pip possibly suspects otherwise; in the first shock of his discovery, for instance, he says that "for anything [he] knew, [Magwitch's] hand might be stained with blood" (Chapter 39). But even supposing that Pip did accept Magwitch's account of events, he would probably still regard his money as tainted simply because of Magwitch's social status and past crimes. When Herbert questions Pip about keeping the fortune, he simply says "Think of him! Look at him!" (Chapter 41).
In fairness to Pip, of course, there is something unsettling about Magwitch claiming him as "[his] gentleman" (Chapter 40). The phrase implies ownership, and Pip probably feels that taking Magwitch's fortune would mean giving Magwitch some kind of power over him; Pip talks, for instance, about feeling burdened by the "gold and silver chains" Magwitch has placed on him (Chapter 39). Still, Pip ultimately comes to regard Magwitch with affection, and to see Magwitch's generosity (though misguided) as sincere, so it seems likely that prejudice was at the heart of his earlier objections. By the time Pip comes around, though, the entire question of accepting the fortune is moot, because Magwitch's status as a convict makes the money forfeit to the Crown.