How can I create a hook for my essay about Hephaestus?

Without knowing in exactly which direction the essay is going to go, I can't dial in a perfectly tailored hook for the essay. However, I can help get you started by briefly discussing four generally effective writing hooks for essays.
A "hook" is what I call an "attention-getter" to my classes.  It's the first few sentences of a speech or an essay. It's critical that the hook grabs a reader's attention right from the very beginning. If the reader is bored after two sentences, he or she isn't likely to be a motivated reader.  The reader might not even continue reading at all. The hook needs to excite and motivate your reader to read more.  Here are four types of hooks that work well.
Use a quote. Quotes tend to get readers' attention, because readers assume that the quote must be of supreme value if the author of the paper is deciding to use it instead of his or her own words.
Use a bold, slightly controversial statement. This hook is effective because it attempts to get an emotional rise out of the reader. Be careful to not offend your reader. That might actually cause the reader to stop reading right away, or that reader will just be antagonistic to everything that you are trying to prove.
Ask a question. This is a simple and easily implemented hook. It works because it immediately forces your reader to mentally engage and answer the question. It could be something as simple as "Who was Hephaestus?" Or try this one: "Despite being the son of Zeus, why is Hephaestus not more well-known?"
Use a definition. This is similar to a quote, but it tends to target a reader's logic center instead of their emotional core. For an essay on Hephaestus, I would actually recommend that you steer clear of this hook.  I recommend this because the definition hook works better when the essay topic is about something other than a person, character, or mythological figure; however, you could perhaps define "fire" or "masonry" or "blacksmithing," because Hephaestus is the god of those things.
https://www.georgebrown.ca/uploadedFiles/TLC/_documents/Hooks%20and%20Attention%20Grabbers.pdf

What is she talking about when she mentions a smell creeping in the house

The narrator mentions that, in addition to its sickly and grotesque appearance, she hates the wallpaper's smell. She says that she did not really notice it much when the weather was nice and she could keep the windows open, but after a week of wet weather, the smell hangs heavily in the room.  She says, "It creeps all over the house." She can find it in the dining room and parlor, the hallway and stairs, and even on her own person. Notice, however, that when she is finished describing the wallpaper's terrible "yellow smell," she says,

There is a very funny mark on this wall, low down, near the mopboard.  A streak that runs around the room. It goes behind every piece of furniture, except the bed, a long, straight, even smooch, as if it had been rubbed over and over.  I wonder how it was done and who did it, and what they did it for. Round and round and round—round and round and round—it makes me dizzy!

If we put two and two together (something the narrator seems no longer capable of doing), we can surmise that she has caused the "smooch" around the room. How else would she know that it goes behind almost all the furniture? How else would she become dizzy unless she herself were going in circles around the room? We do not get dizzy just by looking at circles.
As if to confirm this, the narrator reports near the story's end that "[her] shoulder just fits in that long smooch around the wall."  So, the narrator has been crawling around the room—or "creeping," as she calls it—and she is rubbing against the wallpaper, making it so that she smells it in her hair and on her clothes. Even Jennie, the narrator's sister-in-law, says, "that the paper stained everything it touched, that she had found yellow smooches on all [the narrator's] clothes."  So, the smell appears to creep all over the house, wherever the narrator goes, because the smell of the paper is actually on the narrator.  

How does the narrator feel after leaving the signalman following his second visit?

When the narrator leaves the signal man's hut for the second time, he is extremely concerned, for several reasons. First of all, he is pained on behalf of the signal man as a person: he is evidently struggling with his conscience, and possibly with, the narrator seems to indicate, some kind of mental strain, and the narrator doesn't want him to suffer in this way. Secondly, he is also concerned for "public safety" as a result of his concern for the man's state of mind—in his position, he is responsible for the safety of everyone on and near the railway line, and should something happen to him, terrible consequences could arise. The narrator feels burdened by the knowledge of what a state the signal man is in, and is tortured as to what he should do. He feels partially as if he should tell the man's superiors what he knows, but ultimately decides that this would be treachery on his part. Instead, he decides to take a "middle" ground and accompany the man to a doctor.

After his second visit, the narrator feels very concerned for the emotional and psychological well-being of the signalman. Note, for example, that the narrator offers to spend the night in the signal box but that the signalman will not hear of it. This shows that the narrator feels a genuine sense of compassion toward the signalman.
Moreover,  after their conversations, the narrator knows that the signalman is an "intelligent" and  "vigilant" person. However, given the events that have happened, the narrator wonders how long the signalman will remain this way.
It is clear, then, that the narrator believes the signalman's story and is worried about the signalman's state of mind. You will notice that the narrator looks back at the red light more than once as he leaves the signal box, a sign that he understands and shares the signalman's fears and concerns. 
The narrator plans to return to the signalman the next day and accompany him to a medical doctor to prove his version of events. This desire to help the signalman further reinforces the narrator's genuine sense of concern toward the signalman.

Find reasoning for why Atticus is courageous.

Different readers will likely find slightly different reasons for why Atticus Finch is a brave and courageous character.  For me, two things stand out more than anything else.  
I think the most courageous thing that Atticus does is take the Tom Robinson case.  Atticus is a good and experienced lawyer.  He knows full well that he is likely to lose the case, but that's not the only reason taking the case is courageous.  By taking the case, Atticus is risking his reputation and good standing in the community.  He's even putting himself at risk of physical harm.  People could very well do harm to Atticus (or his family) for no other reason than because he is the man defending someone whom everyone assumes is guilty.  
The other courageous act that really stands out to me is when Atticus decides to go to the jail and wait for the lynch mob to show up.  

A long extension cord ran between the bars of a second-floor window and down the side of the building. In the light from its bare bulb, Atticus was sitting propped against the front door. He was sitting in one of his office chairs, and he was reading, oblivious of the nightbugs dancing over his head.

Atticus knew that putting Tom in that jail was a bad idea, and Atticus knew that people would make an attempt on Tom's life in order to get their own sense of justice.  He went to the jail in order to protect Tom from the lynch mob.  He had to have known that he wasn't likely going to be able to hold them off on his own.  He had to have known that reasoning with them wasn't likely to be successful, and he had to have known that he would have lost any kind of physical fight against a group that far outnumbered him.  It took a great deal of courage for him to stand up for what he knew to be the right thing, even in the face of physical harm.  Fortunately, Scout and Jem showed up, and Scout was able to convince Mr. Cunningham to go home.  

Atticus said nothing. I looked around and up at Mr. Cunningham, whose face was equally impassive. Then he did a peculiar thing. He squatted down and took me by both shoulders.
“I’ll tell him you said hey, little lady,” he said.
Then he straightened up and waved a big paw. “Let’s clear out,” he called. “Let’s get going, boys.”

Calculus: Early Transcendentals, Chapter 7, 7.3, Section 7.3, Problem 4

You need to use the following substitution, such that:
x = sin t => dx = cos t dt
1 - x^2 = 1 - sin^2 t = cos^2 t
Changing the variable, yields:
int_0^1 x^3*sqrt(1 - x^2)dx = int_(t_1)^(t_2) sin^3 t*sqrt (cos^2 t)*cos t dt
int_(t_1)^(t_2) sin^3 t*sqrt (cos^2 t)*cos t dt = int_(t_1)^(t_2) sin^3 t*cos t*cos t dt
int_(t_1)^(t_2) sin^3 t*cos^2 t dt = int_(t_1)^(t_2) sin^2 t*cos^2 t*sin t dt
int_(t_1)^(t_2) sin^2 t*cos^2 t*sin tdt = int_(t_1)^(t_2) (1 - cos^2 t)*cos^2 t*sin tdt
You need to make the next substitution, such that:
cos t = u => -sin t dt = du
int_(u_1)^(u_2) (1 - u^2)*u^2*(-du) =- int_(u_1)^(u_2)u^2 du + int_(u_1)^(u_2)u^4du
int_(u_1)^(u_2) (1 - u^2)*u^2*(-du) =(-(cos t)^3/3 + (cos t)^5/5)|_(t_1)^(t_2)
Since x = sin t => t = arcsin x
int_0^1 x^3*sqrt(1 - x^2)dx = (-(cos (arcsin x))^3/3 + (cos (arcsin x)^5/5)|_(0)^(1)
int_0^1 x^3*sqrt(1 - x^2)dx = (-(cos (arcsin 1))^3/3 + (cos (arcsin 1)^5/5 + (cos (arcsin 0))^3/3 - (cos (arcsin 0))^5/5)
int_0^1 x^3*sqrt(1 - x^2)dx = -(cos (pi/2))^3/3 + (cos(pi/2))^5/5 + (cos 0)^3/3 - (cos 0)^5/5
int_0^1 x^3*sqrt(1 - x^2)dx = 1/3 - 1/5
int_0^1 x^3*sqrt(1 - x^2)dx = 2/15
Hence, evaluating the definite integral yields int_0^1 x^3*sqrt(1 - x^2)dx = 2/15.

What is the strange series of events that begins for Richard Hannay?

One day, when Richard Hannay is going back home as usual, a man who lives in a flat on the top floor of the same building asks to speak to him in Richard’s flat. Richard lets him in and the man named Franklin Scudder tells him a strange story. He says a wicked group is plotting to get European countries at war by assassinating the Greek Prime Minister Constantine Karolides when he visits London on June 15. He is being chased by that group because he has learned of the plot. He has planted a body in his flat, hoping that people will think he’s dead. Richard agrees to provide shelter for Scudder, but a few days later, he finds him murdered in his flat. Richard immediately realizes that the group has found Scudder and will probably murder him too, so he flees to Scotland with an important notebook Scudder has hidden in his tobacco jar and starts a patriotic adventure.

Many of the social tensions of the early republic were rooted in conflict between humane considerations and the desire for economic and political growth. Where can you see these tensions at work? Is there any instances of successful resolution?

The early republic was marked by tensions between an effort at reform (a humane consideration) and the desire of the country to grow economically and politically. The Second Great Awakening, a religious movement which occurred around 1800, gave rise to many different types of reform movements, including abolitionism, temperance, and women's rights. However, these movements struggled to achieve their goals in the midst of the national fervor for economic and political growth.
Abolitionism in particular ran up against the fervor for growth. While many people came to believe that slavery was morally wrong, slavery was integral to the agricultural economy of the South. Cotton in particular became very profitable following the development of Eli Whitney's cotton gin in the late 1700s, as the gin made it possible to remove seeds quickly from different varieties of cotton plants that grew all over the South. Cotton was the "king" of Southern agriculture, and abolitionists were met with the refusal of the South to give up a labor system that fed the growth of cotton. In addition, abolitionism ran up against political demands for western growth. As settlers moved west, they often brought slavery with them (in particular to Texas over time), and the desire for westward growth caused slavery to grow rather than to be eradicated.
There were few successful resolutions of this conflict, as compromises such as the Missouri Compromise of 1820 only caused a delay in outright warfare rather than resulting in a compromise that pleased both sides. In the Missouri Compromise, one state (Missouri) was admitted to the Union as a slave state while another state (Maine) was admitted to the Union as a free state. This only delayed the outbreak of the Civil War and did not prevent it. As a result, humane considerations were in opposition to political and economic demands in the early republic, and this conflict in part led to the Civil War.

sum_(n=1)^oo 1/n^5 Use the Integral Test to determine the convergence or divergence of the p-series.

The Integral test is applicable if f is positive and decreasing function on the infinite interval [k, oo) where kgt= 1 and a_n=f(x) . Then the series sum_(n=1)^oo a_n converges if and only if the improper integral int_1^oo f(x) dx converges. If the integral diverges then the series also diverges.
For the given series sum_(n=1)^oo 1/n^5 , the a_n = 1/n^5 then applying a_n=f(x), we consider:
f(x) = 1/x^5 .  
As shown on the graph for f(x), the function is positive on the interval [1,oo). As x at the denominator side gets larger, the function value decreases.

Therefore, we may determine the convergence of the improper integral as:
int_1^oo 1/x^5 = lim_(t-gtoo)int_1^t 1/x^5 dx
Apply the Law of exponent: 1/x^m = x^(-m) .
lim_(t-gtoo)int_1^t 1/x^5 dx =lim_(t-gtoo)int_1^t x^(-5) dx
Apply the Power rule for integration: int x^n dx = x^(n+1)/(n+1)
lim_(t-gtoo)int_1^t 1/x^5 dx =lim_(t-gtoo)[ x^(-5+1)/(-5+1)]|_1^t
                            =lim_(t-gtoo)[ x^(-4)/(-4)]|_1^t
                            =lim_(t-gtoo)[ -1/(4x^4)]|_1^t
Apply the definite integral formula: F(x)|_a^b = F(b)-F(a) .
lim_(t-gtoo)[ -1/(4x^4)]|_1^t=lim_(t-gtoo)[-1/(4*t^4) -(-1/(4*1^4))]
                             =lim_(t-gtoo)[(-1/(4t^4))-(-1/4 )]
                            =lim_(t-gtoo)[-1/(4t^4)+1/4]
                           = 1/4 or0.25
Note: lim_(t-gtoo)[1/4] =1/4 and lim_(t-gtoo)1/(4t^4) = 1/oo or 0
The integral int_1^oo 1/x^5  is convergent therefore the p-series sum_(n=1)^oo 1/n^5 must also be convergent. 

In John Wyndham’s book The Chrysalids, why are mutations so important, and how are they related to religion?

Waknuk society was established in the wake of a nuclear holocaust, which has significantly affected the world's landscape and genetic pool. The citizens of Waknuk are religious fanatics, who consider any deviation or genetic mutation a blasphemy against the true Image of God. All forms of genetic mutations are considered Offences in Waknukian society and must be severely punished. Mutations in plants or animals are referred to as Deviations, which are immediately destroyed once they are discovered. A human with a genetic mutation is labeled a Blasphemy and sent to the Fringes of society, where they struggle to survive among other individuals with mutations or deformities. Religion plays a significant role in Waknukian society, and the citizens strictly adhere to the Bible and Nicholson's Repentances. Their ideology and intolerance towards individuals and other living things with mutations are based on their narrow interpretation of the true image of God. David's father, Joseph Strorm, is the foremost adherent of Waknuk's religion and is depicted as an intolerant zealot, who ruthlessly persecutes deviants and any person he feels is not behaving morally. Genetic mutations are significant to the Waknukian religion because it provides the fanatics like Joseph Strorm a target and allows them to increase their authority and status as a religious leaders.

Mutations are important in this book because they are something that the society abhors and actively seeks to root out and destroy. Any changes in the gene pool that are deemed outside the normal range are eliminated. These people are called "Deviants," and they are killed, kicked out of society to the Fringes, or sterilized. Regardless of the method, that person's genetic code has been effectively removed from society. To Waknuk society, mutations are important because they are dangerous and subversive societal elements. If you wanted to, I suppose you could substitute "mutations" and "mutants" for "religion" and "religious followers." In that case, religion and anybody associated with it would be deemed a subversive element of a given society, and the society would actively seek to eliminate any kind of religion in order to protect the rest of society. If by "religion" the question is asking about Waknuk religion, then the answer does not change much. The Waknuk society's religion reveres genetic purity, so any mutations are seen as a threat to that particular aspect of their religion. The persecution of Deviants is therefore a holy war.

Intermediate Algebra, Chapter 3, 3.4, Section 3.4, Problem 12

Illustrate the linear inequality $x + 4y \geq - 3$ in two variables.

To graph $x + 4y \geq -3$ we must graph the boundary line $x + 4y = - 3$ first. To do this, we need to find the
intercepts of the line

$x$-intercept (set $y = 0$):

$
\begin{equation}
\begin{aligned}
x + 4 (0) &= - 3\\
\\
x &= -3
\end{aligned}
\end{equation}
$


$y$-intercept (set $x = 0$):

$
\begin{equation}
\begin{aligned}
0 + 4y &= -3 \\
\\
4y &= -3 \\
\\
y &= - \frac{3}{4}
\end{aligned}
\end{equation}
$


Now, by using test point. Let's say point $(0,0)$ from the right of the boundary line.

$
\begin{equation}
\begin{aligned}
x + 4y &\geq - 3\\
\\
0 + 4(0) &\geq -3 \\
\\
0 &\geq -3
\end{aligned}
\end{equation}
$


Since the inequality symbol is $ \geq $, then the boundary line must be solid.
Moreover, since the test point satisfy the inequality, then we must shade the right
portion of the boundary line. So the graph is,

What impact did the Vietnam War have on the American people?

The Vietnam War had lasting impacts on the American people. This war not only impacted individuals, but society and government as well. The effects of the Vietnam War continue to show themselves today. 
The Vietnam war had tremendous impact on individuals. Many soldiers were drafted and forced to leave their families behind. A large number of these soldiers did not return. The Vietnam Was was one of the deadliest American wars of all time. The men who returned from had experienced something horrific and were often physically injured as well as being traumatized. The families of soldiers were also significantly impacted, not only while their soldier was gone, but upon their return as well. Families worked to help rehabilitate these soldiers, whose lives would be forever changed. Other individuals and families were impacted by the efforts ro avoid the draft. Many people chose to leave the country rather than accept their draft orders. This had tremendous impact on these men and their families.
The wars also had a serious effect on American society. The Vietnam War created a rise in protest culture across the country. Many people were unsure about the reasoning and information being put out about the war. Young people especially opposed the war and the draft very openly. The Vietnam Was was the first war to be broadcast on television, this meant that Americans were able to see what was happening in Vietnam. Many people felt that the methods being used in Vietnam were brutal, and being able to see it happening only intensified protests. People also began to loose faith in the government as discrepancies between what politicians were saying and what was actually happening came to light. For example, the US government claimed to have never bombed Cambodia, but it was soon shown that this was not the case. The protest culture that intensified during the Vietnam War continues to show itself today, especially on college campuses and within young people today.
The Vietnam war led to several policy changes as well. The draft system was eliminated after the Vietnam War in exchange for an all volunteer military force. To this day, the draft has not been implemented again. The voting age was also lowered to 18, which is the voting age which holds to this day. People argued that a person who was sent to fight a war for their country should be allowed to vote in their country. Several restrictions relating to how long soldiers could remain in a war zone at a time were also passed after the war ended. These policy changes were implemented in response to the work protestors were doing, and all worked to serve soldiers who had volunteered or been drafted to fight a complicated and often perplexing war. 
It is clear that the Vietnam War had lasting effects on the American People. Though many of the effects were horrible and life changing, policy change and a society that seeks out the truth and fights for what they believe in was also brought to life as a result. 
 
 
 

The Vietnam War had a tremendous impact on the American people. One impact was that many young Americans were drafted and had to go and fight in the conflict in Vietnam. Many of these soldiers either were killed, injured, or experienced lifelong trauma as a result of being in the conflict. Eventually, there were massive protests throughout the country regarding American participation in the Vietnam conflict. Some of these protests turned deadly, such as the one at Kent State University.
Many Americans began to distrust the government as a result of its actions during the conflict. Since this was the first conflict covered by television news programs, Americans could see with their own eyes what was happening in Vietnam. The images that were shown and the stories that were told did not match what the people were hearing from the government. For example, the government kept saying how the conflict was going well and was nearing an end. However, the North Vietnamese launched the Tet Offensive in 1968. The discrepancy between what the government was saying and what people were seeing and hearing led to the development of a credibility gap. It could be argued that this credibility gap still exists today.
The conflict in Vietnam was very costly for the United States in economic terms. The United States spent about $168 billion on the conflict. The United States also spent a lot of money on President Johnson’s War on Poverty programs. This led to increased inflation in the United States.  
Americans were significantly impacted by the conflict in Vietnam.

Is Beowulf an epic?

Beowulf is considered one of the oldest English poems. It is a narrative poem that tells the story of Beowulf, a brave warrior who voluntarily sails to Denmark with several fellow warriors to protect King Hrothgar and his friends. The king and his friends are gathered at Heorot, a mead-hall, feasting and celebrating. Unfortunately, their jubilant noises draw the attention of the demon, Grendel, who comes each night to kill and destroy. Beowulf defeats the first demon; however, the peace is short-lived, and he soon faces further trials.
The story was originally transmitted orally and was not written down for several centuries. Though the story was set in the sixth century, many scholars estimate that the earliest existing manuscript was likely written in the eleventh century. After Beowulf was written down, there was a time when the poem was seemingly forgotten. Thankfully, more recent scholars, including J.R.R.Tolkien and Seamus Heaney, felt this historical piece was an important monument in the English literary canon and translated Beowulf from Old English (which is incomprehensible to today’s readers) into modern English. The poem’s long and complex history has inspired many scholarly debates.
One prevalent debate is about whether Beowulf deserves to be categorized as an epic.  An epic is generally a long narrative poem that focuses on a journey to a distant land. Most focus on a hero who goes on a journey to defeat a monster, often with the help of several loyal friends; this journey typically concludes with the hero winning a great victory.  Additionally, epics often include examples of supernatural figures, often gods, intervening in the chaos and aiding the hero’s efforts. They usually involve themes such as loyalty to one’s leaders, courage in the face of great trials, human mortality, and returning home. Some of the most famous epics include The Iliad and The Odyssey, written by Homer during the 8th century. Interestingly, like Beowulf, The Iliad and The Odyssey were originally oral stories. These stories were written down by Homer centuries later. Another well-known epic poem is The Aeneid, written in Latin by Virgil in the first century.
It can be argued that Beowulf has enough similarities with its predecessors to be deemed an epic. This can be justified by pointing out:


Its great length—the poem is over 3000 lines long.

Its brave hero—Beowulf faces monsters and risks his life to save many lives.

Its mighty monsters—Beowulf defeats three terrifying monsters: Grendel, Grendel’s mom, and a dragon.

Its great journey—Beowulf departs from his homeland, Geatland, to fight the monsters in Denmark.

Its inclusion of companions—Beowulf takes several of his companions from Geatland to fight beside him.

Its epic themes—Beowulf includes the theme of homecoming when Beowulf returns to his homeland and rules as king for fifty years after defeating Grendel. Loyalty is seen in Beowulf’s decision to defend King Hrothgar and his kingdom; loyalty is also seen when Wiglaf stays by Beowulf’s side and helps battle the dragon. Courage is shown as Beowulf fights three treacherous monsters. Human mortality is seen both in the deaths of King Hrothgar’s subjects (by Grendel) and in Beowulf’s eventual death (by the dragon).

These are some of the characteristics that Beowulf shares with other epic poems.
However, some scholars rebut this argument by citing Beowulf’s death, which was caused by wounds he received battling the dragon. Though he kills the dragon first, it is unusual for a hero to be defeated in epic poetry.  Additionally, some believe that Beowulf is too selfish to be considered an epic hero. Though he goes to protect King Hrothgar and his friends early in the poem, it can be argued that he is motivated by a selfish desire to demonstrate his power rather than a desire to help others. It can also be argued that Beowulf’s decision to fight the dragon was prompted by a selfish desire for dragon plunder, rather than a selfless desire to protect a kingdom. Most epic heroes fight to help others, rather than focusing on themselves.
https://www.cliffsnotes.com/literature/b/beowulf/about-beowulf

What does blood symbolize for Macbeth and his wife in Shakespeare's Macbeth, particularly immediately following Duncan’s murder and late in the play?

Blood is a very important symbol in Macbeth. It seems to symbolize guilt, specifically guilt pertaining to the murder of Duncan. Lady Macbeth in particular seems to imagine that the metaphorical blood on her hands (the indication of the pair's guilt) may have been transmogrified into something literal that might be perceived by others.
Before he murders Duncan, Macbeth hallucinates a dagger "bloody" with Duncan's blood. This bloody dagger is the instrument of the murder and serves as testament to Macbeth's guilt. Later, as she spirals into madness, Lady Macbeth becomes preoccupied with the idea that the blood of her guilt will never be washed from her hands—"will these hands ne'er be clean?"—and that the "damned spot" of her guilt cannot be eradicated from her.
Of course, the blood is no longer there—it is in Lady Macbeth's mind only. Indeed, Lady Macbeth did not physically commit the murder and therefore was never bloodied to begin with. However, she sees the blood on her hands as evidence of her significant part in killing Duncan, whether or not she physically participated in the act.

Blood traditionally symbolizes violence.  For the Macbeths, blood also symbolizes guilt resulting from violence.  They kill Duncan in a fit of ambition and then have great regret about doing so.  They often imagine blood that is not there or remember seeing blood, symbolizing their mixed feelings about their deed.
When Macbeth is trying to decide whether or not to go through with the plan to kill the king, he imagines a bloody dagger hanging in the air.  Hallucination is not unusual for the Macbeths.  He hasn’t even committed the act yet, but he already feels conflicted and overrun with guilt about it.

… I see thee still,And on thy blade and dudgeon gouts of blood,Which was not so before. There's no such thing:It is the bloody business which informsThus to mine eyes. Now o'er the one halfworldNature seems dead, and wicked dreams abuseThe curtain'd sleep … (Act 2, Scene 1)

Blood and the visions of it follow him.  Macbeth imagines the bloody ghost of Banquo at the banquet after sending murderers to kill him and his son.  The sight so disturbs him that they have to send their guests home early with excuses about how it’s no big deal because Macbeth is just having a fit.
Lady Macbeth is not immune to the bloody visions.  She did not kill Duncan, but she was involved in the planning and saw the body. After the murder, she took the bloody daggers from Macbeth, chiding him for not following the plan and leaving them there to complete the frame-up job.  She covers for him when he sees Banquo's ghost, but she does not really know about his murder spree.  
Lady Macbeth completely breaks down mentally, imagining that the blood that was on her hands that night is still there.

LADY MACBETH
Out, damned spot! out, I say!--One: two: why,then, 'tis time to do't.--Hell is murky!--Fie, mylord, fie! a soldier, and afeard? What need wefear who knows it, when none can call our power toaccount?--Yet who would have thought the old manto have had so much blood in him. (Act 5, Scene 1)

She eventually dies, apparently of suicide.  Macbeth is shaken, and her death makes him ponder the frailty and brevity of life.  It does not stop him from going to battle with Malcolm's men, a battle he is destined to lose because he is outnumbered and following contradictory supernatural advice from witches.
The witches told Macbeth that he could not be harmed by a man "of woman born," so he figured he was safe.  The other prophecies seemed mostly crazy, such as the forest coming after him, but he was also told to beware Macduff.
Macbeth loses his confidence when Macduff tells him that he was not born of woman, and therefore sees him as a threat.  That is the end of Macbeth.  He cuts off Macbeth's head, and Malcolm becomes king.

Single Variable Calculus, Chapter 2, 2.5, Section 2.5, Problem 25

Explain using theorems of continuity why the function $h(x) = \cos ( 1 - x^2)$ is continuous at every number in its domain. State the domain


We can rewrite,
$\quad h(x) = f(g(x))$

Where,
$\quad f(x) = \cos x \text{ and } g(x) = 1-x^2$


The functions $f(x) = \cos x$ and $g(x) = 1 - x^2$ are examples of the functions that are continuous on every number in its domain according to the definition.
Also, from the definition, the composite function $h(x)$ will be continuous on every number on its domain as well.

Therefore,

$\quad $The domain of $h(x)$ is $(-\infty, \infty)$

What makes The Castle of Otranto a Gothic fiction?

The Castle of Otranto is considered the Ur-text of all subsequent gothic fiction, as it established many of the tropes and imagery which would come to define the genre. Here are a few of them:
It takes place in an exotic past. For the eighteenth-century audience, the Middle Ages was a distant time period associated with pre-enlightenment attitudes. For the specifically English audience Horace Walpole was writing for, the Catholicism of these characters was another exotic element, as England was firmly Anglican by this time. This lends the story both an escapist element and a sense of the unfamiliar.
It focuses on terror and suspense. From the beginning of the story, Otranto's atmosphere is steeped in foreboding and dread. Gothic fiction is known for inspiring feelings of unease in its audience, even sometimes through the setting alone. Characters are thrust into uneasy situations: being trapped in a dark castle, being threatened with violent acts, and being frightened by supernatural elements.
The characters in Otranto have plenty of reasons to be terrified: Isabella is threatened with rape at the hands of Manfred, Manfred is terrified of supernatural forces which seek to end his line, and Theodore is almost killed by Manfred's insatiable paranoia and tyranny.
It combines the uncanny with depictions of normal life. While much of Otranto might seem outlandish today, what made it unique during its original publication was its combination of supernatural terror with grounded characters and setting. This is no fairy story, but a relatively realistic medieval setting with characters who largely possess some depth to them (particularly Manfred and Matilda). This element of gothic literature would be much more emphasized in later incarnations of the genre, such as in the gritty setting of Wuthering Heights or the realistic London streets of The Strange Case of Dr. Jekyll and Mr. Hyde.
It features supernatural elements. Otranto's titular castle is a labyrinth of dark corridors, doors that open and shut of their own accord, paintings that move and sigh, and other such bumps in the night. Inspiring fear in the audience has been a big part of gothic fiction's legacy, and Otranto did that thoroughly for its original audience.

Walpole's Castle of Otranto is considered the first Gothic novel and contains many of the elements that would become standard in Gothic fiction.
For example, the story takes place in the Middle Ages and is set in a suitably creepy and mysterious castle complete with secret passages, towers, and trapdoors.
Further, the novel merges a realistic story with supernatural elements. These include a giant helmet falling from the sky and crushing Manfred's son Conrad, the animated portrait of Ricardo, doors that open and shut by themselves, and frightening, mysterious sounds. Many of these elements (though not the giant helmet) have become standard features of Gothic novels.
In addition, the book features a cruel and frightening paternal figure in the character of Manfred, along with a female who has to escape the clutches of the cruel male. In this novel, it is Isabella, who was engaged to marry Conrad before he was crushed. She has to escape Manfred when he decides to wed her against her will. In another motif typical of the Gothic, she takes sanctuary in a church and is protected by a friar.
Finally, the novel is characterized by an atmosphere of fear, foreboding, and terror, perhaps the chief characteristic of the Gothic genre.

Single Variable Calculus, Chapter 3, 3.6, Section 3.6, Problem 8

Determine $\displaystyle \frac{dy}{dx}$ of $2x^3 + x^2y - xy^3 = 2$ by Implicit Differentiation.

$\displaystyle \frac{d}{dx} (2x^3) + \frac{d}{dx} (x^2y) - \frac{d}{dx} (xy^3) = \frac{d}{dx} (2)$


$
\begin{equation}
\begin{aligned}
2 \frac{d}{dx} (x^3) + \left[ (x^2) \frac{d}{dx} (y) + (y) \frac{d}{dx} (x^2) \right] - \left[ (x) \frac{d}{dx} (y^3) + (y^3) \frac{d}{dx} (x) \right] &= \frac{d}{dx} (2)\\
\\
(2)(3x^2) + \left[ x^2 \frac{dy}{dx} + (y) (2x) \right] - \left[ (x) (3y^2) \frac{dy}{dx} + (y^3)(1) \right] &= 0\\
\\
6x^2 + x^2y' + 2xy - (3xy^2y'+y^3) &= 0\\
\\
6x^2 + x^2 y' + 2xy - 3xy^2y' - y^3 &= 0
\end{aligned}
\end{equation}
$



$
\begin{equation}
\begin{aligned}
x^2y' - 3xy^2y' &= y^3 - 6x^2 - 2xy\\
\\
y'(x^2-3xy^2) &= y^3 - 6x^2 - 2xy\\
\\
\frac{y'\cancel{(x^2-3xy^2)}}{\cancel{x^2-3xy^2}} &= \frac{y^3-6x^2-2xy}{x^2-3xy^2}\\
\\
y' &= \frac{y^3-6x^2-2xy}{x^2-3xy^2}
\end{aligned}
\end{equation}
$

How did the Progressives respond the the myriad of issues they saw in early 20th century America?

The Progressive Era ushered in many changes to American society. Progressives rejected Social Darwinism and believed government should be used as a way to counteract the problems faced by society.
In urban locations, political machines had become a source of corruption and deceit. These organizations offered jobs to immigrants in exchange for votes. They were propped up by local businesses who supported them in exchange for kickbacks. Political Progressives fought these machines and advocated for change in local government in an effort to improve efficiency. Initiatives, referendums and recall were all political reforms supported by Progressives. 
Social evils of the day were attacked as well. Journalists known as "muckrakers" exposed the public to the plight of life in the slums. These investigative journalists published stories of poverty, unsafe labor conditions and corruption in government.  Upton Sinclair exposed the vile meatpacking industry in his book, "The Jungle." 
Progressives sought to enforce prostitution laws and improve sanitation. The tragedy of the Triangle Shirtwaist Factory fire in 1911 sparked a movement toward better safety laws in the workplace. 
Alcohol was blamed as the influence behind many of the domestic problems of the day and found itself in the cross-hair of the Progressives. The Temperance movement led to the passage of the 18th amendment which banned alcohol.  
Other Progressive Era amendments include the 16th amendment which gave Congress the power to tax income, the 17th amendment which provided for the direct election of Senators, and the 19th amendment which finally gave women the right to vote across the entire nation.
Progressives attacked the problems they saw in society. They aggressively sought to improve life for the poor by using the power of the government to force social change. Improvements in education, regulation in the marketplace and food and water sanitation were gained by the Progressives. There is no doubt the lives of many Americans were improved by this era in American History.

What similes are used in the poem "To Autumn" by John Keats?

Similes are comparisons using "like" or "as." This makes them easy to locate in a work of literature, because in the absence of the words "like" and "as," there is no simile. However, not every use of "like" or "as" is comparative, so once we locate these words, we have to evaluate how they are being employed in order to determine if we are in the arena of a simile.

To be like Sherlock Holmes (that's a simile), let's go through this poem analytically. Since it contains one use of the word "like" and one of "as," there are at most two possible similes in the poem. The first is the following:

And sometimes like a gleaner thou dost keep

Steady thy laden head across a brook

"Like a gleaner" is the first potential simile. In this case, it truly is a simile, or comparison. Autumn is likened to a gleaner, a person who gathers the fruit or grain left behind by the harvesters.

The second possible simile is "sinking as the light wind." Is Keats comparing the "small gnats" to a light wind? Here, the answer is no. "As" can also mean "according to" or "because." In this case, Keats is using imagery, saying the the swarm of gnats (which he calls a "choir,") sinks or rises as the wind grows stronger or dies down:


Among the river sallows, borne aloft
Or sinking as the light wind lives or dies

John Keats' "To Autumn" is full of rich figurative language, and similes are certainly included (as a reminder, similes are comparisons that use "like" or "as"). In fact, one of my favorite literary similes occurs in the second stanza of Keats' poem: "And sometimes like a gleaner thou dost keep / Steady thy laden head across a brook" (19-20). This is a particularly virtuosic example of a simile, as it also includes some elements of personification. Keats compares the season of autumn to a "gleaner," someone who collected any leftover food from a field after the reaper finished his harvest. As such, while this example of figurative language is certainly a simile, it also employs some personification, as Keats is giving autumn human qualities. This example is just one of the masterful ways that Keats uses figurative language to describe the season of autumn, and I'd encourage you to read the piece for yourself to look for the other inventive ways Keats brings autumn to life. 
https://www.poetryfoundation.org/poems/44484/to-autumn

Why does Pachuco antagonize Henry?

In Valdeiz's play Zoot Suit, El Pachuco is a mythical, idealized figure who represents the spirit of the zoot-suited Chicano rebel of 1940s Los Angeles. In the play, he functions as a kind of Greek chorus, the name of a Chicano gang and an alter ego for Henry Reyna, the lead character.
When Henry (Hank) is wrongly accused of murder in the so-called "Zoot Suit Riots," he struggles with his Chicano identity and police brutality as they try to obtain a confession. In times of stress, Henry conjures up El Pachuco, who goads him with pride in his identity and honesty not to give in, despite the beatings, and to represent himself and his people with pride.
While the dialogues with El Pachuco encourage Hank, it seems he is convicted anyway, but Valdez offers multiple outcomes to the story, reminding us that Hank is a kind of Chicano everyman.

How would you describe each brother?

The eponymous Sonny decides to follow his dreams after he serves in the military. He's less settled and more transient than the narrator but still kind and, as the narrator says, not crazy. He's passionate about music. He was still in school the first time he tried heroin, and it's that which separates him from the narrator. The narrator stayed on the straight and narrow; Sonny veered off the path and into drugs. This was partially because of his attraction to music. The music scene was filled with people doing heroin, and it was expected that he would too. He uses music to express his pain and rage at the world. Sonny also gets emotional about music; when his brother doesn't know popular music artists, he rages at him and then insists he doesn't care what music the narrator listens to.
The narrator is different than Sonny. Rather than express his pain, he worked to overcome it; he wanted to provide a safe and successful life for his family. He follows a traditional path to success, joining the military, getting a college degree, and finding a steady career. He is cared for and respected. He dislikes the crowd that Sonny spends time with and is frustrated by Sonny's repeated drug use. Though he walks away from Sonny for a while, his loyalty eventually wins out and he contacts Sonny again. By the end of the story, he's made strides toward understanding Sonny's passion.

The narrator is a man who has accepted the responsibilities of being an older brother, a husband, and a father. It is arguable that in doing so, he has put his own needs and desires on the back burner. It begins when he promises his mother that he will always look after Sonny after she passes. He joins the military, marries, completes his education, pursues a career as a teacher, and looks after his family. Though he and Sonny go through periods of estrangement, he keeps his promise to his mother and works to understand and connect with his younger brother.
Sonny is a bit of a dreamer, and he is an artist. Like his older brother, he joins the military, but instead of attending college afterward, he seeks to learn all he can about playing jazz through listening, practicing, and becoming a denizen of New York's jazz scene. Unfortunately, that extends to the culture of heroin use that was prominent in the bop era in which Baldwin sets the story. Sonny finds his place in the world through his piano playing and the camaraderie with and understanding of his fellow musicians.

My question pertains to the movie by David Fincher based on the book. The protagonist has Dissociative Identity Disorder. Can you give some examples of how you feel the movie portrays this mental illness accurately, and also some ways that this movie makes a mockery of the illness—ways the illness is portrayed unrealistically—only adding to the already negative stigma attached to the disorder?

In David Fincher's adaptation of Chuck Palahniuk's satirical novel Fight Club, an unnamed narrator (Edward Norton) suffers from insomnia and depression in a materialistic world. He is weak and submissive with no life direction. When he "meets" the charismatic macho-man Tyler Durden (Brad Pitt), he begins to feel free. Durden is everything he is not: confident, masculine, and free-spirited. As it turns out, Durden is simply another personality of the narrator that the narrator imagined and mentally projected. When the narrator falls asleep, Durden takes over. The accuracy in the film's portrayal of Dissociative Identity Disorder is minimal. The narrator's creation of his other personality as a coping mechanism is realistic, for most cases of DID are acts of desperate coping. Yet, what Fight Club lacks is a severe mental trauma to cause the narrator to need Durden. In most cases, DID stems from some sort of childhood trauma that becomes too difficult to cope with. In Fight Club, the only traumas the narrator experiences are insomnia and existential depression.
One way in which the film—as many others similarly do—mocks mental illness is through its portrayal of Pitt's Tyler Durden as a violent psychopath. In addition to the brutal medieval-style violence of the fight clubs, Durden starts a terrorist organization called Project Mayhem. Mental illness in film and television frequently stigmatizes mental illness as being inherently violent or something for the general public to be afraid of. This is wholly unfair to those diagnosed with mental illnesses, for the categorization and dehumanization strays from offering actual help.
Another instance of making a mockery of mental illness comes from the physical manifestation of Tyler Durden—in other words, the fact that the narrator communicates with and sees Durden as another tangible being outside of his body. At the end of the film, the narrator begins to recognize Durden to simply be a split personality of his own, another fictionalized account, for few, if any, diagnosed with DID suddenly snap into the realization of their own illness. The narrator shoots himself in the mouth, "killing" Durden. Once again, the illness is trivialized, fictionalized, and mocked in order to provide a satisfying ending. Cures for mental illness such as Dissociative Identity Disorder are not as simple as recognizing the illness and causing self-harm to "kill" the other identity.
While an entertaining and iconic film, Fight Club certainly doesn't stand as a medically or psychologically accurate testament to a real mental disorder.

Why does Margaret Fuller structure her initial paper as a lawsuit?

Imagine life as a female intellectual in the nineteenth century. Margaret Fuller (Ossoli) was born in Massachusetts and was given an intense classical education by her father, who treated his daughter, academically, as though she was a young boy. Her education started at home but included a short period in her teens where she went away to school. She was urged to learn about fine arts, literature, and history, and she learned to enjoy thinking about and discussing academic topics. Yet, this type of education for females was frowned upon by the average American at this time in history, meaning that she had very few fellow women to discuss her intellectual wonderings with.
Life could be lonely for a female academic in that time. In fact, even though she was surrounded by scholars, including several transcendentalists, such as Ralph Waldo Emerson, she was rarely welcome in academic discourses. Many male scholars found her manner of speaking overly assertive and intense for a woman and were reluctant to invite her into their social circles. It was this widely prevalent disbelief in women's academic and social potential that led Fuller to write "The Great Lawsuit: Man versus Men, Woman versus Women," the precursor to her full-length book, Woman in the Nineteenth Century. This animosity toward women and their intellectual and social potential led Fuller to write her text in the form of a legal lawsuit. 
Fuller's friendship with Emerson was instrumental in developing both of their ideas. Though they did not always agree, they urged one another to consider ideas from new perspectives. Fuller was first acquainted with Emerson when she was invited, by his wife, to the Emersons' home in Concord, Massachusetts. (She was already curious about him, recognizing his growing fame as a local scholar.) From that point on, they maintained a frequent correspondence throughout her life, until she died in a shipwreck off the coast of the United States. This friendship allowed both Margaret Fuller and Ralph Waldo Emerson to grow in their views. It is arguable that Emerson's friendship with Fuller, filled with many intellectual conversations and debates, led him to advocate for women's rights in a couple of speeches, including his speech "Woman," which he gave in 1855.
Fuller was bold, intelligent, and unafraid to be a bit different. This is seen in her personal life as well, as she moved to Europe as a single woman in her thirties, joined the Roman Revolution of 1848, got romantically involved with a Roman Catholic man (though she was Protestant), had a child with him, and later married him. Fuller was a free-thinking woman of the nineteenth century. She challenged the intellectuals around her, including prominent scholars such as Emerson, to think more seriously about the capabilities of women through her words and actions. Her passionate belief in women's abilities to change the world is what led her to structure her literary piece in the form of a lawsuit. As Rebecca Rix, of Reed College, remarked:

"The Great Lawsuit" allowed Fuller to perform in text what she could not in reality: a sermon and a quasi-legal 'case' . . ."

As a woman, Fuller did not have many opportunities to preach the truths of women's capabilities or to present a case for their improved treatment. Since she couldn't actually speak this type of argument, she wrote out her case instead.
https://www.biography.com/writer/margaret-fuller

What is the difference between being innocent and being found not guilty?

When a person is accused and tried for a crime, the prosecution, the state, must prove beyond a reasonable doubt that the accused's actions have met all the requisite elements of the crime for a finding of guilt, generally that a crime has actually been committed by the accused and that the accused had the requisite intent.  When a person is found "not guilty," this means that the requisite elements have not been proven beyond a reasonable doubt, which is the standard in the United States in a criminal trial. This does not mean the person did not commit the crime.  It means there is insufficient evidence in some way, perhaps no physical evidence to connect the defendant to the crime or no means of establishing intent, for example, some sort of reasonable doubt.   But a finding of "not guilty" does not necessarily imply innocence.  A judge or a jury is in no position to judge that a person is innocent of a crime because the evidence presented by the defense need not prove that at all. The burden is on the state to prove that a defendant did commit the crime. There is no burden on the defense to prove that the defendant did not commit the crime.  The finding of "not guilty" speaks only to the evidence presented, not to the fact of innocence or guilt.  In Scotland, there is actually a distinction made in criminal trial verdicts such that the verdict may be "not guilty" or "not proven."  While I am by no means an expert on Scottish jurisprudence, it is my understanding that "not guilty" is meant to signal something closer to what might be considered innocence, while "not proven" signals that only that the prosecution could not make its case.      

What is the proper role of the government? What are its central responsibilities? What are the limits to governmental power?

The proper role of a democratic government is to govern for the people. The government's duties include, to establish justice, to form a more perfect union, to insure domestic tranquility, to provide for the common defense, to promote the general welfare, and to secure the blessings of liberty.
The Democratic Government should be a representation of its general population as well as representing what the people want and need. The central responsibilities of our government are protecting its citizens, and contributing to sustainable economic development. This means that the government should work toward bettering the lives of its citizens.
There are limits to governmental powers. The government, just like its citizens, is restricted by law. The rights and regulations of government are detailed in the constitution.

Many people have written about the proper role of government over the past several thousand years, and they have offered up a wide range of different opinions on the topic. For example, in Mesopotamian law codes, the ruler was thought to be an intermediary between the divine and the human and was understood as a protector of his people. Some of this attitude, with its inherent paternalism, was seen in notions such as the "divine right of kings" in the Renaissance, in which the Christian monarch combined secular and religious powers.
In the Enlightenment, many philosophers began to regard government as representing the will of its citizens and being in service to them. A government's legitimacy was contingent on the consent of the governed. John Locke was particularly influential in this line of political thought, and his work influenced the Constitution of the United States.
In modern democratic societies, government functions to perform tasks which are necessary for the collective good in a way representing the will of the governed. For example, governments are involved in police work and are responsible for dealing with crime, firefighting, and utilities, such as building aqueducts or other systems to provide cities with water. Governments may also enforce property rights. Defense, whether this involves the maintenance of standing armies or the establishment of militias in times of conflict, diplomacy, and relations with other countries are also typical functions of governments.
Governments vary in their economic roles: some economies are directed or managed by the state, while others simply provide legal frameworks within which free enterprise can operate. Some governments are organized to interfere as little as possible with the liberties of their citizens so long as those liberties do not harm others, while other governments attempt to regulate many different aspects of citizens' lives.

Is Luke O'Neill in The Thorn Birds more like Amir in The Kite Runner or Rasheed in A Thousand Splendid Suns?

Luke O'Neill in The Thorn Birds is more like Rasheed in A Thousand Splendid Suns. Luke is a heartless man who romances Meggie and gets her to marry him. Once married to Meggie, he is heartless and cold. He leaves her to harvest sugarcane and hires her out to be a housemaid to another family. Luke thinks mainly of money, and refuses to have a child until he is well established with a station (a ranch). Even after Meggie tricks him into having a child, he is not interested in raising the child and is loveless toward his wife.
Rasheed in A Thousand Splendid Suns marries Mariam out of expedience rather than love, similar to the reasons Luke marries Meggie in The Thorn Birds. Like Luke, Rasheed is loveless and impatient towards Mariam. Also like Luke, Rasheed sees women as sexual objects but not as objects deserving of love, and is impatient and abusive towards Mariam after they marry. Unlike Luke, Rasheed wants to have a child and is displeased when his wife has several miscarriages. After his second wife, Laila, gives birth to a daughter, Rasheed abuses the daughter and eventually gives her to an orphanage. He shows the same disregard for his daughter that Luke O'Neill shows toward his daughter. At first, Amir in The Kite Runner is an unethical boy who betrays his friend, Hassan. Unlike Rasheed and Luke, who are unredeemed, Amir eventually rescues Sohrab, Hassan's son. In the end, Amir is loving toward a child and redeems himself, unlike Rasheed and Luke. 

Calculus: Early Transcendentals, Chapter 7, 7.3, Section 7.3, Problem 16

int_(sqrt(2)/3)^(2/3)1/(x^5sqrt(9x^2-1))dx
Let's first evaluate the indefinite integral by integral substitution,
Let x=1/3sec(u)
=>dx=1/3sec(u)tan(u)du
int1/(x^5sqrt(9x^2-1))dx=int(1/((1/3sec(u))^5sqrt(9(1/3sec(u))^2-1)))1/3sec(u)tan(u)du
=int(1/(1/243sec^5(u)sqrt(sec^2(u)-1)))1/3sec(u)tan(u)du
Now use the identity:sec^2(theta)=1+tan^2(theta)
=int(243/(3sec^5(u)sqrt(1+tan^2(u)-1)))sec(u)tan(u)du
=int(81sec(u)tan(u))/(sec^5(u)sqrt(tan^2(u)))du
=81int1/(sec^4(u))du
=81intcos^4(u)du
Now let's use the identity:cos^2(theta)=(1+cos(2theta))/2
=81int((1+cos(2u))/2)^2du
=81int(1+cos^2(2u)+2cos(2u))/4du
=81int(1/4+(cos^2(2u))/4+1/2cos(2u))du
=81(int1/4du+int(cos^2(2u))/4du+int(cos(2u))/2du)
=81(u/4+1/4int(1+cos(4u))/2du+1/2intcos(2u)du)
=81(u/4+1/4int(1/2+cos(4u)/2)du+1/2(sin(2u))/2)
=81(u/4+1/4(int1/2du+intcos(4u)/2du)+1/4sin(2u))
=81(u/4+1/4(u/2+1/2sin(4u)/4)+1/4sin(2u)) =81(u/4+u/8+sin(4u)/32+sin(2u)/4)
=81((3u)/8+sin(4u)/32+sin(2u)/4)
Now recall that we have used x=1/3sec(u)
=>sec(u)=3x
=>cos(u)=1/(3x)
=>u=arccos(1/(3x))
Substitute back u and add a constant C to the solution,
=81(3/8arccos(1/(3x))+1/32sin(4arccos(1/(3x)))+1/4sin(2arccos(1/(3x))))+C
Now let's evaluate the definite integral,
int_(sqrt(2)/3)^(2/3)dx/(x^5sqrt(9x^2-1))=81[3/8arccos(1/(3x))+1/32sin(4arccos(1/(3x)))+1/4sin(2arccos(1/(3x)))]_(sqrt(2)/3)^(2/3)
=81[3/8arccos(1/2)+1/32sin(4arccos(1/2))+1/4sin(2arccos(1/2))]-81[3/8arccos(1/sqrt(2))+1/32sin(4arccos(1/sqrt(2)))+1/4sin(2arccos(1/sqrt(2)))]
=81[3/8*pi/3+1/32sin(4*pi/3)+1/4sin(2*pi/3)]-81[3/8*pi/4+1/32sin(4*pi/4)+1/4sin(2*pi/4)]
=81[pi/8+1/32sin((4pi)/3)+1/4sin((2pi)/3)]-81[(3pi)/32+1/32sin(pi)+1/4sin(pi/2)]
=81[pi/8+1/32(-sqrt(3)/2)+1/4(sqrt(3)/2)]-81[(3pi)/32+1/32(0)+1/4(1)]
=81[pi/8+sqrt(3)/2(-1/32+1/4)-(3pi)/32-1/4]
=81[pi/8-(3pi)/32+sqrt(3)/2(7/32)-1/4]
=81[pi/32+(7sqrt(3))/64-1/4]

What is the irony about Bob Ewell's response to Mr. Gilmer's question about being ambidextrous in To Kill a Mockingbird?

The irony attached to Bob Ewell's response to Mr. Gilmer's question about his being ambidextrous is that Ewell denies that he is "certainly not" ambidextrous, but adds, "I can use one hand good as the other," so he admits to it.
Of course, it is obvious that the uneducated and ignorant Ewell has no idea what the word ambidextrous means since he has inadvertently re-defined it when he asserts that he can use one hand as well as the other. In actuality, he thought that he was contradicting its meaning, not affirming it, by saying that he can use both his hands equally well.
As Scout listens to him on the witness stand, it becomes apparent to her just how backward and crude this man actually is as he uses vocabulary that is inappropriate to the courtroom. His descriptions, for instance, of what has occurred with Mayella is described in low terms, to say the least. At one point, for instance, Judge Taylor finds it necessary to tell Ewell to confine his testimony within the confines of Christian English Usage.

What material could I use to transition between teaching my students Shakespeare and the Augustan Age?

Given the additional details, I'd think about setting up the transition by establishing some sort of narrative arc for the course as a whole on the first day. One possibility would be to talk about genre in light of literacy levels. Poems and drama can appeal to a primarily illiterate audience because they are normally performed (lyric poetry was originally accompanied by music), while the proliferation of prose depended on the rise of vernacular literacy. For this sort of approach, you might choose some songs such as "Fine Knacks for Ladies" or "Drink to me only with thine eyes" that are widely available on YouTube in your Elizabethan section and then move on to talking about Defoe's prose appealing to middle class Dissenters.
For a technical school, you might use some of Defoe's The Complete English Tradesman, and talk about the rise of the novel as part of training the ambitious tradesman in the manners needed to succeed in retail business, linking the rise of the novel to conduct and politeness literature such as etiquette and letter-writing manuals. Swift would then fit as a satirist teaching correct behavior by criticizing improprieties. Students in a technical college might respond well to this very pragmatic understanding of literature as offering behavioral models, as they are dealing with this issue in their own lives. Especially for first-generation college students, part of succeeding in careers is learning the unspoken codes of certain types of middle class society (clothing, body language, accent, etc.) and you could ask your students to compare their own situation to that of the 18th century rising middle classes.

There are several possibilities. I think you might want to use a brief lecture as a bridge and talk about the Puritans, the Restoration, and the move toward tolerance after the traumas of the religious wars of the intervening period. 
A few works might help with this. A Letter Concerning Toleration by John Locke might be a good example of the shift in values towards reason and restraint. On a more literary level, one might use Pope's "Essay on Criticism" as a way of showing how literary tastes changed. His "Essay on Man" contrasts well with Milton, but is less important if you skipped over Milton. 
Some of how you handle the transition depends on what you are doing in your class. If you are focusing on poetry, this was a great age for satire, and Pope would be a good focus. If you are thinking about the rise of the novel, Watts is a bit dated but a good starting point for the conversation. Essays by Addison or Steele might also be a good way of establishing the new ideals of taste. 
To answer this more fully, I'd need a sense of the pedagogical context. The strategies that might work for a seminar in drama wouldn't fit an introductory lecture course. 

What is Grim's opinion of Maxwell's father in Freak the Mighty?

Grim and Gram are Max's grandparents and legal guardians. They are his legal guardians because his mother is dead, and his father is in jail. Max's dad, Killer Kane, is in jail because he murdered his wife. Readers do not find out that information until fairly late in the story; however, we are clued into the fact that Max's dad is not well liked by either Gram or Grim. In fact, Killer Kane is both hated and feared at the same time. He is either never talked about, or he is talked about in hushed tones. Their hatred for him runs so deep that Grim actually refuses to say his name. Pronouns are used instead. This aversion to speak Killer Kane's real name and general hatred makes sense because he killed their daughter.

Which is the way he always talked about my father, who married his dear departed daughter and produced, eek eek, Maxwell. Grim never says my father's name, just Him, like his name is too scary to say.

Some of the first things the reader hears about Max's father come from the character of Grim. Grim, of course, is the nickname Max gives to his grandfather who has taken him in. Grim's opinions about Max's father all revolve around fear of Killer Kane as a dangerous criminal.
First, Grim says that Max's father's name is “too scary to say.” As the plot moves on to the rising action, the reader learns that Max's Father (Killer Kane) is being released from prison. As a result, Grim reacts further. Grim wants to obtain a gun, but Gram is against it. Finally, Grim's opinion of Killer Kane is confirmed when Grim obtains a restraining order against Kane.

If [Killer Kane] does try to come here, they’ll send him back to prison. ... Everything is going to be okay.

Although this statement is designed to make Max feel safe, Grim still insists that Max stay inside for days. Of course, Grim's opinions are confirmed when Max's dad shows up and ties Max to a boiler.

Using the book, Night, by Elie Wiesel, discuss Elie's guilt after Shlomo's death.

When Elie and his father arrived at Buchenwald, they were all weak, tired and emaciated. A siren at the camp made Elie forget his father, and instead he rushed into the barracks with the mob. In the morning Elie looked for his father and a thought crossed his mind. He wished that he did not find his father because the situation would relieve him of the responsibility and allow him to focus on his own survival. Elie felt ashamed of himself, and the guilt of his thoughts followed him even after his father’s death.
In another instance, Elie grudgingly gave his father some soup after he realized that his father was not given any food. The situation reminded him of Rabbi Eliahu’s son, who left his father behind during the march out of Buna. According to Elie, he had failed the test just like the Rabbi’s son. The Blockalteste in Buchenwald made matters worse by asking Elie to abandon his father and take his ration of food. The thought that he could take his father’s portion of food left Elie feeling guilty.

What is one question and answer (not a summary) that is revealed in the chapters three and four?

It appears that the most important question in chapters 3 and 4 is as follows: "Are lies always morally objectionable, or are they permissible on the right occasion?"
The answer, according to the author, will depend upon who makes the choice and the procedures to arrive at such a choice. Depending upon our beliefs, we may choose to agree or disagree with the author, who rejects absolutist views about lying. He argues that some lies, when told to protect the innocent, are not to be classed with those that have malicious intent.
The author discusses both utilitarian and absolutist views about lying. He concludes that there is no homogeneity of opinion in both camps. Even among the absolutists who maintain that all lies occasion divine punishment, consensus is lacking when it relates to endangerment of life. The author contrasts Wesley, Augustine, and Kant's "single-minded upholding of truthfulness" with the utilitarian position of common-sense morality. To the utilitarian, a lie is permissible so long as it results in more happiness than unhappiness. In other words, a lie is permissible if it results in positive consequences.
However, the author maintains that utilitarians can only defend this stance on an individual basis. He argues that it is indefensible when the principle of utilitarianism must account for complex situations that involve a large group of people. Furthermore, the author rejects the tendency to render moral equivalence to a lie and falsehood that achieve the same utility. He maintains that, since most lies result in negative consequences and the loss of personal integrity, such a generalization is dangerous.
The question remains: are lies always morally objectionable, or are they permissible on the right occasion? The answer should rest on a case-by-case basis. Because of the complexities of human nature and of life itself, the author insists that both absolutists and utilitarians account for uncertainties that surround the moral alternatives.

What frightens Miss Caroline? Based on context clues, what do you think a “cootie” is?

One could argue that Miss Caroline is frightened of her own lack of teaching ability as much as anything. She's way out of her depth teaching a first grade class and so doesn't quite know how to deal with the children. Because of this, she makes a big mistake in offering to lend the dirt-poor Walter Cunningham a quarter for his lunch money. As Miss Caroline doesn't know anything about his background, she doesn't realize just what an insulting gesture this is to a member of the fiercely proud Cunningham clan. Scout helpfully tries to point this out to Miss Caroline, but all she gets is a rap across the hand with a ruler for her trouble.
The very prim, well-dressed Miss Caroline is also more than a little spooked at the large colony of "cooties," or hair-lice, that thrives on top of Burris Ewell's head. When she sees one of the little critters crawling out of Burris's filthy, matted hair, she jumps up and screams in terror.

In Chapter 3, Miss Caroline is teaching when suddenly a tiny bug jumps out of Burris Ewell's hair. The small bug scares Miss Caroline who steps back and begins to scream. Initially, the students find her reaction amusing, and Little Chuck Little informs her that it is only a "cootie" before getting her a cool glass of water. A "cootie" is simply a slang term for a small bug, in particular, a head louse. Scout goes on to mention that Burris Ewell is the dirtiest person she has ever seen. Miss Caroline finally settles down and tells Burris that he needs to go home and wash up. Burris then disrespects Miss Caroline and begins to call her rude names before he leaves the classroom.

Who is Maureen Peal? What does she represent in the novel?

Maureen Peal represents the problem of colorism, which exists in the black community but is not limited to it. Colorism is the discrimination that can occur among a race or ethnic group due to the tendency to prescribe value, usually, to those who have lighter skin.
Maureen is a little girl who knows that she has social value and she knows why: black people who have proximity to whiteness are deemed more beautiful and respectable than those who don't.
Maureen exists in the novel as a foil to Pecola Breedlove. This isn't merely because Pecola is very dark-skinned and Maureen is very light-skinned but also because Maureen is, as the previous educator noted, popular and charismatic, as well as intimidating (the narrator, Claudia, notes how the boys' eyes "genuflect" when they are around her), and vain. Everyone wants to be around her and Morrison reflects this in her name, Peal, which is the clear beckoning of a bell. Pecola is much nicer than Maureen, but no amount of sweetness or desire to be loved draws anyone toward her. Maureen's clothing is described as fashionable and neat, while Pecola's aren't. Maureen's hair curls in ringlets; Pecola's tightly-curled hair is in plaits that would be described as "nappy."
Claudia dislikes Maureen but also wants her approval. During a conversation about which Hollywood stars they love the most. Claudia expresses her distaste for Shirley Temple, whose saccharine-sweet image and ringlets remind her of Maureen. She expresses a preference instead, for the exotic beauty of Hedy Lamarr. The girls' friendship with Maureen ends with Maureen mocking them for being darker-skinned and acting as though she was doing them a favor by associating with them.
Maureen is one of the most distasteful characters in the novel, but it's easier to forgive her than, say, Geraldine, because she's a child. However, the fact that she's already internalized the tenets of racism, which teach her to believe that she is prettier, more lovable, and better than Claudia, Frieda, and Pecola because she's lighter-skinned reveals how pervasive and corrosive white supremacy is.

Maureen Peal is the new girl in school. She's attractive, charismatic, popular, and comes from a good family. Most significantly of all, however, she also happens to be light-skinned. This means that she approaches more closely to white society's notion of what is beautiful.
Maureen's introduction in the novel reinforces a number of important themes. For one thing, Maureen instills feelings of self-loathing in Claudia, who comes to hate herself on account of her dark skin. Maureen's so much better, she thinks, and all because of light skin.
Morrison's making a general point here. The prevailing standards of beauty in white society lead to African Americans not accepting themselves and their skin color. In this society, white is considered good and black bad. The only way that African Americans can become more accepted in this society is if they display the same kind of characteristics associated with white people, whether it's light skin, wealth, or high social status, all of which are possessed by Maureen Peal.

A balance and a graduated cylinder are used to determine the density of a mineral sample. The sample has the mass of 14.7 g and the volume of 2.2 cubic cm. What is the density of the mineral sample?

The density of a material is defined as a mass per unit volume. So if an object has a mass m, and the volume V, its density can be found as
D = m/V .
As described in the question, a balance can be used to measure the mass of the mineral sample. The volume of the sample can be determined by placing the sample in the graduated cylinder filled with water or another liquid. The level of the liquid in the cylinder rises as the sample displaces some of the liquid. The change of the level, measured by the markings on the cylinder, indicates the volume of the displaced liquid and thus, the sample.
The density of the sample with the given mass and volume then equals
D = m/V=(14.7 g)/(2.2 cm^3) = 6.68 g/(cm^3) .
Converted to the SI of the units of measurements, the density would be 
D = 6.68*10^3 (kg)/m^3 .
The density of the given sample is 6.68 gram per cubic centimeter.
 
http://hyperphysics.phy-astr.gsu.edu/hbase/dens.html

Why is The Seagull a naturalist play?

Literary naturalism is not the same as realism. Naturalism strives to depict humans as a part of nature—that is, subject to their environment—in a way that is detached or even clinical. Often the purpose of naturalist writers is to observe a social phenomena closely, like a scientist, in order to suggest a social critique. So it is with Chekhov.
The Seagull is a play about playwrights and actors, so in that sense the "phenomenon" it observes is its own production, or the artistic impulse that gives rise to plays. Chekhov observes his characters acutely. Their petty squabbles and unrequited loves form what amounts to the "action" of the play, but Chekhov's purpose is to show the friction between their personal desires (for artistic fame, or for a particular lover) and the social and class prejudices that make achieving happiness impossible, in the first place, but also how inadequate literary productions (like The Seagull itself) are at articulating that truth. An example of this is when Treplev kills the seagull (Nina's symbol of freedom) and lays it at her feet. Nina accuses Treplev of talking "in symbols," a charge that could just as easily be aimed at Chekhov. The dead bird is a symbol of Nina's lost freedom; she is "caught" by Treplev even though he does not love her; the dead bird is also a symbol of Treplev's inability to truly understand Nina; you can also think of the dead animal as way in which humans pervert nature in an attempt to make it mean what they want. None of these interpretations really speak to the problem these characters have, however, which is that they exist in a society that prevents actual human connection.

The Seagull (1895) is a play written by the Russian writer Anton Chekhov, and it is representative of his dramatic style. Naturalism in theater is a style that aims to create verisimilitude, or the illusion of reality, through character, acting, language, and dramatic structure.In naturalism, the actions of each character arise directly from the environment and time period that the playwright sets them in. In The Seagull, we see no clear protagonist but an array of characters who are quietly desperate to transcend their personal sense of failure and dissatisfaction. Similar to the Russian zeitgeist of the late nineteenth century, these characters complain and joke about needed personal and societal changes but are ineffectual in making these changes. True to naturalism, these characters represent the working class, artist class, and the bourgeoisie. Furthermore, the acting style employed in many productions of The Seagull is psychological realism, which is focused on the motivations of the characters.The language in The Seagull mimics reality by presenting speech that you might overhear out of the mouths of late nineteenth century Russian bourgeoisie. This speech is full of unfinished sentences, interruptions, pauses, and conversational phrases. Moreover, underneath the speech there is frequently a subtext at work, revealing that characters do not always say what they mean—just like people in real life. The dramatic structure of The Seagull does not follow a traditional Aristotelian arc, where the action of the play culminates in a singular climax and then resolves. Instead, the structure is closer to a feeling of real life, where dramatic tension is pulled taught by the conflicting desires of a network of characters.

How does the poem bring out the relationship between man and nature?

William Carlos Williams's modernist poem "Spring and All" does not explicitly describe the relationship between man and nature. The only real reference to the human world is at the very beginning of the poem when Williams references "the contagious hospital" in line 1. Williams was a doctor in addition to a poet, so he could be referring to observations he has had when going to or from his work at the hospital. The human observer expresses his attitude toward nature and specifically spring, but his relationship with nature is only implied.
The speaker describes nature in winter, with spring approaching. Of the trees the speaker observes, he says,

Lifeless in appearance, sluggishdazed spring approaches—They enter the new world naked,cold, uncertain of allsave that they enter. All about themthe cold, familiar wind (14-19)

The trees are "lifeless" and "uncertain" now, but as spring approaches, "objects are defined" (22). The spring will give nature a more solid identity. The speaker elaborates on this idea in the last several lines of the poem:

But now the stark dignity ofentrance—Still, the profound changehas come upon them: rooted theygrip down and begin to awaken (24-27)

This "profound change" that spring bring with it allows nature "to awaken." The way the speaker phrases this truth makes it sound like the trees will come into their own, embracing and defining their identities in a way that is not possible in winter when they are so new and "uncertain." The speaker describes the trees almost as though they have a human identity and are capable of understanding their power and potential. The speaker is inspired by his observations of nature to consider metaphysical concepts such as life and death.

How does the story "Where Are You Going, Where Have You Been?" show how women are oppressed in a patriarchal society?

From the very outset of the story, Oates implies that women are expected to adhere to traditional gender roles. In the first paragraph, she indicates that Connie meets society’s expectations for women by prioritizing physical beauty above all else, as Connie thinks “she was pretty and that was everything.” Connie notes that she is compared unfavorably to her sister, who “saved money and helped clean the house and cooked”; these activities also reflect traditional roles for women. Ultimately, though, looks seem to be more important (“Connie thought that her mother preferred her to June because she was prettier”), which suggests that women in this world are objectified rather than having agency of their own. This provides the backdrop for the larger action of the story.
The tension between Connie and the ironically named Arnold Friend serves as the most obvious representation of the oppression of women within a patriarchal society. Friend finds Connie at her home, a place that is supposed to be safe and secure, and threatens her family. Throughout the characters’ interactions, Oates carefully chooses words that highlight the unwanted aggression of men toward women. Arnold initially approaches Connie “grinning at her,” while Connie is on the defense, “careful to show no interest or pleasure.” As Arnold becomes more and more insistent that Connie bend to his will, she experiences “another wave of dizziness and fear rising in her,” viewing him as “just a blur” and feeling “light-headed.” Connie is “panting” and her fingers are “shaking” as Arnold tells her, “I’m always nice at first, the first time” and then “gently” questions why she would bother to lock the flimsy screen door. As he points out, “This place you are now—inside your daddy’s house—is nothing but a cardboard box I can knock down any time.” Ultimately Connie does give in, recognizing her body “wasn’t really hers.” Symbolically, Arnold Friend represents male desire for women, and Connie is forced to yield to his will against her wishes, just as women have so often been forced to do what men want.

How did the Homestead Act and the Morrill Act open up the West?

The Homestead Acts were a series of laws passed by the United States government between 1860 and 1930. They opened up over 10%, or 270 million acres, of the total land in the United States to applicants free of charge. Each homestead law had its own requirements for applicants, but the most famous one, the Homestead Act of 1862, said that any adult citizen who had no history of violence against the government was allowed to apply for a piece of land, called a homestead, which was usually 160 acres in size. The land was given to applicants free of charge; all they had to pay was a small application fee. Most of this land was west of the Mississippi River, so the laws led to a massive increase in the number of Americans living in the western part of America. People who received a homestead were required to farm the land, build a home on the land, and live on the land for at least five years.
The idea behind the series of homestead laws was to encourage individuals to farm their own land without the use of slave labor in order to increase productivity in America and to expand the number of American citizens living in areas that previously were not occupied by American settlers.
There are two Morrill Land-Grant Acts: one passed in 1862 and another in 1890. The Morrill Act of 1862 was signed into law by President Abraham Lincoln two months after the Homestead Act of 1862. This act was not passed primarily to encourage expansion into the West (they provided land grants for colleges in every state, east or west), but it nonetheless helped support many of the new farmers on their newly acquired western land. Here's why: Under the Morrill Acts, the United States government provided land to each state on which to build colleges. These colleges were expected to teach agricultural skills. The agricultural focus of the colleges taught farming and other mechanical skills to many of the new homesteaders living west of the Mississippi River.
These two acts, especially the ones passed in 1862, together provided farmland and agricultural training to farmers willing to live on tracts of land west of the Mississippi.

We can infer that Nick is a well-behaved, reserved young man. Why can we make this inference?

The first interaction we see between Nick, Tom, Daisy, and Jordan provides some good clues. Despite the bad behavior of the others, Nick remains polite and well-mannered. When Daisy blames him, for example, for missing her wedding— because of the fact that he was in the war—he doesn't call her selfish or lose his composure. When Tom takes a call from his mistress, Myrtle Wilson, during dinner—while his wife sits in the next room—Nick doesn't say a word about it, ask her any questions, or seem to make any judgments. (For that matter, when Tom takes him—without asking—to meet this woman with whom Tom is cheating on Daisy, Nick's cousin, Nick keeps his opinions to himself about Myrtle, the dog Tom buys her, and the apartment he keeps for her.) He doesn't even laugh at Tom when Tom spouts his ridiculous racist opinions or claims to hate the word "hulking." Nick could speak up about, to laugh at or object to, any one of these situations, but he reservedly keeps his opinions to himself and behaves politely and discreetly.

What is the verbal irony in "The Story of an Hour"?

There are several examples of verbal irony in "The Story of an Hour" which contribute to the climactic ending.
One example is found in the very first sentence:

Knowing that Mrs. Mallard was afflicted with a heart trouble, great care was taken to break to her as gently as possible the news of her husband's death.

Mrs. Mallard's "heart trouble" is implied to be a medical condition as the story opens. Her health therefore seems a thing of fragility that must be guarded. As the story progresses, however, the reader learns that Mrs. Mallard has another kind of heart trouble:

And yet she had loved him—sometimes. Often she had not. What did it matter! What could love, the unsolved mystery, count for in the face of this possession of self-assertion which she suddenly recognized as the strongest impulse of her being!

Mrs. Mallard doesn't truly love her husband; that is her real "heart trouble." Instead, she has lived with him out of a sense of duty and is fairly thrilled with the prospect of living life on her own terms.
Another example is found when Mrs. Mallard takes a moment to herself to consider the news of her husband's death. A surge of emotions begins to rise up in her, and she is overcome with one thought:

She said it over and over under her breath: "free, free, free!"

The verbal irony is that Mrs. Mallard proclaims her freedom from a marriage that she has come to view as a burdensome obligation; the reality is that her husband is very much alive, and the only freedom that she will find will be through her own death.

Verbal irony is when a character says something but means something else. Taken literally, the character seems to mean one thing. Actually, they mean to communicate something completely different than what their words literally mean. Verbal irony is different than other kinds of irony because the speaker uses this double meaning intentionally.
In "The Story of An Hour," the first example of verbal irony happens when Josephine is kneeling outside her sister's door, begging her to come out so she can comfort her. 

Josephine was kneeling before the closed door with her lips to the keyhole, imploring for admission. "Louise, open the door! I beg; open the door—you will make yourself ill. What are you doing, Louise? For heaven's sake open the door. 
"Go away. I am not making myself ill." No, she was drinking in a very elixir of life through that open window. 

When Louise says, "I am not making myself ill," she actually means that she has never felt better. She realizes that her sister will not understand the double meaning of her words, but she says it anyway. Her relief and joy at her husband's death evoked a profound sense of freedom inside her. When she says, "I am not making myself ill," it is a statement to herself. In fact, it is possible that what had really been making her ill was her unhappy marriage. At the beginning of the short story, we are told that Louise has heart trouble. 

Knowing that Mrs. Mallard was afflicted with a heart trouble, great care was taken to break to her as gently as possible the news of her husband's death.

If her heart trouble was actually caused by the stress of an unhappy marriage, then Louise's statement "I am not making myself ill" is even more ironic, since the relief she feels after she is told of her husband's death is actually making her well. 
The next example of verbal irony happens after Brently Mallard returns, alive and well. At the prospect of being married to this man of "powerful will" again, Louise dies from shock and despair. 

When the doctors arrived they said she had died of heart disease—of the joy that kills.

The doctors said she had died of "the joy that kills." They thought her joy was the joy of seeing that her husband was actually alive. In fact, her reaction to his appearance was the opposite. This is an example of verbal irony because what the doctors said was actually true, but not in the way they thought. Louise died because she had been exposed to a pure, living joy that she would never have experienced if her husband had simply come home that day like usual. It was not her day-to-day unhappiness that killed her. Experiencing freedom and happiness for the span of one hour and then realizing that she was still trapped resulted in her death.

What is the role of wealth in the pot of gold?

The role of wealth is crucial in The Pot of Gold. The title of the play itself is both literal and figurative. Euclio, an old miser, hoards his pot of gold, constantly afraid that one day it will be stolen. Euclio is so covetous of his miser's hoard that it becomes an obsession, distorting his mind to such an extent that he becomes intensely paranoid. He regularly starts moving the pot of gold around and hiding it in different places in an increasingly desperate attempt not to lose it. However, despite his best efforts, it is eventually stolen; Strobilus, Lyconides' servant, is the one who makes off with it.
Phaedra, Euclio's daughter, like the titular pot of gold, also has great monetary value, indicating the economic worth placed upon marriageable young women at the time. Essentially, Phaedra is regarded as a piece of property to be bought and sold as part of a business transaction. However, in time, Euclio recovers his stolen pot of gold. And then he realizes that his daughter is valuable in herself, worth infinitely more than his miser's hoard. We see this when Euclio gives the pot of gold to Lyconides on his betrothal to Phaedra by way of a dowry.

What life lesson in Bleachers by John Grisham is relevant today?

A relevant life lesson from Bleachers is that a coach should teach their players to be more than wins and losses.
Coach Rake was responsible for tremendous success. This is seen in his win-loss record, unmatched number of championships, and the way he transformed football in Messina. His intensity translated to his players, some of whom credit the coach with their being able to face down life's challenges.
However, it is clear that a number of his players were damaged through Coach Rake's approach to the game. Coach Rake valued success on the field more than anything else. As a result, he created a system where his players struggled to understand the demands of life away from it:

You count the years until you get a varsity jersey, then you're a hero, an idol, a cocky bastard because in this town you can do no wrong. You win and win and you're the king of your own little world, then poof, it's gone. You play your last game and everybody cries. You can't believe it's over. Then another team comes right behind you and you're forgotten.

Neely enhances this when he wishes that he "never saw a football." Coach Rake encouraged a system that shielded athletes from the reality of the world. They embraced his singular focus on football. This entitlement helped make some of them unable to fully cope with the reality of life when their time on the gridiron had passed. Coach Rake defined his players' lives in terms of success in football being the only metric that mattered. Even if only one player suffers from this condition, it means that Coach Rake failed his athletes. The dangers of this metric are evident in how Coach Rake's methods led to Scotty Reardon's death. Such an instance immediately provokes reevaluation of Coach Rake's approach.
I think that this emphasis on the game being more important than life outside of it is where we see Coach Rake as myopic. The role of a coach should transcend their sport. Their purpose is to lead. Especially in youth sports, a coach should use the game to teach lessons about life. Wins and losses are important. However, the coach's true responsibility is to prepare their athletes for life outside of the game. When Paul says that "another team comes right behind you and you're forgotten," it is an indictment of the world that Coach Rake created. Nothing can justify a coach whose players feel left behind or incapable of dealing with the world that awaits them once their playing days are done. Little can justify the death of a child under a coach's watch. Recognizing the limitations of Coach Rake's worldview is a very relevant life lesson from Bleachers.
In a world where so much of youth sports hinges on wins and losses, a life lesson from Bleachers is that there has to be more. Coaches must recognize that their job is to make athletes better people. Coaches must remind their athletes that no matter what happens on the field of play, they will be loved and that their job is to take that love with them into the outside world. Their ultimate job is to ensure that the young people they take under their wing become better people first and improved athletes second.

Intermediate Algebra, Chapter 2, Review Exercises, Section Review Exercises, Problem 56

Evaluate the compound inequality $-5x + 1 \geq 11$ and $ 3x + 5 \geq 26$. Give the solution set in both interval and graph form.


$
\begin{equation}
\begin{aligned}
-5x + 1 - 1 &\geq 11 - 1 && \text{or} & 3x + 5 - 5 &\geq 26 - 5\\
\\
-5x &\geq 10 && \text{or} & 3x &\geq 21\\
\\
\frac{-5x}{-5} &\leq \frac{10}{-5} && \text{or} & \frac{3x}{3} &\geq \frac{21}{3}\\
\\
x &\leq -2 && \text{or} & x &\geq 7
\end{aligned}
\end{equation}
$



The graphs of these two inequalities are






Since the inequalities are joined with $or$, find the union of two union of the two solution. The union is shown and is
written as $(-\infty, -2] \bigcup [7 ,\infty)$

What was the underlying purpose of the Alien and Sedition Acts of 1798?

The background of the Alien and Sedition Acts starts with the undeclared war between the US and France in 1798, also sometimes called the Quasi-War. The United States owed France a financial debt from money borrowed in the American Revolution but refused to pay it once the French Revolution created a major regime change. The US position was that this debt was not owed to the new leaders in France. The Quasi-War was a shipping war on the seas and ended with a treaty in 1800.
Now, to the Alien and Sedition Acts. They were passed by Federalist president John Adams in 1798. They created a series of immigration and citizenship laws. The Federalists were opposed to adhering to old treaties with France and to sympathizing with the French and French immigrants. The Democratic-Republicans opposed the Federalists in these views. Thomas Jefferson was a Democratic-Republican. You can see some primary source materials about the Alien and Sedition Acts at the links below.
https://guides.loc.gov/alien-and-sedition-acts

https://www.ourdocuments.gov/doc.php?flash=false&doc=16

How does the character of Robinson Crusoe develop?

Over the course of his adventures, Robinson Crusoe becomes much more mature and more responsible in his interactions with the world around him.
At first, he's a bit of a young tearaway, heading out into the world against his father's wishes to make himself a fortune. In his single-minded obsession with wealth, Crusoe shows himself utterly indifferent to morality. He happily gets himself involved in the slave trade, despite the enormous suffering it brings to others. Though a throughly immoral trade, it also happens to be a very financially lucrative one—hence Crusoe's involvement with it. Even after a brief firsthand experience of life as a slave when his ship is taken over by pirates and he's enslaved by a Moor, he still remains committed to making money out of this evil trade.
Crusoe is so obsessed with his various business enterprises that he forgets all about God. He will continue to do so until long after he's shipwrecked on a desert island. Then, thanks to a sudden religious conversion, he will come to see the error of his ways. Realizing his arrogance in neglecting to praise God for his safe deliverance after the shipwreck, he vows to make amends and immediately gets down on his hands and knees and gives thanks to the Almighty.
This dramatic conversion changes Crusoe's whole character, precipitating his transition from selfishness and isolation to self-actualization and social reintegration by way of a renewed commitment to Protestant Christianity.

Defoe is particularly interesting in his tracing of Robinson Crusoe's moral development over his long stay on the island. Crusoe starts out an unbeliever, but as he survives against all the odds on the deserted island he comes to see the hand of providence in his life.
At first, he leaves on his shipboard adventure without telling his parents. He starts off on the wrong foot:

without asking God's Blessing, or my Father's, without any Consideration of Circumstances or Consequences and in an ill Hour, God knows.

His involvement in the shipwreck, by implication, is his punishment for heading out recklessly on his own. In fact, his father had warned him of such consequences.
Once on the island, Crusoe keeps a journal and, being alone, has plenty of time to reflect on what has happened to him and to engage in self-examination and examination of conscience, both important aspects of Protestantism. At first, he blames God for his situation. He expects to die soon and wonders what sense it makes for God to give people life only to make them suffer so:

I had great Reason to consider it as a Determination of Heaven, that in this desolate Place, and in this desolate Manner I should end my life; the Tears would run plentifully down my Face when I made these Reflections, and sometimes I would expostulate with my self, Why Providence should thus completely ruine its Creatures, and render them so absolutely miserable, so without Help abandon'd, so entirely depress'd, that it could hardly be rational to be thankful for such a Life.

Crusoe, however, finds Bibles on the abandoned ship and as he reads one, begins to believe that it was God's plan for his redemption that brought him to this island. Finally, he becomes a complete convert to Christianity and decides that moral redemption from the mental anguish brought on by sin is more important than relief from physical sufferings. His moral regeneration is complete when he decides that forgiveness of sins is more important than being rescued from his island home:

Now I look'd back upon my past Life with such Horrour, and my Sins appear'd so dreadful, that my Soul sought nothing of God, but Deliverance from he Load of Guilt that bore down all my Comfort: As for my solitary Life it was nothing; I did not so much as pray to be deliver'd from it, or think of it; It was all of no Consideration in Comparison to this: And I add this Part here, to hint to whoever shall read it, that whenever they come to a true Sense of things, they will find Deliverance from Sin a much greater Blessing, than Deliverance from Affliction.

Crusoe, having developed into a mature Christian due to his solitude and trials, is able to convert Friday to Christianity. Crusoe's moral change and his development of a relationship with God is a crucial aspect of the novel.

In the book Robinson Crusoe, the character of Crusoe develops through the necessity of his finding ways to survive on the island. He first uses his skills and evident knowledge of some survival techniques to find shelter for himself and security from any possible predators. Crusoe's first night is spent in the trees, and after that, he painstakingly builds a shelter against a high cliff, even carving out more room within it over time. Crusoe next revisits the stranded ship he arrived on and scavenges supplies and parts of the ship after constructing a raft for this purpose. He finishes saving the needed supplies just before the ship is carried off by a storm.
Crusoe wards off what could have been impending insanity by keeping himself busy with finding ways to survive. His character develops further as he fences in and domesticates a goat. His evolving friendship with his found friend, Friday, adds depth to his character as the two learn to communicate and cooperate.

What was the role of indentured servants and the development of slavery in colonial America?

Indentured servants were used as an alternative to black slaves in colonial America. The indentured servants could not pay for their passage to the New World so they had to pay for their passage with labor upon arrival. The indentured servants had finite contracts and therefore were not a stable source of labor for the plantations. The indentured servants were mainly poor people from Ireland and England and many of them died due to tropical diseases such as malaria and yellow fever. As conditions in England improved, more people could afford their own passage, and this led to fewer people signing up for servitude.
African slaves proved to be the better long-term solution to plantation labor needs. The African slaves did not catch tropical diseases as often, and one could keep them until they either died or sold to someone else. One could also breed one's African slaves and enslave the offspring. Plantation owners treated the African slaves poorly and justified the bad treatment by stating that they were not European. Some plantation owners justified keeping slaves by saying that their were providing Christian training and promoting good working habits for their African slaves. African slaves were also easier to catch if they escaped since most of the English colonies were populated by white citizens.
All of these conditions led to indentured servitude largely vanishing by the Revolutionary War. African slavery would supply plantation labor needs until the end of the Civil War.

Indentured servants and slaves became an integral part of the agrarian plantation economy that developed in colonial America. Landowners needed labor to work in fields of rice, tobacco, indigo, and other crops. At first, this manpower was provided by European workers in indentured servitude.
In exchange for free passage aboard ships across the Atlantic as well as room and board, indentured servants would sign contracts agreeing to serve plantation owners for periods of time ranging from four to seven years. Although the work was difficult and punishments were harsh, at the end of their periods of service, indentured servants would receive rewards such as land, food, clothes, and livestock. In this way, plantation owners obtained the cheap labor that they needed, and poor Europeans had a chance to own their own land and become free citizens of the new colonies.
The first contingent of 20 black Africans arrived in Jamestown, Virginia, in 1619. These Africans were taken on as indentured servants and given their freedom when their period of labor had expired. However, within a few decades, slavery became an established institution in the colonies, and Africans were no longer given the opportunity to be indentured servants.
Slaves performed the same role as indentured servants on the plantations. They did the difficult, backbreaking work in the fields that enabled the plantations to remain prosperous. However, it was more economical for plantation owners to keep slaves rather than to contract with indentured servants, and slaves gradually replaced indentured servants as agricultural laborers in the colonies. Historians estimate that up to 7 million people were forcibly removed from the African continent and brought to America as slaves in the 1700s alone.
http://www.pbs.org/opb/historydetectives/feature/indentured-servants-in-the-us/

https://www.history.com/topics/black-history/slavery

https://www.ushistory.org/us/5b.asp

As people traveled to the Americas to build new lives—to experience freedom of religion and have the opportunity to become economically successful— indentured servants and slaves made up a large part of the work force to galvanize these efforts forward, not only with the settlement of towns, but also the development of industry (providing goods and services) which offered a lifestyle either similar to or superior than what the settlers were accustomed to.

Slavery existed in North America almost from the beginning of British colonization.

While slavery eventually settled more to the South, it was valuable to the early settlers of the British colonies.

Slavery was practiced throughout the American colonies in the 17th and 18th centuries, and African slaves helped build the economic foundations of the new nation. 

Unfortunately, owning men and women to build, establish farms, provide services, and so on, was more economically sound than hiring people for a wage. In this way, the overhead of developing a colony was lower, and those able to purchase and keep slaves realized greater wealth and social recognition.
Indentured servants, like slaves, were often treated quite badly, and often they lived lives of drudgery; the biggest difference, however, was that people willingly sold years of their lives and their skills or services for a specific amount of time, with the understanding that after the agreed upon number of years, the indentured servant would be free. For slaves, freedom (at the time) was not an option.

The idea of indentured servitude was born of a need for cheap labor. The earliest settlers soon realized that they had lots of land to care for, but no one to care for it. With passage to the Colonies expensive for all but the wealthy, the Virginia Company developed the system of indentured servitude to attract workers. Indentured servants became vital to the colonial economy.

This was often what poorer people did in order to travel to America. In exchange for transportation across the ocean, men and women would agree to work for the person or persons that purchased their fare, for a term of years—often four to seven.
What the slaves and indentured servants had in common was the degree to which landowners and business owners relied upon them. Not only was their work absolutely necessary for towns to develop and thrive in the wilderness of the Americas, but they also played a key role in supporting the growing economy of Colonies that would one day become perhaps the most powerful nation in the world.
http://www.pbs.org/opb/historydetectives/feature/indentured-servants-in-the-us/

https://www.history.com/topics/black-history/slavery