y=12 Write the standard form of the equation of the parabola with the given directrix and vertex at (0,0)

A parabola with directrix at y=k implies that the parabola may opens up towards upward or downward direction.
The position of the directrix with respect to the vertex point can be used to determine in which side the parabola opens up.
If the directrix is above the vertex point then the parabola opens downward.
If the directrix is below the vertex point then the parabola opens upward.
The parabola indicated in the problem has directrix of y=12 which is located above the vertex (0,0) .
Thus, the parabola opens downward and follows the standard formula: (x-h)^2=-4p(y-k) . We consider the following properties:
vertex as (h,k)
 focus as (h, k-p)
 directrix as y=k+p
 Note: p is the distance of between focus and vertex or distance between directrix and vertex.
 From the given vertex point (0,0) , we determine h =0 and k=0 .
Applying directrix y =12 and k=0 on y=k+p we get:
12 =0+p
12=p or p=12 .
Plug-in the values: h=0 ,k=0 , and p=7 on the standard formula, we get:
(x-0)^2=-4*12(y-0)
x^2=-48y  as the standard form of the equation of the parabola with vertex (0,0) and directrix y=12.

What is the poem "Ozymandias" talking about? How does it relate to Frankenstein?

The overarching theme of the poem "Ozymandias" is the transience of human life and its achievements. Ozymandias was a great Egyptian pharaoh, otherwise known as Ramasses II, who once built a huge statue of himself. But now, due to the passing of several centuries, the statue lies in ruins, reduced to a sad collection of fragments decaying in the desert. However, the pedestal still remains, and the inscription on that pedestal reads as follows:

'My name is Ozymandias, king of kings:Look on my works, ye Mighty, and despair!'

The inscription is an expression of the pharaoh's monumental arrogance. He genuinely believed that his deeds upon this earth would make him immortal. Yet his great statue lies in ruins, showing that however grand, however important we think we are, we must all one day succumb to the ravages of time.
One of the most important themes of Frankenstein is closely related to this. Victor is every bit as arrogant as Ozymandias. He, too, wants to achieve immortality through the construction of a monument to his enormous ego. In his case, however, it's not a statue but a monster that he builds. People do indeed look upon Frankenstein's "works, and despair," but not in the way that he'd hoped. They don't see the monster as representing an awe-inspiring scientific breakthrough, but rather as the expression of monstrous evil, a monument to one man's overweening vanity, ego, and intellectual hubris.

The poem "Ozymandias" is about the broken statue of Ozymandias, who was once the mighty and feared ruler of an important kingdom. By the time of the poem, all that is left of Ozymandias is a ruined statue. His kingdom has disappeared entirely and has become an empty desert. On his statue, these words appear:

Look on my Works, ye Mighty, and despair! 

The words are ironic, meaning the opposite of what Ozymandias meant them to communicate. The mighty should despair not because Ozymandias and his kingdom are  powerful and terrifying, but because the great works of today's tyrants will likewise come to nothing. 
Frankenstein dreams of grandeur as he works in a frenzied way, day and night, to be the first to create life from inanimate body parts. He succeeds, but the life he creates is so monstrous to him he flees it in horror. He wants to destroy it. 
Both Ozymandias and Frankenstein end up "shattered." They both represent the pitfalls of excessive pride and ego. They also represent the problems that can arise from not excercising foresight. 
As noted in the other answer, Percy Bysshe Shelley and Mary Shelley were husband and wife. 

First, you should note that the poem "Ozymandias" was written by Percy Bysshe Shelley and the novel Frankenstein by his wife, Mary Shelley. One is a poem and the other a novel and they are quite different in style and written by different authors.
The poem "Ozymandias" describes a narrator hearing a tale by a traveler who encountered a fallen monumental statue in the desert. It was a statue of an Egyptian pharaoh, with a grandiose claim inscribed on its pedestal:

My name is Ozymandias, King of Kings;
Look on my Works, ye Mighty, and despair!

When encountered by the traveler, the statue is shattered and the great kingdom Ozymandias ruled has been conquered by colonial powers, suggesting that such greatness is fleeting.
The novel Frankenstein also employs layered narration and shares one similar theme, that of human arrogance and overreach. Victor, the scientist who creates the monster, also is trying for a level of power and immortality that are a form of arrogance, and that lead to his ultimate failure and misfortune. Both works thus suggest the importance of our understanding our limitations.

In the novel The Namesake, what were some generational struggles that Gogol faced with dating girls, changing his name, and choosing his university?

The protagonist of Jhumpa Lahiri's The Namesake, Gogol (or Nikhil) Ganguli, is born to Indian parents who moved to the United States shortly before having him. He is an American citizen who grows up going to American schools and speaking English, but at home, his parents still use Bengali, abide by traditions of their culture, and expect Gogol to do the same.
When Gogol begins dating, he finds that it is awkward to introduce himself to women with the name "Gogol." He introduces himself to a young woman at a college party as "Nik" and later legally changes his name to this more traditional name. His parents named him Gogol after Ashoke's favorite author (Ashoke is Gogol's father) and because Ashoke was reading Gogol's story collection during the train crash that he was lucky to survive. It is not an Indian name, but it was chosen because the tradition of having a grandparent choose the name could not be completed; apparently, the name was lost in the mail on its way from India. When he enters school for the first time, his parents want him to go by Nikhil, but Gogol is used to being called Gogol at home; he keeps the name. When he is 18, he legally changes his name, which is somewhat controversial because it feels a bit like a rejection of his parents. This obviously causes conflict and tension between the generations.
When Gogol is involved with Maxine, the generational and cultural differences between his Indian family and her American parents come to the forefront. Gogol likes spending time with Max's family, as they are more liberal and laidback than his conservative, traditional parents. Max's parents are openly affectionate toward one another, while Ashoke and Ashima are not, though they do love one another. When Maxine finally meets Gogol's parents, he tells her not to kiss or hug them because they will be uncomfortable, but she does so anyway. This makes Gogol feel awkward and feel like he cannot make his relationship with Max fit in with his relationship with his family. He is somewhat estranged from his parents as a result and spends most of his time with Maxine until his father dies suddenly. Then, Gogol immerses himself in family life again and goes on to marry a childhood acquaintance whose parents are also Indian.
Gogol finds that his ambitions and preferences do not match with those of his parents in terms of his choice of romantic partner, school, career, or even his name. The tension between first generation immigrants, like Ashoke and Ashima, and their American-born children forms a central theme of The Namesake.

Explain how the character of Macbeth changed after the killing of King Duncan.

Prior to killing Duncan, Macbeth felt guilty and unsure.  He told his wife, Lady Macbeth, "We will proceed no further in this business" (1.7.34), and he even hallucinates a dagger, first clean and then bloodied, because he is so anxious and guilt-ridden at the thought of the murder he's about to commit.  However, once Macbeth has done the deed, and after he gets over his initial concern for his soul, he becomes a great deal more ruthless and feels a lot less guilty about the violent steps he takes. 
Once he's killed Duncan in order to acquire the throne, he soon begins to feel that he must get rid of Banquo and Banquo's son if he is to keep his new position and power.  The Weird Sisters had said that Banquo would not be king, but he would father kings, and Macbeth doesn't want to lose the throne to anyone of Banquo's line.  He promptly decides to kill his once-best friend; he convinces two murderers that it is Banquo's fault that they are poor and destitute, and thus persuades them to murder him (and Fleance, though Fleance escapes).  Further, Macbeth feels no guilt about this action, and he no longer considers the state of his soul. 
Descending into even greater ruthlessness and tyranny, Macbeth eventually murders the family and servants of Macduff, as a way of sending a message to his political enemy.  Macbeth has murdered Duncan and Banquo, and attempted to murder Fleance, and now he actually murders an innocent woman and her children as well as a great many innocent servants, simply because of their connection to Macduff.  It is a despicable move that showcases just how much worse a person Macbeth has become; he's abandoned every loyalty and he seems to have no conscience left. 

What was apartheid all about?

Apartheid, which means "being apart" in Afrikaans, was the system of racial separation that was implemented in South Africa after the Second World War (although it had roots in the earlier twentieth century.) Like segregation in the American South, it was cast as an enlightened measure to keep mutually antagonistic races separate, but it was, as was always clear, about maintaining white supremacy in the country. It outlawed marriage and sex between the races, and actually forced black farmers off of lands designated for whites. Apartheid was enforced by state-implemented violence, with white policemen violently putting down peaceful protests against the institution, especially beginning in the 1970s. This system, which finally came to an end in 1994 under the leadership of F.W. de Klerk, was consistently challenged by black South Africans led by Nelson Mandela (who spent decades in prison for his efforts) and others. It was among the most flagrantly racist legal and social systems to exist anywhere in the world in the late twentieth century.
https://www.history.com/topics/africa/apartheid

In Chapter One of Guns, Germs, and Steel by Jared Diamond, where could I find the answer to the following question: "What was the Great Leap Forward, which peoples did it impact, and what probably catalyzed this change?"

The answers that you are looking for can be found beginning on p. 39 of Guns, Germs, and Steel.  This is where Diamond starts to discuss the Great Leap Forward.
Your first question had to do with what this leap actually was.  Diamond answers this on p. 39, though he does not define the leap in one single sentence.  As you can see on p. 39, Diamond says that humans before the leap lived very simple lives.  This changed with the leap.  After the leap, humans started to have more sophisticated stone tools, tools made of things other than stone, multi-piece weapons, sewn clothing, houses, jewelry, and even art.  The Great Leap Forward was the change in humans that allowed them to become so much more sophisticated.
I will address your third question next, since this is how Diamond does it.  On p. 40, he speculates about what led to this leap.  He is not certain, but he thinks it was an anatomical change.  He says that he has argued in the past that the leap was caused by

the perfection of the voice box [which was] the anatomical basis of modern language, on which the exercise of human creativity is so dependent. 

He says that other people think it was brain development that led to language.  In either case, it appears to be the development of modern language that catalyzed the Great Leap Forward.
Finally, you ask which people were affected.  Diamond poses this question on p. 40.  He asks whether one group of people experienced the leap and then moved out around the world and spread their culture or whether people everywhere experienced parallel changes.  Over the rest of p. 40 (and a little bit of p. 41) he says that we still do not know the answer to this question.
Diamond’s answers to the questions you pose are not stated very explicitly in the text, but you can find them beginning on p. 39.

Why are many ancient texts from the Eastern Mediterranean so similar? How do they still display their culture-specific ideology within the narrative framework?

The main reason for the similarities has to do with the high level of contact the eastern Mediterranean societies had with each other. The region is crisscrossed with trade routes that have existed since the Bronze Age. Throughout history, people from one culture interacted with those from different cultures, sharing stories and, later, literature.
Additionally, this region saw frequent conquests and invasions by numerous empires. Many of these civilizations absorbed the peoples that they conquered into their empires. This meant that ideas were further shared, borrowed, appropriated, and adapted.
Since literature is often a reflection of culture, it is no surprise that similarities in writing reflect similarities in the culture of the different civilizations of the eastern Mediterranean. Since many of these peoples belonged to highly organized societies, their writings often include themes pertaining to social order and a group identity that sets them apart from their numerous neighbors.
Even though major themes are similar between the different societies of the region, their texts still strive to set them apart. This is often done by establishing particular customs and laws codified in writing or by alluding to a legendary past with heroes who represent the ideals of their people.

The first reason for their similarities have to do with direct influence. This was a fairly limited geographic area, in which people traded with each other and exchanged stories as well as material goods. Also, rather than nations having fixed and unchangeable boundaries, many of the groups in this area existed in a world of constant conquests and realignment of borders of various empires, with different groups dominating at different times. 
Most of the cultures in this period were extremely patriarchal and socially stratified, something that is reflected in many of their literary texts, which tend to glorify male leadership. Many of the common religious texts and law codes attempt to codify some notion of justice as a principle for social organization that substitutes law for personal retribution. This grows out of the need to organize cities and eventually empires in a way that permits them to function efficiently. 
Although both monotheistic and polytheistic religions existed, they shared in common a manner of expressing religious belief through narrative. The reason for this is that literacy levels were quite low outside a restricted scribal class and thus important cultural information needed to be disseminated in a form that was memorable. 

What are the ethical differences between "good" and "bad" knights in Morte d'Arthur?

On the surface, the difference between "good" knights and "bad" knights in Malory's Le Morte d'Arthur depends on those knights' adherence to the chivalrous code, the code of ethical behavior that a knight errant was supposed to follow. Knights errant were, ideally, knights that traveled the countryside looking to perform chivalrous acts. In general, the knights of the Round Table were supposed to be knights errant.
Knights errant stood in contrast to knights who sought personal glory or gain from their actions. Such knights fought for their own purposes and did not follow the chivalrous code. Sometimes these "bad" knights were knights that were fighting against the king; or knights that took women against their will; or knights that killed other knights by magic or treachery; or knights that did not treat fallen enemies with courtesy or mercy, as dictated by the chivalrous code.
The problem with Malory's depiction of the knights errant in Le Morte d'Arthur is that none of the "hero" knights (e.g., Sir Gawain, Sir Lancelot, Sir Gareth, Sir Tristram, etc.), save for Sir Galahad, consistently behave in a manner in keeping with the chivalrous code. While none of these hero knights are as "bad" as the evil knights found in Malory, they at different times exhibit behavior that ranges from mild violations of the code to outright villainous behavior, even behavior that goes against their king and cohort.
In this sense, the line between the behavior of the "good" knights and the "bad" knights in Le Morte d'Arthur is blurred. The knights errant who are supposed to be following the chivalrous code often violate that code for their own purposes, and in this way they are nearly as unethical as the "bad" knights, i.e. those who do not follow the code at all. The difference between the "good" knights and the "bad" knights is that the knights errant who stray from the code may be able to make amends, as Sir Lancelot attempts to do, whereas those knights who do not at all follow the codes make no such attempts.
 

Analyze the formal elements like line, shape, form, value, texture, space, and color, as well as the historical precedence of The Death of General Wolfe. How would you interpret it?

Each of the formal elements serves its own purpose and place in the piece pictured. To know how to identify their specific usage, one should first consider what each of these elements is.
Line: A line is an obvious path that one can follow from point to point. Lines vary in length, width, and direction, and are often used as a means to identify where the boundaries of one object begin and the boundaries of another end.
Shape and form: These two elements are used to define the existence of an object in a two-dimensional or three-dimensional space (respectively). Shape is usually defined by the line and has height and width. Form has height, width, and depth.
Color: Color comes from the light that's reflected off objects and is created from hue, intensity, and value.
Value: Value refers to the brightness of a color, which is used to suggest the existence of light (or lack thereof).
Texture: Texture is how we perceive an object's quality through touch. In the case of the painting above, since you can't touch it, the type of texture used is two-dimensional and exists to suggest to us the qualities the painting would have if we were to touch it.
Space: There are both positive and negative versions of space. Positive space is used to define the area in which an artist's objects exist in the painting while negative space describes the unused area around said objects.
So you can see how each of these elements works together to create the painting. Researching the principles of art will allow you to see how those principles fit in with the elements and ultimately help you answer the questions posed.
http://www.getty.edu/education/teachers/building_lessons/formal_analysis.html

There are many questions asked here, so this response will essentially be a summary and an analysis of the work in question. This painting, The Death of General Wolfe, was painted by Benjamin West. It depicts the death of British General James Wolfe at the moment of his greatest triumph—the defeat of French forces on the Plains of Abraham outside the city of Quebec in 1759. The battle was a decisive moment in the Seven Years War, known as the "French and Indian War" in the American colonies, and Wolfe died a hero. Stylistically, the painting is a sort of mixture of classical and emerging Romantic elements. It was criticized in its own time, as the historian Simon Schama points out, because the general was depicted in his army uniform rather than allegorically in classical Roman garb, as was typical of neoclassical painting. In any case, the central drama of the painting is the death of Wolfe itself. Wolfe is expiring from his wounds, surrounded by figures that represented the British Empire. He seems bathed in light amid the smoke and chaos of the battle, and his pose seems reminiscent of Christ being brought down from the cross. Several British officers in their red coats stand around the fallen Wolfe. Isaac Barre, his second-in-command, clutches his chest in grief and shock on the left, and the general's closest advisor and aide-de-camp holds his right arm. Behind them the battle rages, and Schama claims that most English viewers of the painting assumed that Wolfe was receiving news that a British volley had broken a last-ditch French assault. While it is unknown whether West intended this, it does heighten the drama of the painting. Another fascinating element of this painting is the Native American man to the left. A Mohawk allied with the British, he is stoically contemplating the death of Wolfe. This was intended to invoke the raw, unspoiled, uncorrupted nature of Britain's American empire (West himself was American). This painting, with its heroic depiction of Wolfe's death, is intended to invoke the combination of Old and New World sensibilities that characterized the British Empire.
https://www.history.com/topics/native-american-history/battle-of-quebec-1759

https://www.nytimes.com/1991/05/12/arts/art-wolfe-must-not-die-like-a-common-soldier.html?pagewanted=all

What were three events in the book Hatchet?

Three of the most important events from the book are the crashing of the plane, the finding of food, and the finding of the survival pack.
The plane crash is pretty obvious, but it is important because nothing else in the book could have happened without it. Brian is on his way to see his father because his parents have recently divorced after his mother’s affair. His father is in Canada. Brian takes a small plane, and it is just him and the pilot. The plane crashes in the wilderness when the pilot has a heart attack. 

But between the seventeenth and eighteenth radio transmissions, without a warning, the engine coughed, roared violently for a second and died. There was sudden silence, cut only by the sound of the wind milling propeller and the wind past the cockpit. (Ch. 2) 

Once the plane crashes, Brian is on his own. He has no way of calling for help and no one knows where he is. He must find his own sources of food and shelter. At first, he finds some berries. He eventually calls them gut cherries because they make him so sick. Brian eventually figures out how to use a bow and arrow to fish.

With his bow, with an arrow fashioned by his own hands he had done food, had found a way to live. The bow had given him this way and he exulted in it, in the bow, in the arrow, in the fish, in the hatchet, in the sky. (Ch. 13) 

Brian is able to eat better once he can fish, and not live off of berries. It is not enough, though. He wants the survival kit. The survival kit is in the plane, which is half in the lake. Getting it is a feat. Once he does, it is like winning the lottery.

TREASURE.
Unbelievable riches. He could not believe the contents of the survival pack.
The night before he was so numb with exhaustion he couldn't do anything but sleep. . . . But with false gray dawn he had awakened, instantly, and began to dig in the pack—to find amazing, wonderful things. (Ch. 19)

Once he finds the survival pack, the tide turns for Brian. It has many handy survival tools, of course, including food, a gun, and cooking pans. What it also has is an emergency radio that sends out a signal. Until then, no one was even looking for Brian anymore. They had given up.

In what way does the postmaster feel out of place in the remote village?

In the second paragraph of "The Postmaster," Rabindranath Tagore tells the reader:

Our postmaster belonged to Calcutta. He felt like a fish out of water in this remote village.

Calcutta is not only one of the largest cities in India, it is an intellectual and cultural centre, home to many writers, poets, and philosophers including, of course, Tagore himself. The Postmaster would have been surrounded by people and lived with his mother and sister, who also cooked for him—something he now has to do for himself.
The Postmaster has no peer group in the small village of Ulapur. The men who work at the indigo factory are not suitable companions for a respectable, educated man, and in any case, Tagore says, the Calcutta boy is not "adept in the art of associating with others," appearing either proud or ill-at-ease.
The Postmaster also has little work to do, since the village is so small and scarcely needs a post office in any case. Everyone else there is busy which means that they lack both time for friendship and leisure reflection, both of which serve to separate them from the Postmaster.

The short story "The Postmaster" tells of a young man from the city of Calcutta who arrives at the small village of Ulapur to take up his position of postmaster. He feels out of place in this remote location for several reasons.

First of all, the postmaster comes from the big city of Calcutta. Whether he was well-to-do or not there, he would have lived in a normal house surrounded by many other houses, shops, and offices. In the village, he stays in a thatched shed near a slimy pond surrounded by wild foliage.

In Calcutta he lived with his mother and sister, and he misses them. In the remote village, he has only the orphan girl Ratan, who does odd jobs for him, for company. Additionally, in Calcutta his mother and sister did the cooking, but now he has to cook for himself.

The postmaster from Calcutta does not socialize easily with strangers, and as a result he is lonely. This also makes him feel out of place. Tagore writes:


Nor is a Calcutta boy an adept in the art of associating with others. Among strangers he appears either proud or ill at ease. At any rate, the postmaster had but little company; nor had he much to do.


This brings up another point: the postmaster's boredom causes him to feel out of place. He tries writing verses and eventually resorts to conversing with Ratan and attempting to teach her to read.

After the postmaster's illness, he can't stand to remain in the remote village any longer. When his request for a transfer is rejected, he decides to quit and go home, bringing about the tragic ending of the story in which Ratan feels abandoned.

The postmaster feels out of place due to the fact that he must interface on a daily basis with strangers. Essentially, the postmaster finds it difficult to relate to the villagers, who possibly represent the kinds of people he has never had to associate with before.

The men employed in the indigo factory had no leisure; moreover, they were hardly desirable companions for decent folk. Nor is a Calcutta boy an adept in the art of associating with others. Among strangers he appears either proud or ill at ease. At any rate, the postmaster had but little company; nor had he much to do.

Perhaps the factory employers come from dissimilar castes; the narrator doesn't say, but the implication is clear. The postmaster considers the workers "hardly desirable companions for decent folk" like himself. In the story, he has "little company" because he finds it difficult to integrate into the fabric of daily life among the villagers. Also, since he has little to occupy him, the postmaster feels ill at ease.
Aside from these difficulties, the postmaster also misses his family. This is another reason he feels out of place: his family isn't with him. They are back in Calcutta.

On some evenings, seated at his desk in the corner of the big empty shed, the postmaster too would call up memories of his own home, of his mother and his sister, of those for whom in his exile his heart was sad,—memories which were always haunting him, but which he could not talk about with the men of the factory...

What are some symbols in "The Birds" by Daphne Du Maurier?

In "The Birds," Du Maurier employs a number of symbols. Here are a few to consider:

The gun symbolises how man underestimates the power of nature. Mr Trigg thinks that shooting the birds will be fun, for example, and will solve the problem of the birds' attacks. But, as Nat predicted, guns are powerless against them. In fact, the birds continue their attacks unabated and they kill Mr Trigg. When Nat finds Mr Trigg's body, Du Maurier draws our attention to the gun lying by his side.

The silent radio represents man's helplessness in the face of nature. Early in the story, for example, the radio acts as a source of information and comfort to Nat and his family, by stating that they are not the only victims and by instructing them what to do. But once the programmes stop, it becomes clear that Nat's society is completely unable to cope with the birds' attacks. Nat and his family are, therefore, alone in their struggle to survive. The closing image of the story, in which Nat listens to the silent radio, is a poignant reminder of this.

Write the solution of the initial value problem and use it to find the population when t=20 ? (dP)/(dt)=0.1P(1-P/2000) P(0)=100 When does the population reach 1200? Please explain as thorough as possible, thank you.

This is a separable differential equation. This means we can completely separate dependent and independent variables into two expressions. General form if such equation is
dy/dx=f(x)g(y)
and the solution is obtained by solving the following integrals
int dy/g(y)=int f(x)dx+C
Let us now return to the problem at hand.
dy/dt=0.1P(1-P/2000)
Now we need to put everything containing P on the left and everything containing t to the right side.
(dP)/(0.1P-P^2/20000)=dt
Let us first simplify the expression on the left.
(dP)/((2000P-P^2)/20000)=dt
(20000dP)/(P(2000-P))=dt
We shall write the term on the left using partial fractions to make integration easier.
(20000dP)/(P(2000-P))=A/P+B/(2000-P)
2000A=20000 
B-A=0
A=B=10
(2000dP)/P(2000-P)=10/P+10/(2000-P)
We can now integrate the equation.
int 10/P dP+int 10/(2000-P)dP=int dt
10ln P-10ln(2000-P)+10ln C=t

In the line above we have written the constant term as 10ln C in stead of just C. This is often used to make the expression easier to manipulate.
ln P-ln(2000-P)+ln C=t/10
Use formulae for logarithm of product and quotient:
log_a (xy)=log_a x+log_a y
log_a(x/y)=log_a x-log_a y
ln((CP)/(2000-P))=t/10
Take antilogarithm.
(CP)/(2000-P)=e^(t/10)
CP=2000e^(t/10)-e^(t/10)P
P(C+e^(t/10))=2000e^(t/10)
P=(2000e^(t/10))/(C+e^(t/10))
We can now calculate C by using the initial value.
P(0)=100
(2000e^(0/10))/(C+e^(0/10))=100
Since e^0=1, we have
2000/(C+1)=100
C+1=2000/100
C=20-1
C=19
The solution to the initial value problem is
P(t)=(2000e^(t/10))/(19+e^(t/10))   
We can now calculate population when t=20.
P(20)=(2000e^2)/(19+e^2)approx560
Population is approximately 560 at time t=20.
 
To find when the population reaches 1200, we need to solve the following equation
(2000e^(t/10))/(19+e^(t/10))=1200
Multiply by the denominator.
2000e^(t/10)=22800+1200e^(t/10)
800e^(t/10)=22800
e^(t/10)=28.5 
Take logarithm.
t/10=ln28.5
t=10ln28.5approx33.499  
The population will reach 1200 at time t=33.499. 

In Bud, Not Buddy by Christopher Paul Curtis, what is it that enables Bud to survive? Is it luck, skill, or something else?

Bud begins the story in Flint, MI.  The story ends with him in Grand Rapids, MI, but I don't think that your question is only asking about the physical start and end settings.  
When the reader is introduced to Bud, he is living in an orphanage, and a new family has just been found to adopt Bud.  Right from the start of the story, it is clear that Bud does not have a permanent home or a loving family.  The Amos family doesn't end up being either of those two things, so Bud decides to strike out on his own and track down his father.  He scrapes to get by, has some successes, has some setbacks, and he eventually makes his way to Grand Rapids.  It is there that he meets Herman Calloway and his band.  Bud believes that Calloway is his father, but it turns out that Calloway is Bud's grandfather.  Although the story did begin with Bud being without a family and a home to call his own, the story ends with Bud finding both in Calloway and the rest of his band.  
Bud is able to achieve his happy ending through a mixture of luck, skill, and determination.  Bud is extremely lucky that Lefty Lewis is the man that found Bud on the road that night.  There could not have been a kinder man than him.  The Great Depression is in full swing, so it's possible that the car that pulled over for Bud contained a "bad guy" looking to rob Bud of all of his possessions.  Instead, Lefty Lewis feeds Bud, takes him to his home, and drives him to Grand Rapids.  
Bud shows skill at times too.  For example, Bud's repeated use of the library to obtain information to help him succeed shows resourcefulness on his part.  Additionally, the book is full of Bud's rules that help him to better survive and navigate the dangerous world that he inhabits.  Bud skillfully applies each of those rules to cleverly maneuver various situations.  
Lastly, Bud shows a dogged determination throughout the novel.  He is unwilling to give up.  This is especially evident when Calloway clearly shows that he wants nothing to do with Bud, yet Bud remains persistent in his efforts to win over Calloway.  Bud wins the hearts of each band member one by one, and eventually a situation is presented that teaches Bud and Calloway their true relationship to each other. 

What are the character traits of Digory in The Magician's Nephew?

Along with being bold and curious, Diggory is adventurous. Rather than fearing new places and experiences, he is eager to learn and discover. Additionally, he is both brave and imaginative, as is seen as Diggory encourages Polly to explore the attics of their row houses:

"I expect someone lives there in secret, only coming in and out at night, with a dark lantern. We shall probably discover a gang of desperate criminals and get a reward. It's all rot to say the house would be empty all those years unless there was some mystery. . . . Grown-ups are always thinking of un-interesting explanations." (ch. 1)

Diggory often predicts what might come next, as he does when exploring the attic; this shows his imagination.
His love of adventure is seen again when Diggory eagerly selects a pool to enter to travel to another world. He says to Polly in the Wood Between the Worlds,

"There! . . . That's all right. Now for the adventure. Any pool will do Come on. Let's try this one!" (ch. 3)

Diggory makes his decisions with confidence and bravery. Polly urges Diggory to slow his decisions down and to think through the logistics of their plans. She encourages them to mark a pool, so they will be able to determine which pool will take them back to earth at the end of their adventure. After the pool is marked, Diggory's eager enthusiasm to explore returns:

"Well don't keep on gassing about it . . . Come along, I want to see what's in one of the other pools." (ch. 3)

Diggory also demonstrates bravery and immense compassion toward the needs of others. His compassion and bravery is seen when he asks Aslan for something to help cure his mother, despite his fear of Aslan's massive claws. His bravery continues to be seen when he accepts Aslan's commission to get Aslan a seed from a magic tree, before he knows what this mission will require. He was not even sure that he would be able to complete this task, but after Aslan gives him a Lion's kiss, Diggory "felt that new strength and courage had gone into him" (ch. 12).
Diggory's decision to ask Aslan for help, and his continued willingness to get the seed from a magic tree (as Aslan asked) shows Diggory's great bravery and compassion.

Digory is bold, curious, stubborn, and rash.  He also has a healthy skepticism.  These are the traits that drive the story.  Digory also has some softer traits, such as love for his mother, sorrow that she is dying, and a sense of honor and respect for authority.  
We see Digory's boldness and curiosity when he urges Polly to help him explore the attic and to use it to get down into the abandoned house.  These traits, plus his rashness, come up again when the children get into the Wood Between the Worlds.  Digory wants to explore the other worlds the pools lead to.  Polly, who is more cautious, has to be convinced to do this.  (Digory is stubborn during their many little fights.)  Then, when Polly finally does agree, Digory almost charges off to another pool without marking the one that they needed to go back by.  This would have left them lost in other worlds forever.  
These same traits of Digory's come up again when the children discover the bell and hammer, with its warning rhyme, in the ruined palace in Charn.  Digory is curious and wants to ring the bell.  Polly tries to stop him, but being stubborn, bold, and rash, he wrestles with her and rings it anyway.  This is what awakens the evil Empress Jadis, releasing her on London and eventually, on Narnia. 
Digory's boldness and stubbornness come in handy later, when he must approach Jadis on her rearing horse in order to grab her ankle and put on the ring so as to get her out of London. 
Digory is skeptical enough not to just believe anything that he is told.  For example, when Uncle Andrew is telling Digory that as a magician, he (Uncle Andrew) is above the ordinary moral rules, adding, "Ours, my boy, is a high and lonely destiny," Digory realizes that Uncle Andrew simply means he should be able to do whatever he wants.  He recognizes this same attitude later in Jadis.  It is Digory's skepticism (and his loyalty to Polly) that later help him to resist Jadis when she tempts him in the hilltop garden. 
These traits of being curious, stubborn, bold, and skeptical are exactly what make Digory such a good researcher and philosopher in later years, when he grows up to be "Professor Kirk."  
Despite being somewhat rebellious, Digory has been well brought-up and he has a soft heart.  Thus, he loves his mother and keeps trying to save her.  He keeps his promise to Aslan, and though not impressed by just any adult (such as Uncle Andrew), he is able to submit to the authority and goodness of Aslan, recognizing that Aslan is worthy of his service.  After meeting Aslan, Digory will carry the lion's influence with him all his life. 
 

What does Bulosan's memoir tell us about America's empire and its effects on American society?

Carlos Bulosan, a Filipino poet born in 1913, writes about his early years growing up in the Philippines in his 1946 memoir America is in the Heart. He writes of the time right after World War I: "it seemed like the younger generation, influenced by false American ideals and modes of living, had become strangers to the older generation" (5). When he is growing up, the Philippines were becoming more and more Americanized. For example, the author's older brother, Macario, attends the school far from his village, and he is indoctrinated in American ways. When he sees Allos (or "Carlos"), Macario wants to cut his brother's hair in the American way. 
Later, after Bulosan sees the plight of the peasants in his hometown of Luzon, he dreams of going to America and learns about Abraham Lincoln. He thinks, "A poor boy became President of the United States!" and he is fascinated by this story (69). He believes the United States represents equality. This is the idea of America that people in the far-flung parts of the empire believe, and this dream draws them to immigrate to the United States.
When he arrives in the U.S. in the early 1930s, Bulosan finds life entirely different from what he imagined. He writes, "There seemed to be tragedy and horror everywhere I went" (175). He works at menial jobs in the American west, where he is treated with prejudice and disrespect by the white world around him. He develops a hatred and distrust of white people, and he says of his Filipino community: "we hid cynically behind our mounting fears, hating the broad white universe at our door" (164). Finally, he turns to becoming part of the Filipino civil rights movement. His early dreams of American equality help motivate him to push for equality in American society. Therefore, Bulosan, an immigrant, dedicates himself to making America more egalitarian and more true to its promise of equality. 

Single Variable Calculus, Chapter 7, 7.2-1, Section 7.2-1, Problem 6

How are the graphs of $y = 0.9^x, y = 0.6^x, y = 0.3^x$ and $y = 0.1^x$ related. Graph them on the same plane.







Based from the graph, all functions pass through the point $(0,1)$. Since they all have positive exponents, it means that the functions are all increasing. Also, all the functions approaches as $x \to \infty$ and approaches $\infty$ as $x \to - \infty$.

How much money can McDonald's make in a year?

In answering this question, we will focus on McDonald’s annual revenues over the years, and use various sources to get estimates of these values.
According to this infographic from Statista, McDonald’s Corporation made approximately $19.12 Billion in 2005, $20.9 Billion in 2006, $22.79 Billion in 2007, $23.52 Billion in 2008, $22.75 Billion in 2009, $24.08 Billion in 2010, $27.01 Billion in 2011, $27.57 Billion in 2012, $28.11 Billion in 2013, $27.44 Billion in 2014, $25.41 Billion in 2015 and $24.62 Billion in 2016. This gives an average of about $24.4 Billion per year, over the period 2005 to 2016. These figures are based on the corporation’s total revenues worldwide. It is important to note that McDonald’s had 30766 restaurants worldwide in 2005, 31046 restaurants in 2006, 31377 restaurants in 2007, 31967 restaurants in 2008, 32478 restaurants in 2009, 32737 restaurants in 2010, 33510 restaurants in 2011, 34480 restaurants in 2012, 35429 restaurants in 2013, 36258 restaurants in 2014, 36525 restaurants in 2015, and 36899 in 2016.
According to Owler, McDonald’s Corporation makes revenues of about $23.5 Billion per year.

How are pearls created by oysters?

Pearls are made of nacre, which on its own is commonly known as "mother of pearl" (because it is the substance from which true pearls are birthed). Oysters do not actually make pearls deliberately, as it were; pearls are a by-product of the oysters' need to protect themselves from invaders and irritants. For example, if a piece of grit or sand makes its way into the oyster's sensitive internal area, it will begin to coat that piece of grit in layer upon layer of nacre in order to shield itself from the irritation that would otherwise result. Sometimes, when pearls are made deliberately by "pearl farmers," an irritant will therefore be introduced into an oyster's shell to encourage this process. Essentially, however, the process of an oyster making a pearl is similar to the process by which our eyes begin to water when a piece of grit touches the soft surface of the eyeball and needs to be washed away.
https://www.livescience.com/32289-how-do-oysters-make-pearls.html

Who is "a soldier, and afeard" in Macbeth?

In act five, scene one, Lady Macbeth's waiting gentlewoman (a servant) and her doctor see Lady Macbeth sleepwalking and talking, apparently the result of Lady Macbeth's guilty conscience. Lady Macbeth appears to be reliving, in part, the night her husband murdered the king when she says, "Fie, my lord, / fie, a soldier and afeard?" (5.1.38–39). She appears to be addressing her husband, Macbeth, similar to the way she did just after he killed Duncan. At the time, she shamed Macbeth for feeling guilt and remorse, for being too afraid to return the bloody daggers to Duncan's room so that others would believe that Duncan's chamberlains actually murdered him. The word "fie" is sort of an exclamation that is used to convey the speaker's anger or disgust. Therefore, when she relives that night (in her dreams), she seems to be expressing her disgust at Macbeth's weakness once again, shaming him for being a soldier who is afraid. He is the soldier in the quotation, and he feels fearful (or "afeard"), having murdered Duncan. Lady Macbeth seems to feel that it is incongruous and ridiculous that Macbeth could lead a charge in battle with bravery and still be completely frightened by the idea of killing one single person.

Lady Macbeth is talking to herself in Act V, Scene 1 of the play and is evidently sound asleep. At one point, she imagines she is talking to her husband and they are back in the past, in the time before he has actually murdered Duncan. She is using her familiar tactic of appealing to his sense of manhood to convince him to do what she wants him to do. 

Fie, my lord, fie, a soldier, and afeard?

She pretends to believe all Macbeth's misgivings about going through with the murder are due to cowardice and have no logical substance. In the line that follows her question, she is still addressing her husband in her dream.

What need we fear who knows it, when none can call ourpow'r to accompt?

If they can become king and queen of Scotland, Macbeth and Lady Macbeth would not be questioned about how they acquired their authority. After Macbeth becomes king, everyone treats him with the greatest respect. This includes Banquo, who thinks Macbeth obtained the crown by murdering King Duncan, as he says to himself in the soliloquy which opens Act III, Scene 1.

Thou hast it now: King, Cawdor, Glamis, all,As the weird women promised, and I fearThou play'dst most foully for't:

Lady Macbeth struggled to persuade her husband to go through with the assassination. Shakespeare uses Lady Macbeth's sleepwalking scene in the final act of the play to remind his audience that she shares in Macbeth's guilt. For example, back in Act I, Scene 7, when Macbeth told her,

We will proceed no further in this business:He hath honor'd me of late, and I have boughtGolden opinions from all sorts of people,Which would be worn now in their newest gloss,Not cast aside so soon.

She responded,

Was the hope drunkWherein you dress'd yourself? Hath it slept since?And wakes it now, to look so green and paleAt what it did so freely? From this timeSuch I account thy love. Art thou afeardTo be the same in thine own act and valorAs thou art in desire?

What is the plot of Chapter One in The Silver Sword by Ian Serraillier?

In Chapter One, the plot involves Joseph Balicki's escape from prison in the mountains of South Poland.
During the first winter of his incarceration, Joseph is too ill to attempt an escape. In the summer, he feels better and tries to escape with five other prisoners. The attempt fails, however, and Joseph is sent to solitary confinement.
During the second winter, Joseph is ill again. It isn't until the spring that he tries to escape once again. This attempt is successful. When a guard slides Joseph's food through a slot in the door, Joseph is ready for him with his catapult. His catapult is fashioned from sticks and "from the elastic in the sides of his boots." Meanwhile, his "ammunition" consists of a smooth, round stone. Joseph manages to render the guard unconscious with a well-placed shot from his catapult.
Then, with a bent nail tied to a piece of blanket, Joseph manages to retrieve the guard's keys. Once he has the keys, Joseph pulls the guard into his cell and changes into the guard's uniform. Then, he prepares to march out of the prison with the other guards on a routine prison roll call.

What seems to be the basis for their attraction to each other?

Romeo and Juliet's initial attraction seems to be founded on appearances.  Before Romeo ever speaks to Juliet, he says,

O, she doth teach the torches to burn bright!It seems she hangs upon the cheek of nightAs a rich jewel in an Ethiope's ear --Beauty too rich for use, for Earth too dear. (1.5.51-54)

He is immediately affected by Juliet's beauty.  He says that she "burn[s] bright[er]" than a torch, and he compares her to a "rich jewel" being worn by night.  He even says that her beauty is actually too much for the Earth to deserve.  Romeo goes on and on about how beautiful Juliet is, and so it seems clear that this is what first attracts him to her.
The first time Romeo speaks to Juliet is to ask to kiss her hand.  They speak very briefly and then they actually do kiss.  Juliet's nurse pulls her away, and Juliet asks her to find out Romeo's name.  When the nurse is away, Juliet says, "If he be married, / My grave is like to be my wedding bed" (1.5.148-149).  Then, when she learns that he is a Montague, she laments, "My only love sprung from my only hate!" (1.5.152).  In other words, she now feels herself to be in love, and considering she has only had one verbal interaction and one kiss with Romeo, her love for him must be, mostly at least, based on appearances at this point.

What is one of the themes of The Orchid Thief?

Money is a major theme in The Orchid Thief by Susan Orlean. When she goes to investigate an unusual arrest involving a plant dealer and three Seminole tribe members, Orlean inadvertently stumbles into the high-stakes world of plant breeding. Though most of the dealers and breeders Orlean speaks to are driven by their obsession and love for rare plants, money is also an undeniable part of the equation. The best example of this is John Laroche, the white man who was arrested for stealing rare orchids from a preserve in Florida. Though Laroche thought he was not technically breaking the law (he believed that he was exploiting a legal loophole by having Seminole tribesmen actually remove the flowers), his quest for the rare ghost orchid was primarily driven by his desire to turn a profit. If he could successfully clone and breed the ghost orchid to make it a suitable houseplant, Laroche believed that he and the Seminoles would be able to make millions. Laroche is not alone in his desire for fame and money; many of the other plant breeders Orlean meets hope to create a new breed of orchid that will make them rich. Some of the breeders have even transferred their horticultural knowledge into other business ventures such as Orchid Jungle, a popular tourist attraction run by a famous orchid grower named Tom Fennell.

What social issue in Death of a Hero by Richard Aldington and All Quiet on the Western Front by Erich Maria Remarque was a concern during WWI and is still present in society today?

One thing you could point to is that both books are critiques of the tendency for Western societies to embrace violence as a positive trait, or as the only way to resolve conflicts. In Death of a Hero, for example, young George is browbeaten into getting a gun license -- the hope is that this "will make a man" out of him. His experience with shooting, however, is horrifying -- he wings a bird, and, in trying to wring its neck, tears its head completely off. This episode is emblematic of George's disgust with bourgeois values, his desire to become a bohemian, and his embrace of "free love." None of these values serve him very well at the front, however, where he becomes a kind of automaton. In All Quiet on the Western Front, it's clear that Paul's teacher Kantorek is urging his students to enlist without fully understanding what the war will be like. Kantorek's betrayal lies in his using his position of authority to advocate for violence. Both books describe, with shocking detail, exactly what the cost of this love of violence is in human terms.
It's also pretty clear that we can trace the origins of the US's current "get tough" rhetoric about immigration or terrorism to the same nationalist ideologies and love of violence condemned in these books.

Why is the narrator left in despair at the end of the story The Old Man at the Bridge?

The narrator is left in a state of despair at the end of the story because he is worried about the old man but is unable to offer him any help. The narrator is a scout of sorts for the camp of soldiers fighting against the fascists. His work involves exploring various places beyond the bridge to check on the movement of the advancing enemy. It is while doing this that he observes the old man sitting by the roadside even as everybody else hurries to cross the bridge to move to safer places.
The old man is seventy-six years old and does not have any close relatives, except for “two goats, a cat, and four pairs of pigeons,” which he had to leave behind in his hometown of San Carlos, because of the artillery. He is tired after walking about twelve kilometers and does not have the strength or the desire to walk any further. The narrator urges him to walk on at least until he can get to the trucks further up the road which will hopefully take him to Barcelona. However, the old man is too weak to walk any further. He tries to stand up, “sways from side to side and then sits down backwards in the dust.” The whole scene paints a picture of sad hopelessness in the reader’s mind. The narrator is saddened by the plight of this old man who is surely a victim of a war that he does not understand, for, as he states “he is without politics.”

What are the causes of urban-rural migration?

This question is vague and could be approached from a number of angles. I would argue that one of the most significant examples of rural-urban migration in history is provided by the industrial revolution, which began in Great Britain in the early to mid-19th century before spreading to France, the rest of Western Europe and the United States. The emergence of major industrial factories in cities, and in many cases the springing up of new cities around such factories, led to a dramatic alteration in the way of life of the entire population. Not only were large numbers of people drawn to urban areas to take advantage of job opportunities, but the way of life for those in the country was severely undermined. The manufacturing economy that had existed in England, for example, where workers and their families would produce goods in a cottage or small community, was largely undermined by technological advances and the superiority of factory production in terms of efficiency.
Industrialization has had a similar impact in other parts of the world in more recent times, such as in China. In fact, many see the current rate of urbanization as unprecedented. The total number of people living in urban areas is expected to grow from 3.4 billion to 6.3 billion by 2050. That being said, there is an urban-rural component to migration as well, as this question suggests. One cause of this is the cost of living in cities. In many large urban areas, property prices and other necessities for life have risen dramatically, meaning rural life offers an affordable alternative. This can be particularly attractive to families, for example, who are considering the quality of life for their children. A desire to contribute to the improvement of biodiversity and the environment also plays a role among some urban-rural migrants (see the story about Daniel and Johanna at the link below). Other reasons can be more immediate. The United Nations University notes the example of the response by 600,000 residents of the Haitian capital Port au Prince to the 2010 earthquake. As a result of the collapse of food supply systems and other services, they left the city for the country’s rural areas in order to survive. A final reason worth mentioning here is technology. The rapid spread of the internet and other forms of communication means that people who want to live in rural areas can still stay connected with work and educational opportunities or with friends or family in urban centers.
https://unu.edu/publications/articles/return-to-rural-communities-resilience-over-efficiency.html

How did the Sighet Jews fail to anticipate Nazi brutality?

When Moishe returns to Sighet with stories of the Nazi brutality he witnessed and experienced firsthand, the Jews do not believe him. "They think I'm mad," he tells Elie (page 7). After foreigners are expelled from the town and witness the madness of the Nazis, life returns to normal. In the spring of 1944, as news of the Russian victories arrive in the town, the Jews believe that the Russians will soon defeat the Nazis. The Jews also believe that it's impossible for Hitler to exterminate an entire people and that such brutality is unthinkable in the 20th century. Most of the Jews speak about possibly emigrating to Palestine, though they do not do so, and they believe that the Nazis will never invade Hungary. Once the Nazis invade Hungary, the Jews believe that the Nazis will never reach their town. Even once they reach the town, the Jews believe the Nazis are polite until they start passing anti-Semitic laws. The Jews of Sighet react with disbelief to every bit of news and live in denial until they can't do so any longer.

a_n = nsin(1/n) Determine the convergence or divergence of the sequence with the given n'th term. If the sequence converges, find its limit.

a_n=nsin(1/n)
Apply n'th term test for divergence, which states that, 
If lim_(n->oo) a_n!=0 , then sum_(n=1)^ooa_n diverges
lim_(n->oo)nsin(1/n)=lim_(n->oo)sin(1/n)/(1/n)  
Apply L'Hospital's rule,
Test L'Hospital condition:0/0
=lim_(n->oo)(d/(dn)sin(1/n))/(d/(dn)1/n) 
=lim_(n->oo)(cos(1/n)(-n^(-2)))/(-n^(-2))
=lim_(n->oo)cos(1/n)
lim_(n->oo)1/n=0
lim_(u->0)cos(u)=1 
By the limit chain rule,

=1!=0 
So, by the divergence test criteria series diverges.  

Early in "The Cask of Amontillado," how does Montresor describe Fortunato's strengths and weaknesses?

Early on in "The Cask of Amontillado," Montresor tells of his plans to get revenge against Fortunato for unspecified insults. Montresor knew Fortunato's biggest weaknesses, his love and knowledge of great wines and his tendency to drink too much and become intoxicated. Montresor used Fortunato's love for wines against him by convincing him that he had been given a rare cask of amontillado wine. Fortunato, being the proud man and wine connoisseur that he was, did not allow Montresor to ask Luchresi for help in determining wether the amontillado was authentic or not. Montresor, by being able to identify Fortunato's strengths and weaknesses, was easily able to trick Fortunato into following him into the vaults. Had Fortunato not been so quick to become intoxicated and so prideful in his knowledge of wines, he might have been able to save himself from Montresor's revenge. 

Listed below are six essay prompts: create a 400-600 word essay. Be sure your essay follows the MLA style of formatting. 1. How are specific physical symbols used to characterize the essential nature of Stanley Kowalski? 2. Characterize the essential differences between the Kowalski and the DuBois worlds. 3. Using evidence from the play, try to determine which is the real Blanche--the innocent and charming Blanche or the degenerate and promiscuous Blanche. 4. Show how each subsequent meeting between Blanche and Stanley increases in violence and antagonism. 5. In spite of Blanche's past life, her deceit, and her artificiality, most readers and viewers tend to sympathize with and align themselves with her. How can this emotional reaction (or attachment) toward Blanche be justified? 6. Show how a Mitch-Blanche marriage could have been a perfect marriage if Stanley had not interfered.

On your point 3, I would argue that in viewing Blanche, to use words such as "degenerate" and "promiscuous" is somewhat unhelpful. The value judgments attached to such terms in her case, I believe, are unrealistic and unfair. But an awareness of what I would consider a problem with the way the question is worded can lead to an answer to the "deeper" question that lies behind Blanche's personality and that of Stanley, and of Stella, as well.
Like every real person, the characters in Streetcar are a mixture of different qualities, both "good" and "bad." Even Stanley, though the emphasis is on his crudeness and abusiveness shown in his physically violent behavior, appears to love Stella in his way. The Kowalskis are a working-class couple, removed from the rarefied world Stella and Blanche originally are from. Blanche is, in fact, charming and sensitive. Her love for her husband, whom she discovered to be gay, was genuine, and the shock of finding this out about him and his subsequent suicide threw her life off course. A reader, especially in our time, who does not sympathize with her would have to be extremely cold-hearted and unforgiving, in my opinion.
It is not surprising that the antagonism between Blanche and Stanley should increase as the play progresses and they continue to interact with each other, given that the two of them are not "on the same page" to begin with. Whether she and Mitch could have had a successful marriage is anyone's guess. Mitch is a blue-collar person like Stanley, but without the latter's cruelty. Though he and Blanche come from different social backgrounds, such a difference is not always an impediment to a successful pairing in real life, so it's possible that these two could have been successful as well had not Stanley destroyed it for both of them.

What would be a method for finding a thesis statement about JFK's assassination?

The first step might be to determine where your interests lie – in the motive?  In the political fallout? In the missed presidential opportunity? etc.  Then examine your bias or attitude or opinion about that area of inquiry – was there a conspiracy?  Did Johnson do a good job?  etc.  Then word that area and attitude in a question that has two sides to research and argue – What is the evidence for a Cuban conspiracy?  Who would benefit by Kennedy’s death?  What might have been accomplished by his presidency? etc.  This approach to a thesis statement gives you plenty of room to explore the subject and solidify your ideas as you research and write.  Leave room for discoveries during the process. Avoid being too specific at the outset of wording your thesis statement, but be exact and specific in the final draft.  Your final draft thesis statement should not be in question form, of course, but instead an arguable point of view, with researched evidence as support.  The questioning in an early draft is a way to make your final statement convincing. This project deserves your creative abilities as well as your organizational skills.

How does Buckingham's speech in act 3, scene 7, lines 24-41 support the Scrivener's speech at the beginning of the scene? What other characters in this scene act in ways that bear out the Scrivener's speech?

The Scrivener is an important minor character in Richard III. Formally, the Scrivener's role is to draw up documents. But in relation to the play, his dramatic role is to provide a running commentary on events, in particular drawing attention to the devious machinations of Richard and Buckingham. His speech in act 3, scene 7 is an example of this.
The Scrivener is also presented to us as a man of the people, someone with his finger on the pulse of public opinion. The Scrivener, much like the common folk of England, knows that Richard and Buckingham are up to no good. Yet the latter is largely unaware of this, expressing great surprise at the mute hostility of the crowd in response to his speech. But their reaction is entirely predictable, and is foreshadowed earlier in the scene by the Scrivener when he complains about spending practically a whole day drawing up Hastings's indictment. The whole thing is a sham, and the Scrivener, for one, can see right through it:

Who is so gross
That cannot see this palpable device?
Yet who so bold but says he sees it not?

You'd have to be pretty stupid not to see through this blatant ploy, says the Scrivener, but who would dare to come right out and say this? The behavior of the citizens, the Lord Mayor, and Catesby later on in the scene would certainly appear to bear out the Scrivener's words. They are indeed stupid enough not to see Richard's theatrical rejection of the crown for the gigantic con trick that it is. The common people, like the Scrivener, are on to Richard, but not the worthies of the city. They are completely taken in by Richard's fake reluctance to accept the crown of England and by his loud protestations of loyalty to young King Edward.

What is 60 Earth Hour? Is it a good idea? Considering all of the global turmoil going on right now, are you surprised at the reach this movement has had considering the different countries/regions participating?

Earth Hour is an international movement whose main aim is to advocate for action on climate change. It is coordinated by the World Wide Fund for Nature, an international non-governmental organization concerned with environmental conservation work. Its website details that it is a non-profit organization that is based in Singapore and whose mission involves “uniting people to protect the planet.” It first started out as a “lights off” event in Sydney, Australia, in 2007, and it has since expanded to over 172 countries situated in various regions of the world. A core component of its advocacy is to encourage people to turn off their lights for a period of one hour between 8:30 pm and 9:30 pm on a given day in the month of March every year.
I think you could make a good case that the 60 Earth Hour initiative is a good way of drawing attention to climate change, an issue of major concern to people globally. Though turning off lights for an hour may have negligible effects on energy consumption levels, the very action encourages dialogue on the need to reduce energy consumption and pushes people to commit to behavior that achieves this goal beyond the hour. It helps to sensitize people to the need for energy conservation: What is to be achieved from an hour of darkness? A Google search for this question yields answers that point to the connection between our energy use and the environment. One realizes that when they use less energy, they reduce the quantity of toxic fumes emitted by power plants and conserve natural resources.
According to Earth Hour’s website, the 2017 event was commemorated in 187 countries, where more than 3000 landmarks and monuments turned off their lights. Clearly, the Earth Hour movement has managed to reach a large number of people since its inception. The movement’s mission is an issue that touches the lives of many people across the globe. Most of us have experienced the effects of climate change in the form of long droughts, heat waves, and rising sea levels. As such, Earth Hour’s message resonates with many people. Also, technology has perhaps helped the organization to push its message more quickly across the globe.
https://www.earthhour.org/

Finite Mathematics, Chapter 1, 1.1, Section 1.1, Problem 30

Determine a equation in slope intercept form (where possible) for the line that goes through $(2,-5)$ and parallel to $y - 4 =2x$

If we transform the given line into point slope form, we have

$
\begin{equation}
\begin{aligned}
y - 4 &= 2x \\
\\
y &= 2x + 4
\end{aligned}
\end{equation}
$

Now that the line is in the slope intercept form $y = mx + b$. By observation, $m = 2$
And if the line is parallel to the line we are looking, then we can say that both lines have the same slope
By using the point slope form,the equation of the line will be $y - y_1 = m(x - x_1)$

$
\begin{equation}
\begin{aligned}
y - (-5) &= 2(x - 2)\\
\\
y + 5 &= 2x - 4 \\
\\
y &= 2x - 9
\end{aligned}
\end{equation}
$

In "Half a Day," what is the concept of time and how does it connect with death?

Naguib Mahfouz's short story "Half a Day" is about a reluctant young man who goes off to his first day of school. The story is a metaphor for life and how short a life can be. No sooner has the boy gotten through his first day of school than he is pictured at the end of the story as an old man who has to be helped across the street. During the course of the story the first person narrator gives hints that this is no normal day and that time is passing. He talks of learning new things, of struggle, and of the entanglements of relationships, some involving love and some hatred. Just before this figurative day of school is over, the narrator seems to acknowledge that a great deal of time is passing and that the world is changing:

In addition, the time for changing one's mind was over and gone and there was no question of ever returning to the paradise of home. Nothing lay ahead of us but exertion, struggle, and perseverance. Those who were able took advantage of the opportunities for success and happiness that presented themselves amid the worries.

This paragraph, which in a short number of words, sums up a person's life, is quickly followed by a paragraph which transports the narrator to the day when school is out and he must return home. Instead of the calm, tranquil streets of his childhood, the city has become crowded and bustling, symbolic of the fact that many years have passed and that the city has greatly changed. For the narrator, only death awaits after only "half a day." Life is short and before the narrator knows it time has ebbed away, school is out and people are suddenly referring to him as "Grandpa."  

What is the relationship between the French and Indian War and the movements for American Independence?

As a result of the French and Indian War, the British had accrued a significant amount of debt.  Paying back the interest alone was going to require a significant amount of the empire's yearly budget.  Many in England felt that the colonists were not paying their fair share of the burden of taxation, especially considering the rewards that the colonists were reaping from the protection of Britain's powerful navy.  
The colonists, on the other hand, were beginning to feel culturally and politically distant from the mother land.  Decades of lax governance by the Brits had engineered an independent spirit in the thirteen colonies.  For this reason, when Parliament started to expect more revenue in the form of enforcing new and existing tax legislation, the colonists were not willing to pay.  The colonists felt that if they were to be taxed, they should have representation in Parliament to decide what the taxes would be and how the revenue would be spent.  
http://www.let.rug.nl/usa/essays/before-1800/french-and-indian-wars/effects-of-the-war.php

What federal actions were taken to resolve the Great Depression? How was the working class impacted? (Not including Hoover's unsuccessful actions.)

Federal actions to combat the Great Depression were part of a massive effort known as the "New Deal" that followed a campaign speech by Franklin Roosevelt. The New Deal consisted of hundreds of government programs, bureaus, agencies, and spending initiatives, each of which was intended to address the problems created by the Depression.
There were far too many of these programs to list in this space, but many were implemented in the so-called "Hundred Days" after Roosevelt's inauguration. These included measures taken in 1933 to address the bank failure crisis that gripped the nation, emergency loans to state governments, low-interest housing loans, and the Civilian Conservation Corps (CCC), one of the New Deal programs that attempted to create work for jobless men. Many other programs were passed in 1935–1936, the so-called "Second New Deal," that included the Works Progress Administration, the Social Security Administration, and the Wagner Act, which protected the rights of unions to organize.
The New Deal in general tried to resolve the Depression through government action, which took several different forms. Historians usually accept that New Deal programs had three broad aims, sometimes categorized as the "three Rs": providing relief, promoting recovery, and reforming the American economy. Of the three, the final aim was the most successful. Reforms like the Wagner Act, the Social Security Act, the Securities Exchange Commission, and the Federal Deposit Insurance Corporation fundamentally changed the relationship between the American people, the economy, and their government. These reforms created a "New Deal order" that persisted for much of the twentieth century.
As for how they affected the working class, the Wagner Act in particular had profound consequences, as it essentially established collective bargaining as a fundamental right. Unemployment rates declined in the short-term (with several blips) during the 1930s, partially due to New Deal spending. But American workers only saw the end of the Depression with the outbreak of World War II.
http://www.digitalhistory.uh.edu/disp_textbook.cfm?smtid=2&psid=3439

https://www.history.com/topics/great-depression/new-deal

How did the government policies of the Revolutionary and Napoleonic Era shape French national identity?

The French Revolution began the establishment of social and economic rights for all citizens, affording them voice and some control over their political destinies. The Napoleonic Era established the Civil Code, the first modern legal code. This was a code that influenced many European countries.
Prior to the Revolution of 1789, there were three estates in France:
The First Estate - The clergy
The Second Estate - The nobility
The Third Estate - All other French citizens, which was composed of the middle class (otherwise known as the bourgeoisie, which included bankers, merchants, lawyers, doctors, journalists, and professors), the peasants who worked on the lands of the nobility, and the city workers. Only the Third Estate paid taxes.
Here are three ways that the French Revolution and Napoleonic Era shaped the national identity of France:
1. The establishment of democratic policies.
The government that was formed did not adhere strictly to the French Revolution's ideals of liberty, equality, and fraternity; rather, all citizens began to have some control over their individual political destinies. People began to be afforded equal representation and they possessed social and economic rights, rights that are the foundations of democracies.
2. The introduction of secularism
Secularism was instituted into the government. Before the Revolution, the clergy of the Catholic Church wielded great power and influence. Religious rule was eliminated after the Revolution. Thus, public and political decisions were no longer influenced by religious beliefs.
3. The institution of the Napoleonic Code 
During the Napoleonic era, the Napoleonic Code was established, which introduced an organized legal system into the government -- a system the Revolution had not provided. The Napoleonic Code provided the French government with its first orderly and consistent set of laws that covered colonial affairs, the family, property, and the rights of the individual. This code prohibited judges from making decisions independent of any clearly defined system. It also affected other areas:

It codified several branches of law, including commercial and criminal law, and divided civil law into categories of property and family. The Napoleonic Code made the authority of men over their families stronger, deprived women of any individual rights, and reduced the rights of illegitimate children (https://www.boundless. com/world-history/concepts/the-napoleonic-code-0-17755/).

In short, the Napoleonic Code replaced the many fragmented laws of pre-revolutionary France that were not reformed, and it recognized the principles of civil liberty for some along with the non-religious character of the state.
https://www.britannica.com/event/Napoleonic-Wars

https://www.history.com/this-day-in-history/napoleonic-code-approved-in-france

https://www.history.com/topics/france/french-revolution

How does Edgar Allan Poe use darkness and gloom to make "The Tell-Tale Heart" a Gothic Story?

Gothic texts combine fiction, horror, and death to prompt readers to feel extreme emotion, and "The Tell-Tale Heart" employs darkness and gloom to this effect. When the narrator describes the way he approaches the old man's darkened room each night, just at midnight, slowly inserting his head and his "dark lantern" through the door, we know what his intention is. His obsessive repetition of these actions, undertaken in darkness, only adds to the growing tension. Further, on the night the old man hears the narrator and sits up wide awake in bed, we know the narrator is waiting in the gloom, increasing our anxiety and terror for the old man's well-being. It's quite terrifying when the narrator says the old man tried to comfort himself in vain "because Death, in approaching him had stalked with his black shadow before him, and enveloped the victim." The old man seems to know, intuitively, that he is in danger, and the fact that the narrator associates himself with Death (he is right at home in the darkness and gloom with which we often associate death) confirms the man is, indeed, in mortal danger. This all heightens our anxiety and horror, in parallel with how the old man's feelings of terror increase as well, and these feelings are the hallmark of Gothic literature.

Why do the animals of Animal Farm confess to being traitors?

Things are going horribly wrong with the Animalist experiment. There are chronic food shortages on the farm; everyone has to work harder for fewer rations; and the rickety old windmill has collapsed. But Napoleon cannot admit that he is any way responsible for what's happening, despite being dictator. So he creates a scapegoat, namely Snowball. Napoleon makes out that Snowball is the evil genius behind everything that goes wrong on the farm. And any animal found to be in league with Snowball is history.
Napoleon assembles all the animals in the yard. There follows a grotesque, bloody spectacle of false confessions and summary executions. So why do the animals confess to something they haven't done? There all kinds of reasons. Fear would be one of them. Although the animals are not actually guilty of anything, some of them are worried that if they don't confess, they'll end up getting in trouble sooner or later.
However, the most important factor is that the animals, for all their troubles, have come to believe in the ideals of the Animalist revolution; they've invested themselves body and soul in its success. If things are going wrong, then it can't be the fault of Animalism; it must be because of conscious acts of sabotage. According to the dominant ideology, the individual is ultimately of no importance; the collective is everything. This inculcates a mindset of individual sacrifice for a higher cause, and it is this, more than anything, that prompts animals to come forward and confess to crimes that they never committed.

An ultracentrifuge accelerates from rest to 100,000 rpm in 2.50 min. (a) What is its angular acceleration in rad/s2? (b) What is the tangential acceleration (in m/s2) of a point 11.50 cm from the axis of rotation?

a) Angular acceleration:
First, convert the speed in rpm to rad/s as follows:
omega = 100,000 rev/min x 2pi rad/rev x 1 min/60 sec = 10,472 rad/sec
Since the ultracentrifuge starts from rest,
angular acceleration, alpha = omega /time
where time = 2.5 min = 2.5 min x 60 sec/min = 150 sec
Thus, angular acceleration, alpha = 10,472 rad/sec / 150 sec = 69.81 rad/s^2

b) Tangential acceleration can be calculated by using the following formula:
a_t = alpha r
where r is the distance from the axis of rotation. This distance is given as 11.50 cm.
In other words, r = 11.50 cm = 11.50 cm x 0.01 cm/m = 0.115 m.
Substituting the values of alpha and r in the above equation, we get:
a_t = (69.81 rad/s^2) x 0.115 = 8.03 m/s^2

Thus, the angular acceleration is 69.81 rad/s^2, and the tangential acceleration is 8.03 m/s^2.
Hope this helps.

Calculus of a Single Variable, Chapter 8, 8.5, Section 8.5, Problem 8

int(3-x)/(3x^2-2x-1)dx
Let's use partial fraction decomposition on the integrand,
(3-x)/(3x^2-2x-1)=(3-x)/(3x^2+x-3x-1)
=(3-x)/(x(3x+1)-1(3x+1))
=(3-x)/((3x+1)(x-1))
Now form the partial fractions using the denominator,
(3-x)/((3x+1)(x-1))=A/(3x+1)+B/(x-1)
Multiply equation by the denominator (3x+1)(x-1)
=>(3-x)=A(x-1)+B(3x+1)
=>3-x=Ax-A+3Bx+B
=>3-x=(A+3B)x+(-A+B)
comparing the coefficients of the like terms,
A+3B=-1 ----------------(1)
-A+B=3 ----------------(2)
Now let's solve the above equations to get A and B,
Add the equations 1 and 2,
4B=-1+3
4B=2
B=2/4
B=1/2
Plug in the value of B in equation 1,
A+3(1/2)=-1
A+3/2=-1
A=-1-3/2
A=-5/2
Plug in the value of A and B in the partial fraction template,
=(-5/2)/(3x+1)+(1/2)/(x-1)
=-5/(2(3x+1))+1/(2(x-1))
So, int(3-x)/(3x^2-2x-1)dx=int(-5/(2(3x+1))+1/(2(x-1)))dx
Apply the sum rule,
=int-5/(2(3x+1))dx+int1/(2(x-1))dx
Take the constant out,
=-5/2int1/(3x+1)dx+1/2int1/(x-1)dx
Now let's evaluate both the above integrals separately,
int1/(3x+1)dx
Apply integral substitution:u=3x+1
=>du=3dx
=int1/u(du)/3
Take the constant out,
=1/3int1/udu
Use the common integral:int1/xdx=ln|x|
=1/3ln|u|
Substitute back u=3x+1
=1/3ln|3x+1|
Now evaluate the second integral.
int1/(x-1)dx
Apply integral substitution: u=x-1
du=1dx
=int1/udu
Use the common integral:int1/xdx=ln|x|
=ln|u|
Substitute back u=x-1
=ln|x-1|
int(3-x)/(3x^2-2x-1)dx=-5/2(1/3ln|3x+1|)+1/2ln|x-1|
Simplify and add a constant C to the solution,
=-5/6ln|3x+1|+1/2ln|x-1|+C

In the book Chains by Laurie Halse Anderson, what is Isabel's first act of bravery?

Isabel first demonstrates her bravery on the night of Mr. Lockton’s meeting in the library, when Mrs. Lockton’s aunt visits. At bedtime, Ruth breaks into tears for being mistreated by Mrs. Lockton earlier on that day, which deeply disturbs Isabel.
She feels desperate, because her situation has rendered her powerless and she cannot protect her sibling from harm, yet she is fully responsible for her. She, therefore, decides to take Curzon’s offer to become a spy on behalf of the rebels, in order to secure freedom for herself and Ruth. That night, she sneaks out of Locktons’s estate to seek Curzon despite the grave repercussions in the event that she is caught. In addition to that, she betrays her master by revealing the clandestine details of his meeting to Curzon, placing herself in greater jeopardy. She then bravely sneaks back into the mansion without anybody’s knowledge.
There are other incidents that happened earlier and may show signs of courage on the part of Isabel. However, these incidents can also be seen as responses to sibling responsibility. The moment she decides to become a spy is definitively brave because, despite having a choice to stand down, she makes the bold move to meet with Curzon. She makes a conscious decision to stand up against her aggressors because she cannot take the abuse anymore. At that moment she makes the first move.
https://onlinelibrary.wiley.com/action/cookieAbsent

This is a tough question because Isabel is brave throughout the book, and I'm not sure what the defining line for an "act of bravery" is in regards to this question.  
I have three possibilities that I feel work.  Each involves Isabel putting herself in greater danger than the previous act.  
The first occurs in chapter three.  The Locktons are deciding whether or not to purchase Isabel and Ruth.   Madam Lockton is fairly confident in purchasing Isabel, but she can see that Ruth is mentally handicapped.  Madam Lockton asks Mr. Robert about it, and Isabel answers before Mr. Robert can answer.  It's a bold, brave move for Isabel because she's a black slave.  Some people even consider blacks equivalent to animals.  By merely speaking out of turn, Isabel is risking a possible beating.  Madam Lockton even comments on it.  

"She's [Ruth] prettier than you," Missus said. "And she knows how to hold her tongue." 

The second act of bravery that I believe Isabel displays is when Ruth has a seizure in front of Madam Lockton.  Madam Lockton believes that Ruth is possessed by the Devil, and she begins to beat Ruth with a broom.  Isabel throws herself down on top of Ruth in order to take the blows for Ruth.  

''NO! I threw myself on top of my sister. The broom came down my back once, twice, but still it didn't matter. I had to keep my sister safe until the storm passed.'' 

Both of those previous acts are a bit reactionary on Isabel's part.  She is responding to a situation in order to immediately protect Ruth.  There really isn't a choice to be defiantly brave.  The first time that Isabel chooses to be brave through an act that she very easily could have chosen not to do is when she sneaks out of the Lockton house the first time.  She sneaks out in order to report to Curzon what she heard about Lockton's plans to bribe Patriot soldiers.  Slaves can be captured and killed for being out at night, and Isabel tells readers that she wants to be brave like Queen Esther from the Bible.  

What are some race-related events that are foreshadowed throughout Harper Lee's To Kill a Mockingbird and really remind the reader the underbelly of racism in America is never far away?

One race-related event in Harper Lee's To Kill a Mockingbird is the outcome of Tom Robinson's trial. Robinson's innocence in the crime he's being accused of is made evident the moment during the trial we learn that Mayella Ewell had been bruised on the right side of her face, which could only have been accomplished by a left-handed man facing her, whereas Robinson has been crippled in his left arm and hand since he was a boy and got his arm caught in a cotton gin. What also convinces the reader of Robinson's innocence is the fact that Atticus proves to the court that Bob Ewell is ambidextrous. Since Robinson is innocent, it is clear he has been brought to trial and declared guilty by the jury simply because of the color of his skin.Robinson's guilty verdict, despite his innocence, is foreshadowed in the book's title and the scene in which the meaning of the title is explained to the reader. In Chapter 9, Scout and Jem are given air rifles for Christmas. In Chapter 10, Atticus expresses his wish that Scout and Jem would only shoot "tin cans in the back yard" but, knowing they'll shoot birds, gives the the following warning:

Shoot all the bluejays you want, if you can hit 'em, but remember it's a sin to kill a mockingbird (Chapter 10).

When asked, Miss Maudie explains to Scout that Atticus is correct in saying the above because mockingbirds don't cause mischief like other birds; all they do is "sing their hearts out" all day long (Chapter 10). Therefore, the mockingbird symbolizes all innocent beings in the story, such as Robinson, and Atticus's warning not to kill them foreshadows Robinson's defeat in his trial despite his innocence, a defeat incited by racial hatred.In this same chapter, the death of the rabid dog named Tim Johnson foreshadows Robinson's death after his trial, a second race-related event. Though Robinson would be on death row for quite a while and Atticus had hoped to overturn his sentence—possibly even his conviction, upon appeal—Robinson gave up all hope of being served justice by white men and, immediately after his trial, decided to try to take justice into his own hands by attempting to escape prison. He was shot to death while trying to escape and shot far more times than really necessary, which shows he was shot and killed out of racial hatred, not out of the guards' necessity. Just as Robinson was shot to death as an innocent man, Tim Johnson was shot to death as a helpless, innocent dog. Dogs certainly don't become infected with rabies intentionally, nor do they mean to cause the harm and death they can cause once infected; therefore, Tim Johnson, though rabid, also symbolizes an innocent being, a being society thinks must be killed because the being has become violated by something evil, something like racism. The death of Tim Johnson foreshadows Robinson's upcoming death. We especially see what Tim Johnson's death foreshadows when Scout remembers his death just after the lynch mob scene. In bed that night, Scout reflects in her narration:

I was very tired, and was drifting into sleep when the memory of Atticus calmly folding his newspaper and pushing back his hat became Atticus standing in the middle of an empty waiting street, pushing up his glasses. The full meaning of the night's events hit me and I began crying (Chapter 16).

Standing, waiting, and pushing up his glasses in the middle of a street is exactly what Atticus did while waiting with Sheriff Tate for Tim Johnson to come within shooting distance. If Scout associates shooting Tim Johnson with Atticus guarding Robinson from a lynch mob, then we know Scout has realized the death of an innocent being is about to take place a second time, and Atticus is doing his best to prevent it, despite its inevitability, just as he at first refused to shoot Tim Johnson.

How do the members of Jess's family feel about Leslie in Bridge to Terabithia?

In general, Jess's family does not have a big problem with Jess being friends with Leslie. That does not mean they are all completely supportive of Jess, though. Jess's dad is probably the least supportive of the friendship. He has some fairly archaic ideas about how boys and girls should associate. He also doesn't like how Leslie tends to pull his only son away from doing "manly" things. Brenda and Ellie don't seem to have a problem with Jess and Leslie being friends, either. They tease Jess a lot about it, but I don't believe that means they are against the friendship. I would say that they like that Jess and Leslie hang out together because it gives Brenda and Ellie the opportunity to tease Jess more. May Belle is the most positive about the friendship between Jess and Leslie. That's why she is always trying to tag along and find out what they do together in the woods.

What actions take place at certain times? Does any event or action happen only once? Is there a plot in “Girl”? If so, how would you summarize it?

Plot in literature is loosely defined as the main events in a story linked by a structure or pattern. As you may already know, the main events of a story in plot structure are said to flow as follows: the exposition or introduction, where characters and setting are established; rising action, during which a series of events build up to the conflict; the climax, or the turning point of the story; falling action, or the winding up of the story; and finally, the resolution or ending.
However, it is not necessary that all stories follow this pattern. If we strictly insist on this definition of a plot, we may struggle to locate a narrative structure in unconventional stories, such as Jamaica Kincaid’s “Girl” (1978), which is set up like a breathless monologue. That’s because our understanding of plot is of something happening, whereas “Girl” is all dialogue. But if we allow that plot elements do not always follow a prescribed flow and shift the focus from on-stage action to action by habit, we will clearly be able to see a plot emerge in “Girl.”
Part of your question is about certain actions in the story taking place at specific times, and certain actions that are one-time occurrences: I think both these aspects are interesting and, in fact, build the story’s plot. “Girl” is plotted as a series of instructions given by an older, female voice—presumably a mother—to a daughter.
The instructions (or orders, or life lessons, depending on how you look at them) are about how to maneuver the difficult experience of being a girl and a woman. These life lessons don’t take the typical form they may between a parent and a child in contemporary times, such as “Be yourself” or “Eat your vegetables.” Instead, they are more about the tasks the girl must perform, indicating that being a girl in the story’s context is more about duty and social roles than about being your individual self. Repetition plays an important role in outlining these duties. Variants of the same duty are repeated:

this is how you iron your father’s khaki shirt so that it doesn’t have a crease; this is how you iron your father’s khaki pants so that they don’t have a crease . . .

Similarly, a warning is repeated at different times in the story, such as the mother’s anxiety about the daughter being seen as sexually promiscuous:

this is how to hem a dress when you see the hem coming down and so to prevent yourself from looking like the slut I know you are so bent on becoming . . . this is how to behave in the presence of men who don’t know you very well, and this way they won’t recognize immediately the slut I have warned you against becoming . . .

Repetition also works in the form of the mother’s specific instructions to the girl for certain days of the week:

Wash the white clothes on Monday and put them on the stone heap; wash the color clothes on Tuesday and put them on the clothesline to dry . . .

Repetition works both as exposition and rising action to tell us that the women’s lives in the story are completely bound by their tasks, social roles, and duties. These duties can never be abandoned, and being a woman is a full-time job and responsibility. The girl can never slack on her watch, lest she be “seen as a slut”; neither can the mother abdicate her duty of being a good mother who has raised an obedient daughter.
Certain events are referred to less often, which in itself is very significant. For instance, this particular instruction of the mother’s is given only once:

don’t squat down to play marbles—you are not a boy, you know . . .

This indicates that it was quickly obeyed, and the daughter’s playfulness was quelled almost immediately.
The daughter’s voice, which is heard only twice and is rendered in the story in italics, marks both the climax and falling action. In behaving like a boy and asserting her voice, the girl presents a brief conflict in the story, a counterpoint to the mother’s litany of instructions:

but I don’t sing benna on Sundays at all and never in Sunday school . . .

Toward the end of the story, when the mother instructs the girl to always squeeze the bread to check if it’s fresh, she responds:

but what if the baker won’t let me feel the bread?

Yet the sparseness of her voice and the mother’s quick dismissal of it indicate that the conflict is overcome quickly, and the action begins to fall towards the expected, tragic resolution, expressed in the mother’s response to the question about the bread:

you mean to say that after all you are really going to be the kind of woman who the baker won’t let near the bread?

The tragic end of the story is that the girl cannot escape her social role; she will grow up to be a particular “kind of woman,” a woman her mother is shaping and raising, a suitable sort of girl who watches her every step.

Jamaica Kincaid's short story "Girl" relates a series of commands, obligatory tasks, and fears, directed at the titular "girl" by presumably some older female relative. The tasks listed in this short directive are ones that should be repeated, so I don't know that I'd say any are onetime instructions.
Take for example some tasks associated with specific days of the week. The narrator insists,

Wash the white clothes on Monday and put them on the stone heap; wash the color clothes on Tuesday and put them on the clothesline to dry

and later,

on Sundays try to walk like a lady and not like the slut you are so bent on becoming; don't sing benna in Sunday school

These tasks are associated with days of the week, but the assumption is that these tasks are repeated every Monday, Tuesday, and Sunday. The narrator is giving the girl instructions on how to live her life daily and what needs to be completed on what day. The Sunday instructions belie a fear on the part of the narrator: that the girl will develop a reputation and will thus not be marriageable. She is concerned that the girl will get involved in sexual activity before marriage and warns her against it by predicting that the girl wants to become a "slut."
Many of the other instructions, though not falling on particular days, are laying out how to complete household duties. The narrator says, for example,

this is how you iron your father's khaki shirt so that it doesn't have a crease;this is how you iron your father's khaki pants so that they don't have a crease; this is how you grow okra—far from the house, because okra tree harbors red ants

These instructions indicate that the girl is still young and living with her parents. She will perform chores for her father, and presumably, this will train her to do the same for her eventual husband. She is also told how to grow okra, which she will then presumably need to learn to cook.
The story reads like a list of directives rather than a narrative with a plot. The narrator's repeated use of the phrase "this is how you" seems bossy but informative. The training she is getting here indicates that the girl's life will be all about serving others and staying out of trouble. There seems to be little to no room left for what the girl may want for herself.

Summarize an imaginary adaptation (film, tv show, script, etc.) changing some aspects of Shakespeare's Hamlet, while sticking with one of the themes. (Make changes to the characters, their roles, maybe the setting, etc.) Summarize what changes you have made and the justification for these changes. Also relate these changes back to the theme you chose. (Break down the script / cast of characters).

Adapting a Shakespearean play into a different setting/theme is a popular way to explore the important aspects at the root of the play with modern settings and dialogue, making it more accessible to modern audiences. Famous examples of this kind of adaptation are 10 Things I Hate About You (a retelling of The Taming of the Shrew), Get Over It (an adaptation of A Midsummer Night's Dream), and West Side Story (Romeo and Juliet, set in New York). Many film buffs argue that The Lion King is a version of Hamlet. This theory is grounded in the fact that both stories are about kings who are murdered by their brothers so that the brother can take the throne. In both, the son of the slain king takes revenge on the murderous uncle.
The first step in deciding how to rewrite Hamlet is choosing the setting. You might choose to set the play in the Wild West, modern-day England, Byzantine China, or any easily understood environment. A good choice is a setting with enough gimmick to inform other elements of the story but not so much as to distract from the story itself.
Next, apply the general character profiles to those who might stand out in the setting you chose. Using the Wild West as an example, it might make sense to replace the king with a sheriff, Hamlet with the sheriff's son, and Claudius with the Assistant Sheriff. Other characters could be Wild West mainstays such as saloon bartenders, dancers, or cowboys.
Finally, each scene should be rewritten to adhere to the new theme/setting. Using language and phrasing popular in that environment, rewrite scenes so that the meaning and gravitas is the same as the original play, but the dialogue and setting feel on-brand for your chosen theme. Using West Side Story as an example, the Montagues and Capulets have been replaced with the Sharks and the Jets, since ethnic gangs are more at home in our New York setting than dueling families would be.
https://lfq.salisbury.edu/_issues/first/adaptation_shakespeare_and_world_cinema.html

https://www.telegraph.co.uk/film/macbeth/best_shakespeare_adaptations/

https://www.theguardian.com/stage/2015/oct/09/10-best-shakespeare-screen-adaptations

In "A Very Old Man with Enormous Wings", how is there a theme of isolation?

There is a theme of isolation in "A Very Old Man with Enormous Wings." Since no one knows exactly what or who "that nightmare" is after he appears at the home of Pelayo and Elisenda, the old man, "impeded by his enormous wings," becomes isolated as an oddity. He then later becomes a mere inconvenience. 
At first, Pelayo and Elisenda overcome their surprise, and they "find him familiar." However, when they speak to him, he answers in "an incomprehensible dialect with a strong sailor's voice." They then conclude that the winged old man is a castaway from a foreign ship that has been wrecked in a storm. However, when onlookers arrive, numerous conjectures are made about this winged man. The priest, Father Gonzaga, promises to write to the Supreme Pontiff for the final decision on the determination of the old man's identity. However, others interpret his identity in their own ways.
Not long after the old man's appearance, other oddities come to Pelayo's home; it becomes a virtual circus. This demonstrates that the irrational is a real part of life and that it should be accepted as such without futile attempts to assign definitive limits to what is in the world. Moreover, by trying to define the old man with enormous wings, people have stripped him of his fantastic elements that are inexplicable but real. 

What literary awards has Chinua Achebe received?

In October of 1999, Chinua Achebe was awarded the thirty-second Saint Louis Literary Award, joining other previous winners such as Tennessee Williams, Eudora Welty, and Saul Bellow. Three years later, in 2002, Achebe won the Peace Prize of the German Book Trade, an international peace prize awarded by a foundation whose aim is to promote tolerance and understanding throughout the international community.
Just five years later, in 2007, Achebe was awarded the prestigious Man Booker International Prize; this is a prize awarded biennially—every two years—to an author of fiction who has produced a distinguished body of work. Three years later, in 2010, Achebe won the Dorothy and Lillian Gish Prize, awarded to an individual who has contributed to the world's beauty and to humanity's experience of life.

Chinua Achebe received numerous literary awards over the course of his long and successful writing career. He won the Dayton Literary Peace Prize in 2010 for his collection of autobiographical essays The Education of a British-Protected Child. His first major literary honor was the Margaret Wong Memorial Prize in 1959 for arguably his most famous work, Things Fall Apart. His general contribution to literature was honored in 2007 with the award of the prestigious Man International Booker Prize.
As well as being honored on the international stage, Achebe also received a number of prizes in relation to this work as an author from a Commonwealth country. In 1964 he was awarded the New Statesman Jock Campbell Award for Commonwealth Writers for Arrow of God, the third instalment in his African Trilogy. In 1972 he was the joint winner of the Commonwealth Poetry Prize for his collection Beware Soul Brother.

Single Variable Calculus, Chapter 5, 5.2, Section 5.2, Problem 26

a.) Determine the approximation to the integral $\displaystyle \int^4_0 \left( x^2 - 3x \right) dx$ using Riemann Sum with right end points and $n = 8$
Let $f(x) = x^2 - 3x$
With $n= 8$ the interval width is $\displaystyle \Delta x = \frac{b-a}{n} = \frac{4-0}{8} = \frac{4}{8} = \frac{1}{2}$

And the right end points are $x_1 = 0.5$, $x_2 = 1.0$, $x_3 = 1.5$, $x_4 = 2.0$, $x_5 = 2.5$, $x_6 = 3.0$, $x_7 = 3.5$ and $x_8 = 4.0$

So the Riemann Sum is

$
\begin{equation}
\begin{aligned}
R_8 &= \sum\limits_{i = 1}^8 f(x_i) \Delta x\\
\\
R_8 &= f(0.5) \Delta x + f(1.0) \Delta x + f(1.5) \Delta x + f(2.0) \Delta x + f(2.5) \Delta x + f(3.0) \Delta x + f(3.5) \Delta x + f(4.0) \Delta x\\
\\
R_8 &= \left( \frac{-5}{4} \right) \left( \frac{1}{2} \right) + (-2) \left( \frac{1}{2} \right) + \left( \frac{-9}{4} \right) \left( \frac{1}{2} \right) + (-2) \left( \frac{1}{2} \right) + \left( \frac{-5}{4} \right) \left( \frac{1}{2} \right) + (0) \left( \frac{1}{2} \right) + \left( \frac{7}{4} \right) \left( \frac{1}{2} \right) + (4) \left( \frac{1}{2} \right)\\
\\
R_8 &= \frac{-5}{8} - 1 - \frac{9}{8} - 1 - \frac{5}{8} + \frac{7}{8} + 2 \\
\\
R_8 &= \frac{-5-8-9-8-5+7+16}{8}\\
\\
R_8 &= \frac{-12}{8}\\
\\
R_8 &= \frac{-3}{2}\\
\\
R_8 &= -1.5
\end{aligned}
\end{equation}
$


b.) Sketch a diagram to illustrate the approximation in part(a)



Evaluate $\displaystyle \int^4_0 \left( x^2 - 3x) \right) dx$
Using the definition of the integral
$\displaystyle \int^b_a f(x) dx = \lim\limits_{n \to \infty} \sum\limits_{i = 1}^n f(x_i) \Delta x$

$
\begin{equation}
\begin{aligned}
\Delta x &= \frac{b-a}{n}\\
\\
\Delta x &= \frac{4-0}{n}\\
\\
\Delta x &= \frac{4}{n}\\
\\
x_i &= a + i \Delta x\\
\\
x_i &= 0 + \frac{4}{n} i\\
\\
x_i &= \frac{4i}{n}
\end{aligned}
\end{equation}
$


$
\begin{equation}
\begin{aligned}
\sum\limits_{i = 1}^n f(x_i) \Delta x &= \sum\limits_{i = 1}^n f \left( \frac{4i}{n} \right) \left( \frac{4}{n} \right)\\
\\
\sum\limits_{i = 1}^n f(x_i) \Delta x &= \sum\limits_{i = 1}^n \left[ \left( \frac{4i}{n} \right)^2 - 3 \left( \frac{4i}{n} \right) \right] \left( \frac{4}{n} \right)\\
\\
\sum\limits_{i = 1}^n f(x_i) \Delta x &= \sum\limits_{i = 1}^n \left( \frac{16i^2}{n^2} - \frac{12i}{n} \right) \left( \frac{4}{n} \right)\\
\\
\sum\limits_{i = 1}^n f(x_i) \Delta x &= \sum\limits_{i = 1}^n \left( \frac{64i^2}{n^3} - \frac{48i}{n^2} \right)
\end{aligned}
\end{equation}
$

Evaluate the summation

$
\begin{equation}
\begin{aligned}
\sum\limits_{i = 1}^n f(x_i) \Delta x &= \sum\limits_{i = 1}^n \frac{64i^2}{n^3} - \sum\limits_{i = 1}^n \frac{48i}{n^2} \\
\\
\sum\limits_{i = 1}^n f(x_i) \Delta x &= \frac{64}{n^3} \sum\limits_{i = 1}^n i^2 - \frac{48}{n^2} \sum\limits_{i = 1}^n i \\
\\
\sum\limits_{i = 1}^n f(x_i) \Delta x &= \frac{64}{n^3} \left[ \frac{n(n+1)(2n+1)}{6} \right] - \frac{48}{n^2} \left[ \frac{n(n+1)}{2} \right]\\
\\
\sum\limits_{i = 1}^n f(x_i) \Delta x &= \frac{32(n+1)(2n+1)}{3n^2} - \frac{[24(n+1)]}{n}\\
\\
\sum\limits_{i = 1}^n f(x_i) \Delta x &= \frac{32(2n^2+n+2n+1)}{3n^2} - \frac{(24n+24)}{n}\\
\\
\sum\limits_{i = 1}^n f(x_i) \Delta x &= \frac{64n^2+96n+32}{3n^2} - \frac{(24n+24)}{n}\\
\\
\sum\limits_{i = 1}^n f(x_i) \Delta x &= \frac{64n^2 + 96n + 32 - 72n^2 - 72n}{3n^2}\\
\\
\sum\limits_{i = 1}^n f(x_i) \Delta x &= \frac{-8n^2 + 24n + 32}{3n^2}
\end{aligned}
\end{equation}
$


Evaluating the limit

$
\begin{equation}
\begin{aligned}
\int^4_0 \left( x^2 - 3x \right) dx &= \lim_{n \to \infty} \sum\limits_{i = 1}^n f(x_i) \Delta x\\
\\
\int^4_0 \left( x^2 - 3x \right) dx &= \lim_{n \to \infty} \left( \frac{-8n^2+24n+32}{3n^2} \right)\\
\\
\int^4_0 \left( x^2 - 3x \right) dx &= \lim_{n \to \infty} \left( \frac{\frac{-8\cancel{n^2}}{\cancel{n^2}} + \frac{24n}{n}+\frac{32}{n^2} }{\frac{3\cancel{n^2}}{\cancel{n^2}}} \right)\\
\\
\int^4_0 \left( x^2 - 3x \right) dx &= \lim_{n \to \infty} \left( \frac{-8 + \frac{24}{n}+\frac{32}{n} }{3} \right)\\
\\
\int^4_0 \left( x^2 - 3x \right) dx &= \frac{-8 + \lim\limits_{n \to \infty}\frac{24}{n}+ \lim\limits_{n \to \infty} \frac{32}{n^2} }{3}\\
\\
\int^4_0 \left( x^2 - 3x \right) dx &= \frac{-8+0+0}{3}\\
\\
\int^4_0 \left( x^2 - 3x \right) dx &= \frac{-8}{3}
\end{aligned}
\end{equation}
$