What are the differences and similarities between skin and plant epidermis?

Let's start with a similarity. Regardless of whether the epidermis belongs to a plant or an animal, the epidermis is the outermost layer of cells that covers other cell and tissue types. In both types of organisms, the epidermis is a barrier layer. One simple difference between plant epidermis and the skin's epidermis is that the plant's epidermis is also covered in a waxy coating called the cuticle. The cuticle plays a large part in reducing and preventing water loss. In animals, the epidermis also plays an important water role. It is a waterproof layer that prevents water from moving into the body. If skin didn't do this, we would swell up every time we went swimming or took a bath. Another difference is that plants have two layers of epidermis. They have an upper and a lower epidermal layer.
https://www.britannica.com/science/epidermis-plant-tissue

What is the rising action in The Bass, The River, and Sheila Mant

The rising action of the story begins when Sheila agrees to go with the narrator on his canoe to Dixford. He knows that this is his golden opportunity to impress her. Quite meticulously, he spends a day rubbing and polishing his canoe “until it gleamed as bright as aluminum ever gleamed.”
The actual suspense, however, begins to build up as soon as a huge bass gets hooked to the narrator’s fishing rod. This happens when he is already out on a date with Sheila. Only a few moments ago, he heard her contemptuous and dismissive remarks about fishing: she loathes his favorite pastime activity.
The rod has bent double, in all probability, by the weight of the big bass. The narrator doesn’t want to lose it as it’s going to be his biggest catch ever. But Sheila is on the boat, and at no point can she know about the catch, as “at that fragile moment,” he can’t just do anything that might vex her.
The author of the story, W. D. Wetherell, illustrates the narrator’s dilemma beautifully. The fourteen-year-old narrator puts to use all his might and skills not to lose the enormous bass. Overcoming all the hurdles, he manages to cling to it until they’re almost at Dixford.
Meanwhile, he keeps Sheila engaged in the conversation. While she continues talking about herself, he doesn’t give her the slightest hint that he’s tugging a giant bass.
All these events comprise the rising action of the story.
In this way, the narration beautifully sways between the fourteen-year-old narrator’s struggle to hold on to the giant fish and his efforts to make an impression on Sheila. Finally, the story reaches its peak with the arrival of the moment when he has to make a final choice between his biggest catch and the beautiful Sheila.

What is the hook in The Graveyard Book?

In literature, a "hook" is the part of a story that grabs the reader's attention. Usually found in a book's opening scene, the hook serves to pull the reader into the world of the novel and keep them reading, as they want to know what's going to happen next.
Neil Gaiman's The Graveyard Book starts not by introducing a character or setting, but rather by introducing a knife. Right from the beginning, you know this is a story in which threats are real, and the anticipation of what's going to happen keeps you reading. As the chapter continues, readers are introduced to Jack, the man who wields the knife, who has killed the entire family living in a home he's invaded, except for the youngest child. We enter the story as he's moving to murder the baby, but, as we find out, the baby is not in the crib.
The hook, surprisingly, is not the murder; that takes place before the story begins. Instead, the hook is the mystery of where the baby has gone, why it's so important to Jack to find him, and why the murder took place at all. The opening scene sets up many questions, so readers want to keep reading to find out the answers. The moment when Jack discovers the baby is missing serves as the hook for The Graveyard Book, as it takes a scene with a finite ending where all the characters except Jack are dead and makes it a mystery instead, driving readers to continue.

In the poem "To His Coy Mistress," what is the speaker's basic argument?

The basic argument of this poem is that if time were limitless, the woman's coyness would not matter. She keeps putting off the narrator of the poem, but the narrator argues that her coyness is wasting time, as time is finite.
The poet says that if time were limitless and they were immortal, they could walk, even to the Ganges in India, and he could spend centuries admiring her beauty. She could also continue to refuse him to the "conversion of the Jews" (which means forever). However, as they are not immortal, if she keeps putting him off, she will die before they can get together as a couple. All her coyness will be for naught, as they will never get to enjoy their love. They should instead find love when they are young and can enjoy it. In simple terms, the message of the poem is "carpe diem," or seize the day.

Andrew Marvell's "To His Coy Mistress" is an especially famous example of seventeenth-century "carpe diem" poetry. Like other works in the genre, Marvell's poem centers on the fleeting nature of life and youth and the consequent need to make the most of them while they last. In this particular poem, the speaker is leveraging this argument to persuade his "coy" (shy or hesitating) lover to sleep with him. He begins by acknowledging that the woman "deserves" a long and extravagant courtship, and he speaks hyperbolically about devoting hundreds of years to praising each of her body parts (19). At this point, however, the speaker switches strategies and reminds his lover that time is constantly passing ("at my back I always hear / Time's wingèd chariot hurrying near") and that death is inevitable; in the end, the woman will lose her beauty, and "worms" will take her "virginity" (21–22, 27, 28). That being the case, the speaker says, there is no time to waste on slow, leisurely lovemaking. Instead, he uses urgent and even violent language ("tear our pleasures with rough strife") to convince his mistress to accept his advances; by snatching what pleasure they can from the moment, the couple can defy (if not stop) the progression of time ("though we cannot make our sun / Stand still, yet we will make him run" (43, 45–46).

What is the conflict in "The Bass, the River, and Sheila Mant"?

At one level, the central conflict in W.D. Wetherell’s short story “The Bass, the River, and Sheila Mant” seems to be between the narrator’s longing for Sheila and his longing for the bass. However, I think Sheila and the bass—a species of fish—are actually stand-ins for two aspects of the narrator’s nature and his choice between the two is critical for the development of his self. If we look closely at the way Sheila is described, we get a clue into what really attracts the narrator to her: her beauty and poise, of course, but also her popularity and her family’s social status.

There was a summer in my life when the only creature that seemed lovelier to me than a largemouth bass was Sheila Mant. I was fourteen. The Mants had rented the cottage next to ours on the river; with their parties, their frantic games of softball, their constant comings and goings, they appeared to me denizens of a brilliant existence.

The fact that Sheila is courted by older boys and sportsmen, the entire “Dartmouth heavyweight crew,” adds to her appeal. Because Sheila is such a rare commodity, the narrator too covets her. In this, Sheila represents the part of the narrator’s nature that is easily seduced by the superficial and the glitzy. It is important to note that his crush on Sheila is not based on who Sheila is as a person.
On the other hand, fishing is a great passion for the narrator, an activity he is perfectly happy doing in solitude. He doesn’t need an audience for fishing; thus, like reading or hiking often is for other people, this is an activity arising from his deeper nature.

Automatically, without thinking about it, I mounted my Mitchell reel on my Pfleuger spinning rod and stuck it in the stern. I say automatically, because I never went anywhere that summer without a fishing rod.

From these lines we can see that the narrator almost feels incomplete without his fishing rod. Thus, fishing, the river, and the bass represent the more authentic, less self-conscious aspect of the narrator’s nature. The clash between the two aspects of his nature is comically highlighted when he actually manages to get Sheila—the object of his affection—out for a date in his canoe. While Sheila is talking to him, his attention is entirely on the bass he has accidentally pulled in and on trying to keep Sheila from discovering this. Earlier, Sheila has emphatically confessed she thinks fishing is “dumb,” which make sit even more urgent for him to conceal the hooked bass from her. But like the narrator’s subconscious, the bass makes its presence felt.

Downstream, an awesome distance downstream, it jumped clear of the water, landing with a concussion heavy enough to ripple the entire river. For a moment, I thought it was gone, but then the rod was bending again, the tip dancing into the water. Slowly, not making any motion that might alert Sheila, I reached down to tighten the drag.

The narrator’s frequent use of fishing words such as “drag” and “tugging” also embody the push-pull he feels between Sheila and the bass. Similarly, much as the “fish” is lured to the bait, the narrator too is lured by the glitter of all that Sheila represents. It is also interesting to see how the bits of conversation the narrator recalls with Sheila paint her as a self-absorbed and vain person. This could have little to do with Sheila herself and more to do with the little interest the narrator discovers in her company and his distracted state of mind.

I have to be careful with my complexion. I tan, but in segments. I can’t figure out if it’s even worth it. I wouldn’t even do it probably. I saw Jackie Kennedy in Boston, and she wasn’t tan at all.

Sheila’s empty words above are in contrast to how the narrator sees he physicality, “her lithe figure” and “the proud tilt of her shoulders.” Again, we see the narrator judge Sheila less by her personal qualities and more by her appearance.
When he finally cuts the line and lets the fish go, the effort it costs him is almost spiritual, as if he is amputating his soul. Although he doesn’t know it himself quite yet, the reader understand Sheila is already lost to him. We know the narrator’s enjoyment in the evening is ruined even before it begins; so much so that when Sheila decides to go home in Eric Caswell’s Corvette, all he can mumble is an indifferent okay.
Wetherell resolves the narrator’s psychological conflict with a neat lesson, with the narrator declaring that “he never made the same mistake again.” The mistake wasn’t about Sheila or the bass but about not listening to his heart and pretending to be someone other than he is. He now understands that he has to choose his deeper self over artificial glamour or the social pressure of seeming cool. Another lesson he learns is to value people by more than their appearance. Thus, as a young 14-year-old, he learns important, foundational lessons in self-hood.

W. D. Weatherell's short story "The Bass, the River, and Sheila Mant" is about a fourteen-year-old boy who develops a crush on a seventeen-year-old girl named Sheila Mant. 
Sheila is clearly out of his league. She is older, beautiful, and has captured the attention of an Ivy League rowing team. This causes an internal conflict on the part of the narrator. Should he ask her out? Here's how he describes his feelings about that conflict:

It was late August by the time I got up the nerve to ask her out. The tortured will-I's, won't I's, the agonized indecision over what to say, the false starts toward her house and the embarrassed retreats--the details of these have been seared from my memory.

Another internal conflict develops later as the narrator must choose between Sheila and the magnificent bass he secretly caught while on the date. He chooses Sheila, a decision he will soon regret.
You would expect to see an external conflict between Sheila and the narrator, since their date wasn't particularly successful. But Weatherell isn't as interested in the conflict between them as he is in the conflict that takes place inside the narrator. When Sheila goes home with another guy in his Corvette, the narrator doesn't object.
Weatherell resolves the internal conflict in the story's final paragraph, as the narrator comes to a personal realization:

Before the month was over, the spell she cast over me was gone, but the memory of that lost bass haunted me all summer and haunts me still. There would be other Sheila Mants in my life, other fish, and though I came close once or twice, it was these secret, hidden tuggings in the night that claimed me, and I never made the same mistake again.

Henry points out that the British have recently sent armies and fleets to the colonies. According to Henry, what does their presence mean?

Patrick Henry gave his famous speech in 1775.  The years leading up to this speech had been a time of unrest in the Thirteen English Colonies.  There were boycotts due to new taxes and a stronger military presence, among other things.  Henry was specifically concerned about the increasing military presence in the Colonies.  King George III had been sending more British troops to supposedly keep order in the Colonies.  Henry thought that the colonists should be prepared to defend themselves from the British soldiers.  He asked his fellow Virginia delegates to consider the situation at hand.  He warned them to not be fooled:

Suffer not yourselves to be betrayed with a kiss.  Ask yourselves how this gracious reception of our petition comports with these war-like preparations which cover our waters and darken our land.  Are fleets and armies necessary to a work of love and reconciliation?   Have we shown ourselves so unwilling to be reconciled, that force must be called in to win back our love? (Speech to the Virginia Convention)

He warned the men that the King had no intention of reconciling.  Instead, he thought that the King had intended to wage war against the rebellious colonists.  He told the men that he thought military force would be used to bring forth a sort of reconciliation.

Where can I get more information about the idea that gender roles for our particular sex are imprinted during our early childhood years? (Not just learned, because if they were just learned, we could unlearn them later, and thereby not have any pride or shame that goes along with gender roles)

There's actually considerable debate and ongoing research on exactly when and how gender roles are acquired, and how much they can change over the lifespan. I've linked Gender Roles: A Sociological Perspective, which is a standard text in the sociology of gender and seems like it might be a good place to start.There are a number of different theories of gender role acquisition, which vary in how much they ascribe gender development to social environment versus genetics. We do have experimental evidence that some concept of gender roles is formed very early, well before speech, which suggests some genetic component. But clearly some gender roles vary substantially between cultures, so there must be a component due to social environment as well. The idea that gender roles are imprinted at a very young age and henceforth are very difficult to change---akin to how language is imprinted---could account for both phenomena, but is by no means universally accepted.As for the pride/shame issue, be careful: almost any violation of social norms is going to trigger feelings of shame, regardless of how those social norms were learned. I know that the proper placement of salad forks is absolutely a learned behavior, usually acquired in adulthood; but I'd still feel ashamed if I did it wrong when arranging an important business dinner. What's important is not how I learned the norm, but how I perceive others will react if I violate it.
https://books.google.com/books/about/Gender_Roles.html?id=qoQEAQAAIAAJ

In Shakespeare's Hamlet, what does Hamlet mean when he says, "The time is out of joint" in act 1 scene v?

This seemingly simple phrase that Hamlet utters after his horrifying meeting with his father’s ghost is actually another example of Shakespeare’s genius with words. Let’s begin by unpacking the basic meaning of the phrase itself. “The time” would refer to all current events that Denmark is encountering -- domestic, commercial, political, and international. For the phrase “out of joint,” imagine a dislocated shoulder. A joint in the wrong position is extremely painful and needs to be corrected immediately, or permanent damage will result, which could be crippling to the whole body. Anything described as "out of joint" is functioning incorrectly somehow, and requires fixing.
We can look at what this phrase might mean in the context of Hamlet’s situation. He feels he cannot tell the guards or Horatio exactly what the Ghost has revealed to him, but he wants them to know the kingdom is “out of joint,” meaning it is in peril. The Danish people believe that with the late King Hamlet’s brother Claudius on the throne, all is well in Denmark. In truth, there has been a major political upheaval of the throne, which is now in the hands of a murderer. Also, the domestic joining of Hamlet’s queen-mother to her former brother-in-law is rather incestuous.  While somewhat accepted for political purposes during the late middle ages (the time period in which Hamlet is set), it was still religiously frowned upon.
Additionally, the guards and Horatio are already aware that something is amiss internationally, as they have been discussing the rumors about why Denmark is frantically preparing for war. The appearance of the ghost confirms in their superstitious minds that “something is rotten in the state of Denmark” (Marcellus, Act I, Scene 4). Their new king is already clearly doing a disjointed job of running the kingdom if he hasn’t even informed his guards about the threats of Norway’s Prince Fortinbras to reclaim his kingdom’s land. 
With the ghost’s revelation that he was murdered by Claudius, Hamlet becomes horrifyingly aware of just how “out of joint” the whole kingdom is. This is so painful for him to hear that he laments, “Oh cursed spite / That ever I was born to set it right!” (Act I, Scene 5). He has little choice, however, for if he doesn't put the political joint back in place, it will indeed be crippling to the whole kingdom. Sadly in the end, it seems the only way to heal the kingdom is to wipe out the entire royal family--replace the joint, if you will--and allow Denmark to be ruled by the much better-hinged Fortinbras.

What was King Henry Viii famous for?

Henry VIII ruled England for much of the first half of the 16th century (1509-47). While perhaps most infamous for his multiple marriages and executions, his breaking with the Catholic church and dissolution of the monastic houses had a far stronger impact on English society and history. In 1534 the Act of Supremacy finalized the break from Rome and established the Britsh Monarch as head of the Church of England. By 1536 the monastic houses were falling across the kingdom. In 1540 as many as fifty institutions came down each month. The motivations behind the Act of Supremacy were personal, financial, and punitory. First, Henry wished for an annulment which the Pope refused to grant. Second, many of the monasteries held great wealth, which went to the crown. Finally, corruption was said to be common among the wealthiest monasteries with the inmates neglecting their vows of poverty to live like lords. The loss of the religious houses left a gap in Engish society. Many had served as hospitals and asylums for the ill and vulnerable, while others regularly provided alms for the destitute. The nobility to whom the crown granted or sold the former monastic lands had no call to continue these services. Perhaps most painful for modern historians and antiquarians was the destruction of libraries associated with the monasteries, especially significant when books were hand-lettered and quite rare.

Henry VIII served as King of England from 1509-1547. He is most known for his six marriages and his changes to the Church of England. After taking the throne in 1509, Henry married Catherine of Aragon, who was the widow of his brother. Catherine bore Henry three sons and three daughters, but all of his children except for one, Mary, died in infancy. Believing his marriage was cursed, worrying Catherine could not bear him a son to succeed him as king, and having become infatuated with another woman, Anne Boleyn, Henry sought an annulment of his marriage from the pope, which would allow him to end his marriage to Catherine and marry Anne. Catherine's nephew, however, was Holy Roman Emperor Charles V, and he held considerable influence over the pope. The pope therefore refused Henry's request for an annulment at the request of Charles V and due to the fact that marriages were considered sacred contracts in the Catholic Church.
Frustrated, Henry decided that he did not need the pope's permission to make religious decisions. In 1534 he signed the Act of Supremacy, which established him as head of the Church of England (now called the Anglican Church) and required English subjects to recognize his marriage to Anne Boleyn. The Act of Supremacy therefore severed English ties with the Roman Catholic Church. The act also meant that the pope no longer served as head of the English church. Henry went on to marry four more women in his quest to have a male heir to the throne, and he had two of these women beheaded. His son Edward VI eventually succeeded him in 1547.
https://www.history.com/topics/british-history/henry-viii

Why do plants in water-logged soil have to use anaerobic respiration?

Aerobic respiration is when a cell uses oxygen molecules to generate usable energy for itself. Anaerobic respiration is when a plant is using something besides oxygen molecules to generate usable energy. The reason a plant submerged in water needs anaerobic respiration is because the plant has no oxygen molecules available. 
Plants prefer aerobic respiration, as anaerobic respiration provides much less usable energy than its oxygen powered counterpart, but in a pinch can resort to anaerobic respiration. 
Other creatures can use anaerobic respiration as well. Yeasts, for example, produce alcohol when engaging anaerobic respiration. This is one method used to make alcoholic drinks.
Some other organisms use anaerobic respiration as their primary method of generating usable energy, like archeabacteria. Rather than oxygen, these processes use chemicals like sulfates and nitrates.

int sin(sqrt(x)) dx Find the indefinite integral by using substitution followed by integration by parts.

To evaluate the given integral problem int sin(sqrt(x))dx using u-substitution, we may let:u = sqrt(x) .
 Square both sides of  u = sqrt(x) , we get: u^2 =x
Take the derivative of u^2 =x , we get: 2udu =dx .
Plug-in the values: u =sqrt(x) and dx = 2u du , we get:
 int sin(sqrt(x))dx =int sin(u)* 2u du
Apply the basic integration property: int c*f(x) dx = c int f(x) dx .
int sin(u)* 2u du =2int sin(u)* u du
Apply formula for integration by parts: int f*g'=f*g - int g*f' .
Let: f =u  then f' =du
       g' =sin(u) du then  g= -cos(u)
Note: From the table of integrals, we have int sin(theta) d theta= -cos(theta) +C .
Following the  formula for integration by parts, we set it up as:
2int sin(u)* u du= 2 * [ u *(-cos(u)) - int (-cos(u)) du]
                                 = 2 * [ -u cos(u)) + int (cos(u)) du]
                                 = 2 * [ -u cos(u)) + sin(u)]+C
                                 = -2ucos(u) +2sin(u) +C
Plug-in u=sqrt(x) on -2ucos(u) +2sin(u) +C , we get the complete indefinite integral as:
int sin(sqrt(x))dx=-2sqrt(x)cos(sqrt(x)) +2sin(sqrt(x)) +C .
 

What arguments were made in favor and against the 15th Amendment in 1870?

The 15th Amendment to the Constitution, ratified in 1870, prevented the denial of the vote based on race, color, or previous circumstance of servitude. In essence, it gave African American men the vote and was a cornerstone of the Reconstruction era. The Republican-dominated Congress ratified the Amendment, although it was opposed by then President Andrew Johnson, who attempted to veto it.
Still, it passed and had an almost immediate impact on the political culture of the US. For the first time, several African Americans were elected to Congress only a few years after being freed from slavery.
Much of this transformation was too drastic for the entrenched culture of racism in the Southern United States. Southerners fought back against the imposition of the 15th Amendment with laws that prevented African Americans from voting at the state and local level. These Jim Crow and segregation laws more generally rolled back the advances pushed forward with the 15th Amendment.
These discrepancies were only fully resolved when the Voting Rights Act was passed in the US in 1965, ending all the limitations on the African American vote, once and for all.

Telemachus, is not behaving heroically at the opening of homer's Odyssey. He does, however, say or do several things that indicate he has the potential to become the man he needs to be, a man like his father. Identify at least three specific things--words or actions--in Book 1 that reveal Telemachus' underlying heroic potential and explain how they do so.

Though Telemachus is caught up in his own thoughts about his father's absence, he understands that according to Greek tradition for men, he must show hospitality to guests. When Athena arrives in disguise, a stranger to Telemachus, he stores her spear for her, shakes out a tapestry for her, and seats her on a chair with a footrest, away from the noise the suitors are making as he gives her his full attention. At the end of the visit, he offers her a fine and valuable gift, though he still does not know he has been counseled by a goddess. He has assumed the grown-up responsibility of a Greek son of a king.
Athena, in disguise, counsels Telemachus that he must no longer be a boy, and that he must travel to seek word of his father from Nestor and Menelaus. If he finds that Odysseus is still alive, he must hold things together at the palace in Ithaca for at least one more year to give Odysseus time to travel home. If he hears that his father is dead, he must prepare to hand over his mother to a new husband after honoring his father with burial rites. Telemachus readily agrees that he will do as Athena counsels, though the journey will be difficult and the news may be bad. Without Odysseus to counsel him, he accepts the counsel of the person he thinks he is talking to, Mentes, a trusted friend of his father's.
When Athena has gone, Telemachus goes to his mother, Penelope, and takes a firm stand with her, telling her to busy herself with weaving, have courage, and that he, Telemachus, will take charge of the house. Telemachus then confronts the suitors, telling them to leave the house and stop badgering his mother. He invokes the power of Zeus to pay them back for their greed and insolence and speaks of his acceptance of the kingdom of Ithaca if it is Zeus's will.

When Athena arrives at Ithaca, Telemachus is sitting around brooding about how much he hates all his mother’s suitors, and how he wishes his father would come home and make all these men clear out. Athena arrives at the gate, disguised as a stranger, and none of the (many, many) suitors who are milling about as if they own the place take any notice of her, which is a serious violation of hospitality rules. Telemachus goes up to her and welcomes her, takes her by the hand, offers her food, and leads her to the hall, where he gives her a seat, a footstool, water to wash her hands and feet, bread, meat, and wine.
Here are three examples of Telemachus revealing his heroic potential:
1. He is instinctively hospitable, which is good, because this stranger is actually Athena, Odysseus’s greatest friend and ally.
Telemachus asks for news of his father, and she asks him about the suitors, and he explains the whole sorry situation to her—how Odysseus hasn't come back, they no longer believe anyone who claims to have seen him, and these suitors are eating him and his mother out of house and home. Athena advises Telemachus to tell the suitors to go away and then go searching for his father by visiting Nestor and Menelaus (who were in the war with Odysseus). If he finds out Odysseus is still alive, he should keep looking for him, but if he finds out his father is dead, then he should hold funeral rites, marry off Penelope once and for all, and move on with life. Telemachus is really cheered by this advice and says he’ll give her a gift for it, but Athena declines and turns into a bird and flies away. Telemachus knows this means she was a god, so he takes her advice very seriously and immediately goes out where the suitors are lying around and tells them to leave.
2. Like Odysseus, he asks for advice from Athena, goddess of wisdom (although in his case, he is unaware of her identity), and when he receives the advice, he heeds it—this is why Odysseus is so successful: because he listens to what Wisdom tells him.
He also announces to the suitors that his father is definitely dead and he, Telemachus, is therefore now master of the house and they had better do as he says. He tells Penelope to stop crying and prevaricating and to get back to her daily work as the woman of the house, because she is not the only one who lost a husband in the war and they’re all moving on with their lives, so she should too. He is effectively lying here in order to buy time for his search for Odysseus.
3. Like Odysseus, Telemachus tells a tactical untruth to accomplish his goal—in this case, to get just enough time to successfully set off in search of his father without the suitors taking his absence as a kind of carte blanche to ruin the household. He's saying he's in charge now, so he can afford to be away for a while in search of his father.

How does Saki develop the central idea of friendship and revenge in "The Interlopers"?

"The Interlopers" is a story that begins with enmity, transitions toward reconciliation, and transitions again with its ending, in which both characters are left helpless against forces entirely outside of their control.
Saki's story begins with an image of Ulrich von Gradwitz hunting in the forest—not for animal game, but rather for a human opponent. From this first paragraph, Saki then proceeds to detail the backstory of the two families and the boundary dispute that is the source of the hostility between Ulrich and his adversary, Georg Znaeym.
The story changes abruptly, however, after the two come face to face. (Keep in mind, the sheer depth of their mutual hatred for one another.) Saki writes, "each had a rifle in his hand, each had hate in his heart and murder uppermost in his mind." However, the scene takes an abrupt when one of the trees collapses down on them, leaving both men trapped and vulnerable.
As the two men are trapped, gradually their attitude shifts. Initially, each man swears to kill the other, should his men find them first. But being trapped in this helpless situation cools that hostility. Ulrich is the first to reach out an olive branch—offering Georg some of his wine—and then, after Georg refuses the offer, he declares that he has changed his mind on his earlier vow: should his men find them first, he would have them both be rescued. He asks that they end their hostility and become friends, and Georg accepts this offer. Out of their shared plight, the two enemies are reconciled and become friends.
That being said, however, even if they are resolved to become friendly with one another, they remain trapped and helpless. This brings about the ending—where both men are shouting for help in order to be rescued, only to watch as wolves approach.

The feud between the families of the von Gradwitzes and Znaeyms began with a lawsuit in the days of the grandfathers of Ulrich and Georg, but the animosity and ill will between the two young men is exacerbated by Ulrich von Gradwitz's strong hatred for Georg Znaeym. It is only an act of Nature that brings them together.
Because of this ill will, Ulrich goes into the forest where there is "a disturbing element," and he comes face-to-face with his enemy. A force of nature brings a huge beech tree's limbs down upon them, leaving the two men pinioned beneath it. At first, they curse each other and boast that each one's men will arrive before the other's and revenge will be served. As they wait to be rescued and their discomfort increases, Ulrich reconsiders his feelings. The wine in his flask is warming, so he offers it in a gesture of friendship to the other man, Georg Znaeym: "Let us drink, even if tonight one of us dies." At first, Georg rejects this offer from an enemy." As they lie in pain, though, the two men reconsider what is important in life. Ulrich says to Georg,

I've come to think we've been rather fools; there are better things in life than getting the better of a boundary dispute. Neighbor, if you will help me to bury the old quarrel, I—I will ask you to be my friend.

After some thought, Georg speaks in reconciliation,

What peace there would be among the forester folk if we ended our feud tonight. . . Ulrich von Gradwitz, I will be your friend.

Then, in a gesture of true friendship, each man offers to have his men help the other if they arrive first.

Justify the title of the story "Lamb to the Slaughter."

The title is justified since, firstly, in a direct and literal sense, the object used to kill Patrick Maloney is a frozen leg of lamb. Patrick is essentially "slaughtered" with a leg of lamb as the murder weapon. In this sense, then, the lamb, or rather, a part of it, is brought to the slaughter.
The title also has a metaphorical connotation. It generally refers to someone who goes innocently and unconcernedly into a dangerous or life threatening-situation. Patrick Maloney is a good example of this. Mary Maloney is described as someone who is meek and mild-mannered. She is a doting and loving wife who takes care of her husband's every need. She is, therefore, the last person anyone would suspect of committing a heinous crime, but that is precisely what she does. She kills the unsuspecting Patrick.
One can, furthermore, describe Mary as being "as gentle as a lamb." Ironically, it is this very same meek and mild-mannered person who, after killing her husband, coldly sets about creating an alibi to cover herself. She acts as if she is the traumatized victim of an offensive act when, indeed, she is the one who committed the deed. The fact that her gentle nature is not doubted adds credence to the title. Mary Maloney looks like the proverbial gentle lamb—but she is the one who committed the slaughter in this instance. 
Furthermore, given of Dahl's physical description of her having calm, dark, large eyes and his explanation of her behavior toward Patrick, one would expect him to be good-natured and loving toward her. However, she becomes an unsuspecting victim of his selfish and uncaring attitude. He plans to leave her even though she is pregnant with his child. In this sense, then, Mary, who naively believes in her husband's loyalty and commitment, becomes an innocent victim of his ruthless attitude. She is essentially also, like an unsuspecting lamb, led on by Patrick until he divulges his heartbreaking intention. The news devastates her and she, without any forethought, lashes out. She also becomes, in the instant that she kills him, a victim of her own inner malice—a trait she most surely did not know she had until after she had killed him.
Finally, the unsuspecting detectives and other investigators, like lambs, innocently destroy the evidence by ingesting the murder weapon. They are unaware that the murderer is within their midst. Mary, to them, cannot possibly be held accountable for what happened to Patrick. She, however, takes morbid pleasure in the fact that, with each bite, the men are demolishing the only proof of her crime. She begins to laugh in the other room when she hears them talking about the evidence while they're actually eating it.
It is for all these reasons that the title aptly reflects the main and sub themes of Dahl's brilliant tale. 

The title of "Lamb to the Slaughter" is rather ingenious because it has so many possible meanings. "Lamb to the Slaughter" is more than a double-entendre; it might be called a "quadruple-entendre." A frozen leg of lamb is used by Mary Maloney to "slaughter" her husband. That weapon once belonged to a real lamb that was "slaughtered" in order to be used as food. Patrick is the one who is "slaughtered" in the story. He is an easy victim of his enraged wife because, like a lamb going to the slaughter, he is completely unsuspecting. Mary, who does the slaughtering in the story, behaves very much like a meek lamb until her husband shatters her illusions by telling her that he wants out of their marriage. The police who arrive on the scene do not suspect Mary because they have always considered her a very meek, mild, gentle, patient woman, not unlike a lamb. The whole story is based on the fact that the murder weapon is never found because no one would ever think of a murderer using a frozen leg of lamb for the "slaughter."

What does the reader learn about the narrator's mother in the exposition of the story "The Leap"?

One thing the reader quickly learns about Anna Avalon is that she "lives comfortably in extreme elements." Anna is confident where others would be fearful. Most notably, she is half of a high-flying trapeze circus act and performs with calm skill even while seven months pregnant. More prosaically, though, Anna moves from country to country at a young age, learns to read as an adult, navigates the death of her first husband and the stillbirth of her first child, and faces blindness caused by cataracts, all with courage and grace. Her calm confidence is seen in her daughter, the narrator, as well. The narrator remains calm during the house fire, performing all the correct steps to lead to her rescue.
The reader also learns that Anna is resourceful. Twice in the story she finds a solution in the heat of a panicked moment that saves someone's life—first her own, then the narrator's. As Anna herself would put it, "[you'd] be amazed at how many things a person can do within the act of falling." First, during the circus accident, she realizes something has gone wrong and pulls off her blindfold just in time to see her husband falling to the ground. Instead of succumbing to panic or grief and falling after him, Anna quickly turns the other way and grips a guy wire until she can descend slowly. Later, during the house fire, Anna realizes her child is trapped upstairs while the house burns down. Again, instead of feeling panicked or helpless, Anna climbs a tree, leaps to the window, and saves her child.
Finally, the reader learns that Anna Avalon is practical and no-nonsense. Most importantly, as outlined above, she does what needs to be done to save herself and her child during both fires. She does so without fear of pain (she severely burned her palms holding the guy wire but did not let go) or embarrassment (she stripped to her underwear in front of the crowd to save her child, because she knew she needed maximum agility to leap to the window). Anna also moves past grief and nostalgia throughout the transitions in her life. After the loss of her husband and first child, Anna is able to recover and start a new family. After she leaves the trapeze act, she does not hang on to costumes and fliers or constantly relive her memories but instead moves into the second act of her life, living on the farm and becoming a voracious reader. When she loses her sight, she does not complain or grieve but simply learns to get around without sight.

In the exposition, the reader of "The Leap" learns that the narrator's mother, Anna Avalon, is a very resourceful woman, as well as a quick thinker.
Central to the theme of this story is the mother's remark to her daughter that she would be 

...amazed at how many things a person can do within the act of falling.

While it does feel as though time slows while one is mid-air, Anna Avalon means that

...in that awful doomed second [when the circus tent collapsed], she could think, for she certainly did.

When lightning struck the main pole of the circus tent, her husband Harry, who was toppled forward from his swing as the tent buckled swept past her, Anna of the Flying Avalons could have caught his ankle and fallen with him, but, instead, she changed direction by twisting her body toward a heavy wire which she grabbed and held despite the burns to her hands.Three people died this night, but Anna Avalon survived because of her quick thinking. She opted to live rather than to die with her husband, who was plummeting to the ground.

College Algebra, Chapter 1, 1.4, Section 1.4, Problem 46

Evaluate the expression $\displaystyle \frac{(1+2i)(3-i)}{2+i}$ in the form of $a + bi$.


$
\begin{equation}
\begin{aligned}
&= \frac{(1+2i)(3-i)}{2+i}\\
\\
&= \frac{3-i+6i-2i^2}{2+i} && \text{Use FOIL method}\\
\\
&= \frac{3+5i -2 (-1)}{2+i} && \text{recall that } i^2 = -1\\
\\
&= \frac{5+5i}{2+i} && \text{Simplify the numerator}\\
\\
&= \left( \frac{5+5i}{2+i} \right) \left( \frac{2-i}{2-i} \right) && \text{Multiply by the denominator of the conjugate}\\
\\
&= \frac{10-5i+10i-5i^2}{2^2 - i^2} && \text{Apply FOIL method}\\
\\
&= \frac{10-5i+10i-5(-1)}{4-(-1)} && \text{recall that } i^2 = -1\\
\\
&= \frac{15 + 5i}{5} && \text{Simplify and group terms}\\
\\
&= 3 + i
\end{aligned}
\end{equation}
$

Were there political motives for the colonization of Africa?

The colonization of Africa that kicked off in the late nineteenth century had many motivations. Some nations wanted to gather all the raw materials they could get; others had a desire to spread their ideology. Politically, though, every nation wanted to increase the size of its empire. More territory means more power.
This same fundamental idea fed the political aspect of African colonization, just as it had fed political rivalries for thousands of years. What made the Scramble for Africa different was the region's vast reserves of raw materials. European empires weren't just fighting for the immediate political status bump that accompanies colonization; they were fighting to win Africa's abundant natural resources that they believed would cement their position as a global super power for centuries to come.
http://webs.bcp.org/sites/vcleary/modernworldhistorytextbook/imperialism/section_6/causesmotivations.html

How can we use the three sociological paradigms to help solve the problem with the football players disrespecting the flag by kneeling? The three paradigms are structural functionalism, conflict theory, and symbolic interactionism.

One of the powerful aspects of being a sociologist is the ability to analyze various social phenomena from different perspectives. Paradigms provide sociologists with a framework from which to orient themselves philosophically and to analyze society. The three primary paradigms used today include structural functionalism, symbolic interactionism, and conflict theory.
Before we analyze the current event you have mentioned, let's acknowledge something: this event will be viewed vastly differently from these different perspectives. In some of these paradigms, the football players' kneeling will be considered, as you have written, as an act of disrespect toward the flag; however, in other perspectives, the kneeling will be viewed as an empowered act of social change. Please remember to keep an open mind when considering this event from all three perspectives.
Structural functionalism, also known as the functionalist perspective, views all parts of society as interdependent and as providing necessary contribution to the holistic (or "whole") functioning of that society. This perspective is often criticized as being complicit in maintaining the status quo; in other words, it does not motivate members of society to actively change their social environment, even when doing so will directly benefit them. From this perspective, social change is, in fact, undesirable, because it operates on the belief that other parts of society will organically compensate for issues that arise.
In viewing the current event of football players kneeling during the national anthem through the lens of structural functionalism, the answer to this "problem" would be to end acts of social activism during football games. Functionalists would see this act—which began with Colin Kaepernick of the San Francisco 49ers taking a knee during the national anthem to protest police brutality against black Americans—as a futile and undesired action against an issue that should be allowed to be organically solved by society, believing that everything will "work itself out."
The conflict perspective is far more focused on the ever-changing nature of society and the negative conflicts that impact. This perspective advocates for social change (which eventually results in social revolution) in order to prevent the wealthy and powerful from taking advantage of the poor and weak. It acknowledges that the diversity between groups (in terms of gender, socioeconomics, race, politics, etc.) causes these groups to compete against each other to uphold their opposing values. Viewing the kneeling football players from the conflict perspective, we would see their act as a significant act of outcry against inequality—one that is natural given the opposition between the polarized difference between black and white Americans. This perspective would not see this event as particularly surprising or astounding and would allow it to continue, understanding that society is ever-shifting. They would not see it as disrespect for the flag but rather as an organic part of cooperation to impact social change.
The symbolic interactionist paradigm views society with an emphasis on the symbolic, acknowledging that humans attach meanings to symbols and act according to their interpretation of these symbols. This perspective interprets words as requiring intention and interpretation and views dialogue as the interaction of symbols. A symbol within this context can be anything that represents something other than its literal self. From this perspective, the most interesting part of the players kneeling would be how it impacts the symbol of the American flag—a symbol of patriotism, freedom, democracy, and liberty, but also of free speech. Some may argue through this perspective that kneeling during the national anthem is a sign of disrespect to what the flag represents. What's interesting about this interpretation is related to a criticism of this paradigm—that the focus on symbols neglects the influence of institutions and social forces on how an individual may choose to behave. For example, rather than intending to insult the flag and what it represents, perhaps these football players are merely reacting to the institutions around them (say, the militarization of police forces, the Trump administration, etc.) and social forces (the growth of the Black Lives Matter movement).

Beginning Algebra With Applications, Chapter 6, 6.2, Section 6.2, Problem 36

Solve the system
$
\begin{equation}
\begin{aligned}

3x+y =& 4 \\
4x-3y =& 1

\end{aligned}
\end{equation}
$

by substitution.



$
\begin{equation}
\begin{aligned}

3x+y =& 4
&& \text{Solve equation 1 for $y$}
\\
y =& 4-3x
&&
\\
4x-3y =& 1
&& \text{Substitute $4-3x$ for $y$ in equation 2}
\\
4x-3(4-3x) =& 1
&&
\\
4x-12+9x =& 1
&&
\\
13x =& 1+12
&&
\\
13x =& 13
&&
\\
x =& 1
&&

\end{aligned}
\end{equation}
$


Substitute value of $x$ in equation 1


$
\begin{equation}
\begin{aligned}

y =& 4-3(1)
\\
y =& 4-3
\\
y =& 1

\end{aligned}
\end{equation}
$


The solution is $(1,1)$.

College Algebra, Chapter 7, Review Exercises, Section Review Exercises, Problem 4

Given the matrix $\left[ \begin{array}{cccc}
1 & 3 & 6 & 2 \\
2 & 1 & 0 & 5 \\
0 & 0 & 1 & 0
\end{array} \right]$.

a.) State the dimension of the matrix.


$
\begin{equation}
\begin{aligned}

& \text{Matrix} && \text{Dimension} &&&
\\
\\
& \left[ \begin{array}{cccc}
1 & 3 & 6 & 2 \\
2 & 1 & 0 & 5 \\
0 & 0 & 1 & 0
\end{array} \right]
&& 3 \times 4
&&& \text{3 rows by 4 columns}

\end{aligned}
\end{equation}
$


b.) Is the matrix in row-echelon form?

No, the matrix is not in row-echelon form.

c.) Is the matrix in reduced row-echelon form?

Not, the matrix is not in reduced row-echelon form.

d.) Write the system of equations for which the given matrix is the augmented matrix.

The equivalent system of equations of the augmented matrix is


$
\left\{
\begin{array}{ccccc}
x & +3y & +6z & = & 2 \\
2x & +y & & = & 5 \\
& & z & = & 0
\end{array}
\right.
$

Calculus: Early Transcendentals, Chapter 6, 6.3, Section 6.3, Problem 5

The shell has the radius x, the cricumference is 2pi*x and the height is e^(-x^2) , hence, the volume can be evaluated, using the method of cylindrical shells, such that:
V = 2pi*int_0^1 x*e^(-x^2) dx
You need to use substitution method to solve the integral, such that:
-x^2 = u => -2xdx = du => xdx = -(du)/2
V = 2pi*int_(u_1)^(u^2) e^u*(-du)/2
V = -pi*e^u|_(u_1)^(u^2)
V = -pi*e^(-x^2)|_0^1
V = -pi*(e^(-1^2) - e^(-0^2))
V = -pi*(1/e - e) => V = pi*(e - 1/e)
V = ((e^2-1)*pi)/e
Hence, evaluating the volume, using the method of cylindrical shells, yields V = ((e^2-1)*pi)/e.

What quote should I use to support the theme in the short story "Cranes" by Hwang Sunwon?

In "Cranes," two childhood friends find themselves on opposite sides of the Korean War, with most of the conflict occurring at the 38th parallel, which is referenced in the story. Friendship is certainly a theme and has been referenced here. Also worth noting is another theme: War creates ideological conflict based on circumstances that may not represent individual beliefs.
After all, these two boys are childhood friends. They intimately know each other's families and the struggles they have overcome. They share memories, like sneaking out to smoke dried gourd leaves, hidden from the adults. They also share a time when younger Tokchae plucked chestnut needles out of Songsam's bottom. Yet here they are under governments that tell them that they have nothing in common and that any person on the opposing side of war deserves death.
One quote that illustrates this:

They made me vice-chairman of the league because I was one of the poorest and I was a hardworking farmer. If that constitutes a crime worthy of death, so be it.

Here it is clear that Tokchae is not selected as a military leader due to his passion for the governmental policies or because he has proven himself a fierce warrior. Instead, he is a victim of the government itself; they know that he is a man of few resources and simply take advantage of his situation.
Another quote that illustrates this theme is as follows:

But his father had said the same thing! Where can a farmer go, leaving all his chores behind? . . . Fortunately, his family was safe then, as now.

The fact that Songsam's family is safe seems to be a matter of luck more than anything. Their stories are so similar, and being on the winning side seems a matter of chance. Songsam's family is "fortunately" safe—but the situation could have easily been flipped as the 38th parallel changed hands so many times.
War creates deep lines of division that do not always reflect the values of individuals. As this short story shows, perspective is important in determining fault and responsibility in areas of conflict.

Before identifying a quote that supports a theme from the story, we first need to identify a theme.  I think the main theme of "Cranes" is about the power of friendship.
Tokchae and Songsam are on opposite sides of a conflict, and Tokchae is Songsam's prisoner.  As the story progresses, the reader learns that Tokchae and Songsam grew up together and were childhood friends.  Readers learn that the boys shared much of their lives with each other and got into mischief together as well.  One such incident involved them capturing a crane. Fearing that they would get in trouble for capturing the crane, the two boys freed it.  The flashback foreshadows the ending of the story when Songsam unties Tokchae and invites him to go on a crane hunt.  It takes Tokchae a few moments to realize that Songsam is setting him free in the same way that they freed the crane as boys.  Despite being on opposite sides of an ideological conflict, the power of their friendship was able to overcome that divide.  
Because the theme of friendship is so closely tied to the crane and the men's childhood, I think that the quote for the theme should highlight both the crane and their childhood.  I like the following quote. 

But the next moment, as another crane from a nearby bush fluttered its wings, the boys’ crane stretched its long neck with a whoop and disappeared into the sky. For a long time the two boys could not take their eyes away from the blue sky into which their crane had soared.

The quote works well for the theme because it takes place during their childhood.  It shows the two boys together in happier times, and the quote emphasizes the freedom of the crane.  That freedom is then mirrored when Songsam frees Tokchae. 

What is the supernatural element of Tell-Tale Heart?

Until we analyze what the narrator is experiencing, it does seem as though there is a supernatural element to the story; however, what at first appears to be supernatural can actually be explained naturally. After the narrator has murdered the old man, dismembered him, and buried him beneath the floorboards, the police arrive to investigate the old man's cry, which a neighbor heard in the night. While the officers are there, the narrator believes that he can hear the old man's heartbeat from underneath the floor. However, we know that this is not possible because, for one reason, the old man is certainly very dead. The narrator's description of the sound helps us to identify its natural cause. He says,

It was a low, dull, quick sound –– much such a sound as a watch makes when enveloped in cotton.

We know that the narrator's adrenaline is racing because he fears discovery. Earlier in the story, when the narrator was about to murder the old man, he believed that he hears the man's heartbeat. He said,

[...] there came to my ears a low, dull, quick sound, such as a watch makes when enveloped in cotton.

His adrenaline was racing then, too. As his fury grew, he said, the sound "grew louder, [...] louder every moment." Thus, we can interpret this sound as the narrator's own heart beating. It is not possible to hear another person's heart beat from across the room with one's naked ears, and it is not possible for a person's heart beat to continue after they've died. Therefore, there is no supernatural origin of the heartbeat, just a misguided and mentally ill narrator who misinterprets his own heartbeat.

What are three examples of figurative language used in Stave 1 of A Christmas Carol?

The first paragraph of the story uses several figures of speech. The paragraph runs:

Marley was dead: to begin with. There is no doubt whatever about that. The register of his burial was signed by the clergyman, the clerk, the undertaker, and the chief mourner. Scrooge signed it: and Scrooge’s name was good upon ’Change, for anything he chose to put his hand to. Old Marley was as dead as a door-nail.

The first and most obvious figure we encounter here is amplification. A single piece of information—the death of Marley—is delivered to us in several sentences, each minor variations upon a single fact. The purpose of this figure is to emphasize the significance of his death and its importance to the people around Scrooge. 
The extended description of the certification and confirmation of Marley's death is an example of the rhetorical figure of enumeration (Latin: enumeratio), which explains a complex point or concept by breaking it down into simple steps or details and listing them. 
Finally, Dickens uses a simile in the phrase "dead as a door-nail," a phrase that compares a dead person to an inanimate object that never lived to emphasize absence of life. 

In Lord of the Flies, what are some good examples of figurative language that show themes such as Fear and Good vs Evil?

Golding uses simile, pathetic fallacy, symbolism, and allusion to depict fear and evil among the boys on the island. Near the beginning of the story, the boys inadvertently set fire to a large swath of island when their bonfire gets out of control. As the boys come to the realization that at least one littlun was killed in the fire, Piggy goes into an asthmatic panic attack, and "the crowd was as silent as death."
This simile is followed by a pathetic fallacy and symbolism:

"Tall swathes of creepers rose for a moment into view, agonized, and went down again. The little boys screamed at them. "Snakes! Snakes! Look at the snakes!"

Giving the creepers emotion such as agony is a pathetic fallacy that voices the fear the boys have of the consuming fire. The allusion to snakes recalls the account of the Garden of Eden when the devil appeared in the form of a snake or serpent. This symbol foreshadows that the island is not a paradise; the boys are already beginning to turn it into a hell because of their innate evil.
When the evening meeting after the missed rescue from the passing ship deteriorates into talk of ghosts, Golding uses pathetic fallacy again: "Two grey trunks rubbed each other with an evil squeaking that no one had noticed by day." The fear the boys have is reflected in Golding's description of the sound of the trees. 
The most prominent symbol of evil in the book is the pig's head on a stick, which becomes the Lord of the Flies during Simon's vision. When Simon first sees it, "the half-shut eyes were dim with the infinite cynicism of adult life. They assured Simon that everything was a bad business." The head's mocking tone and threatening manner personify evil.
Another symbol of fear and evil is the dead parachutist. Although, as Simon discovers, "the beast was harmless and horrible," it is the embodiment of the boys' fear and at the same time a representation of man's inhumanity to man, as the parachutist was shot down as part of the war that is engulfing the outside world. Golding has the rotting parachutist, freed from its bondage by Simon, float out to sea over the dead body of the recently murdered Christ-figure, combining allusion and symbolism. What could be more evil than killing an innocent man with their bare hands--a man who was only trying to share the good news? 
Golding uses figurative language--including simile, pathetic fallacy, symbolism, and allusion--to portray fear and evil on the island.

Why was Doug Hoo stationed outside the Westing house?

I believe that this question is asking about events that happen at the very beginning of chapter 4. It is Halloween, and Turtle Wexler is planning on spending the night in the Westing house. The second paragraph of this chapter tells readers that Doug Hoo is up on the top of the cliff where he had taken his "station" behind the maple tree. Doug Hoo is the chosen timekeeper for Turtle Wexler's time spent in the Westing house. Doug Hoo is the chosen timekeeper because he's a track star that can run faster than anybody else in the entire state. Turtle is absolutely planning to spend the entire night in the house because it will make her a lot of money. She's being paid two dollars per minute for being in the house. Unfortunately, her time is cut short, and she is only in there for twelve minutes. She runs out of the house screaming because she finds a dead body.

Turtle had seen the corpse in the Westing house, but it was not rotting and it was not sprawled on an Oriental rug. The dead man was tucked in a four-poster bed.

Who receives the chess set for Christmas?

In Amy Tan's short-story "Rules of the Game," Waverly and her brothers attend an annual Christmas party at the First Chinese Baptist Church, which is located at the end of their alley. During the party, a man dressed as Santa Claus begins passing out random small gifts to each child in attendance. Waverly receives a twelve-pack of Life Savers as a present while her brother Vincent receives a used chess set from Santa's bag. Despite the fact that Vincent's chess set is missing two pieces, Waverly and her brothers are intrigued by the game and immediately read the rules when they get home. Waverly begs her brother to play and ends up sharing several Life Savers to get a chance to play. Waverly becomes fascinated by the game of chess and quickly learns the rules and secrets to the game. Waverly turns out to be a chess prodigy and becomes the youngest champion from her side of town.

In Amy Tan’s, Rules of the Game, Waverly’s brother, Vincent, is the initial recipient of the chess set. The game, which later has a significant impact on Waverly’s life, comes into Vincent’s possession completely by chance: it is a Christmas gift bestowed by a Santa-costume-clad man at the church the San Francisco-based Jong family attended. As this was an act of charity—a gift for less fortunate children—Waverly’s mother, a woman as poor as she is proud, wants to destroy it. Fortunately for Waverly, her brothers rescues the chess board and starts playing the game before Mrs. Jong can toss it on the trash heap. Although her two brothers quickly lose interest in the game, Waverly excels, becoming a national chess champion by the age of nine.

What does Blake mean by "To See The World in a Grain of Sand"? How can we see the world in a grain of sand?

"Auguries of Innocence" is a poem about perception, as is much of Blake's work. This poem lists seemingly impossible sights to an experienced eye (the world in grain of sand, for instance) that the innocent perceive routinely. To extend the poem beyond that first line, we see further paradoxes:

To see a World in a Grain of Sand
And a Heaven in a Wild Flower
Hold Infinity in the palm of your hand
And Eternity in an hour
A Robin Red breast in a Cage
Puts all Heaven in a Rage
A Dove house filld with Doves & Pigeons
Shudders Hell thr' all its regions
A dog starvd at his Masters Gate
Predicts the ruin of the State

To Blake and the Romantics, innocence and childhood are usually synonymous, and a child might well see in something as minute as a grain of sand the wonder of the universe or in a flower that an adult easily passes by an image of Heaven. These are intellectual and spiritual orientations, and the person of experience is blind and numb to the potential for wonder all around. As a result, the adult or experienced person grows numb to injustices such as the starving dog. If a grain of sand can reveal a world, a starving dog can indict a society.


The poem continues for several lines, falling into an almost trance-line condemnation of contemporary life and its degradation. These are auguries of doom. The poem ends with a stronger affirmation of this claim about the importance of choosing our mode of perception in spiritual terms:


Every Morn and every Night
Some are Born to sweet delight
Some are Born to sweet delight
Some are Born to Endless Night
We are led to Believe a Lie
When we see not Thro the Eye
Which was Born in a Night to perish in a Night
When the Soul Slept in Beams of Light
God Appears & God is Light
To those poor Souls who dwell in Night
But does a Human Form Display
To those who Dwell in Realms of day

Blake’s opening line is a way of saying that every part of the natural world is important, and that we humans are connected to all of it. The foundations of our planet are rock and water. Sand represents both entities. These grains are tiny bits of rock that have been worked upon by the centuries-long action of water. So, yes, they are indeed representative of the world, in the physical sense. And if you look at a handful of sand, you can see variety and diversity in the size and shape and origin of the particles – mirroring the range of people who populate our earth. Yet from a distance, the sand on a beach looks like a solid surface made up of only one color. The individual and unique grains coalesce to form that whole. This is an apt metaphor and lesson for us. We ARE the grains of sand. I see us here. Do you?
https://www.poetryfoundation.org/poems/43650/auguries-of-innocence

What are the objectives of the Vet to Vet program?

The Vet to Vet program trains veterans to work as peer advisors to other veterans. The study by Barber et al. (2008), cited below, looked at anonymous surveys of 1,847 people from 38 veteran peer support programs and found that there was a positive association between program satisfaction and recovery and the duration and frequency of peer support. As the article states, peer support has been an important part of mental illness recovery programs in recent years. Research has suggested that peer support can be an important tool in the recovery of people with serious mental illness, including chronic illness. The objectives of this article were to document the delivery of peer support as part of mental health treatment and to monitor its implementation and outcomes.
Vet to Vet was developed by Moe Armstrong, a celebrated Vietnam veteran, and the program uses peer education and support at a range of VA (Veterans' Administration) locations, including VA hospitals, community clinics, and residential centers. The peer supporters are independent from the VA but receive support from the VA. The researchers in the article by Barber et al. found that participants viewed their experience positively. Participation in peer support was also associated in the study with stronger recovery attitudes and a stronger sense of engagement.
Source:
Barber, J.A., Rosenheck, R.A., Armstrong, M., Resnick, S.G. "Monitoring the dissemination of peer support in the VA healthcare system." Community Ment Health J (2008) 44:433–441. DOI 10.1007/s10597-008-9146-7.

Piggy comes up with the idea to make a list of the boys on the island. What does this reveal about his character?

Piggy's strongest and most valuable characteristics are also the ones that inspire the most mockery; after all, his practical intelligence makes him seem like a grown-up, which sets him apart from the other boys and makes him a target for their meanness.
Piggy's idea to make a list of the boys is something a teacher would do, so that they would know who is absent and who is late for meetings, for example. Though Piggy intends the idea to help everyone stay organized and safe, the idea makes him appear less spontaneous and fun. Piggy desperately wants to survive this perilous time, and he wants to contribute to the effort to help everyone else survive, but his methods are too much like something an adult would do. This side to his personality enhances the rough-and-tumble attitude of Jack and the thoughtful coolness of Ralph, as Piggy, though bright and intelligent, lacks the self-awareness to understand why his approaches are not as well-received as those of the other boys.

In Chapter 1, Piggy suggests to Ralph that they make a list of names of the boys on the island. After Ralph blows the conch, the remaining boys on the island group together and hold an assembly. During the assembly, Piggy tries desperately to get everyone's name but is unable to do so. Piggy's suggestion to make a list of names illustrates his affinity for structure and civilization. Piggy is the most intelligent boy on the island and understands the importance of maintaining order. Creating a list of names also demonstrates that Piggy has his priorities in the right order. Piggy is pragmatic and attempts to organize the boys. Unfortunately, he is not able to list the littluns, and a young boy goes missing after they accidentally set the forest on fire. As the novel progresses, Piggy's representation of civilization, structure, and intelligence becomes more evident.

Calculus of a Single Variable, Chapter 9, 9.3, Section 9.3, Problem 82

To evaluate the series sum_(n=2)^oo ln(n)/n^3 , we may apply Direct Comparison test.
Direct Comparison test is applicable when sum a_n and sum b_n are both positive series for all n where a_n lt=b_n .
If sum b_n converges then sum a_n converges.
If sum a_n diverges so does the sum b_n diverges.
Let b_n=1/n^2 and a_n =ln(n)/n^3
It follows that a_n < b_n
Graph:
Note: f(x) =1/x^2 for red graph and g(x)=ln(x)/x^3 for green graph.
Apply the p-series test where kgt0 : the sum_(n=k)^oo 1/n^p is convergent if pgt1 and divergent if plt=1 .
For the sum_(n=2)^oo 1/n^2 , we have the corresponding value p=2 . It satisfies the condition pgt1 since 2gt1 .Therefore, the series sum_(n=2)^oo 1/n^2 converges.
Conclusion:
Because a_n < b_n and sum b_n converges, then sum a_n = sum_(n=2)^oo lnn/n^3 converges

Calculus: Early Transcendentals, Chapter 7, 7.4, Section 7.4, Problem 14

int 1/((x+a)(x+b)) dx
sol:
int 1/((x+a)(x+b)) dx
let [u= x+a] => du = dx
so ,
int 1/((x+a)(x+b)) dx
=int 1/((u)(x+b)) du
As u =x+a => x= u-a , on substituting in the above equation we get ,
=int 1/((u)(x+b)) du
=int 1/((u)((u-a)+b)) du
=int 1/((u)(u+b-a)) du
Taking partial fractions we obtain,
=int 1/((u)(u+b-a)) du
=int ((1/((a-b)(u+b-a)))+ (1/(u*(b-a)))) du
=int (1/((a-b)(u+b-a)))du+ int (1/(u*(b-a))) du -----------------(1)

Now let us consider
int (1/((a-b)(u+b-a)))du
let v=u+b-a => dv =du
so,
int (1/((a-b)(u+b-a)))du
= (1/(a-b)) int (1/(u+b-a))du
=(1/(a-b)) int (1/(v))dv
=(1/(a-b)) ln(v)
=(1/(a-b)) ln(u+b-a)
=(1/(a-b)) ln(x+b) as [u-a =x] ----------------------(2)
Now consider ,
int (1/(u*(b-a))) du
As similar to above we obtain as follows,
int (1/(u*(b-a))) du
= (1/(b-a))int (1/(u)) du
=(1/(b-a)) ln(u)
= (1/(b-a)) ln(x+a) as u=x+a -------------(3)
substituting (2) and (3) in (1) we get,
int 1/((x+a)(x+b)) dx
=int (1/((a-b)(u+b-a)))du+ int (1/(u*(b-a))) du
= (1/(a-b)) ln(x+b) +(1/(b-a)) ln(x+a) + C

is the solution :)

Who was George Grenville, and what did he hope to accomplish in America? Was he successful?

George Grenville was a British Whig politician who served as prime minister from 1763 to 1765. Grenville's tenure as prime minister was brief but disastrous. He did not get along with King George III, who found Grenville tiresome. His decisions to enforce the Sugar and Molasses Act of 1764, also known as the American Revenue Act and the Stamp Act of 1765, were some of the events that led to the American Revolution.
The Sugar Act, as it is usually called, was designed to end the smuggling of molasses and to address tax evasion on imports of sugar and molasses from the French and Dutch West Indies. Grenville reduced the tax on molasses from six pence per gallon to three pence per gallon but strictly enforced it. Protests from the American colonies insisted that the tax should not be any more than one pence, or one penny, per gallon, as that was all the market would tolerate. Grenville refused to listen and instituted the tax. Other items were also taxed, such as sugar, some wines, coffee, and fabrics. The tax on molasses led to the decline of the rum industry in some colonies, which then reduced the number of colonies with which others could trade. Not having as much revenue from trade made some colonies unable to afford manufactured goods from Great Britain.
Distillers in New England benefited from the hole left in the market. However, they did not appreciate the increased interference from the British, who also had the right to seize and confiscate ship cargoes if ship masters did not pay duties or violated a trade rule. The Sugar Act was a scheme to increase revenues for the British Empire and to recoup losses from the French and Indian War.
Whereas the Sugar Act benefited American colonists while still limiting their trade and freedom on the seas, the Stamp Act was a more direct imposition. It placed a tax on "every piece of printed paper they used." This included shipping documents, legal documents, newspapers, other publications, licenses, and playing cards. The revenue was to be used to protect and defend the American frontier near the Appalachian Mountains. Ten thousand troops had been stationed there.
The tax was small but escalated quickly, especially since each piece of paper one used was taxed. What offended colonists was that the act was an attempt to levy taxes on the colonies without going through colonial legislatures. Colonists saw it as the British legislature overstepping its bounds and disallowing autonomous rule. Furthermore, if they could pass this tax with little to no resistance from colonists, other taxes—bigger taxes—could be imposed in the future.
It seems that Grenville's hope was to establish order in the colonies. He wanted to ensure that colonists paid their taxes on goods. He enforced taxation not only to ensure order, but also to pay for the crown's wars and to secure colonial borders. Though he was decisive, he lacked talent as a politician. He failed to listen to people's concerns and failed to maintain good relationships with people, including the king. Grenville was already out of office by the time the first grumblings of revolution swept the American colonies, but his tax policies had initiated those grumblings.
https://www.britannica.com/event/Sugar-Act

https://www.history.org/history/teaching/tchcrsta.cfm

https://www.ushistory.org/declaration/related/sugaract.html

How is "The Road Not Taken" interpreted in today's society?

If we take "today's society" to mean the current culture of America, 2017, then quite often the poem is considered a call to push past boundaries, to step outside one's comfort zone and do something new! It has a very particular calling of "going against the grain," by taking a path that is "less traveled by." References to this poem are often used in the context of desiring not to be just another sheep in the herd, but to separate oneself and do what most of society does not.
Especially in the context of the millenial society, this poem is an encouragement to turn away from the 'worn path' (though the speaker does not necessarily describe the paths as one being worse for wear than the other), and go a separate way.

People typically interpret the fork in the road in this poem to be symbolic of the choices we make. We may have a few options at each of these moments of decision, but ultimately we cannot really know where each choice would take us, just as the speaker cannot see where the roads lead.
The speaker examines both choices, noting that the second is "just as fair" as the first, and he admits that "the passing there / Had worn them really about the same." In other words, the two roads are worn pretty equally, implying that approximately the same number of people have taken them: neither one, then, is actually "less traveled." In fact, the speaker also says that "both [roads] that morning equally lay / In leaves no step had trodden black" (my emphasis). He chooses the second option, knowing that he'll probably never come back to try the first road.
Finally, he claims that he will tell this story in the future, perhaps to his grandchildren, since it will be "ages and ages" from now. He will say that there were

Two roads diverged in a wood, and I—I took the one less traveled by,And that has made all the difference.

Thus, he is planning to lie. He will tell people that one of the roads was clearly "less traveled" than the other and that he took that road. We might assume it is because he wants to seem brave, as though he made a difficult and relatively unique choice. However, if you recall, there IS no road less traveled—he described them as equal in many ways—and so we are left to consider the possibility that there are, perhaps, no real unique choices to be made.
Many people interpret this poem to mean that it is possible and good to take the road less traveled. However, it is difficult to find evidence for this interpretation since the speaker so clearly describes the roads as equals. Perhaps this interpretation says more about us, actually confirming the conclusions we might draw from the narrator's desire to lie and make himself sound unique.

Why is it good to be Thane of Glamis in Macbeth?

The three witches greet Macbeth in act 1, scene 3 as "Thane of Glamis," "Thane of Cawdor," and tell him "thou shalt be king hereafter." Macbeth answers, "By Sinel's death I know I am Thane of Glamis." This is the seat he has inherited rightfully at the beginning of the play. He cannot understand how he is to be also Thane of Cawdor, or king—not knowing that Duncan is later to appoint Macbeth Thane of Cawdor.
The idea is that each position is more powerful than the one before. As Thane, or lord, of Glamis, Macbeth has an authority position within the feudal system of early medieval Scotland. The men who live in the land he controls owe their loyalty to him, and its wealth belongs to him. Glamis Castle still stands today and is considered one of Scotland's most beautiful castles; it now belongs to the Earl of Strathmore and Kinghorne. Glamis is in a highly defensible position, giving its thane a military advantage.
Macbeth describes the Thane of Cawdor prior to himself as "a prosperous gentleman." In becoming Thane of Cawdor, in addition to Thane of Glamis, then, Macbeth would likely inherit this wealth, as well as the additional power, land, and men attached to Cawdor.

When Lyddie's mother decides to go to her sister's farm, what do Lyddie and Charlie do? What does this show about Lyddie's relationship with her brother?

The answer to this question can be found in Chapter 1. Early in the chapter, a bear enters the house that Lyddie and her family lives in. Lyddie bravely fends off the bear to keep her family safe; however, Lyddie's mother takes the event with the bear as a bad sign. She no longer feels safe in the house, and she wants her entire family to go to her sister's place. Lyddie is not on board with that idea because she and Charles are worried that their father will come home to find his family gone. 

"But how will Papa find us if we've left home?" Charles asked. 

Lyddie tells her mother that she is unwilling to go to the other farm. She and Charlie agree to stay behind, take care of the farm, and wait for the possible return of their father. 

"I can't stop you to go," Lyddie said, "but I can't go with you.  I can't leave the farm." 

Charlie leaves with the family for two weeks to make sure that they make it safely to Uncle Judah's farm, and then he returns. Lyddie and Charlie successfully take care of the farm, feed themselves, and birth a calf.  All of this shows that Lyddie and her brother are close with each other. They get along with each other, and they are capable of working together as a team. It also shows that they have a similar work ethic and emotional attachment to their home. Finally, it shows that Charlie and Lyddie have a lot of trust in each other. They are each essentially placing their welfare, health, and safety in the hands of the other sibling.  

1-2 paragraph about the purpose of Dr.King's I have a Dream Speech , and why it was important and still important today?

The purpose of Dr. Martin Luther King Jr.'s speech was at least twofold: it was an integral part of the August 28, 1963 march on Washington, DC for the realization of economic and civil rights for blacks, and it provided much-needed support for civil rights legislation that President John F. Kennedy had proposed to Congress two months prior, in June. 
The speech was important in 1963 because the country was still legally segregated.  It was not until the Civil Rights Act of 1964 that it became illegal for state and local authorities to segregate Americans on the basis of their race. Because blacks had no federal protection, they were denied access to schools, businesses, and other organizations because of their race. Moreover, discrimination was holding black people back from equal access to jobs. King's speech was a call to follow through on the promises of the Emancipation Proclamation one hundred years before and the Declaration of Independence's claim that "all men are created equal."  King refers to these seminal documents along with the Constitution to point out that American blacks were denied many of the basic human rights that their citizenship guaranteed for them.
The speech is still important today because it reminds us that in America, the promises our government makes in its founding documents are not always carried out for all people.  Though blacks have legal protection from discrimination, America still has social problems centered on race. Evidence used to support this argument include findings that blacks are incarcerated at higher rates than other races and are treated unfairly by police and the judicial system. Blacks applying for mortgages and other loans find it more difficult to borrow. Unemployment  and poverty rates are higher for African Americans than for other races. The Black Lives Matter movement was founded after the murder of a black teenager and subsequent acquittal of his killer. It labors to move black Americans forward in American society. 
Though the Civil Rights Act was passed in 1964 and America elected its first black president in 2008, many of the inequities Dr. King cited in his speech continue to trouble America. The "I Have a Dream" speech reminds Americans of the continued work required to deliver social justice to all Americans. 

What are the advantages of banning computers?

Banning computers completely would surely be disastrous for any society. We would lose so much if we did so. We would lose the ability to have computer-controlled machines make things for us at low price. We would lose the ability to store huge numbers of records (including those at banks and hospitals) in easily accessible ways. We would lose the internet and, with it, our ability to access huge amounts of information easily and to contact people around the world via email. All of this would be terrible for our society.
I can come up with at least three potential benefits of banning computers, though. First, repressive governments would find it easier to prevent the spread of information and opinions. Without computers, people would have to spread opinions through actually talking to one another or printed materials. It is harder to spread information and ideas this way than through computers, making it is easier for the government to crack down on people spreading information. Thus, some repressive governments might like to ban computers.
Secondly, if we ban computers, we would open up many more jobs for people. If there were no computers, we would again need large numbers of secretaries, typists, and clerks in every office. They would be needed for filing papers and finding papers people needed. We would need more people to do the jobs of machines currently controlled by computers. There would be many more jobs in these areas than we have now. Of course, we would lose all the jobs that we have that depend on computers, so this might not be a net benefit.
Finally, we could argue banning computers would make our society more human once more. Today, people can avoid face-to-face interactions with other people more than ever before. They can also say horrible things anonymously through the internet. These behaviors make our society worse because they loosen the bonds between people. If we banned computers, we might have a more civil and polite society in which people interacted more with one another than we do now.
These are some possible benefits of banning computers, though such an idea is surely absurd in today’s world.

What other crimes have Sam and Bill committed?

At one point during the story, Bill tells Sam that they have been together in many adventures, which include natural disasters such as fires, floods, cyclones, and earthquakes. In addition, they have experienced police raids and have been involved in poker games. He also mentions that they've been in train robberies together. Therefore, they seem to have been involved in gambling and theft in the past.
Bill and Sam are now attempting to commit what Sam refers to as a "a fraudulent town-lot scheme." To get the money necessary to carry out this scheme, they are trying to kidnap Ebenezer Dorset's ten-year-old son, who refers to himself as Red Chief, and to charge a ransom of $2,000. While they want to add fraud and kidnapping to their list of crimes, they are entirely unsuccessful as kidnappers. They wind up having to pay Dorset to take his horribly behaved child back at the end of the story.

We get the impression that Sam and Bill are career criminals although it isn't spelled out as such in the story. When the story opens, our two would-be kidnappers have managed to scrape together about $600 which they're going to put towards a town-lot scam they're planning in Western Illinois. But it's not enough. Sam and Bill figure they're going to need another $2,000 to swing the deal—hence, their ingenious kidnapping plan.
Although the two men prove themselves hopelessly incompetent, they do give the impression that they have prior experience of criminal activity. Sam goes into a lot of detail about the preparations that he and Bill Driscoll made when they first decided to kidnap a little boy in Summit, Alabama. It's instructive that he seems to know just what kind of response they can expect from the local sheriffs. This would appear to indicate that Sam and Bill have encountered law enforcement officials in semi-rural communities before.

Single Variable Calculus, Chapter 3, 3.4, Section 3.4, Problem 8

Differentiate $\displaystyle y = u(a \cos u + b \cot u)$


$
\begin{equation}
\begin{aligned}

y' =& au \cos u + bu \cot u
&&
\\
\\
y' =& au \frac{d}{du} (\cos u) + \cos u \frac{d}{du} (au) + bu \frac{d}{du} (\cot u) + \cot u \frac{d}{du} (bu)
&& \text{Derive each term}
\\
\\
y' =& (au) (-\sin u) + (\cos u) (a) + (bu)(-\csc^2 u) + (\cot u) (b)
&& \text{Simplify the equation}
\\
\\
y' =& a \cos u + b \cot u - au \sin u - bu \csc^2 u
&& \text{}

\end{aligned}
\end{equation}
$

When did Saint-Domingue become Haiti?

Saint-Domingue became Haiti on January 1, 1803. On this day, rebels led by Jean-Jacques Dessalines declared their independence from France. This event was the culmination of a long and bloody struggle against the French colonial leaders, one which had frequently taken the form of a civil war fought not just along racial lines, but with free people of color sometimes siding with whites. Its initial leader, Toussaint L'Ouverture, was imprisoned in Europe at this point, and would die just a few months later. Dessalines declared independence after defeating a French force sent by Napoleon Bonaparte to recover the island several years after L'Ouverture had concluded a peace agreement with the French revolutionary government. With this declaration, Haiti became the second independent republic in the Western hemisphere, after the United States. This revolution, not simply a by-product of the French Revolution, had global ramifications, not least because it ran counter to many racial assumptions. The idea that people of African origin could establish a free government was anathema to proslavery ideology.
https://www.history.com/this-day-in-history/haitian-independence-proclaimed

How are the characters affected by the outcome of Tom Robinson's trial?

The outcome of the trial is critical to Jem and Scout's process of maturation. Scout and Jem believe that Tom will be acquitted because the evidence is in favor of his acquittal. When he is found guilty, they know that the legal system in Maycomb is unjust and that the adults who made the decision are flawed and racist. They develop the idea that life is not always ideal, and their disappointment makes them more mature and wiser about the world.
Atticus is also disappointed by the verdict, as he held out hope for a fair trial. However, he takes comfort in knowing that the jury did not decide immediately but took a little while to render their verdict. To Atticus, this means that they actually did some deliberating, which is a step forward in his view.
The verdict causes Tom Robinson to try to escape from prison, and he is shot and killed. Bob Ewell is angered by the trial and later tries to attack Scout and Jem as a result.

The outcome of the Tom Robinson trial drastically affects various members of Maycomb's community. Jem, Scout, and Dill lose their childhood innocence after witnessing racial injustice firsthand. Jem becomes jaded with his prejudiced community members, Dill is extremely upset at the treatment of Tom, and Scout gains perspective regarding the duality of human nature. Scout's tolerant attitude towards her community and awareness of the prominent racial prejudice throughout Maycomb influence her to protect innocent individuals. Atticus is upset at the verdict but understands that significant steps were made towards racial equality. Bob Ewell was exposed as a liar and abusive father throughout the trial. Even though Tom was found guilty, Bob Ewell seeks to avenge Atticus for "ruining" his reputation. Following the guilty verdict, Tom Robinson loses hope and does not try to appeal the sentence. Tom eventually attempts to escape from prison and is shot to death. Helen Robinson is forced to provide for her children, and Bob Ewell tries to intimidate her while she walks to work. Aunt Alexandra also shows empathy for her brother following the trial and becomes more understanding of Atticus.

What is the tone of Lincoln's Gettysburg Address?

Lincoln's brief but powerful address at Gettysburg in 1863 has a reverent, humble, and fervent tone. As Lincoln begins the speech, he refers to the founding fathers and references the founding document, the Declaration of Independence. He shows reverence for these men and their work. Everyone in the audience would realize that the men and document started a bloody but crucial war, similar to the one that then ravaged the country.
As he moves on to discuss the then-ongoing conflict, he mentions that the stakes are high. The purpose of his speech is to dedicate a cemetery to bury those who fought and died at Gettysburg. With great reverence, he notes that he and those in attendance don't have the power to "consecrate . . . this ground." The men who shed their blood there are the ones who hallowed it. Through this first part of the address, Lincoln displays great respect for the founders, the country, and the dead soldiers.
Next, he displays his own humility and extends it to his listeners. By stating, "The world will little note, nor long remember what we say here, but it can never forget what they did here," he takes the focus off himself and defers to the soldiers as the truly important people.
Toward the end of the speech, Lincoln becomes fervent as he outlines the response he hopes to gain from his listeners. He wants the citizens of the Union to stay committed to "the great task remaining before us," that is, winning the war, reuniting the country, and healing the nation's wounds. He calls for "a new birth of freedom" and invokes God as the overseer to protect the democracy in perpetuity.
Lincoln's tone of reverence, humility, and fervency conveyed the president's emotions and aptly reflected the hearts of his countrymen during those trying times.

The "Gettysburg Address" by none other than Abraham Lincoln is very complex is in its overtones. The speech serves several purposes, and it is through these purposes that the tones are best expressed. First, it takes a somber, morose tone, because it is meant to respect the dead from the Battle of Gettysburg. Second, it is meant to be invigorating, because it is an attempt to stir up the passions and force of the Union people and soldiers to embolden them to fight harder for their cause. Finally, and perhaps most prominently, it is hopeful. Lincoln uses this speech as an opportunity to look forward at a United States that is unified and free and serves the people to the best extent possible. All of these tones are mixed well throughout its text.

President Abraham Lincoln delivered the "Gettysburg Address" on November 19, 1863. This was in the middle of the Civil War. The occasion of the speech was the dedication of the Soldiers' National Cemetery in Gettysburg, Pennsylvania. Since this was the dedication of a memorial and burial ground of fallen soldiers, the occasion was solemn. As well as the mourning occasioned by the deaths of soldiers in the past, the mood was made even more somber by the awareness of both Lincoln and his audience that the war was still going on and that many more soldiers would die and be buried in the cemetery.
As is appropriate to such a solemn occasion, Lincoln's tone is formal and hortatory. Although Lincoln expresses sorrow for the fallen soldiers, the tone is not uniformly mournful, but rather encourages his audience to honor the soldiers' sacrifice by continuing to fight for the values for which the soldiers made the ultimate sacrifice. The conclusion of the speech shows determination and even optimism, arguing that the war should not simply be mourned but also seen as a beacon of hope, that the war was not only an emblem of death but of birth of a new political tradition, and:

that these dead shall not have died in vain—that this nation, under God, shall have a new birth of freedom—and that government of the people, by the people, for the people, shall not perish from the earth.

 

"Gettysburg Address" was solemn yet hopeful. Lasting only a few minutes, it is considered one of the most eloquent speeches in American history. At the beginning of his speech, Lincoln spoke about the founding of the nation and its commitment to liberty. In the middle of the speech, he spoke about the Civil War in very brief terms, but the bulk of this short speech was dedicated to thinking about the future. Lincoln mentioned the "unfinished work" that the soldiers who fought and died at Gettysburg advanced, and he committed the country to "a new birth of freedom." As Gettysburg was the campaign that ended the Confederate advance northward in the summer of 1863, Lincoln began to look forward to the end of the war. This speech is a brief but solemn memorial to the people who died at Gettysburg and an eloquent and hopeful look at the future. 

x=2+t^2 , y=t^2+t^3 Determine the open t-intervals on which the curve is concave downward or concave upward.

x=2+t^2
y=t^2+t^3
First, take the derivative of x and y with respect to t.
dx/dt =2t
dy/dt =2t + 3t^2
Then, determine the first derivative,dy/dx . Take note that in parametric equation, the formula of dy/dx is:
dy/dx= (dy/dt)/(dx/dt)
Applying this formula, the first derivative is:
dy/dx = (2t+3t^2)/(2t)
dy/dx= (2t)/(2t) + (3t^2)/(2t)
dy/dx=1+3/2t
Then, determine the second derivative of the parametric equation. To do so, apply the formula:
(d^2y)/(dx^2)= (d/dt (dy/dx))/(dx/dt)
So the second derivative is:
(d^2y)/(dx^2) = (d/dt (1+3/2t))/(2t)
(d^2y)/(dx^2) = (3/2)/(2t)
(d^2y)/(dx^2) = 3/2 * 1/(2t)
(d^2y)/(dx^2) = 3/(4t)
Take note that the concavity of the curve changes when the second derivative is zero or does not exist.
(d^2y)/(dx^2)= 0     or     (d^2y)/(dx^2)= DNE
Since the second derivative of the given parametric equation is
(d^2y)/(dx^2) = 3/(4t)
there are no values of t in which it results to zero.
However, the second derivative does not exist when its denominator is zero. Setting 4t equal to zero yields
4t=0
t=0/4
t=0
So the concavity of the parametric curve changes at t=0.
Now that the inflection is known, apply the second derivative test.
Take note that when the value of the second derivative on an interval is positive, the curve on that interval is concave up.
(d^2y)/(dx^2)gt0       :.  concave up
And when the value of the second derivative on an interval is negative, the curve on that interval is concave down.
(d^2y)/(dx^2)lt0     :. concave down
So assign a test value for each interval t<0 and t>0. And plug-in the test values to the second derivative.
For the interval t<0, let the test value be t=-1.
(d^2y)/(dx^2) = 3/(4t)
(d^2y)/(dx^2) = 3/(4(-1))=3/-4=-3/4
So the parametric curve is concave down on the interval t<0.
For the interval t>0, let the test value be t=1.
(d^2y)/(dx^2) = 3/(4(1))=3/4
So the parametric curve is concave up on the interval t>0.
 
Therefore, the graph of the given parametric equation is concave down on the interval t<0 and it is concave up on the interval t>0.

What are the significant characters in The Ramayana?

There are many significant characters in The Ramayana.  
Whenever addressing a sacred text vital to a spiritual tradition, there will be many important characters.  This is especially so with The Ramayana, as a case could be made that every character mentioned is important in their own way.  This is to emphasize that what follows is by no means comprehensive. 
Lord Rama is probably the most important character in The Ramayana.  He is an avatar of Lord Vishnu, and his narrative forms the basis of the text. Born to King Dasaratha, he is the example of dharma, or adherence to the overarching structure of the universe.  Lord Rama carries himself as the perfect son, prince, warrior, husband, and brother.  His defeat over the demon-king Ravana establishes how human beings must live their lives with duty and honor.
Sita is Lord Rama's wife.  Born to King Janaka of Mithila, she is an avatar of Goddess Lakshmi.  As Lord Rama's wife, Sita devi demonstrates an equal commitment to dharma.  As beautifully honorable as Lord Rama is as a husband, she is as much an equal as a wife.  She is kidnapped by the demon-king Ravana, setting in motion the confrontation between her husband and her tormentor.  While in Lanka as Ravana's captive, Sita devi demonstrates her strict virtue in refusing to acquiesce even in the slightest to Ravana's gestures. Sita is the perfect daughter, wife, sister, daughter-in-law, and sister-in-law.
Lakshmana is one of Lord Rama's brothers.  Along with Shatrughna and Bharata, Lakshmana is very devoted to his brother.  Lakshmana is the avatar of Adi Sesha, the reclining serpent upon which Lord Vishnu rests.  When Rama is exiled to the forest for fourteen years, Lakshmana feels it his duty to accompany him.  He is a vigilant protector of Rama and Sita.  When Sita is kidnapped, Lakshmana accompanies Rama to confront and eventually kill the demon-king of Lanka.
Ravana is the antagonist of The Ramayana.  While Rama represents structure, honor, and adherence to a structure that envelops human beings, Ravana represents self-indulgence and excess.  Ravana is the demon-king of Lanka. Through extreme penance to Lord Brahma and Lord Shiva, he acquired boons of incredible power. He used this power to consolidate his control over the universe.  Rama is incarnated from Lord Vishnu in order to defeat the existential threat that Ravana posed to justice and goodness.  Ravana kidnaps Sita as a way to showcase his power because he covets her beauty.  His kingdom in Lanka is the very embodiment of ostentatiousness and sensory gratification.  Ravana has many wives, to which he wishes to add Sita.  He is defeated by Lord Rama at the end of the epic, representing justice's triumph over injustice.
Hanuman is the commander of the monkey army that pledges to serve Lord Rama in his quest to retrieve Sita. Lord Hanuman was born to Vayu, god of the winds, and Anjani.  As a child, Lord Hanuman was incredibly brilliant, but also very mischievous.  His lack of focus ceased the moment he met Lord Rama. Hanuman immediately devoted himself to Lord Rama, and was willing to do anything and everything for his guru.  
Hanuman's devotion to Lord Rama is an important part of The Ramayana.  Through his immense strength and skill, he is able to jump across the ocean to enter Lanka, and collect vital intelligence that he relays to Lord Rama. He is the first one to find Sita devi, reminding her not to lose faith in Lord Rama.  Hanuman orders the army of monkeys, the Vanaras, to build a bridge to Lanka made of floating stones that allows Lord Rama, Lakshmana, and the army to enter Lanka and challenge Ravana.  When Lakshmana is struck down by Ravana's potent arrows, Hanuman saves him by bringing an entire mountain to Lanka that contains a precious herb.  Hanuman's selflessness is the example that human beings are meant to follow.
These are the primary characters in The Ramayana. There are many more that play vital roles in the development of the narrative.  In temples all over the world, shrines are built to Lord Rama, Devi Sita, Lakshmana, and Hanuman in acknowledgement of their efforts in overcoming the injustice that Ravana represented.