What could be another title for "The Last Leaf"?

The first title that comes to mind is "Staying Alive." This short story shows how life is based on hope as much as science or medicine. Johnsy has contracted pneumonia. She believes she will die when the last leaf falls from the tree growing against the wall outside her window.
Her friend Sue persuades their neighbor, Mr. Behrman, to paint a leaf on the wall behind the tree. Because this leaf doesn't fall, Johnsy stays alive long enough to recover fully from her pneumonia. Ironically, however, Mr. Behrman himself dies of pneumonia caught from being outside painting the leaf. This kind of irony is typical of O'Henry's method. The leaf becomes Mr. Behrman's final masterpiece. This leads to another possible title for this story: "The Masterpiece."

What is the Northwest Ordinance of 1787?

The Second Continental Congress adopted the Northwest Ordinance in 1787 as a result of settlers spilling into the area after the U.S. had gained the territory in the Revolutionary War with the 1783 Treaty of Paris. The ordinance stated that the new territory would be admitted to the union as no more than 5 and no less than 3 states. This territory went from the Ohio River in the south to the Great Lakes in the north and to the Mississippi River to the west. The territories would use a three-step process of becoming states. First, they would be administered by a governor, secretary, and three judges appointed by Congress. Then, in the second phase, they would have a non-voting member of Congress and an elected assembly when the male voting population reached 5,000. When the population reached 60,000 (in all), the territory would draft a state constitution and ask to be admitted as a state to the union. In addition, the ordinance stated that rights would be granted to members of the territory, including the right of free speech and religion, the right of habeas corpus, and right to a jury trial. This process of becoming a state was used for all subsequent states that came into the union. Finally, the ordinance stated that slavery was not allowed in the Northwest Territory, so the Ohio River became the dividing line between slave and free states until the Civil War.

Why does the nurse mark the medicine down as charity?

Although she's dealt with Phoenix on a number of previous occasions, the nurse still looks at her as just a frail, little old lady, one of many who turn up to the clinic on a regular basis. To the nurse, Phoenix is just "Aunt Phoenix," a slightly bothersome granny who turns up a couple of times each year to pick up some medicine for her grandson. The nurse marks the medicine down as charity as she assumes that Phoenix is poor, a charity case, so to speak. The attendant has the same impression, which she confirms by giving Phoenix a nickel from her purse, as it's nearly Christmas.
Phoenix says that she'll use the money (plus the nickel she picked up from the hunter earlier in the story) to buy her grandson a paper windmill. Despite what Phoenix says, we're not actually sure that her grandson really is still alive. If he has indeed passed away, then Phoenix's acceptance of both the medicine and the money on his behalf, and not hers, is a way of maintaining her pride and dignity in extreme old age.

I need detail about Greek hero Herakles with its labors.

Here are more details about each of Herakles's labors:
1) Killing the Nemean Lion
The Nemean lion was said to target warriors. Accordingly, it kidnapped beautiful women and used them to lure unsuspecting warriors to its lair. The women would turn into lions and kill the warriors once the men approached. When Herakles reached Nemea in Argolis, a young boy presented him with a challenge. If Herakles killed the lion within 30 days, a lion would be sacrificed to Zeus. If Herakles failed, the boy would be the sacrifice.
Herakles succeeded within 30 days. After he strangled the lion to death, he used (on the advice of the goddess Athena) the lion's claws to remove its skin. Herakles then fashioned a cape for himself out of the lion's skin.
2) Killing the Lernaean Hydra
The Hydra was the offspring of Echidna and Typhon, the ancestors of all monsters. Typhon was an immortal giant, and Echidna was a half-woman, half-snake monster. The Hydra had anywhere between 6 to 100 heads at a time.
Herakles defeated this creature with his nephew Iolaus's help. After Herakles chopped off each head, Iolaus would cauterize it with a torch. When Hera realized that Herakles was succeeding, she was furious. She sent a giant crab to stop the hero, but Herakles crushed the crab under his foot. In the end, Herakles used Athena's golden sword to chop off the Hydra's last head, which was immortal. King Eurystheus claimed that Herakles failed this mission because he needed Iolaus's and Athena's help. This is part of the reason the king asked for two extra labors (in addition to the original ten).
3) Capturing the Ceryneian Hind
The Hind was the goddess Artemis's sacred deer. It had golden antlers and bronze hooves. The Hind could outrun any flying arrow. In the end, Herakles was able to capture the creature by targeting his arrow between its legs. When the deer tripped, Herakles grabbed it and trussed it up. Seeing that Herakles had succeeded, the king attempted to add the Ceryneian Hind to his collection of exotic animals.
However, Herakles devised a plan so that the Hind could return to Artemis. A split second before King Eurystheus grabbed the rope that held the deer, Herakles let the animal go. When the king protested, Herakles proclaimed that the royal was just not fast enough to capture the creature.
4) Capturing the Erymanthian Boar
When Herakles set off for this mission, he made a detour to visit Pholos, one of his centaur friends. The two began drinking, and the smell of the wine attracted all the other centaurs. The centaurs came and began to imbibe of the wine; eventually, they became drunk and violent. Herakles was forced to shoot poisonous arrows at them. The centaurs fled to Chiron, also one of Herakles' friends.
It was Chiron who told Herakles how to capture the boar. Herakles first lured the animal into deep snow. The snow considerably slowed down the animal's movements, and this eventually allowed the hero to capture it.
5) Cleaning the stables of Augeas in one day
Herakles completed this task by first making large holes in the walls of the cattle-yard. Then, he dug two deep trenches to two rivers, thus redirecting the waters to the cattle-yard. Once the waters reached the yard, it washed through the stables. Augeas, however, refused to pay Herakles a tenth of his cattle, which had been promised as a reward. Our hero then took Augeas to court to receive his payment. Because of this reward, King Eurystheus claimed that this mission did not count toward the required labors.
6) Killing the Stymphalian Birds
These birds were created by Ares, the god of war. Their dung was poisonous, and they had sharp feathers, which could be weaponized. Athena gave Herakles a special rattle made by the god Hephaestus. Our hero used the rattle to scare the birds out of their nests. When the birds tried to escape, Herakles shot most of them with arrows that were dipped in the Hydra's poisonous blood.
7) Capturing the Cretan Bull
This bull was said to be the progenitor of the Minotaur. Herakles made short work of this quest by wrestling the bull and then choking it to death. King Eurystheus wanted to sacrifice the bull to his benefactor goddess, Hera. However, Hera, who hated Herakles (because he was the illegitimate son of her husband, Zeus), wanted no part of the sacrifice. The bull was then released. It eventually made its way to Marathon and became known as the Marathonian Bull.
8) Stealing the mares of Diomedes
These horses needed human flesh to keep them calm. They were extremely dangerous creatures. To fully gain control of them, Herakles first cornered the horses on a peninsula. Then, he dug a trench around the peninsula and filled it with water, turning the peninsula into an island. Next, Herakles killed Diomedes. Then, he fed the flesh of the dead man to the cornered horses. After eating, the horses became tame enough for Herakles to lead them back to King Eurystheus.
9) Stealing the girdle of Hippolyta, Queen of the Amazons
The girdle represented Hippolyta's authority over the Amazonians; it was a symbol of her power. After hearing Herakles' story about his labors of atonement, Hippolyta reluctantly decided to give the hero her belt. However, Hera was angered that Herakles had obtained the girdle so easily. The goddess then disguised herself as an Amazonian warrior. Then, she warned the rest of the Amazonians that Herakles and his men meant to kidnap Hippolyta.
The Amazonians lost no time in attacking Herakles's ships. Some stories say that Herakles killed Hippolyta during the attack, thinking that she had betrayed him. He escaped with her girdle after the short battle.
10) Stealing the monster Geryon's cattle
Geryon was a three-headed monster. He had a two-headed dog named Orthrus which was the brother of Cerberus (guardian of the Underworld). Herakles reportedly stole Geryon's cattle by first killing Orthrus with a club. Our hero also killed Eurytion, Geryon's servant, who tried to stop him from taking the cattle. When Geryon heard about the killings, he tried to use his three shields, spears, and helmets to destroy Herakles. However, Herakles felled Geryon with an arrow that had been dipped in the Hydra's poisonous blood.
11) Stealing the apples of the Hesperides
These golden apples bequeathed immortality to all who consumed them. The tree that bore the apples belonged to Hera, and she jealously guarded the fruits with the help of the hundred-headed dragon named Ladon. Herakles was said to have subdued Ladon by giving him an intoxicating herb. Another version of the story has Atlas (who held the heavens on his shoulders) retrieve the apples for Herakles while the latter (with the help of Athena) supported the heavens in his absence.
12) Capturing Cerberus
Cerberus was a fearsome hellhound. The hound, however, met his match in Herakles. Herakles's thick lion cape was so strong that Cerberus' claws and teeth could not penetrate it. Eventually, Herakles wrestled Cerberus into submission and brought him back to King Eurystheus. Shocked that Herakles had succeeded, the king made Herakles take Cerberus back: he was simply too frightened of the dog to let it stay.
After Cerberus was returned, Hades cornered King Eurystheus and demanded to know why he wanted the hellhound. Fearing for his life, the king admitted that he was acting under Hera's orders. Hades then had an audience with Hera, promising her that if she ever made life difficult for Herakles again, she would have to contend with him (Hades).
https://www.ancient.eu/hercules/

https://www.greekmythology.com/Myths/The_Myths/Labours_of_Heracles/labours_of_heracles.html

Herakles (better known by his Roman name, Hercules) is a hero in ancient Greek mythology. He was the son of the god Zeus and Alcmene, a mortal woman.
Zeus was a legendary adulterer. He had many affairs with mortals, which angered his jealous wife, the goddess Hera. When Hera found out about Herakles, she tried to kill him by placing snakes in his crib—but even as an infant, he was so powerful that he overcame them.
As an adult, Herakles asked Apollo how he could make amends for murdering his own wife and children (crimes he had committed after Hera threw him into a fit of insanity—she never did stop trying to take revenge on Zeus by interfering with his child’s life). Apollo’s reply (via the Oracle at Delphi) was that Herakles had to serve King Eurystheus for twelve years. During this time, the King (who was sympathetic to Hera) assigned him twelve tasks that seemed insurmountable—but in every case, through his own virtues (and with some help from other deities), Herakles was able to complete the job.
Many of these myths are immortalized to this day in the night sky. Most of our constellations are named after Greek characters, including Herakles and several of the beings he encountered in these Labors.
1. Kill the Nemian Lion
First Herakles was told to take care of this beast, which was terrorizing the land of Nemia. Its hide could not be pierced by any weapons, so Herakles strangled it with his own brute strength. He then took its hide to wear as his own armor.
The constellation Leo is named after the Nemian Lion.
2. Kill the Lernean Hydra
Hera created this monster specifically to defeat Herakles. It had nine heads, one of which was immortal. The others, if severed, would be replaced by two more. To make matters worse, the Hydra’s blood was poisonous, as was the mist in the swamp where it lived. Herakles needed help from his nephew Iolaus to defeat this creature, as well as a magical sword (from Athena) to kill the immortal head. Afterward, he dipped his arrows in its blood.
This battle is depicted in the constellations Hydra, as well as Cancer (because Hera sent a giant crab to fight alongside the Hydra).
3. Capture the Hind of Ceryneia
A hind is a kind of deer. This one belonged to Artemis, the goddess of hunting, so Herakles knew better than to kill or injure it. After chasing it for a year, though, he became desperate and had to shoot it. Luckily it didn’t die, and though Artemis was angry, she forgave him when he explained that he only acting under orders from the Oracle.
4. Capture the Erymanthean Boar
This animal was also sacred to Artemis. Capturing the boar was actually quite easy for Herakles (he drove it into a thick patch of snow and ensnared it in his net). The drama in this story really comes from Herakles’s visit to his friend Pholos, a centaur, on his way to capture the boar. The other centaurs resented the two drinking all the wine, there was a fight, and Herakles’s poison arrows killed many of them (including Pholos, who dropped one on his foot).
The centaur Chiron, who was the wisest and kindest of them all, is now the constellation Sagittarius.
5. Clean the Augean Stables
Herakles was given only one day to clean out the vast cattle stables of King Augeas. Instead of grabbing a shovel, he re-directed two rivers into the yards. The rushing water quickly flushed all the dirt and filth from the stables. As a bonus, Herakles tricked Augeas into giving him one tenth of the herd as a reward.
6. Kill the Stymphalian Birds
These enormous birds, vicious creatures with metal wings and beaks, belonged to Ares, the god of war. They ate humans and had been terrorizing the area around Lake Stymphalia. Herakles was unable to get through the swamps where they roosted, so the goddess Athena gave him a set of krotala (loud rattles) to flush them out, and he was able to shoot them with his poison arrows.
7. Capture the Cretan Bull
This creature was rampaging throughout the island of Crete, ruled by King Minos (another son of Zeus). The bull itself had been a gift to Minos from the sea-god Poseidon, and had been intended as a sacrifice. Minos loved the bull and refused to sacrifice it, so Poseidon caused it to become a destructive monster. Herakles captured it and sent it back to King Eurystheus, who was so terrified that he hid himself away.
The constellation Taurus has several connections to King Minos and the bull mythology surrounding him, particularly the famous Minotaur.
8. Steal the Horses of Diomedes
Herakles brought some companions to help him capture the flesh-eating horses of King Diomedes. They were able to steal the herd, but Diomedes and his troops chased after them. The horses ate Herakles’s friend Abderus while Herakles was engaged in battle (the city of Abderos is named after him), and some versions of the myth have Herakles feeding Diomedes to his own horses as an act of revenge. After eating, the horses became tame, and he was able to send them back to Eurystheus.
9. Steal the Belt of Hippolyte
Hippolyte was the Queen of the Amazons. Her belt was a gift from her father, Ares, the god of war. Eurystheus’s daughter wanted it for herself. Herakles brought friends on this mission, too, but at first it seemed like they wouldn’t be necessary—at first, Hippolyte agreed to just give him the belt. However, Hera interfered, inciting the other Amazons to attack Herakles’s band. Herakles, thinking that Hippolyte had betrayed him, killed her and claimed the belt.
10. Steal Geryon’s Cattle
Geryon was a monster who lived on the island Erythia “at the end of the world,” and Herakles had several adventures on his way to his realm, including earning admiration and assistance from the sun itself. Upon reaching Erythia, Herakles had to defeat Geryon’s guard dog (Cerberus’s brother Orthrus) as well as Geryon. The real task was driving the cattle all the way back to Eurystheus and keeping track of all of them in spite of Hera’s interference.
11. Steal the Apples of the Hesperides
The apples belonged to Zeus himself and were a gift from Hera, kept in a garden guarded by the dragon Ladon and the nymphs known as the Hesperides. Herakles had to find the garden, defeat several opponents along the journey, and figure out how to steal the apples. Prometheus advised him to ask Atlas to do it for him—this was the Titan (gods who predated the Greek Olympians) who held the world on his shoulders, and he welcomed a break. In fact, after retrieving the apples, Atlas refused to take up his burden again, and Herakles had to trick him into resuming his position.
12. Capture Cerberus
This was the three-headed dog who guarded the gates to the Underworld, Hades’s domain. (Certainly Eurystheus thought that this final task would be Herakles’s undoing.) Herakles needed to learn how to travel to the land of the dead and back without dying himself and petitioned the gods Athena, Hermes, and Hestia for help as well. Herakles was finally able to wrestle Cerberus into submission, and Hades allowed him to take the beast back to the surface if he would promise that it wouldn’t be hurt. This was the last straw for Eurystheus. Cowering in fear, he released Herakles from his service. Cerberus was returned to Hades, and Herakles was free.
http://www.perseus.tufts.edu/Herakles/bio.html

http://www.perseus.tufts.edu/Herakles/labors.html

How does the balcony scene in Romeo and Juliet exemplify the poetics of love?

Although there are many ways we can examine how Romeo and Juliet's love is exemplified through their poetry in the balcony scene, the interpretation is always also your own, as with so much of Shakespeare's work.
This scene, however, is special because Shakespeare has given us a challenge. He has placed the characters far from each other. Juliet is high on a balcony, while Romeo is on the ground speaking up to her.
Though each character does use the word "love" directly several times, there are many other elements we can identify that show that this is not just an everyday kind of love.
In the balcony scene, they are speaking in blank verse. They don't use rhymes, which we usually hear when lovers speak to each other. We might interpret Shakespeare's use of blank verse here as suggesting that the pair are speaking direct and true. No nonsense.

JULIET: "And all my fortunes at thy foot I'll lay
And follow thee my lord throughout the world."

These words seem to represent blank verse very well. What she is saying is very clear and to the point, and also perhaps foreshadows what is to come.
We can also look at the imagery in this scene.

JULIET: "This bud of love, by summer's ripening breath
May prove a beauteous flower when next we meet."

It is best to ask yourself how you feel when you hear the words summer, flower, and breath. Does it seem to signify something sinister and dark or something sweet and innocent?
Lastly, a poetic tool Shakpesare uses often is "O." "O," or more specifically the poetic device called apostrophe, signifies great emotion. For example, when Romeo says,

"O, speak again, bright angel!"

we know he is experiencing something overwhelming.

What are two things that cause us to doubt ourselves, according to Emerson?

Two things that cause us to doubt ourselves are not being true to the inner voice of our souls and failing in our first endeavor.
Emerson contends that we doubt the divine spark that God has placed within us if we constantly look to the past or the future for inspiration. He advises young men to throw away their books and live in the present moment. He points to plants, saying they are not looking to the past but being true to themselves as they grow and blossom. He writes the following:

Thus all concentrates: let us not rove; let us sit at home with the cause. Let us stun and astonish the intruding rabble of men and books and institutions.

Likewise, while we need to care for our family and friends, we cannot allow them or their ideas of what we ought to do shake us from our true path: 

Say to them, O father, O mother, O wife, O brother, O friend, I have lived with you after appearances hitherto. Henceforward I am the truth’s.

Emerson also writes that,

If our young men miscarry in their first enterprises, they lose all heart.

Instead, he says, we should brush off failure, hop up, and try again. The world is a big place and full of opportunities. If we have not found our destined path on the first try, there are a hundred more paths to explore. The key is to keep trying and to have faith that we will eventually succeed.

What is the role and responsibility of the executive branch?

The executive branch of the federal government is tasked with carrying out laws and enforcing them as defined by Article II of the US Constitution. Once a law is passed by Congress, the executive branch must oversee that the law is implemented and followed. This branch of the government is headed by the President. The President appoints the heads of the various cabinets and other federal agencies so that they may offer advice and implement laws.
The President, as head of the executive branch, also has certain checks over the other branches. The President can veto a bill passed by Congress and can also appoint federal judges. Congress can then refuse to confirm appointments and override a veto.
The military is under the command of the executive branch. The President is the commander in chief of the military, and the President can appoint military commanders.
This branch also has the power to negotiate foreign treaties, although they must be approved by the Senate.
The various government agencies that are part of this branch vary greatly. They include everything from the Department of Interior and the Federal Bureau of Investigations to the Environmental Protection Agency and the national parks. Embassies and diplomatic missions also fall under the umbrella of the executive branch.
The president has the power to grant pardons and commute the sentence of anyone convicted of a federal crime.
https://www.whitehouse.gov/about-the-white-house/the-executive-branch/

What does Mr. Pearson mean when he suggests to Squeaky it would "be a nice gesture if you were . . . to ahhh . . ."?

Previously, in the same paragraph as the given quotation, Mr. Pearson asks Squeaky if she is "going to give someone else a break this year." Squeaky wonders "if he is seriously thinking [she] should lose the race on purpose just to give someone else a break." Mr. Pearson then suggests that there are only "six girls running this year" because Squeaky doesn't give anyone else a chance to win.
In this context, when Mr. Pearson asks (or begins to ask), "Wouldn't it be a nice gesture if you were to . . . ahhh . . ." the implication is that he thinks it would be nice if she gave somebody else the chance to win the race this year. He would see such a gesture as an act of kindness. He might also be thinking of next year's race and the possibly of an even lower turnout if Squeaky wins yet again. Squeaky's reaction to this suggestion is such that Mr. Pearson doesn't even bother finishing the sentence.
Later in the story, Squeaky hears Pearson (or "old Beanstalk," as she calls him) "arguing with the man on the loudspeaker . . . about what the stopwatches say." Perhaps, in this moment, Mr. Pearson is trying to argue that someone else won the race, attempting to achieve himself what he could not persuade Squeaky to do.
Another possible reason that Mr. Pearson doesn't want Squeaky to win the race might be that he just doesn't like her. She does, after all, "call him Jack and the Beanstalk to get him mad"—or at least used to. And she does seem to talk to him in a somewhat disrespectful manner, telling him abruptly to write down her full name on his board; she gives him "such a look" of derision when he suggests that she give someone else a chance to win and storms away from him before he can finish his sentence.

Before Squeaky is about run the fifty-yard dash, Mr. Pearson approaches Squeaky to pin her number on her shirt. As Mr. Pearson checks Squeaky's name off the list and hands her the number to pin on her shirt, he casually asks Squeaky if she is going to let someone else win the race this year. Mr. Pearson proceeds to inform Squeaky that only six girls are running in the race this year and mentions that the new girl, Gretchen, should give her a run for her money. Mr. Pearson then begins to look around for Gretchen and says, "Wouldn’t it be a nice gesture if you were . . . to ahhh . . ." (Bambara, 4). Judging from Mr. Pearson's previous comment regarding the fact that Squeaky should allow someone else to win the race this year, one can infer that Mr. Pearson was going to suggest that Squeaky should allow Gretchen to win the race. Since Gretchen is the new girl and Squeaky has already won races in the past years, Mr. Pearson thinks that allowing Gretchen to win the fifty-yard dash would be a nice gesture on Squeaky's part.

What does the phrase "teach the torches to burn bright" suggest in Romeo and Juliet?

Romeo has fallen head over heels in love with Juliet. And when people fall in love, they're apt to use hyperbole in describing the object of their affection. That's what Romeo's doing here. Words can't adequately describe how beautiful Juliet is, but Romeo's going to have a good old shot at it anyway. According to him, Juliet is so beautiful, so wonderfully radiant, that she outshines any torch, no matter how bright. High praise, indeed!
Romeo's language may seem a little over the top, but his use of the light metaphor to describe Juliet's beauty is useful in giving us a perspective, not just on the strength of Romeo's feelings, but also on life in Verona. Juliet's "light" has penetrated through the "darkness" of daily life in a city disfigured by the long, bloody feud between the Montagues and the Capulets. The light of Juliet's beauty is a rare ray of sunshine amidst the enveloping darkness of a city plagued by violence and hatred.

Juliet is so beautiful that even torches are not as bright as she.
This quote is from this line when Romeo first sees Juliet, before he knows who she is.

O, she doth teach the torches to burn bright! (Act 1, Scene 5)

Basically, with this line Romeo is saying that Juliet is so beautiful that her beauty is brighter than a torch.  She is so bright, that the torches learn to be bright from her.  It is another metaphor on Juliet's beauty.
Romeo is infatuated by Juliet’s beauty and, blinded by her beauty, has not really stopped to consider anything else.  Romeo goes on and on with many beautiful lines about Juliet’s looks, but never once does he mention her personality.  He compares her to the sun, and a jewel, and says in this line that the torches get their light from her.  However, he is not talking about her glowing personality.  He is again talking about her looks.

Beauty too rich for use, for earth too dear!So shows a snowy dove trooping with crows,As yonder lady o'er her fellows shows. (Act 1, Scene 5)

Romeo proposes soon after.  Romeo has only just met Juliet, and he didn’t even have a real conversation with her.  They share a cute conversation that was all in metaphors.  What is she like?  Does she like roses?  Is she allergic to strawberries?  What does she do on weekends?  He has no idea!  He has spent no time with this girl.  He just took one look at her and fell head over heels in love with her.
 

In Coming of Age in Mississippi, what was the most significant single event in Anne's early life that shaped her to become an activist in the movement. In other words, what was the major turning point in Anne's youth?

The most important formative event in Anne's early life was the murder of a 14-year-old African American boy from Chicago named Emmett Till. He was murdered in Mississippi while visiting relatives, and Anne heard fellow students speaking about it right before she entered high school. She then realized that she had spent so much time with her head in a schoolbook that she had not been aware of what was happening around her.
When Anne left her house later that same day to work for a white woman named Mrs. Burke, her mother told her not to mention Emmett Till, which made Anne wonder why her mother was so frightened. When Anne was at work, Mrs. Burke told her that Emmett Till was killed because he was from the North and did not know his place in Mississippi. From these experiences, Anne learned about racial injustice and the fear that white people tried to instill in African Americans. Anne writes, "Before Emmett Till’s murder, I had known the fear of hunger, hell, and the Devil. But now there was a new fear known to me—the fear of being killed just because I was black." This event shaped her identity and her activism in later years. 

Did the Greasers or Socs ever cross territories without asking?

Most readers probably assume that this must true. Rival gang members are not likely to ask permission every single time they might cross the street from the west side to the east side of town or vice versa. This question is also made a bit more difficult because Hinton doesn't give readers an exhaustive list of what locations are in each gang's territory.
The trick is going to be finding interactions between Greasers and Socs where the reader knows that one gang is in the other gang's territory without permission. Chapter 7 is a good location for this kind of instance. Ponyboy and Two-Bit are walking to the hospital to see Johnny, and a blue Mustang follows them. There are some Socs in the car including Randy. Everybody eventually stops, and Ponyboy and Randy have a conversation. It's likely that Ponyboy is in Greaser territory since he left his own home to get to the hospital. This means that the Mustang with the Socs is in Greaser territory without permission since Ponyboy wasn't expecting the visit.
Chapter 11 is another good location for evidence for this question. Ponyboy is at home recovering from his concussion, and Randy comes to visit him. Ponyboy isn't expecting the visit, and Darry doesn't seem to know that Randy was planning on coming; therefore, I think the reader can assume that Randy is in Greaser territory unannounced and without express permission.

Summarize the following primary source to offer historical understanding of what Kollontai believed and hoped to gain. https://www.marxists.org/archive/kollonta/1909/social-basis.htm

Alexandra Kollontai was a revolutionary socialist and a feminist. In this excerpt, she explains the theoretical links between these two strands of her life. One part of her argument is summed up in the following line:

Specific economic factors were behind the subordination of women; natural qualities have been a secondary factor in this process. . . . In other words, women can become truly free and equal only in a world organized along new social and productive lines.

This is an early statement of what would become Marxist feminism. Kollontai (and scholars much later) saw the plight of the working class and the subjugation of women as inextricably connected. She argues in the pamphlet that the efforts of what she calls "bourgeois" suffragettes were incomplete. Participation in politics alone would not bring about equality. Much of the first half of the pamphlet is devoted to tracing the connections between the oppression of women and the working classes with the emergence of capitalism. While she says that gains made in the struggle for political rights are laudable, she points out that the interests of bourgeois women are antithetical to those of working-class women.
Kollontai goes on to argue that the legal structures that undergird the bourgeois family are a source of oppression for women and again argues, without fully explaining, that the roots of this oppression can be found in the "inanimate and mighty forces of production." Struggles to reform these institutions will not liberate working-class women. She does not argue that reforming women's legal, political, and personal lives is completely futile, she argues that these reforms will not fully emancipate working-class women. She hoped that women would gain full equality through the destruction of the capitalist order, which formed the superstructure upon which sexist institutions were built.
https://www.marxists.org/archive/kollonta/1909/social-basis.htm

Great Expectations is a story of the triumph of good over evil, one in which the fantastic dominates over realism. Justify your agreement or disagreement with this observation.

I would agree both that good triumphs over evil in this novel and that the fantastic—I might call it the unlikely—dominates over the real.
Two fantastic events from Pip's childhood come to dominate Pip's adult life. The first fantastic occurrence is Pip helping the escaped convict Magwitch, who is hiding in the fens. This is an unlikely and melodramatic event. Even more fantastic is that a convict would remember Pip and spend his life working and living rough to set Pip up as a gentlemen living the high life. This is one very good-hearted man!
Miss Havisham at Satis Hall is another fantastic character, a fairytale-like figure of a witchlike woman isolated in her "castle" and trapped in the past. The other significant event in Pip's childhood is Miss Havisham inviting him to her home. If Magwitch is good and remembers the past to do good, Miss Havisham is badly damaged by having been been left at the altar and remembers the past in order to do harm.
Both these fantastic characters have a significant impact on Pip's adult life, but the mutual impact is to soften his heart and turn him from a person who bases his life on snobbery to one who can begin to discern true goodness in people.

Precalculus, Chapter 9, 9.5, Section 9.5, Problem 40

We have to expand the expression using the binomial theorem , so use the formula,
(a+b)^n=sum_(k=0)^n((n),(k))a^(n-k)b^k
(4x-1)^3=((3),(0))(4x)^(3-0)(-1)^0+((3),(1))(4x)^(3-1)(-1)^1+((3),(2))(4x)^(3-2)(-1)^2+((3),(3))(4x)^(3-3)(-1)^3
=(4x)^3+(3!)/(1!(3-1)!)(4x)^2(-1)+(3!)/(2!(3-2)!)(4x)^1(1)+(-1)
=64x^3+(3*2!)/(2!)(-16)x^2+(3*2!)/(2!)(4x)-1
=64x^3-48x^2+12x-1
(4x-1)^4=((4),(0))(4x)^(4-0)(-1)^0+((4),(1))(4x)^(4-1)(-1)^1+((4),(2))(4x)^(4-2)(-1)^2+((4),(3))(4x)^(4-3)(-1)^3+((4),(4))(4x)^(4-4)(-1)^4
=(4x)^4+(4!)/(1!(4-1)!)(4x)^3(-1)+(4!)/(2!(4-2)!)(4x)^2(1)+(4!)/(3!(4-3)!)(4x)^1(-1)+(-1)^4
=256x^4+(4*3!)/(1!3!)64x^3(-1)+(4*3*2!)/(2!2!)16x^2+(4*3!)/(3!)(4x)(-1)+1
=256x^4-256x^3+96x^2-16x+1
:.(4x-1)^3-2(4x-1)^4=(64x^3-48x^2+12x-1)-2(256x^4-256x^3+96x^2-16x+1)
=64x^3-48x^2+12x-1-512x^4+512x^3-192x^2+32x-2
=-512x^4+64x^3+512x^3-48x^2-192x^2+12x+32x-1-2
=-512x^4+576x^3-240x^2+44x-3

Discuss the advantages and disadvantages of being an office incumbent in Washington, D.C. Which incumbent is more likely to win an election—a congressional or a presidential incumbent? Why?

As a matter of historical statistics, in the second half of the twentieth century and the beginning of the twenty-first century, incumbents have enjoyed re-election rates of over 80 percent when running to retain the seats they occupy in Congress. Presidents running for second terms also display a significant incumbency advantage. Members of Congress enjoy a slightly larger advantage, but this is within the margin of error caused by a small sample size for presidents.
There are several reasons for this incumbency advantage. The first is that incumbents have the advantage of free publicity and extensive free media coverage. Rather than having to fight bruising primary battles, they can focus on the election itself and are not as likely to be compelled to pander to an ultra-partisan base in primaries in a way that might have an adverse effect on their chances in a general election; although in our current era of hyper-partisanship, this may be changing.
There are a few circumstances in which incumbency can be a disadvantage. While people tend to support incumbents when they feel safe and prosperous, in times of economic downturns or social insecurity, voters can react by voting against the status quo, often for populist or other "outsider" candidates. Midterm elections during an unpopular presidency can also go against incumbents.
http://cstl-cla.semo.edu/rdrenka/ps103/Spring2010/congressional_incumbency.htm

How is gender constructed in Bollywood movies and Indian cinema?

Gender construction in Bollywood films and Indian cinema is as complex an issue as gender-based identity is in India today.
We need to define some terms before delving into the issue of gender construction. "Bollywood movies" reflect the lucrative film industry for which India is known. These films are distributed out of Mumbai. Hindi is their primary language. "Indian cinema" reflects the regional filmmaking industry that represents a significant portion of Indian filmgoers and filmmakers. For example, "Indian cinema" reflects Tamil-, Telegu-, and Malayalam-speaking populations. It is more regional, localized in specific Indian states. For example, most Tamil films are distributed out of Chennai, the state capital of Tamil Nadu in the Southern part of India. These distinctions are important to understand what is being discussed when we talk about the Indian film industry.
As with most media, gender construction is related to commercial profit. For example, both Bollywood and Indian cinema utilize "item songs." These are songs where a woman performs for an audience of men. The item song represents a particular construction of feminine identity. The woman featured is dressed in a provocative way, dances for men, and does not speak outside of the lyrics she sings. She has no depth to her presentation. Women in these songs are seen as objects for men. They are designed to elicit a specific response both in the film's scene and in the audience. Item songs are employed because of their commercial marketability. They are a way to generate "buzz" and publicity for a specific film. In other words, commerce dictates one way in which women are presented in Bollywood films and Indian cinema.
Commercial expectations further affect gender construction in Bollywood films and Indian cinema. Films aimed at mass appeal are designed to generate profit and feature a more conventional and/ or objectified depiction of women. This is based on commercial expectations. A significant number of areas India tend to view women in a "traditional" way. In these areas, a more conventional depiction of women on the screen will generate greater sums of money. In many instances, the filmmakers and producers are not inclined to put forth a message that preaches universal empowerment for women if it cuts into a film's profits. These individuals are more likely to present women in a particular way through particular roles in order to maintain the film's commercial viability.
At the same time, there are examples of films that view themselves as "art" over a vehicle for commercial production. For example, filmmakers like Deepa Mehta are willing to depict a relationship between two women in Earth or a film about the mobilization of widows in Varanasi in Water. These are examples of films that might not experience a wide distribution because they are not intended to profit substantially. Profit is not these films' primary motivation. They are intended to make a statement about social conditions in India. The people who would watch either of these films are fundamentally different than a more traditional Indian film audience member. These audiences are more likely to embrace a challenging of existing social attitudes about gender identity. These audiences will be found in metropolitan centers like Bangalore, Hyderabad, or Calcutta. They are less likely to exist in the small villages that comprise so much of India. Commercial viability plays an important role in gender construction in both Indian cinema and Bollywood films. There is also a growing subsection of artistic films in India that want to challenge how gender identity is perceived, though.
Part of the reason for this divergence is because India is in the midst of questioning its understanding of gender identity. Indian society is wrestling with issues like domestic violence and sexual assault. For a very long time, these issues were seen as "private issues." They were realities that women had to confront silently, away from public view. Through social media and emerging markets, however, globalization has brought different cultural attitudes. As India has become a very active participant on the world stage, new attitudes have entered into the Indian social mindset. This has prompted previously held mores and values regarding gender identity to be challenged. There is an emergence of organizations and collective attitudes which argue that violence against women must be a public issue. It must be legislated in the public arena and should no longer be relegated into silence. It is for this reason that when Bollywood actor Salman Khan compares a difficult film shoot schedule to a "woman being raped," he provoked intense reactions from different parts of society. It is also why Amitabh Bachchan, quite possibly Bollywood's biggest star, makes news when he takes the role of a lawyer defending girls who have been sexually assaulted in the upcoming film, Pink. Gender depiction is a complex reality in Indian films because it is a complex issue in Indian society.
https://www.hindustantimes.com/bollywood/salman-khan-s-rape-comment-how-bollywood-reacted/story-bVR0Y2GNnxdBo686T0wiWM.html

https://www.indexoncensorship.org/2013/01/bollywood-india-gender-women-new-delhi-salman-khan/

"The Fish," "Woodchucks," and "A Blessing" all portray human interaction with nature. Discuss the poem "A Blessing," sharing both your emotional reaction to it and incorporating at least one literary feature such as setting, simile, personification, point of view, tone, onomatopoeia, etc.

"The Blessing" by James Wright is a tender, haunting, and beautiful poem about his interaction with a couple of ponies. It is almost a religious-like encounter, as he and the ponies react with wonder, kindness, and closeness, despite being two different species. And though they are unable to vocally communicate with one another, there is a sense of communication going on. Wright indicates communication when he writes "they have come gladly out of the willows to welcome my friend and me" and "they can hardly contain their happiness that we have come" and "they bow shyly as wet swans." The ponies are in awe of the humans, just as Wright and his friend are in awe of them. In fact, one of the ponies walked over and "nuzzled my left hand." Wright ends on a note of pure delight with the encounter, saying, "Suddenly I realize / that if I stepped out of my body I would break / Into blossom." He is touched and moved by the experience.
There are a few similes (the comparison of two things with a "like" or "as") in the poem, such as "they bow shyly as wet swans" and "the light breeze moves me to caress her long ear / that is delicate as the skin over a girl's wrist"
The point of view is a first person, as indicated with the use of "I", "me," and "we."
A couple other striking instances of figurative language include "And the eyes of those two Indian ponies / darken with kindness" and "That if I stepped out of my body I would break / Into blossom."
Considering the tender but ultimately delightful tone of the poem, the setting—a sunset—is interesting. Sunsets can sometimes be symbolic of an "ending," while sunrises can be symbolic of "new beginnings." But the way he describes the sunset—"Twilight bounds softly forth on the grass"—reinforces the sweet, tender tone.
https://www.poetryfoundation.org/poems/46481/a-blessing

What are the similarities between Flight to Canada and Josiah Henson's narrative on slavery?

Josiah Henson was an escaped slave who wrote The Life of Josiah Henson, Formerly a Slave, Now an Inhabitant of Canada, as Narrated by Himself (1849). Harriet Beecher Stowe is said to have based Uncle Tom in Uncle Tom's Cabin on Henson. One of the points that Henson makes is that slavery corrupts the masters. The slave owners' racism makes them oblivious to any value of the slave save their monetary value and what labor they can offer. Henson writes of slavery, "The natural tendency of slavery is, to convert the master into a tyrant, and the slave into the cringing, treacherous, false, and thieving victim of tyranny." Slavery corrupts the master so that he can no longer see the humanity of his slaves. After working for many years as a devoted and reliable slave, Henson is only valued for his labor. His master attempts to sell him, and Henson writes about his slave owner's family, "My merits, whatever they were, instead of exciting sympathy, or any feeling of attachment to me, seemed only to enhance my money value to them." In other words, his years of hard work are only valued for the financial worth they provide. His owner's family does not value his worth as a human.
In Flight to Canada, Reed satirizes the self-interested and racist perspective of slave owners. For example, Uncle Robin, a parody of a devoted slave, says to Swille, his owner, about Canada, "Canada. I do admit I have heard about the place from time to time, Mr. Swille, but I loves it here so much that...I would never think of leaving here" (page 19). Uncle Robin illustrates the racist way in which slave owners saw slaves merely as objects and dehumanized them as mere property while relying intensely on slaves for their survival. 

Single Variable Calculus, Chapter 5, 5.5, Section 5.5, Problem 40

Find the definite integral $\displaystyle \int^{\frac{1}{2}}_{\frac{1}{6}} \csc \pi t \cot \pi t dt$

Let $u = \pi t$, then $du = \pi dt$, so $\displaystyle dt = \frac{du}{\pi}$. When $\displaystyle t = \frac{1}{6}, u = \frac{\pi}{6}$ and when $\displaystyle t = \frac{1}{2}, u = \frac{\pi}{2}$. Thus,


$
\begin{equation}
\begin{aligned}

\int^{\frac{1}{2}}_{\frac{1}{6}} \csc \pi t \cot \pi t dt =& \int^{\frac{1}{2}}_{\frac{1}{6}} \csc u \cot u \frac{du}{\pi}
\\
\\
\int^{\frac{1}{2}}_{\frac{1}{6}} \csc \pi t \cot \pi t dt =& \frac{1}{\pi} \int^{\frac{1}{2}}_{\frac{1}{6}} \csc u \cot u du
\\
\\
\int^{\frac{1}{2}}_{\frac{1}{6}} \csc \pi t \cot \pi t dt =& \left. \frac{1}{\pi} (- \csc u) \right|^{\frac{1}{2}}_{\frac{1}{6}}
\\
\\
\int^{\frac{1}{2}}_{\frac{1}{6}} \csc \pi t \cot \pi t dt =& \frac{\displaystyle - \csc \frac{\pi}{2}}{\pi} - \frac{\displaystyle \left( - \csc \frac{\pi}{6} \right)}{\pi}
\\
\\
\int^{\frac{1}{2}}_{\frac{1}{6}} \csc \pi t \cot \pi t dt =& \frac{1}{\pi}


\end{aligned}
\end{equation}
$

What does Isabel say Mrs. Lockton is set on doing to her?

I believe that the quote in question can be found at the end of chapter 41:

She was set on keeping my arms and legs dancing to her tune and my soul bound in her chains.

Just before this quote appears, Isabel is imagining a couple of scenarios. Each scenario has one end goal: Isabel wants to be free. At this point, Isabel is thinking of ways to legally accomplish her goal. She has heard of other slaves buying their own freedom from their masters, but Isabel has no way of earning money. She tells readers that some slaves have a day off on Sunday. Isabel wishes that she had that, because it would allow her to hire herself out for pay. She could do that enough times and earn money to buy back her freedom. Unfortunately, Isabel knows that dream isn't likely to happen at all. This is because Madam Lockton controls every single part of Isabel's waking moments.

What was one reason the European settlers came to America?

One of the major reasons that European settlers came to America was to get rich. One should also count the Caribbean settlers as American settlers since they were the first European settlers of the New World. Columbus came to America accidentally, on his way to India in search of spices. The early explorers of America hoped to find a Northwest Passage to reach valuable Asian markets. The Spanish hoped to find the Seven Cities of Gold but instead took Aztec gold back to Madrid. The English settlers of Jamestown hoped to find gold as well; it was not until later were they forced to grow tobacco. The settlers of the Caribbean islands became wealthy sugar planters—no one intended to live in the islands for a long period of time, as the idea was to get back to Europe in order to spend the money in "civilization." The French came to America and found valuable furs which fetched good prices in Europe. The New World's early value was in its wealth of natural resources and the promise of eventually getting to rich Eastern markets.

With Darwin's Descent of Man and Freud's The Structure of the Unconscious, how did these writers change the worldview of Europeans in the 19th century?

While Darwin's Origin of Species (1859), outlining his theory of evolution by natural selection, is his most famous work, Descent of Man (1871), a book that explores the consequences of his theory for humankind, also had a significant impact on the 19th century European's worldview.
In the text he explores the consequences of evolutionary theory for human beings. He argues that civilization has actually insulated humanity from the direct effects of natural selection. Things like altruism and medicine have allowed the weak to survive. In this respect he opens the door to ideas like eugenics and larger expressions of Social Darwinism. Social Darwinism saw various manifestations, from cowboy capitalism to socialist theories of human perfection.
Freud explored the mysteries of the dark corners of the mind, opening a new frontier of human understanding. One of his famous texts in this respect was written at the beginning of the 20th century: The Interpretation of Dreams (1899). He gave us new windows into the mind, arguing that much of how we act and behave is driven by unconscious desires and thoughts.

Even when tired, the family used to end the day with what?

The Robinsons are firm believers in God. And their seemingly miraculous deliverance from a potentially fatal shipwreck merely confirms them in their belief. Whatever happens on the island, however much adversity the Robinsons encounter, William always reminds his sons to say their prayers. The family that prays together, stays together, as they say, and the regular ritual of the evening prayer binds the Robinsons more closely together as a family. This is important, as the Robinsons are all alone on the island and really need to pull together if they're going to survive.
The Robinson family has a lot to be thankful for: they've survived a disastrous shipwreck in one piece; they've landed on a desert island abundant in plant and animal life; they've remained a close-knit, loving family despite all their numerous setbacks. The Robinsons are truly grateful to the Almighty for the many blessings He has so graciously bestowed upon them, and they express their undying gratitude in prayer each night before they go to bed.

What is the theme of the poem "Five Ways to Kill a Man" by Edwin Brock?

The wording of the question seems to assume that there is a single theme to this poem.  I don't believe that is the case.  I believe a reader could see several themes emerge from this poem.  I believe there are themes about war, violence, brutality, dehumanization, technology, time, and/or power.  
Of the above themes, I think the dehumanization of mankind theme is the strongest.  I like this theme choice because I feel that it encompasses some of the other themes with it.  
Each of the poem's first four stanzas focuses on a particularly violent event and/or time period.  The first stanza is about the crucifixion of Christ.  Stanza two is about medieval knights fighting and having their armor pierced.  Stanza three is about World War One's trench warfare, and stanza four is about World War Two's atomic bombs.  
The above scenarios are incredibly violent and even barbaric examples of the violence that humans have wreaked upon each other for hundreds of years; however, the author's tone is cold and blunt.  Sympathy, compassion, and aversion to violence are not conveyed by the poem.  The poem doesn't focus too much on human suffering.  The crowd of people watching Christ's death are not described as showing any emotion.  There is no compassion for the man being brutally executed.  The second stanza continues that cold distance.  It ends with a royal banquet that celebrates the destruction and death heaped upon a battlefield.  

But for this you need white horses,English trees, men with bows and arrows,at least two flags, a prince, and acastle to hold your banquet in.

Stanzas three and four almost completely remove humans from the violence.  Both of them are about how easy killing other men has gotten because of improved technology.  Stanza three says that all you have to do to kill is "blow gas at him."  Stanza four makes killing even easier by saying that only a small button needs to be pushed. 

In an age of aeroplanes, you may flymiles above your victim and dispose of him bypressing one small switch.

By the time the final stanza finishes, it's clear that mankind has continually found more and more efficient ways of killing other people.  Our technology hasn't made us kinder and better humans.  It has allowed us to kill from greater and greater distances, which has had the effect of us not seeing our enemy as a fellow human being.  They are dehumanized targets to be eliminated in an efficient manner.  The sarcasm present throughout the poem clearly indicates that the author thinks the increasing dehumanization of mankind is a bad thing. 

How does Vera set the scene for the perfect reveal?

At the beginning of the short story, Vera asks Mr. Nuttel several questions concerning whether he is familiar with her aunt or the area. After discovering that Framton Nuttel is an absolutely clueless hypochondriac, Vera begins to concoct a false story about her aunt's "tragedy."
Vera takes note of the large French window and is aware that her aunt's husband and two younger brothers left earlier that day to shoot their guns in the country. She proceeds to tell Framton a made-up tale about their tragic deaths, all while knowing that they will return from their trip any minute. Vera convinces Mr. Nuttel that the story is true by acting disturbed and feigning sympathy for her aunt. Vera also remembers to include an exact description of her uncles' attire in her story to set the scene for the perfect reveal. When Vera's uncles arrive, she stares out the open window with "dazed horror in her eyes." Framton then sees the three figures walking towards the window and bolts out of the home without saying goodbye.
Overall, Vera recollects the details of her uncles' appearances, takes note of the open window where they typically enter the home, and is aware that they will return while Mr. Nuttel is visiting. Vera then behaves like a concerned niece and tells Framton the false story regarding her uncles' tragic deaths. When they arrive, Vera acts horrified, which convinces Framton Nuttel that he is actually watching ghosts enter the residence.

College Algebra, Chapter 7, 7.2, Section 7.2, Problem 28

Suppose the matrices $A, B, C, D, E, F, G$ and $H$ are defined as



$
\begin{equation}
\begin{aligned}


A =& \left[ \begin{array}{cc}
2 & -5 \\
0 & 7
\end{array}
\right]

&& B = \left[ \begin{array}{ccc}
3 & \displaystyle \frac{1}{2} & 5 \\
1 & -1 & 3
\end{array} \right]

&&& C = \left[ \begin{array}{ccc}
2 & \displaystyle \frac{-5}{2} & 0 \\
0 & 2 & -3
\end{array} \right]

&&&& D = \left[ \begin{array}{cc}
7 & 3
\end{array} \right]
\\
\\
\\
\\
E =& \left[ \begin{array}{c}
1 \\
2 \\
0
\end{array}
\right]

&& F = \left[ \begin{array}{ccc}
1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 1
\end{array}
\right]

&&& G = \left[ \begin{array}{ccc}
5 & -3 & 10 \\
6 & 1 & 0 \\
-5 & 2 & 2
\end{array} \right]

&&&& H = \left[ \begin{array}{cc}
3 & 1 \\
2 & -1
\end{array} \right]


\end{aligned}
\end{equation}
$


Carry out the indicated algebraic operation, or explain why it cannot be performed.

a.) $BC$


$
\begin{equation}
\begin{aligned}

BC =& \left[ \begin{array}{ccc}
3 & \displaystyle \frac{1}{2} & 5 \\
1 & -1 & 3
\end{array} \right] \left[ \begin{array}{ccc}
2 & \displaystyle \frac{-5}{2} & 0 \\
0 & 2 & -3
\end{array} \right]

\end{aligned}
\end{equation}
$


$BC$ is undefined because the number of columns of the first matrix must equal the number of rows of the second matrix.

b.) $BF$

$\displaystyle BF = \left[ \begin{array}{ccc}
3 & \displaystyle \frac{1}{2} & 5 \\
1 & -1 & 3
\end{array} \right] \left[ \begin{array}{ccc}
1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 1
\end{array} \right]$


$
\begin{equation}
\begin{aligned}

& \text{Entry}
&& \text{Inner Product of}
&&& \text{Value}
&&&& \text{Matrix}
\\
\\
& C_{11}
&& \left[ \begin{array}{ccc}
3 & \displaystyle \frac{1}{2} & 5 \\
1 & -1 & 3
\end{array} \right] \left[ \begin{array}{ccc}
1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 1
\end{array} \right]

&&& 3 \cdot 1 + \frac{1}{2} \cdot 0 + 5 \cdot 0 = 3
&&&& \left[ \begin{array}{ccc}
3 & & \\
& &
\end{array} \right]
\\
\\
\\
\\
& C_{12}
&& \left[ \begin{array}{ccc}
3 & \displaystyle \frac{1}{2} & 5 \\
1 & -1 & 3
\end{array} \right] \left[ \begin{array}{ccc}
1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 1
\end{array} \right]

&&& 3 \cdot 0 + \frac{1}{2} \cdot 1 + 5 \cdot 0 = \frac{1}{2}
&&&& \left[ \begin{array}{ccc}
3 & \displaystyle \frac{1}{2} & \\
& &
\end{array} \right]

\\
\\
\\
\\
& C_{13}
&& \left[ \begin{array}{ccc}
3 & \displaystyle \frac{1}{2} & 5 \\
1 & -1 & 3
\end{array} \right] \left[ \begin{array}{ccc}
1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 1
\end{array} \right]

&&& 3 \cdot 0 + \frac{1}{2} \cdot 0 + 5 \cdot 1 = 5
&&&& \left[ \begin{array}{ccc}
3 & \displaystyle \frac{1}{2} & 5 \\
& &
\end{array} \right]
\\
\\
\\
\\
& C_{21}
&& \left[ \begin{array}{ccc}
3 & \displaystyle \frac{1}{2} & 5 \\
1 & -1 & 3
\end{array} \right] \left[ \begin{array}{ccc}
1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 1
\end{array} \right]
&&& 1 \cdot 1 + (-1) \cdot 0 + 3 \cdot 0 = 1
&&&& \left[ \begin{array}{ccc}
3 & \displaystyle \frac{1}{2} & 5 \\
1 & &
\end{array} \right]
\\
\\
\\
\\
& C_{22}
&& \left[ \begin{array}{ccc}
3 & \displaystyle \frac{1}{2} & 5 \\
1 & -1 & 3
\end{array} \right] \left[ \begin{array}{ccc}
1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 1
\end{array} \right]

&&& 1 \cdot 0 + (-1) \cdot 1 + 3 \cdot 0 = -1
&&&& \left[ \begin{array}{ccc}
3 & \displaystyle \frac{1}{2} & 5 \\
1 & -1 &
\end{array} \right]

\\
\\
\\
\\

& C_{23}
&& \left[ \begin{array}{ccc}
3 & \displaystyle \frac{1}{2} & 5 \\
1 & -1 & 3
\end{array} \right] \left[ \begin{array}{ccc}
1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 1
\end{array} \right]
&&& 1 \cdot 0 + (-1) \cdot 0 + 3 \cdot 1 = 3
&&&& \left[ \begin{array}{ccc}
3 & \displaystyle \frac{1}{2} & 5 \\
1 & -1 & 3
\end{array} \right]

\end{aligned}
\end{equation}
$


Thus, we have


$
\begin{equation}
\begin{aligned}

\left[ \begin{array}{ccc}
3 & \displaystyle \frac{1}{2} & 5 \\
1 & -1 & 3
\end{array} \right]

\left[ \begin{array}{ccc}
1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 1
\end{array} \right]

=

\left[ \begin{array}{ccc}
3 & \displaystyle \frac{1}{2} & 5 \\
1 & -1 & 3
\end{array} \right]


\end{aligned}
\end{equation}
$

Single Variable Calculus, Chapter 1, 1.3, Section 1.3, Problem 34

We need to find (a) $f \circ g$ , (b) $g \circ f $, (c) $f \circ f$ , and (d) $ g \circ g$ and state their domains

$f(x) = \sqrt{x} , \qquad g(x) = \sqrt[3]{1-x}$



$
\begin{equation}
\begin{aligned}

\text{(a)} \qquad \quad f \circ g &= f(g(x))\\

f(\sqrt[3]{1-x})&= \sqrt{x}
&& \text{ Substitute the given function $g(x)$ to the value of $x $ of the function $ f(x)$}\\
\displaystyle f(\sqrt[3]{1-x}) &= [(1-x)^{\frac{1}{3}}]^{\frac{1}{2}}
&& \text{ Simplify the equation}

\end{aligned}
\end{equation}
$



$\displaystyle \boxed{ f \circ g = (1-x)^{\frac{1}{6}} \text{ or } \sqrt[6]{1-x}} $


$\boxed{ \text{ The domain of this function is } (-\infty,1] }$



$
\begin{equation}
\begin{aligned}

\text{(b)} \qquad \quad g \circ f &= g(f(x)) \\

g(\sqrt{x}) &= \sqrt[3]{1-x}
&& \text{ Substitute the given function g(x ) to the value of x of the function f(x) }\\

\end{aligned}
\end{equation}
$


$\boxed{g \circ f = \sqrt[3]{1-\sqrt{x}}} $


$\boxed{\text{ The domain of this function is } [0,1]}$



$
\begin{equation}
\begin{aligned}
\text{(c)} \qquad \quad f \circ f &= f(f(x)) \\
f(\sqrt{x}) &= \sqrt{x}
&& \text{ Substitute the given function $g(x)$ to the value of $x$ of the function $f(x)$}\\

f(\sqrt{x}) &= [(x)^{\frac{1}{2}}]^{\frac{1}{2}}
&& \text{Simplify the equation}\\

\end{aligned}
\end{equation}
$


$\boxed{f \circ f = \sqrt[4]{x}} $


$\boxed{\text{ The domain of this function is } [0,\infty)} $



$
\begin{equation}
\begin{aligned}
\text{(d)} \qquad \quad g \circ g &= g(g(x)) \\
g(\sqrt[3]{1-x}) &= \sqrt[3]{1-x}
&& \text{ Substitute the given function $g(x)$ to the value of $x$ of the function $f(x)$ }

\end{aligned}
\end{equation}
$


$ \boxed{g \circ g=\sqrt[3]{1-\sqrt[3]{1-x}}} $


$\boxed{ \text{The domain of this function is } (-\infty, \infty)} $

How do the Kumalo family members symbolize the growing tension in South Africa?

The Kumalo family, like South Africa on the eve of apartheid, is deeply fractured. Much of the story revolves around Stephen Kumalo's repeated attempts to keep his family together at a time of great upheaval. The tensions within the family mirror those taking place in society as a whole.
Stephen represents a simpler time, a period of greater stability and certainty. His Zulu tribal heritage provides a network of care and mutual support. Sadly, that heritage is under threat of extinction. More and more young people from the village want to leave and seek new opportunities in Johannesburg. In breaking free from their ancestral homelands, they become atomized and rootless as they attempt to make new lives for themselves in the big city.
Stephen's son Absalom is one of them. His fate symbolizes the damage that city life poses to the traditional Zulu culture. Absalom falls in with the wrong crowd and participates in a botched robbery which ends in death. It does not just result in the death of Arthur Jarvis, it also results in his own death by execution. Every such death is a tragedy. This is the case not just for the individuals concerned, but also for the land that dies a little more each time a member of the tribe leaves it untended and open to exploitation.
The rampant corruption of the big city is also embodied in the figure of John, Stephen's brother. One does not just risk political corruption, one also risks the corruption of the soul, of one's very identity. John has become a politician, a powerful spokesman for the rights of oppressed black South Africans. Yet, in the process of developing a racial consciousness, John has lost sense of his tribal roots and the values they represent. His concern for justice is largely abstract; he has no sense of personal responsibility. He has left his wife to live with another woman, and he is prepared to pull strings to absolve his son Matthew from involvement in Absalom's botched robbery, even if it makes things worse for his nephew.
What is especially tragic here is that there is no obvious solution to the growing tensions within both the Kumalo family and in South Africa as a whole. It is not a simple matter of giving up city life and returning to the land. Gertrude Kumalo, Stephen's younger sister, for example, cannot do so. She is presented as a woman not just corrupted by the city, but also as morally eviscerated. By living such a dissolute lifestyle, she has broken the ancient moral code of the village. Zulu society is traditional, and women are expected to perform the roles of homemaker, mother, and wife. Having tasted the forbidden fruit of Johannesburg, it is impossible for Gertrude to return home, even if she was be accepted by the tribe.
There is undoubtedly a religious element to all this. Perhaps there is no earthly salvation for any of the Kumalo family or the rapidly changing South Africa they inhabit. In their own individual ways, John, Absalom, and Gertrude have tried to achieve salvation of sorts. However, all that their efforts have shown is the futility of doing so and the dangers of idolatry, particularly in relation to wealth, power, and status.
It is the meek, simple faith of Stephen Kumalo that tentatively suggests some resolution. This faith is one of quiet strength in the face of suffering and adversity. Stephen's prayer on the mountainside as his son is executed is also a prayer for South Africa. The country is on the verge of massive change that will intensify the already high levels of injustice, bloodshed, and racial intolerance. Stephen's prayer, however naive or forlorn it may be, allows us a brief glimpse of a still point in a rapidly turning world.

Select two quotes from the text to support your explanation of Siddhartha’s simile in the passage. Use one quote to explain the simile of the leaf and one quote to explain the simile of the stars. Explain what people are like a leaf and what people are like a star.

The first reference in Siddhartha to the similes likening people to either leaves or stars occurs in the chapter "Amongst the People," as Siddhartha is telling Kamala why he believes he and she are similar, in contrast to the majority of people:

"Most people, Kamala, are like a falling leaf that
drifts and turns in the air, flutters and falls to the
ground. But a few others are like stars which travel
one defined path: no wind reaches them, they have
within themselves their guide and path." [trans. Hilda Rosner, p. 58]

During his period of living a worldly life, Siddhartha lives largely among people of the first type—except for Kamala. In the same chapter, even before he has defined this separation within humanity to Kamala, Siddhartha makes an observation which describes those he likens to falling leaves:

He saw people living in a childish or animal-like way,
which he both loved and despised. He saw them toiling,
saw them suffer and grow gray about things that to him
did not seem worth the price—for money, small pleasures
and trivial honors. [p. 57]

These are the normal pursuits of everyday life for the overwhelming majority of people. Though Siddhartha has (as it turns out, temporarily) relinquished the lifestyle of a samana and become part of the "real" world, he has not adopted the material values of that world, which all seem part of a childish game to him. And in contrasting himself with the other people, he makes the following observation, which describes those who can be likened to stars that follow their own course:

Like a player who plays with his ball, he played with his
business, with the people around him, watched them,
derived amusement from them; but with his heart, with
his real nature, he was not there. His real self wandered
elsewhere, far away, wandered on and on invisibly and had
nothing to do with his life. [p. 58]

It is not until after he has left Kamala that Siddhartha finally accomplishes a joining of these two mindsets. Kamala has sold her estate and gone away with the son she has had by Siddhartha. After Kamala dies of snakebite, Siddhartha, now working as a ferryman with his friend Vasudeva, takes care of his son, but the boy is spoiled and resentful, disdainful of the simple life his father leads. He runs away, and Siddhartha never sees him again. But Siddhartha, for the first time apparently, has felt love for another person: his son now lost to him. Siddhartha realizes that as a Brahmin and an ascetic, he had only understood things partially, and that it is necessary for him to go into the world and essentially (though he does not express it this way) experience a kind of fusion between the personality of the leaf and that of the star in order to achieve happiness.

Single Variable Calculus, Chapter 2, 2.1, Section 2.1, Problem 9

Given the curve $\displaystyle y= \sin \left(\frac{10 \pi}{x}\right)$ and the point $A(1,0)$ that lies on the curve.

(a) If $B$ is the point $\displaystyle \left( x, \sin \left(\frac{10 \pi}{x}\right) \right)$, find the slope of the secant line $AB$ (correct to four decimal places) for $x=2,1.5,1.4,1.3,1.2,1.1,0.5,0.6,0.7,0.8$ and $0.9$. Do the slopes appear to be approaching a limit?

$
\begin{equation}
\begin{aligned}

\begin{array}{|c|c|c|c|c|c|}
\hline\\
x & B_1 (x) & B_2 \left(\sin \left(\frac{10 \pi}{x}\right)\right) & A_1 & A_2 & \text{slope} = \frac{B_2 - A_2}{B_1 - A_1} \\
\hline\\
2 & 2 & 0 & 1 & 0 & 0 \\
\hline\\
1.5 & 1.5 & \frac{\sqrt{3}}{2} & 1 & 0 & \sqrt{3} \\
\hline\\
1.4 & 1.4 & -0.4339 & 1 & 0 & -1.0848 \\
\hline\\
1.3 & 1.3 & -0.8230 & 1 & 0 & -2.7433 \\
\hline\\
1.2 & 1.2 & \frac{\sqrt{3}}{2} & 1 & 0 & 4.3301 \\
\hline\\
1.1 & 1.1 & -0.2817 & 1 & 0 & -2.817 \\
\hline\\
0.5 & 0.5 & 0 & 1 & 0 & 0 \\
\hline\\
0.6 & 0.6 & \frac{\sqrt{3}}{2} & 1 & 0 & -2.1651 \\
\hline\\
0.7 & 0.7 & 0.7818 & 1 & 0 & -2.606 \\
\hline\\
0.8 & 0.8 & 1 & 1 & 0 & -5 \\
\hline\\
0.9 & 0.9 & -0.3420 & 1 & 0 & 3.42\\
\hline
\end{array}

\end{aligned}
\end{equation}
$


Based from the values we obtain in the table, the slopes of the secant lines do not approach any limit since their values
are not close to each other. Also, some lines have positive slope while most of the lines have negative slope.



(b) Use a graph of the curve to explain why the slopes of the secant lines in part (a) are not close to the slope of the tangent line at $A$.








Based from the graph of the function, the slopes of the secant line are not close to the slope of the tangent line at $A$
it's because of the infinite number of cycles/oscillations; thus, unlike a more linear or hyperbolic relationship,
slopes of the secant lines of the chosen points do not approach the slope of the tangent line at $A$ because they lie
on the part of the graph that is already going to a new cycle/oscillation than the one $A$ is in.

(c) By choosing appropriate secant lines, estimate the slope of the tangent line at $A$







We let the secant line connects the point M(0.95,1) and A(1,0) as shown from the graph. Therefore, slope can be computed as..

$\displaystyle m = \frac{1-0}{0.95-1}$

$m = -20$

To what extent was the NHS a complete success in the years 1946-1979? (20 marks)

To understand the extent to which the NHS was a complete success, you need to understand some of the circumstances surrounding healthcare in England before it was implemented in July of 1948. Prior to then, healthcare was a luxury few could afford. Workers could see a general practitioner for free, but their families could not.  Hospitals had disparate admission policies and practices. Mentally ill and handicapped people were sent away to institutions with horrible conditions, often causing their health to become worse. Seniors who couldn't support themselves did very poorly, and many died in workhouses known as Public Assistance Institutions.
The NHS immediately resolved the problem of patient cost by ensuring the organization was financed almost entirely by taxes. Treatment standards quickly improved as better drugs were introduced and spread through the NHS. These were the years a polio vaccine was created, dialysis allowed people with liver failure to continue living, and chemotherapy began saving cancer patients. All of these new developments were excellent for patients, but they also drove up the cost of the NHS.
By the second decade of the NHS, doctor's low pay became a contentious issue. Negotiations between the government and general practitioners lead to the GP Charter, a new contract that helped provide financial incentives to practice medicine. This lead to better staffed hospitals and doctors joining together in what today is known as group practice.
An oil embargo in 1967 caused the NHS to financially struggle. But while its expansion stalled, meaningful developments continued from within the organization. Transplant surgery became more successful, intensive care units and non-steroidal anti-inflammatory drugs were made available. The NHS began to emphasize care for seniors, the mentally ill, and children. 
Finally, in 1974, the NHS was reorganized, changing many of the relationships between regional healthcare authorities. New authorities were created to intermediate between district authorities and hospitals. This allowed area health authorities to unite into a tripartite service , providing better service in conjunction with local providers. 
Stephen Hawking has said "I wouldn't be here today if it were not for the NHS, I have received a large amount of high-quality treatment without which I would not have survived." His sentiment reflects the extent to which the NHS has been successful through its early years. While the NHS has faced problems, it's a complete success relative to the challenges it's been tasked with solving.
http://www.nhshistory.net/shorthistory.htm

https://www.kingsfund.org.uk/projects/nhs-in-a-nutshell/how-nhs-funded

https://www.telegraph.co.uk/news/worldnews/northamerica/usa/6017878/Stephen-Hawking-I-would-not-be-alive-without-the-NHS.html

What is the rhyme scheme of the poem, "Power of Hope"?

The rhyme scheme of this poem by Leonard Rebello is, as the previous educator said, irregular. For the first half of the poem, he uses end rhyme in every other line, but does not repeat the same rhyming sound, so we see: A B C B D E F E. Then, the amount of rhyme in the poem intensifies somewhat, as we see a GHGH rhyme scheme appear, where the first line of this section rhymes with the third, and the second line rhymes with the fourth. This happens only once, and then the poet returns for four lines to the original poetic structure, where the second and fourth lines of the quatrain rhyme, while the first and third do not. Finally, the poet employs an entirely different kind of rhyme in his final quatrain—in reality, not rhyme at all, but pararhyme or assonance, where the vowel sound of a word is similar to that of the one with which it is paired. In this case, there is assonance on "heart" and "dark."

The second, fourth, and seventh lines make use of end rhyme (rhymes: see, me, company), and the sixth and eighth lines do as well (rhymes: dead, dread). Lines nine and eleven also rhyme (rhymes: soul, goal) as do lines ten and twelve (rhymes: hand, sand). Finally, lines fourteen and sixteen rhyme (rhymes: mind, find). Thus, the poem does not possess anything approaching a regular rhyme scheme.  However, if you need someone to express the end rhyme in the poem in a straightforward way, it would go something like this: abcbdefbfghghijklkmn. Each letter corresponds to a line in the poem, and if that letter has a match or even two in the string, this indicates that those lines possess rhyming words at their ends.

Beginning Algebra With Applications, Chapter 7, 7.4, Section 7.4, Problem 70

Simplify: $\displaystyle (3ab^{-2}) (2a^{-1}b)^{-3}$


$
\begin{equation}
\begin{aligned}

(3ab^{-2}) (2a^{-1}b)^{-3} =& (3ab^{-2}) \left( 2^{-3} a^{-1(-3)} b^{-3} \right)
&& \text{Use the rule for Simplifying Power of Products}
\\
\\
=& (3ab^{-2}) (2^{-3} a^3 b^{-3})
&& \text{Simplify}
\\
\\
=& 3a \left( \frac{1}{b^2} \right) \left( \frac{1}{2^3} \right) (a^3) \left( \frac{1}{b^3} \right)
&& \text{Write the expression with only positive exponents}
\\
\\
=& \frac{3a a^3}{2^3 b^2 b^3}
&& \text{Simplify}
\\
\\
=& \frac{3 a^{1+3}}{2^3 b^{2+3}}
&& \text{Multiply variables with same bases by adding their exponents}
\\
\\
=& \frac{3a^4}{8b^5}
&& \text{Simplify}

\end{aligned}
\end{equation}
$

What kind of love is Touchstone most interested in?

The short answer is the physical kind. Touchstone, the court jester, is a cynical old so-and-so who does not have much time for the courtly, romantic variety of love displayed so fervently by Rosalind and Orlando. Indeed, the much earthier, lust-driven attraction Touchstone feels for his dim country girl Audrey acts as a foil to the passionate love of the two leads.
Touchstone and Audrey are in so much of a hurry to get married that they perform an impromptu wedding ceremony under a tree. Ever the cynic, Touchstone instantly recognizes that since the "wedding" is informal, he may continue to engage in multiple affairs with impunity and one day leave his "wife." Cynicism aside, Touchstone is wise enough of a fool to understand that a relationship based purely on sexual lust cannot last for very long. A similar degree of insight is sadly unavailable to the hapless Audrey.
Contrast this with the long, drawn-out courtship of Rosalind and Orlando, which has all the hallmarks of a traditional romance. And yet even Rosalind eventually comes to tire of Orlando's devoted wooing, wanting something much deeper from their relationship. Touchstone, as we have come to expect, has a cynical contempt for the convoluted game being played out between the two young lovers:

The truest poetry is the most feigning.

To Touchstone, it all seems so terribly dishonest, this love business. Rosalind agrees to a certain extent, which is why she sets out to test Orlando's love. But unlike Touchstone she is not a full-blown cynic when it comes to romantic love; she still believes in its magical properties.
The contrast between the two kinds of love sets up a choice as to which is the more honest. On the one hand, we have the bawdy, unrestrained lust of Touchstone and Audrey. Yes, it is pretty tawdry and more than just a tad indecent, but at least there is a simplistic honesty and openness about it. Say what you like about Touchstone and Audrey but there is nothing remotely artificial about their particular brand of love.
Then there is Rosalind and Orlando. They woo each other so beautifully, reciting love poetry and carving their names on trees. It is all so decorous, so wonderfully romantic. But isn't there just something rather fake and old-fashioned about it? They may well be acting out a long-standing tradition, but since when has tradition had anything to do with the beauties of love, in all their majestic wonder? And where is the honesty when both lovers constantly need to put on emotional masks as part of their tiresome, drawn-out courtship ritual?
Touchstone's idea of love may not be to everyone's taste. But, all things considered, we can still at least appreciate that it has a certain rough-and-ready appeal.

Calculus of a Single Variable, Chapter 3, 3.3, Section 3.3, Problem 9

Given: g(x)=x^2-2x-8
Find the critical values by setting the derivative equal to zero and solving for the x value(s).
g'(x)=2x-2=0
2x=2
x=1
The critical value is x=1.
If g'(x)>0 the function will increase over an interval.
If g'(x)<0 the function will decrease over an interval.
Choose an x value less than 1.
g'(0)=-2 Since g'(0)<0 the function will decrease in the interval (-oo, 1).
Choose an x value greater than 2.
g'(2)=2 Since g'(2)>0 the function will increase in the interval (1, oo).
Because the function changed direction from decreasing to increasing a relative minimum will exist. The relative minimum will occur at the point (1, -9).

Describe the place Narnia.

C.S. Lewis's series, The Chronicles of Narnia, explores the lives of the Pevensie children as they discover a magical land that can be reached through the back of a wardrobe at Professor Digory Kirke's home. The land they discover is called Narnia, and it's full of people, animals, and flora they've never experienced in quite that way before.
Aslan, an anthropomorphic lion, leads the persecuted inhabitants of Narnia, and legend says he created the world in the first place. Geographically, Narnia is mostly forested, with some marsh in the north. The northern border is the River Shribble, the Eastern Ocean flanks the east, Archenland borders on the south, and a series of mountains line the western border. The Great River of Narnia flows through most of the country and creating a natural gathering place for communities along its banks.
Narnia is home to dwarfs, fauns, satyrs, tree people, a variety of animals, witches, giants, centaurs, and dozens of other mythological creatures call Narnia home. Humans are able to enter Narnia in various ways throughout the books including Professor Kirke's wardrobe, Susan's horn, Uncle Andrew's magic rings, Eustace's attic picture, and the Experiment House door.
Narnia has some quirks that separate it from the Earth-like world that it often resembles. The sky in Narnia is a dome, and in The Voyage of the Dawn Treader the place where the sea and sky meet is explored. Stars are alive and can move at will. The sun revolves around the world and some flora and fauna inhabit it. Time on Narnia moves more quickly than on Earth, but not at a constant rate. When the Pevensies return to Narnia in Prince Caspian: The Return to Narnia, 1,300 years have passed in Narnia while on Earth the children are barely older than they were when they left.

What are the major events that occur after the arrival of the trains at Birkenau and before the evacuation of Buna?

Their arrival at Birkenau marks the beginning of Elie's and his father's nightmarish experience at four different Nazi concentration camps. Birkenau acted as a "reception center" for the larger Auschwitz camp. The first major event at Birkenau was the selection. Directed by the infamous Dr. Mengele, Jews were pointed in two different directions, either to their immediate death in the gas chambers or to slow death as workers for the Third Reich. Luckily, just before the selection, Elie is told by another prisoner to lie about his and his father's age. Instead of saying 14, Elie tells the Nazis that he is 18 and that his father (actually 50) is 40. They are pointed to the left, and for a short time, they believe they are being sent to their deaths as they witness the bodies of dead children being tossed into fiery pits. Just short of the pits, they are turned toward a series of barracks. As he enters, Elie proclaims his loss of faith in God:

Never shall I forget those flames which consumed my faith forever. . . . Never shall I forget those moments which murdered my God and my soul and turned my dreams to dust.

Once they reach the barracks, the Jews are told to shed their clothes except for their shoes and their belts. Barbers shave the men, and they are given prison clothes, often of the wrong size. All the while they are being beaten with truncheons by the "Kapos," prisoners who have been chosen to keep discipline. During the night, they are marched a short distance to Auschwitz where signs read "Work is Liberty." They stay at Auschwitz for three weeks with very little to do. Elie and his father encounter a relative who is worried about his family. Elie lies to the man, telling him his family is safe.
At Buna, Elie and his father go to work sorting electrical parts. Elie has a conflict with another prisoner about his shoes, which he ultimately loses in an effort to protect his father from beatings. They live with a group of musicians, including the violinist Juliek who will later die on the forced march to Buchenwald. Another prisoner, Franek, notices Elie's gold crown and demands it. When Elie makes excuses, Franek brutalizes his father, and Elie is ultimately forced to give up the crown, extracted from his mouth with a rusty spoon in the lavatory. Similarly, when Elie accidentally discovers the Kapo Idek having sex with a young Polish girl, he is whipped.
Signs of the impending Nazi defeat are signaled when bombers appear overhead and several of the camp's buildings are destroyed. It is also at this time that a "black gallows" appears in the camp. When a young boy is hanged in front of the prisoners, a man asks, "Where is God now?" to which Elie silently answers, "Where is He? Here he is—He is hanging here on this gallows."
Elie again demonstrates his condemnation of God during the Jewish holidays Rosh Hashanah and Yom Kippur when he does not fast. Not long after, the prisoners are again subjected to the dreaded selection. Elie worries about his father, who has become quite weak during their ordeal. There is a poignant scene in which Elie's father gives his son his knife and spoon as a way of saying goodbye. Miraculously, however, Elie's father escapes the selection. He is in the barracks when Elie returns from work.
In his final days at Buna, Elie's foot becomes badly swollen, and he undergoes surgery. While in the hospital, Elie learns that Russian troops are advancing, and the entire camp will be evacuated. Elie and his father then face a difficult decision: either stay in the camp's infirmary or be evacuated with the rest of the prisoners. They decide to evacuate. Unfortunately, they choose poorly because the camp is ultimately liberated by the Russians. All those who stayed in the camp's hospital were freed. Elie and his father then begin the terrible forced march to Buchenwald.

In Hatchet, Brian felt like he was a new person. Where and how did this take place?

In the novel Hatchet, Brian’s epiphany comes as part of a long process of transformation that has several definite steps. The gradual change in his type of self-awareness from self-pity to pride begins after he admits that the pilot is dead, the plane is useless, and that he is truly alone. One important moment occurs when he glimpses his own reflection while drinking at the lake and chides himself for wasting time with crying (chapter 7). This brief episode of awareness shows Brian’s ability to objectify his situation, an important step in thinking rationally.
Two related steps on the path to transformation occur in regard to his ideas about friendship. Initially, he thinks woefully about being alone and the limited use that the small hatchet will be as a weapon to defend himself in the hostile wilderness. Remembering things he had done with his friend Terry reminds him that back home, he enjoys affection and support. After he throws his hatchet at the porcupine, the next day he recalls the sparks it caused, and he links that concept with his memory of Terry. Together, these metaphorically spark the realization that the hatchet is a tool, not just a weapon (chapters 8 and 9). He no longer feels alone because the hatchet is his “friend,” and he will be able to make fire, which will in turn contribute to his likely survival.
By Chapter 13, after he has considered and rejected suicide, his commitment to rejecting death signals his awareness of his own achievements in surviving. This realization is a turning point that comes as the culmination of his previous moment of recognizing his successes.

In Hatchet, Brian finds himself alone in the wilderness after a plane crash. He must learn to survive by finding food and shelter while hoping to be rescued. In chapter 13, Brian describes the change that makes him a new person. When he realizes that a rescue plane has come and gone, he experiences a despair so great that he wishes for death. He doesn't eat, he allows the fire to burn out, and he attempts to cut himself with his hatchet. However, when he doesn't die, Brian resolves to "not let death in again." Instead of hoping to be rescued, he becomes determined to survive on his own. He learns from his mistakes, has faith in his abilities, and is full of "tough hope." Brian is alone for fifty-four days before he is rescued.

Brian's "rebirth" takes place in the woods where he is stranded after his plane crashes. In chapter 13, we learn that it has been forty-two days since he was reborn as the new Brian. The change comes about after Brian learns how to survive in the wilderness on his own, without all the modern comforts of life.
The new Brian is made up of the sum of his experiences in the woods. In the wilderness, Brian learns how to hunt, fish, and collect wild foods for his meals. He also learns how to fashion a bow and arrows from willow branches, how to make fires, and how to make a sturdy shelter that can withstand the elements.
In short, Brian learns how to survive on his own, despite his fears and reservations about his future. Because of his experiences, Brian feels as if he is now a new person.

What are at least three uses of symbolism in "A&P" by John Updike?

As the girls in bathing suits walk away from their interaction with McMahon, the clerk at the A&P's meat counter, Sammy, observes "old McMahon patting his mouth and looking after them sizing up their joints." The author may be suggesting, for argument's sake, that the girls have offered themselves up to the male gaze, choosing to appear in a grocery store in bathing suits. The fact that McMahon sees them as pieces of meat is symbolic, but in a sly sense. The scene may be intended to raise the question of the girls' complicity in their own objectification.
Sammy's description of Queenie purchasing herring snacks and the mental picture it suggests to him of stylishly dressed upper middle class adults drinking martinis contrasts with his description of his own family's "lemonade and if it's a real racy affair Schlitz in tall glasses with 'They'll Do It Every Time' cartoons stenciled on." The snack symbolically suggests another way Queenie might be out of Sammy's league, so to speak.
As Lengel tries to counsel Sammy into not quitting his job, Sammy punches "the No Sale tab" on his cash register. He is symbolically not buying Lengel's counsel. He has taken a stand on principle and must follow his own moral compass.

How does Ji-li act differently than what she thinks?

Red Scarf Girl is about the experiences of Ji-li Jiang during the Cultural Revolution in China. At this time, Chairman Mao wanted the Chinese people to recommit themselves to Communist principles. As part of this effort, a representative from the Liberation Army comes to Ji-li's school and selects her to audition for the Central Liberation Arts Academy. However, in the end, she must refuse to audition. Her father tells her that it is best for her not to audition. She finds out later that her family used to function as landlords, which is counter to the Cultural Revolution.
Ji-li wants to audition and thinks that auditioning would bring her joy and attention; however, in the end, she does not do so. Ji-li instead hands her principal a note from her father in an action described in the following way:

"Hastily I handed her the note, damp with sweat from my palm. I hurried out of the office before she could look at it or ask any questions. I ran down the hallway, colliding with someone and running blindly on, thinking only that she must be very disappointed" (11).

Ji-li wants to be popular in her school and to please her principal, but she must tell her principal that she does not want to audition for the Central Liberation Arts Academy, because her father tells her she shouldn't. Only later does she understand why. Perhaps you can find other examples in the book of times when Ji-li acts in a way that is contrary to her thoughts and desires.

In The Bronze Bow by Elizabeth George Speare, who is the narrator?

The Bronze Bow centers on Daniel bar Jamin, a young Galilean boy growing up during the time Jesus was on the earth.
This story is told in third person, which means the narrator is an observer, and not necessarily a character in the story (see this breakdown of narrator types). However, the narrator here is an omniscient observer, since he/she knows Daniel’s inner thoughts and feelings (The Narrator). 
So in this case, the narrator is technically an unnamed observer. However, you could say that Daniel is the narrator in a sense, since the entire book is told from his perspective, and the reader has complete access to his emotions, thoughts, struggles, and beliefs—which would not be the case unless you were inside the person’s head, or unless he sat down and told you every thought he had.
But to be completely accurate, you would say that the narrator is an omniscient observer. 
This site goes into detail about seven different types of narrators in a story, and this one mentioned earlier breaks down first, second, and third person narrators.
http://bekindrewrite.com/2011/09/09/the-7-narrator-types-and-you-thought-there-were-only-two/

https://www.reed.edu/english/courses/AnalyzingLit/narrator.html

What would the genre of Fences be?

August Wilson's play Fences is a drama, or more specifically, a family drama. We know this work is a play because there are stage directions and characters speaking dialogue.
The play is about an African-American family and is set in 1957. The main character, Troy Maxson, has a very strong personality and is very demanding of his son, Cory. Troy's behavior is influenced by disappointments in his own life. We can see in the play how Troy takes out his own frustrations on his family. Troy's wife Rose stands by him but also becomes frustrated when she feels like their marriage and family are not satisfying to Troy. All of these details create tension between the characters and initiate the central conflicts of the drama. Later, we learn that Troy has had an affair and his mistress is pregnant. That daughter, Raynell, becomes part of the family, and Troy passes away by the end of the play. We are left to consider how the family will now interact without the influence of its patriarch.
The drama also engages with issues of racial discrimination via the limited opportunities Troy has in his life due to his being an African-American man. So in addition to being a family drama, the play has a sociopolitical context. It is also a work of realism because it portrays the all-too-real struggles of African Americans in the United States between abolition and the Civil Rights era.

What choices has Tom already made when "Contents of the Dead Man's Pocket" opens? Why does he choose to risk his life to retrieve the paper?

Tom Benecke has chosen to stay at home and work on his business proposal rather than to go to the movies with his wife. He knows Clare will be disappointed at having to go to the theater by herself, but this will give him an opportunity to have some privacy for three or four hours to concentrate on writing the final draft of his proposal. Although he lives on the eleventh floor of a Manhattan apartment building and his yellow worksheet containing all his accumulated information has blown out the window, Tom persuades himself it wouldn't be a very serious risk to climb out on the narrow ledge to go after it.

It occurred to him that if this ledge and wall were only a yard above ground — as he knelt at the window staring out, this thought was the final confirmation of his intention — he could move along the ledge indefinitely.

It is only because of the dizzying height that Tom would have any difficulty retrieving his paper. Otherwise, it is just a matter of walking a short distance along a ledge and walking back again. All Tom must do is avoid looking down, although in his situation there is a perverse temptation to do so. Looking down could cause him to have vertigo and fall over backwards into empty space. If the worksheet had simply flown off among the Manhattan skyscrapers, Tom could forget about it, but

he saw that the paper was caught firmly between a projection of the convoluted corner ornament and the ledge. 

How could Tom forget about the worksheet when he wouldn't be able to keep himself from looking out the window every couple minutes to make sure it was still there?

Of all the papers on his desk, why did it have to be this one in particular! On four long Saturday afternoons he had stood in supermarkets counting the people who passed certain displays... From stacks of trade publications... he had copied facts, quotations, and figures onto that sheet. And he had carried it with him to the Public Library on Fifth Avenue, where he'd spent a dozen lunch hours and early evenings adding more. All were needed to support and lend authority to his idea for a new grocery-store display method; without them his idea was a mere opinion. 

Time was of the essence. If Tom procrastinated until Clare came home from the movies, she wouldn't dream of letting him climb out the window onto that ledge. She would think he was utterly insane. It would be better not to tell her he had done such a crazy thing, even after he had actually done it. He wants to be working at the typewriter when she returns home so he can casually ask, "How was the movie?" If he didn't get that worksheet tonight, then tomorrow morning he would have to go to the office. When he returns from work in the early evening and looks out the window, the yellow sheet could be gone forever!
Tom does not believe his life is really in danger until he reaches the paper and must look down for a second to get a grip on it with the tips of his fingers.

He saw, in that instant, the Loew's theater sign, blocks ahead past Fiftieth Street; the miles of traffic signals, all green now; the lights of cars and street lamps; countless neon signs; and the moving black dots of people. And a violent instantaneous explosion of absolute terror roared through him. For a motionless instant he saw himself externally — bent practically double, balanced on this narrow ledge, nearly half his body projecting out above the street far below — and he began to tremble violently, panic flaring through his mind and muscles, and he felt the blood rush from the surface of his skin.

Tom didn't believe he was taking any risk when he got out on that narrow ledge and edged his way to where the paper was stuck. After looking down, though, he feels doomed to die. Tom even imagines his body being found on the sidewalk far below and the police looking through his pockets trying to find out who he was.

All they'd find in his pockets would be the yellow sheet. Contents of the dead man's pockets, he thought, one sheet of paper bearing penciled notations—incomprehensible.

What are parent functions and inverse graphs?

Parent functions are the most basic, or "simplest" form of a given function with no transformations placed upon them.
For example, y=4x^2+2x+5
is a quadratic function. The parent is: 
y=x^2
The inverse graph is the graph that results from switching the (x,y) coordinates of the function.  Inverse graphs are graphs the are reflections across the y= x line.

The graphs above are inverses of each other.

What was a primary outcome of the Dawes Severalty Act?

There were many outcomes of the Dawes Severalty Act, mostly negative—especially for Native Americans. The Dawes Act allowed the president of the United States (Grover Cleveland at the time) to divide the land previously designated as Native tribal territories. At the time, the five tribes recognized by the United States government were Chickasaw, Chocktaw, Muscogee, Seminole, and Cherokee. Allotting land to individuals instead of tribes was an effort to barter freedom for profit. The land allotments again disrupted the Native American way of life by prohibiting free movement throughout territories.
In effect, the primary outcomes of the Dawes Act were: abolishing communal property among tribes, limiting tribal interaction, and forcing Native Americans to assimilate into the American lifestyle that had spread across the continent. The Dawes Rolls, a registry of all residents of Indian territories and their tribal designation, are used today to determine tribal heritage.