Amir and Hassan have a favorite story. Does the story have the same meaning to both men? Why does Hassan name his son after one of the characters in the story?

Amir and Hassan share a love and fascination for the short story “Rostam and Sohrab,” but for different reasons. In the story, Rostam kills Sohrab in battle, not knowing that he is his son. Hassan cries after he hears Amir read the story to him, and Amir notes that he didn’t understand Hassan’s reaction. Amir wonders if all fathers have a desire to kill their sons. For Amir, this story is a lens though which he can try to understand his own dysfunctional relationship with his father, who secretly blames Amir for murdering his wife after she died giving birth to him. In contrast, Hassan reads the story about Rostam and Sohrab as a tragedy that he can’t fully appreciate, as his father, Ali, adores and protects Hassan as his most prized possession. Hassan likely names his son after Sohrab because he was a character from a story that had great significance in his childhood, but it is also a clue from the author of Hassan’s appreciation for and instinct toward sacrifice for one’s family members.

Amir and Hassan enjoyed readings from the Shahnamah, with special emphasis on the story about Rostam and Sohrab. In the story, Rostam killed Sohrab only to learn Sohrab was his son. The emotions evoked by the story brought tears to Hassan’s eyes, but Amir did not know who the tears were for, Rostam or Sohrab.
The story was interpreted differently by the two boys. Amir saw himself as Sohrab, the young warrior, and his father as Rostam. The story reflects his relationship with his father. Amir does not comprehend Rostam’s grief or fate.

Personally, I couldn't see the tragedy in Rostam's fate. After all, didn't all fathers in their secret hearts harbor a desire to kill their sons?

Hassan’s interpretation is not explicitly given, but his emotions suggest he understands the situation between the father and his son. He goes on to name his son Sohrab because he was his favorite character in the story.

In "A Rose for Emily," who was the author writing for, and to what purpose?

It is difficult to pinpoint a single audience or purpose for most literary works, and William Faulkner's "A Rose for Emily" is no exception. First, it may be useful to think about the narrative voice and themes of the story.
The narrator is a sort of communal "we" representing the townspeople who know (or know of, at least) the title figure, Miss Emily Grierson. The narrative voice reports, in a non-chronological order, the major events of Emily's life, as observed from the outside by the town. The story begins with Miss Emily's death and the opening of her home to mourners. Most of the townspeople have never been in the home before this, and they join in the procession mainly out of curiosity. We then hear some background on Emily's relationship with her father and with the town, in which her family was once important and powerful. Eventually, hints are dropped about Emily buying rat poison and a stench coming from her home. At the end of the story, the town discovers that Emily has apparently poisoned a former suitor and kept his body in a bed where she has seemingly slept with him for a number of years. All of the information is presented in an almost gossipy tone. The townspeople talk about Emily but not to her. Their knowledge of her life is based on speculation, rumor, and detached observation. The narrative voice could be addressing any kind of audience. The reader need only be interested in hearing about Emily's story (while also understanding that the story is an interpretation of the character and not necessarily a factual account).
Purpose is another tricky term that seems related to the slippery concept of authorial intent. Many authors do not have one intended purpose, meaning, or message when writing a complex literary text. However, we can discuss some of the themes that emerge from the story and can infer that some of the purposes may be to have the reader think about those themes. First, Emily and her family are considered a tradition in the town, and the outward respect citizens show her is mostly based on her family's previous influence and standing. Now, the house is decrepit and the family is dying out with Emily's demise. The world around the Griersons has evolved and modernized, but Emily tries desperately to hold on to the past. This is seen in several examples but in none more clearly than her symbolic attachment to Homer's dead body. Faulkner is, in large part, drawing our attention to humans' desire to hold on to what they have, particularly when what they have is power and money. Further, in context, Faulkner seems to suggest a larger message about the South trying to hold on to the prosperous society and economy they enjoyed in the antebellum period. More generally, the story could also suggest how little humans really know about one another's lives or psychologies. The story could also possibly be lamenting the human impetus to scapegoat or exile others who are mysterious or different. 

In Rules of the Game, Waverly's mother says the "strongest wind cannot be seen." What does she mean by this? How does this idea show up in the story?

Waverly says she learned the art of invisible strength from her mother. The invisible strength of the strongest wind means she does not always say what she is thinking and she acts as a hidden threat. This is one of the ways she is able to become so successful at chess. She watches and learns. No one really expects a little girl in ribbons to be a chess champion.
Waverly was good at chess because she was intelligent enough to learn from what others taught her. Her mother realizes the value of Waverly becoming good at chess and allows her to play with the men in the park. Waverly watches them.

I learned why it is essential in the endgame to have foresight, a mathematical understanding of all possible moves, and patience; all weaknesses and advantages become evident to a strong adversary and are obscured to a tiring opponent. I discovered that for the whole game one must gather invisible strengths and see the endgame before the game begins.

The wind becomes a metaphor for Waverly's inner voice. She listens to her instincts, the wind inside of her, and she becomes more and more successful. She uses these insights to secretly sneak up on her opponents.

"Blow from the South," it murmured. "The wind leaves no trail." I saw a clear path, the traps to avoid. The crowd rustled. "Shhh! Shhh!" said the corners of the room. The wind blew stronger. "Throw sand from the East to distract him." The knight came forward ready for the sacrifice.

The concept of the strongest wind does not just apply to chess. Waverly uses her wind to give herself a voice. In a way, she was following her mother's own advice when she told off her mother. She just did not quite follow it in the way her mother intended. Waverly was just a little too rude. She was independent, but forgot to be strong and silent.

Did the isolation of the Island of the Blue Dolphins affect its inhabitants?

The Island of the Blue Dolphins focuses on a group of people living on an isolated island off the coast of California. The story is based on the life of a real woman who lived alone on a California island until 1853. During this time period, it would have been more difficult to find and map this tiny island. This causes the characters in The Island of the Blue Dolphins to be cut off from modern advances and technology. For example, they refer to the Russians' ship as a "giant canoe" because they are unaware of the correct term for it.  
The island's inhabitants also rely on hunter-gatherer roles, in which men hunt and women take over more domestic duties. This means that when Karana is left alone on the island in the story, she has to take over the more "male-oriented" responsibilities.    

Single Variable Calculus, Chapter 1, 1.3, Section 1.3, Problem 66

If $g$ is an odd function, let $h = f \circ g$. Is $h$ always an odd function? What if $f$ is odd? What if $f$ is even?


$
\begin{equation}
\begin{aligned}

\text{Let } g(x) =& x^3\\
f_1(x) =& x^5\\
f_2(x) =& x^6\\
\\
h_1 =& f \circ g\\
h_1 =& (x^3)^5\\
h_1 =& x^{15}\\
\\
h_2 =& f \circ g\\
h_2 =& (x^3)^{16}\\
h_2 =& x^{18}

\end{aligned}
\end{equation}
$



It's unpredictable, we must know first the function $f$ ; if $f$ is odd, $h$ will be odd also. On the other hand, if $f$ is even, $h$ will be even as well.

What is the verse form of the poem "The Solitary Reaper" by Wordsworth?

William Wordsworth's poem "The Solitary Reaper" has a mixed rhyme scheme, with the first and last stanzas following an abcbddee pattern and the middle stanzas following an ababccdd pattern. More importantly, the poem is written in iambic tetrameter. Similar to iambic pentameter, iambic tetrameter is slightly more compact, as it uses only four feet per line, rather than five. A foot is a group of two syllables, one of which is stressed and one of which is not stressed. Each line in Wordsworth's "The Solitary Reaper" contains four of these groupings, thus ensuring that a constant, reliable rhythm runs throughout the verse and holds the whole composition together. 
Understanding poetic feet can be difficult at first, so here's a trick to start figuring it out: when looking at a line of poetry, count the number of groupings of two syllables. The ending number will be the total number of feet. Once you get the hang of this, it will be much easier to also identify stressed and unstressed syllables, and also whether something is written in iambic pentameter or not. Try it out with the lines in "The Solitary Reaper," and aim to identify four feet per line. 
https://www.poetryfoundation.org/poems/45554/the-solitary-reaper

In "The Devil's Highway" by Luis Urrea, how and why do you think Urrea describes illegal immigration as "a game"?

In any game, there are always two opposing sides; this is certainly the case in the area of illegal immigration.
In the book, Urrea discusses how the Border Patrol agents (La Migra) often find themselves at odds with the Coyotes (human smugglers) who facilitate the migration of illegals across the Mexican-United States border. Urrea characterizes the conflict between the Border Patrol agents and the Coyotes as a game.
While the Coyotes aim to guide their charges across the border unseen, the Border Patrol agents are paid to "see the invisible." In this daily game of cat-and-mouse, Urrea tells us that the Coyotes "score" when they successfully guide their clients across the border. On the other hand, the Border Patrol agents get to "score" when they manage to stop the Coyotes on any given day. In this dangerous "game," there is a formidable referee, and it is La Muerte (Death). Urrea describes Death as a "masked invader who regularly storms the field to disrupt the game."
With two opposing sides and a referee of sorts, illegal immigration is a game of wits at best and a vicious game of survival at worst. Both sides (as in any game) depend on trusted strategies to win the conflict. The Coyotes and their charges tape blocks of foam rubber to their shoes so as to leave no prints. They also utilize what they call the "brushout." This is when the last man in any group walks backwards and uses a branch to wipe away the footprints of those who've gone before him.
Meanwhile, the Border Patrol relies on in-ground sensors buried in places known only to agents. The agents "cut" the land (checking the sensors) in search of illegal immigrants who've lost their way; so, these agents are the "cutters" in search of "walkers" (the illegals). In their line of work, cutters know that illegal immigrants often cross the Mexican-United States border between the hours of 11pm and 3am. Thus, they scrutinize the tracks left by the migrants as they track them across the border.
Often, the agents rely on signs left by small animals that trample over the footprints just before dawn. The animals make what are known as "bug-signs." If the bug-signs cross over the footprints, Border Patrol agents know that migrants crossed nearer to midnight than to dawn. On the other hand, if the footprints appear to crush out the bug-signs, agents know that migrants may have recently crossed and are probably nearby. If so, with a new day beginning, these migrants will be in trouble once the blazing sun powers its merciless rays against their backs.
Most of time, by using the in-ground sensors, the agents are able to corral the walkers into a tight area, where they can then apprehend them. At other times, as with the Yuma 14 who perished in the desert, walkers can unwittingly wander way "off the map," where La Muerte eventually claims them for his own. So, from Urrea's point of view, illegal immigration often results in a perilous game of life and death.