Discuss Linda Hutcheon motto "hail to the edges" in Foe by J.M. Coetzee and The French Lieutenant's Woman.

Linda Hutcheon's "hail to the edges" motto highlights the pluralistic, ex-centric, composite nature of postmodernist fiction. Both Foe and The French Lieutenant's Woman are what Hutcheon calls historiographic metafiction.
Metafiction, of course, openly highlights the fictitious quality of its storyline. Historiographic metafiction then is an attempt at combining history with metafiction. As historiographic metafiction, both novels explore the margins of a centralized narrative. In doing so, the authors draw attention to the ex-centric, a position from where the prevailing racial, gender, or language framework can be analyzed and critiqued.
In Foe, Friday's tongue has been cut out. This means that he cannot tell his story, let alone the history of his people. His identity, ideology, and background is lost to the world because he cannot speak. Foe tells Barton that she should teach Friday how to write; Foe believes that this is the only way the world can hear Friday's voice. Meanwhile, Barton tries to communicate with Friday through sign and body language.
The experience is unsettling to Barton, however. In the final lines of the novel, Friday is given a sort of mythic, transcendent voice. In life, he was voiceless, but through Friday's surrealistic death throes, the narrator captures the marginalized, ex-centric proclamations of the disenfranchised man. Hutcheon's "hail to the edges" motto is encapsulated in this final scene with Friday, leading us to question historical records that are predicated on colonialist interpretations of the subaltern experience.
In The French Lieutenant's Woman, Fowles explores the ex-centric by drawing attention to gender and relationship issues. The narrator (in true metafiction fashion) provides us with two possible endings for the novel. There is a strong indication of Charles and Sarah reuniting in one but not in the other.
By "interfering" in the lives of his characters, the narrator questions Victorian values from the vantage point of his modern consciousness. He highlights the Victorian novelist's obsession with "clean," definitive endings, where the fate of all characters is decided by a capable narrator, and questions their relevance to the postmodern mind. In this, Fowles embodies the "hail to the edges" mindset (championed by Hutcheon) that embraces multiplicity and hybridity.
 
Sources:
1) Rethinking Borders, edited by John C. Welchman
2) A Poetics of Postmodernism: History, Theory, Fiction by Linda Hutcheon, Professor Department of English and of the Center for Comparative Literature
http://classprojects.kenyon.edu/engl/exeter/Kenyon%20Web%20Site/Richard/Fowles%20as%20Postmodernist.html

What is the significance of the Trojan War outside of the Homer Odyssey?

The Trojan War is in its tenth grueling year when The Iliad takes place, which is significant because it's a catalyst for the desperation and in-fighting amongst the soldiers. The Trojans are still fending off the Achaians, and the Achaians have yet to get Helen back (their "official" goal), or ravage Troy for its riches (their other, more lucrative goal). In short, everybody's feeling stuck and frustrated. The Trojans can't quit because Troy will fall. The Achaians can't quit because they've invested ten years of bloodshed. If they give up now, what was that all for?
The war also drags on because Achilleus enlists the help of his mom, Thetis, a god, and all of her god-friends. The Achaians have the Trojans on the ropes, for example, and then Thetis calls in a favor to Zeus. Ouch.
This war without end influences the characters' actions. They get frustrated; they take risks, and this sets off the chain of events that drives the poem's narrative. Achilleus gives up his girlfriend in a deal with Agamemnon and then gets so mad about it that he refuses to fight. Patroklos then goes into battle in Achilleus' place—even going so far as to wear Achilleus' armor—and gets killed by Hektor (with help from Apollo; there's those meddling gods again). When Achilleus hears what happened to Patrokolos, he kills Hektor.
Hektor's funeral wraps things up for The Iliad, but it's clear that Achilleus is going to die, too, and Troy will fall to the Achaians. By the end, the seemingly infinite nature of the Trojan War wears everyone down to dust.

In Macbeth, how is there a smooth transition from the real world to the world beyond?

Initially, Macbeth's political ambitions seem perfectly normal for someone of his time and class. Yes, there's something deeply treacherous and disturbing about his betrayal of Duncan; but there's nothing out of the ordinary about it. All that changes as the play progresses, however. Once Macbeth's safely established on the throne, his actions go beyond the pale, crossing over into outright evil. His cruel, bloodthirsty behavior towards Banquo and Macduff's family is utterly senseless. In ordering their brutal murders, Macbeth has made a disturbingly smooth transition from the natural to the supernatural world.
But then, this shouldn't really surprise us. For the Weird Sisters' prophecy pertains to both worlds, admitting of interpretations that are consistent with the natural and the supernatural. As Macbeth's tyranny becomes ever more bloody and unhinged, mere earthly ambitions give way, and he takes his stand unequivocally with the forces of darkness, making it easier for his enemies to express their opposition in terms of a struggle between good and evil, instead of as a bid for political power.

In A Long Walk to Water, what is Salva's role to the reader influentially and morally?

In the novel A Long Walk to Water, Salva plays a significant role to the reader in several different contexts. This novel is unique in the sense that it tells the stories of one fictional character and one real person. Salva is the main character, and his story is one of a young Sudanese boy who overcomes tragedy to save thousands of lives through his courage and charity.
Salva's Influential Role
As the main character, Salva's influential role in the story is made clear to the reader from the beginning. After he is separated from his family at the age of 11, Salva is forced to travel a long distance on foot in order to escape other gunmen. Without food or water, he struggles to survive in a harsh environment while helping others. Salva's influence becomes apparent when he takes on a leadership role among other lost boys of Sudan. He leads the group to safety at a refugee camp and is taken to America seven years later. While in America, Salva uses the influence he gained from telling his story and his act of heroism to start a charity called Water for South Sudan.
Salva's Moral Role
Salva is a strong moral character, and his story gives the reader insight into the complex moral issues that caused the conflict in Sudan. Even while struggling to survive in a country torn apart by the Second Sudanese Civil War, Salva demonstrates great moral courage. His voice as a character is strong and compelling, helping the reader understand each decision he makes throughout the story. By the conclusion of A Long Walk to Water, the reader understands the moral importance of investing in charities such as Water for South Sudan.
In addition to his role as an ambassador for the Sudanese water crisis, Salva also helps the reader understand the complex nature of the Sudanese civil war. Salva makes a strong moral argument against the violence that characterized much of his childhood in Sudan and separated him from his family. He also serves as a moral exemplar by caring for the other lost boys of Sudan despite his own fears and all he has suffered.
Salva's Role in Relation to Nya
Throughout A Long Walk to Water, Salva is a strong, influential, and moral character. His true story is engaging and told in a manner that makes it easy or the reader to relate to his emotions and motivations. Nya's fictional account is a poignant complement to his journey, as it carries the moral themes of Salva's story through to the present-day life of a young girl in a Sudanese village. Both stories combine to support Salva's message of compassion, bravery, and the importance of access to clean water as a basic human right.
https://www.lspark.com/books/longwalk/longwalk.html

https://www.waterforsouthsudan.org/

In The Giver by Lois Lowry, what are five rules of the community in which Jonas lives?

The Giver (Lowry) is a story about a community that is kept in order with many rules and few choices.  We learn about some of these in the first few chapters, even on the very first page.  Let's go over five of them.
First, this is a community in which it is against the rules for a pilot to fly an airplane overhead.  We learn, in fact, that a pilot who does so is released, and while we don't know exactly what that means, we are privy to Jonas' thoughts, that this is "...a terrible punishment, an overwhelming statement of failure" (Lowry 3).
Second, there is a rule in school that requires students to apologize publicly if they are late.  Jonas' friend Asher is late for school and he must stand up at his seat to tell his classmates he is sorry for "inconveniencing my learning community" (3).
Third, there are rules governing the justice dispensed in the community when people break the rules.  Jonas' mother, who works for the Department of Justice, must follow the sentencing rules. She must release those who have violated the rules a third time, whether she wants to or not. At this point, we still do not know what release is, but we do know the very idea of it makes Jonas shiver.
Fourth, there is a rule regarding the naming of infants. They must not be named until it has been determined that they are to be kept and placed in a household.  Before that point, they are given numbers.  For example, Lily had been "Newchild Twenty-three" (13).  Remarkably, Jonas' father breaks this rule for a child he is nurturing, by giving him the name Gabe.
Fifth, the children in the community are not, by rule, permitted to ride bicycles until they are nine years old. This rule, though, is frequently broken, since older siblings are always helping younger siblings learn to ride before they are Nines. 
There are many more rules the community must adhere to in this story. These are just a few that the people must obey, a means of keeping the community under control in every facet of their lives, from public safety to the naming of children.
 
 
 
 
 

College Algebra, Chapter 7, 7.1, Section 7.1, Problem 26

The system of linear equations

$
\left\{ \begin{array}{ccccc}
2x_1 & + x_2 & & = & 7 \\
2x_1 & - x_2 & + x_3 & = & 6 \\
3x_1 & - 2x_2 & + 4x_3 & = & 11
\end{array}
\right.
$
has a unique solution.

We use Gauss-Jordan Elimination

Augmented Matrix

$\left[ \begin{array}{cccc}
2 & 1 & 0 & 7 \\
2 & -1 & 1 & 6 \\
3 & -2 & 4 & 11
\end{array} \right]$

$\displaystyle \frac{1}{2} R_1$


$\left[ \begin{array}{cccc}
1 & \displaystyle \frac{1}{2} & 0 & \displaystyle \frac{7}{2} \\
2 & -1 & 1 & 6 \\
3 & -2 & 4 & 11
\end{array} \right]$

$R_3 - 3R_1 \to R_3$

$\left[ \begin{array}{cccc}
1 & \displaystyle \frac{1}{2} & 0 & \displaystyle \frac{7}{2} \\
2 & -1 & 1 & 6 \\
0 & \displaystyle \frac{-7}{2} & 4 & \displaystyle \frac{1}{2}
\end{array} \right]$

$R_2 - 2R_1 \to R_2$

$\left[ \begin{array}{cccc}
1 & \displaystyle \frac{1}{2} & 0 & \displaystyle \frac{7}{2} \\
0 & -2 & 1 & -1 \\
0 & \displaystyle \frac{-7}{2} & 4 & \displaystyle \frac{1}{2}
\end{array} \right]$

$\displaystyle R_3 - \frac{7}{4} R_2 \to R_3$

$\left[ \begin{array}{cccc}
1 & \displaystyle \frac{1}{2} & 0 & \displaystyle \frac{7}{2} \\
0 & -2 & 1 & -1 \\
0 & 0 & \displaystyle \frac{9}{4} & \displaystyle \frac{9}{4}
\end{array} \right]$

$\displaystyle \frac{4}{9} R_3$

$\left[ \begin{array}{cccc}
1 & \displaystyle \frac{1}{2} & 0 & \displaystyle \frac{7}{2} \\
0 & -2 & 1 & -1 \\
0 & 0 & 1 & 1
\end{array} \right]$

$\displaystyle \frac{-1}{2} R_2$

$\left[ \begin{array}{cccc}
1 & \displaystyle \frac{1}{2} & 0 & \displaystyle \frac{7}{2} \\
0 & 1 & \displaystyle \frac{-1}{2} & \displaystyle \frac{1}{2} \\
0 & 0 & 1 & 1
\end{array} \right]$

$\displaystyle R_1 - \frac{1}{2} R_2 \to R_1$

$\left[ \begin{array}{cccc}
1 & 0 & \displaystyle \frac{1}{4} & \displaystyle \frac{13}{4} \\
0 & 1 & \displaystyle \frac{-1}{2} & \displaystyle \frac{1}{2} \\
0 & 0 & 1 & 1
\end{array} \right]$

$\displaystyle R_1 - \frac{1}{4} R_3 \to R_1$

$\left[ \begin{array}{cccc}
1 & 0 & 0 & 3 \\
0 & 1 & \displaystyle \frac{-1}{2} & \displaystyle \frac{1}{2} \\
0 & 0 & 1 & 1
\end{array} \right]$

$\displaystyle R_2 + \frac{1}{2} R_3 \to R_2$

$\left[ \begin{array}{cccc}
1 & 0 & 0 & 3 \\
0 & 1 & 0 & 1 \\
0 & 0 & 1 & 1
\end{array} \right]$

We now have an equivalent matrix in reduced row-echelon form and the corresponding system of equations is


$
\left\{
\begin{equation}
\begin{aligned}

x_1 =& 3
\\
x_2 =& 1
\\
x_3 =& 1

\end{aligned}
\end{equation}
\right.
$


Hence we immediately arrive at the solution $(3,1,1)$.

College Algebra, Chapter 4, 4.1, Section 4.1, Problem 72

A rancher with $750$ ft of fencing wants to enclose a rectangular area and divide into four pens with fencing parallel to one side of the rectangle.







a.) Find a function that models the total area of the four pens.

b.) Find the largest possible area of the four pens.

a.) If the area of one pen is $A = xy$, then the total area of the four pens is $A_T = 4xy$. Since the $750$ ft of fencing material corresponds to the perimeter of the lot, then,


$
\begin{equation}
\begin{aligned}

P =& 8x + 5y
\\
\\
750 =& 8x + 5y

\end{aligned}
\end{equation}
$


Solving for $y$

$\displaystyle y = \frac{750 - 8x}{5}$

Thus,


$
\begin{equation}
\begin{aligned}

A_T =& 4xy = 4x \left( \frac{750 - 8x}{5} \right) = 600x - \frac{32}{5} x^2
\\
\\
A_T =& 600x - \frac{32}{5} x^2


\end{aligned}
\end{equation}
$


b.) The function $A_T$ is a quadratic function with $\displaystyle a = - \frac{32}{5}$ and $b = 600$. Thus, its maximum value occurs when

$\displaystyle x = \frac{-b}{2a} = \frac{-600}{\displaystyle 2 \left( \frac{-32}{5} \right)} = \frac{375}{8}$ ft

Therefore, $A_T$ is maximum at..


$
\begin{equation}
\begin{aligned}

A_T = 600x - \frac{32}{5} x^2 =& 600 \left( \frac{375}{8} \right) - \frac{32}{5} \left( \frac{375}{8} \right)^2
\\
\\
=& \frac{28125}{2} \text{ ft}^2

\end{aligned}
\end{equation}
$