In the book The Giver what are some of the structural guidelines in the book's society?

The society has many structural guidelines because it is an attempt to build a utopia - that is, a perfect society - by controlling all natural human tendencies.  The result is a soulless, totalitarian society. 
Three major areas that totalitarian/utopian governments usually attempt to control are sex, family, and individual liberty.  These three areas cause a lot of trouble in ordinary human society, so they are a natural target for anyone trying to build a utopia.  
In The Giver, the instinct for sex/romantic love is suppressed with the use of pills.  As soon as preteens or teens feel "the stirrings," as they are called (the beginning of interest in the opposite sex), they are to report them, and then they are given pills that suppress the stirrings. 
Families are chosen by the leaders.  Each family has a father, a mother, and children, but they are not biologically related to one another.  Children are borne by birth mothers (also specially selected for that role), then assigned to families.  "The Old" live not with their grown children (who would not really be theirs anyway), but in a special home for old people. 
The idea that suppressing natural family bonds will lead to harmony in society is a very old one.  Plato floated it in his Republic.  In The Giver, putting this idea into practice leads to dull, grey, loveless "families."  These families are not completely without affection, but the father and mother are not sexual partners, and the mothers did not actually give birth to the children they raise.  Even asking about "love" is viewed as using "imprecise language."  
Individual liberty is also basically nonexistent in the society of The Giver.  Children are assigned a vocation - a lifetime career - when they turn 12, based on the leaders' observations of their gifts.  They are assigned their family, their clothes, and so on.  At the beginning of Chapter 13, Jonas expresses to The Giver the reason for this:

"We don't dare let people make choices of their own."
"Not safe?" The Giver suggested.
"Definitely not safe," said Jonas with certainty.  What if they were allowed to choose their own mate?  And chose wrong? Or what if," he went on, almost laughing at the absurdity, they chose their own jobs?" 
"Frightening, isn't it?" The Giver said.
Jonas chuckled.  "Very frightening.  I can't even imagine it.  We really have to protect people from wrong choices."

In the end, even life and death are controlled in the society of The Giver.  Babies are euthanized if they don't gain weight fast enough (or are the smaller of a set of twins).  It turns out that the quest to make things perfect for people often leads to killing quite a few of them. 
 

Glencoe Algebra 2, Chapter 2, 2.3, Section 2.3, Problem 44

The line which we needed is perpendicular to a line whose slope is (-3/2) .
the product of the slopes of two lines which are perpendicular is equal to -1
let the slope of the line which we need to find be m_1 and the slope of the other line be m_2 = (-3/2).
so ,
m_1 * m_2 = -1
=> m_1 = -1/(m_2) = -1 /(-3/2) = 1/(3/2) = 2/3
so , m_1 = 2/3
and the line of slope m_1 passes through the point (-4,1)
then the line is
y = mx+c
=> y = (2/3)x +c
as it passes through (x,y)=(-4,1) so
=> 1= (2/3)(-4) +c
=> 1= -8/3 +c
=> 1+8/3 = c
=> c = 11/3
so the equation of the line is y= (2/3)x+ 11/3 and the graph plotted is as follows in the attachments. the point (-4,1) is spotted with a green dot.

Single Variable Calculus, Chapter 3, 3.3, Section 3.3, Problem 39

Differentiate $\displaystyle y = \sqrt[3]{t} (t^2 + t + t^{-1})$



$
\begin{equation}
\begin{aligned}

y' =& (t)^{\frac{1}{3}} (t^2 + t + t^{-1})
&& \text{Expand the equation}
\\
\\
y' =& t^{\frac{7}{3}} + t^{\frac{4}{3}} + t^{\frac{-2}{3}}
&& \text{}
\\
\\
y' =& \frac{d}{dt} (t^{\frac{7}{3}}) + \frac{d}{dt} (t^{\frac{4}{3}}) + \frac{d}{dt} (t^{\frac{-2}{3}})
&& \text{Apply Power Rule}
\\
\\
y' =& \frac{7}{3} t^{\frac{4}{3}} + \frac{4}{3} t^{\frac{1}{3}} - \frac{2}{3} t^{\frac{-5}{3}}
&& \text{Simplify the equation}
\\
\\
y' =& \frac{7}{3} t^{\frac{4}{3}} + \frac{4}{3} t^{\frac{1}{3}} - \frac{2}{3t^{\frac{5}{3}}}
&& \text{Get the LCD}
\\
\\
y' =& \frac{7 t^{\frac{9}{3}} + 4 t^{\frac{6}{3}} - 2}{3 t^{\frac{5}{3}}}
&& \text{Simplify the equation}
\\
\\
y' =& \frac{7t^3 + 4t^2-2}{3t^{\frac{5}{3}}}
&& \text{}
\\
\\


\end{aligned}
\end{equation}
$

What does Andrea think of the "tricks" that realtors use to convince a client to buy a house? What are some of the "tricks" she uses?

Andrea views the "tricks" that real estate agents use to help sell a house as good, valuable, and useful tactics.  She herself uses the tricks in order to make a house seem more appealing to prospective buyers.  
Andrea uses a variety of tricks to help buyers see a prospective property as "quite special."  The text tells readers that she will frequently light a fire in the fireplace.  Presumably this tactic will make the house feel more cozy and inviting.  She will put pretty flowers in a pitcher in the kitchen, or Andrea will use special aroma drops that vaporize from the heat of a lamp bulb to make the entire house smell clean and fresh.  Andrea has even gone so far as to bring her dog and dog bowl to a house that is being looked at by someone that is an animal lover. Her favorite trick item is a bowl that she places in a key area in each house.  She believes that the bowl brings her luck when she is selling a property because it is a perfect balance of "both subtle and noticeable."  

Calculus: Early Transcendentals, Chapter 4, 4.8, Section 4.8, Problem 21

x^3=tan^-1(x)
f(x)=x^3-tan^-1(x)=0
f'(x)=3x^2-(1/(x^2+1))
To solve using Newton's method apply the formula,
x_(n+1)=x_n-f(x_n)/(f'(x_n))
Plug in f(x) and f'(x) in the formula
x_(n+1)=x_n-((x_n)^3-tan^-1(x_n))/(3(x_n)^2-(1/((x_n)^2+1)))
See the attached graph for finding the initial values of x_1.
The curve of the function intersects the x axis at ~~ 0.9 and -0.9
Let's solve for the first zero x_1=0.9,
x_2=0.9-(0.9^3-tan^-1(0.9))/(3(0.9)^2-(1/(0.9^2+1)))
x_2~~0.90203199
x_3~~0.90202549
x_4~~0.90202549
Now let's solve for the second zero , x_1=-0.9
x_2=-0.9-((-0.9)^3-tan^-1(-0.9))/(3(-0.9)^2-(1/((-0.9)^2+1)))
x_2~~-0.9020443393
x_3~~-0.902025494
x_4~~-0.9020254924
x_5~~-0.9020254924
So the roots of the equation are 0.902025 and -0.902025

How would you paraphrase "The Slave's Dream" by Henry Wadsworth Longfellow?

Henry Wadsworth Longfellow’s poem “The Slave’s Dream” paints the picture of an exhausted slave resting on the ground of a rice field with his “sickle” in his hand, his work unfinished. His head has been in the same place so long, his hair is covered by the sand of the field, which is a symbol for death encroaching on him. As he lays near death, he dreams of his life in his homeland before he became enslaved. His life flashes before him one final time.
When the author describes the Niger River flowing through the land, the reader learns the dying man’s homeland is Africa. The line “Once more a king he strode” indicates he was a leader in his former life before he became a slave. In his subconscious state, he hears the sounds of the “tinkling caravans” as they travel through his homeland.
As the poem progresses, he sees a woman, his “queen,” with his children who adore him. They hold him in great esteem by holding his hand, kissing him, and clutching his neck. This brings the dying man to tears. Although he is dreaming, the tears escape his eyes and flow to the ground around his head.

 He saw once more his dark-eyed queen
 Among her children stand;

The dream continues with him riding his horse with purpose and exhilaration. He carries his warrior’s sword as he guides his horse with “golden chains as bridle-reins.” The beautiful sight of flamingos in flight fills his view as he rides across the land to the sea.

Before him, like a blood-red flag,
The bright flamingoes flew;

The auditory imagery of the next stanza indicates what he is hearing in his dream. He hears cries of the animals, and hears himself thrashing through reeds along the river. Longfellow describes the scene as one of freedom and triumph with the “glorious roll of drums.” This tone of the slave’s dream continues with his dreams of being free. He experiences the sights and sounds of the forests and desert of his homeland. His subconscious thoughts bring a smile to his face.

And the Blast of the Desert cried aloud,
With a voice so wild and free,
That he started in his sleep and smiled
At their tempestuous glee.

Finally, he dies and no longer feels the constraints of slavery. Although he died a broken man, his soul is finally free.

For Death had illumined the Land of Sleep,
And his lifeless body lay
A worn-out fetter, that the soul
Had broken and thrown away!

Beginning Algebra With Applications, Chapter 8, 8.1, Section 8.1, Problem 124

Factor by grouping

a. $3x^2 + 3xy - xy - y^2$


$
\begin{equation}
\begin{aligned}

3x^2 + 3xy - xy - y^2 =& (3x^2 + 3xy) - (xy + y^2)
&& \text{Group the first two terms and the last two terms}
\\
=& 3x(x+y) - y(x+y)
&& \text{Factor out the GCF from each group}
\\
=& (3x-y)(x+y)
&& \text{Write the expression as a product of factors}

\end{aligned}
\end{equation}
$


b. $3x^2 - xy + 3xy - y^2$


$
\begin{equation}
\begin{aligned}

3x^2 - xy + 3xy - y^2 =& (3x^2 - xy) + (3xy - y^2)
&& \text{Group the first two terms and the last two terms}
\\
=& x(3x-y) + y(3x-y)
&& \text{Factor out the GCF from each group}
\\
=& (x+y)(3x-y)
&& \text{Write the expression as a product of factors}

\end{aligned}
\end{equation}
$