In "Letter from Birmingham Jail" by Dr. King, how many paragraphs constitute the introduction, middle, and conclusion?

I think that the number of paragraphs is going to be a
relative concept.  With the transmission of speeches and writings to the web, strict
paragraphing entirely followed.  We can trace the structure of Dr. King’s letter in
specific terms, though.  The introduction to the letter consists of the opening address
to whom King refers in the assertion that King and his followers’ actions were “unwise
and untimely.”  In reference to other organizations, the introduction comes to a close. 
I would say that the middle begins with the idea that Dr. King is in “Birmingham because
injustice is here.”  This helps to launch him into an explanation of the cause and the
need to fight for social justice.  This “middle” goes on for quite a bit.  For my bet,
the conclusion of the letter begins with the simple sentence, “I must close now,” as Dr.
King concludes in demanding that all members of society- White and Black- fully heed the
call for social equity and to hear the cries of others’ sufferings in making Southern
society, and in turn all of America, recognize its promises and possibilities in
creating a system of equal treatment for all.

In "To Build a Fire" as a whole, how do the setting and theme reinforce each other?

The impressive and awesome setting of this incredible
story is of course inextricably intertwined with the theme of the tale, which points out
the frailty of humanity in the face of the might and power of nature. The anonymous
protagonist (which itself supports the theme of how insignificant man is when compared
with nature), in his attempts to reach the camp and his arrogance and belief that he can
make it in spite of the intense cold and the "intangible pall" and "subtle gloom" in the
otherwise "clear day," crucially ignores instinct and all the signs of nature that tell
him not to venture out, which is, ironically, what ensures the survival of the dog, a
creature of "instinct."

In particular, note what we are
told about the landscape, and in particular the cold, and the impact this has on the
man:

Fifty
degrees below zero meant eighty-odd degrees of frost. Such fact impressed him as being
cold and uncomfortable, and tha was all. It did not lead him to meditate upon his
frailty as a creature of temperature, and upon man's frailty in general, able only to
live within certain narrow limits of heat and cold, and from there on it did not lead
him to the conjectural field of immortality and man's place in the
universe.

This passage in a
sense reveals the theme of the story and how it is linked to the setting. Everything
about the intensely cold, barren landscape that the protagonist is about to enter
reinforces man's "frailty," yet this is something that the protagonist is blind to. It
is this blindness that ends up costing his life.

Summarize the basic idea of Emerson's "The American Scholar."

Emerson's fundamental thesis in his speech is the need for
the American academic institutions to have enough gumption and internal strength to
"discover" a new intellectual path.  Emerson seeks to develop the path in the academy to
embrace a new, "American" voice to scholarship.  For so long, Emerson had seen the
academy pattern itself solely after the European intellectual theatre.  In his speech,
Emerson makes clear the basic idea that American intellectualism does exist.  Emerson
identifies the development of Transcendentalist philosophy as a part of this process. 
In embracing this set of ideas, Emerson believes that American intellectualism can take
root apart from Europe, embracing the passion and uniqueness that is located in
American.  For Emerson, this becomes one of the most important elements in his speech. 
American intellectual thought has to branch off from its dependency on European thought
and formulate something that represents the character and distinction of
America.

When Paul is writing about Jewish law in Galatians, does he mean merely circumcision and kosher/dietary laws or the whole Jewish law?

In the book of Galatians in the New Testament, when Paul
is speaking to the people of Galatia about following the old laws, or the Jewish law, he
is speaking of the body of Jewish laws that govern even the smallest aspects of the
lives of the Jewish faith/culture, not just circumcision or eating kosher. The Jewish
law refers to 613 mitzvot, or commandments. These commandments are referred
to...

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...collectively as the "Law of Moses," "Mosaic
Law", or simply "the
Law".

These laws referred to
"instructions" that provide guidance in terms of the things they
should do, and laws against the things they should
not do. The laws are divided specifically in terms of the
"positive" laws—248: based on "the number of bones and significant organs in the human
body;" and, the "negative" laws—365: based upon "the number of days in a solar year." Of
the negative laws, there were three that Jewish law suggested "One should let himself be
killed rather than violate…" including worshipping idols, practicing "unclean" or
"abominable" sexual acts (as outlined in Leviticus), or
murder.

These laws governed the actions of the Jews
throughout the day and year: what one would do upon waking, the foods that were
acceptable to eat ("kosher"), how to dress, how to handle business transactions,
guidelines for choosing a mate, and the observance of Jewish holidays, to mention a
few.

This set
of rules and practices is known as
halakhah.

What is the literary element or device in James Baldwin's short story, "Going to Meet the Man"?

The literary element or device used in James Baldwin's
short story, "Going to Meet the Man" is
flashback.

Flashback is a literary device used to provide
information to the reader by returning to an earlier time. Flashback allows the author
to interrupt the story's flow to provide essential information for better understanding
of a character or a conflict.

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A method of narration in which present action is
temporarily interrupted so that the reader can witness past events--usually in the form
of a character's memories, dreams, narration, or even authorial
commentary...

The story
begins with Jesse, a bigoted, white, deputy sheriff who is trying to recount to his wife
an event of that day whereby he beat a civil rights leader badly. Jesse feels threatened
by the black society and hatred for the race. He feels that his world is out of control
as he watches the changes taking place in the society around him, in particular, the
struggle for blacks to earn the right to vote.

Whereas he
feels he is justified in his actions, a song—a black spiritual—returns Jesse to an event
in the past that has scarred him, perhaps for life. As a child, in an atmosphere of
"entertainment," he and his family "go on a picnic" to watch a black man (accused of
raping a white woman), publicly castrated, burned and mutilated. The boy sees this
moment through the eyes of his parents. His mother has a look of rapture on her face;
his father earns his love and respect because he had:

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...carried him through a mighty test, had
revealed to him a great secret which would be the key to his life
forever.

In this moment, the
child Jesse was believed he was experiencing the "greatest joy of his life." However,
the experience has left him angry and paranoid; his identity as a man is linked to the
murder of another man: steeped in hatred and brutality. It is the flashback that allows
us to see why Jesse is so impotent, not only sexually with his wife, Grace, but also in
terms of his ability to be a decent human being. The flashback brings information to the
forefront of Jesse's brain, allowing that perhaps seeing this memory from a different
place in his life, that he may well be salvageable—better able to understand the
suffering and pain he experiences as an adult, based upon this horrific experience from
his childhood. This knowledge may allow him to escape the damage done to him as a
child.

If
freedom is an escape from one's inheritance, the story offers on assurance that such
escape is possible.

Are the thematic elements similar in Amy Tan's "Two Kinds" and Tellie Olsen's "I Stand Here Ironing"?

In Tellie Olsen's "I Stand Here Ironing" and Amy Tan's
"Two Kinds," the mothers are very
different.

Olsen's story is about a woman who is reflective
of her child (Emily) and her childhood—the images we receive come from the mother's
perspective as she stands ironing—a seemingly endless task. The mother recalls someone
at school once contacting her, worried about Emily. We learn that the child's father had
abandoned them, and that for two years the mother had to leave her daughter with her
in-laws before she could afford to take care of her. Another time she had to put her
daughter in a convalescent home (for eight months) because Emily had measles and could
not be allowed infect the family (including a new baby)—but she failed to thrive
there. The mother recalls the hard years with Emily—the separations, and the mother's
concern that maybe she didn't do enough...though she is adamant that she loved Emily. It
was the during the Depression, and life was hard, and raising a child,
harder.

And while the mother admits that Emily was hard to
get close to, she recalls, too, that her daughter was a beautiful baby, and was later a
gifted entertainer, winning an amateur talent contest at
school.

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Mother, I did it. I won, I won; they gave me
first prize; they clapped and clapped and wouldn't let me
go.

For all of her concern,
her daughter spread her wings and took flight with her newly-realized talent. Emily has
grown up and is graceful and more self-assured. The mother wonders what the caller from
the school had been worried about.

However, the story ends
as the mother almost prays that her daughter will realize "...she is more than this
dress on the ironing board, helpless before the iron." My sense is
that she hopes her daughter will not have the life the mother has had and that she will
know her own self-worth, regardless—or in spite—of her mother's struggles. Or as one
source states "...that she is more than the sum of her
experiences."

Amy Tan's story is told from the
daughter's standpoint, so the reader is only able to assemble
information through the recollections of Jing-Mei (or June). This is a very different
story in that the mother is married and the family lives in comfort. There is not the
distance between mother and daughter her caused by poverty and endless working, but
because Jing-Mei cannot share her mother's American dream for her
future.

In "Two Kinds," the mother and daughter fight.
Jing-Mei's mother has dreams for her daughter so that her life will be better than her
own, but she pushes the child to do things that embarrass this American daughter of
Chinese parents. Jing-Mei's mother believes that she can make her daughter a child
prodigy by having her take piano lessons. Jing-Mei disagrees, and ends up at a recital
where she really has learned nothing and has no talent to share. Both mother and
daughter are embarrassed.

Here the mother does not seem to
worry about the mistakes she may have made, though she does want
her daughter to be successful in life. While she does not seem to worry, it does occupy
her mind, but as with "I Stand Here Ironing," Jing-Mei is also able to find success in
her life.

Olson's mother never seems to quite know her
daughter, but Tan's Jing-Mei grows to know her mother. The piano music, years later
shows that two songs she had played as a child were "two halves of the same song," much
as Jing-Mei realizes that she and her mother were more connected than she could have
known as a child.

Find the integral of the function y=sinx*cos(3x)*cos^2 x-cos(3x)*sin^3 x?

First,we'll factorize by sin x*cos 3x and we'll
get:

y = sin x*cos 3x*[(cos x)^2 - (sin
x)^2]

We recognize the double angle
formula:

[(cos x)^2 - (sin x)^2] = cos
2x

The function will become: y = sin x*cos 2x*cos
3x

Now, we'll transform the product cos2x*cos3x into a
sum:

cos2x*cos3x = [cos(2x + 3x) + cos (2x -
3x)]/2

cos2x*cos3x = [cos(5x) + cos
(-x)]/2

Based on fact that cosine function is even, we'll
replace cos(-x) = cos x.

cos2x*cos3x = (cos 5x+ cos
x)/2

The function will
become:

y = (sin x*cos 5x)/2 + (sin x*cos
x)/2

We'll transform the product sin x*cos 5x into a
difference:

sin x*cos 5x = [sin(x+5x) +
sin(x-5x)]/2

sin x*cos 5x = [sin(6x) +
sin(-4x)]/2

Since sine function is odd, we'll put sin(-x) =
-sin x.

sin x*cos 5x = (sin 6x - sin
4x)/2

The 2nd term of y is sin x*cos x/2 = 2*sin x*cos
x/2*2 = sin 2x/4

We'll evaluate the integral of the
function:

Int ydx = Int (sin 6x - sin 4x)dx/4 + Int sin
2xdx/4

Int ydx = Int (sin 6x)dx/4 - Int(sin 4x)dx/4 + Int
sin 2xdx/4

The integral of the given function
y is: Int ydx = (-cos 6x)/24 + (cos 4x)/16 - (cos 2x)/8 +
C