In Fahrenheit 451, Beatty says "[Fire] is a mystery...Its real beauty is that it destroys responsibility and consquences." How has this been true?

Beatty says this when he and Montag are at Montag's house,
preparing to burn it down.  In the earlier parts of the book, we can see how fire (or at
least the way fire has been used in this society) has destroyed responsibility and
consequences.

In this society, fire has been used to burn
books.  This is part of a larger drive to rob people of their human impulses.  People
have been encouraged to ignore the real problems that come with being human.  They have
been encouraged to simply rid themselves of these problems by pretending they don't
exist.  True human life consists of having feelings and problems and confronting those
things and their consequences.  In this society, by contrast, people run from those
things.  We can see this clearly in how Mildred retreats into her parlor walls and in
how her friends try to forget their families.

When Beatty
says the line you cite, he is speaking figuratively.  His society's default reaction to
every problem is to burn it (literally or figuratively).  He is saying that they rid
themselves of responsibility and consequences by simply destroying their need to make
choices and confront problems.  This society does this by trying to get people to simply
live in the moment and forget that they are human beings.

What does Mrs. Gibbs serve her husband for breakfast?

In Act II when Mr. Gibbs appears for breakfast on the
morning of their son's wedding, his wife "puts a plate before him." He says, "Why, Julia
Hersey--French toast!" She replies, "'Tain't hard to make and I had to
dosomething."

This is one of the little things that go
unnoticed in people's daily lives, but it is filled with significance. Mrs. Gibbs has
been unable to sleep during most of the night and is filled with conflicting emotions in
the morning. The coming wedding has made her sad about losing her young son and the
responsibility of caring for him. She has been thinking about her own wedding and
marriage, which of course has made her think about how much her husband means to her.
From now on she will be turning more of her attention on him because her son will have
another woman to love him and care for him. Mrs. Gibbs doesn't want to talk about her
feelings because she is on the verge of tears already. The French toast, which is
obviously a favorite of her husband's is her way of telling him she loves
him.

Losing their son through his marriage will change the
relationship between the Mr. and Mrs. Gibbs. It will draw them closer. The fact that he
calls her by her maiden name of Hersey indicates that his love for her is being
rekindled, just as the French toast indicates that hers is being rekindled for him.

How does the point of view affect our response to "Cathedral"?

It is clear that the first person point of view selected
is a rather interesting choice for this excellent story. However, I think that
deliberately choosing to tell the story through perhaps the most unsympathetic
character, the husband who appears to be deliberately rude to both his wife and his
guest, we see the transformation that the guest manages to bring about in the character
of the narrator that much more clearly because of his earlier
rudeness.

As the story begins, we see that even though
Robert has just lost his wife, the narrator is still rude about the way that he feels
threatened by the invasion of his personal space. He crassly jokes about taking Robert
bowling, and when Robert comes draws attention to his blindness by asking questions such
as which side of the train he sat on in his journey and then pointedly turns on the TV
when conversation runs dry.

However, in spite of this, it
is clear that the narrator's conversation with Robert, especially when he is asked to
draw a cathedral so that Robert can "see" what they look like, has a big impact on him,
triggering an epiphany as the narrator chooses to keep his eyes closed even when Robert
tells him to open them:

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But I had my eyes closed. I thought I'd keep them
that way for a little longer. I thought it was something I ought to do... My eyes were
still closed. I was in my house. I knew that. But I didn't feel like I was inside
anything.

The narrator for
perhaps the first time in his life is able to empathise with another human being, and
his experience of blindness, albeit temporary, is actually something that is very
liberating for him. To have the story narrated from this character's point of view
allows us to appreciate and understand the massive change that the narrator experiences
through meeting Robert.

Considering Old Major's dream for the future and his warnings to the animals, how is the ending of Animal Farm ironic?

Old Major's dream envisioned an earth of the future with
no humans, where animals ruled the world and determined their own actions. He pointed
out that all of the evil in the world was the result of humanity, and declared that the
animals should all maintain an "enmity" toward humans. The animals should avoid all
human characteristics, even after they have been conquered. By the end of the novel, at
least one part of Old Major's dream had come true: The leaders of Animal Farm were
considered equals among their new human associates, but the pigs had broken nearly every
commandment in the process, from wearing clothes to walking upright. The other animals
were now worse off than they had been under their human masters, working longer hours
for less sustenance. The animals were all equal, but some were just more equal than
others.

Can anyone help me with an essay for A Thousand Splendid Suns with the theme of women's hope? I am doing an essay for school about this and am in...

I think your topic of hope is a good one for A
Thousand Splendid Suns, and most of the women in the story never give up
their desire to better their seemingly hopeless situations. Only Mariam's mother, Nana,
seems to have completely lost faith in anything positive happening to her,
although Laila's mother also loses the will to live after the death of her sons. Despite
the desperate situation of Mariam's life with Rasheed, she clings to the hope that her
life will change for the better. Laila's presence is what keeps Mariam's hopes alive,
and they both enjoy a short burst of independence when they attempt to flee Rasheed's
home. After they are caught, they resume a dismal existence under the brutal hand of
Rasheed, but once Laila discovers that Tariq is still alive, she realizes that future
happiness may still await her. When Mariam kills her husband, she quickly understands
that she will not escape the wrath of Taliban law, but she maintains the hope that Laila
will survive to enjoy a life with the man she loves. Laila's hope never dies, and at the
end, her desire to return to her homeland and begin a new life is built on the hope that
her own child will be brought up in a peaceful world.

According to Tom's story,when did he''bust up the chiffarobe''?

Tom Robinson's first visit to assist Mayella Ewell had
been "way last spring," according to his court testimony.  She had offered him a nickel
to "bust up a chiffarobe", which he had declined; since that time, Robinson claimed that
every time he was in the area, Mayella Ewell had something for him to do to help her. 
Scout observes that Mayella "must have been the loneliest person in the world. .
.lonelier than Boo Radley".  On the day in question, Mayella had sent the children to
town to get ice cream with the "seb'm" nickels it had taken her quite some time to save;
she asked Tom to come in the house and get something off the chiffarobe (a different one
than the one Tom had earlier chopped up for her), and when he stood on the chair,
Mayella tried to hug his legs.  In his surprise, he hopped off the chair, which fell
over, and then Mayella kissed him on the cheek.  This description of the incident
completes the portrait of Mayella as a pitiful girl living a pitiful life; at nearly
twenty years old, she has no friends, no education, has never been on a date or had any
interaction with the opposite sex. 

Given the function f(x)=-2x+4 what is the real number x such as |x|

By definition, we'll
have:

|x|<-7-f(7) <=> -[-7-f(7)]
< x < -7-f(7)

7+f(7) < x <
-7-f(7)

We'll solve the left side
inequality:

7+f(7) <
x

We'll replace f(7) by f(7) = -2*7 + 4 =
-10

7 - 10 < x

-3
< x

We'll solve the right side
inequality:

x <
-7-f(7)

x < -7 -
(-10)

x < -7 + 10

x
< 3

The real values of x, that
accomplish the constraint |x|<-7-f(7), are located in the opened interval (-3 ,
3).