In Life of Pi, how does the use of symbolism and allegory give the readers a better understanding of Pi's descent into savagery?

It seems that the answer to this question is linked with
the "alternative" version of events that Pi gives to Mr. Chiba and Mr. Okamoto in
Chapter 99 of the tale, who are obviously unconvinced by the version that Pi gives them
and us as readers. Trying to come up with a different story, Pi gives a much more
realistic account of what supposedly happened, with each of the animals clearly
represented by a character. Thus it is that the zebra is replaced by a sailor, the hyena
by the cook, and the orangutang by his mother. Interestingly, the only animal that is
absent is Richard Parker, the tiger, which suggests that allegorically Richard Parker in
the "first" tale represents Pi himself. The second tale charts the way in which Pi was
forced to kill the Cook and how he ate human flesh to sustain
himself:

I
stabbed him in the throat, next to the Adam's apple. He dropped like a stone. And died.
He didn't say anything. He had no last words. He only coughed up blood. A knife has a
horrible dynamic power; once in motion, it's hard to stop. I stabbed him repeatedly. His
blood soothed my chapped hands. His heart was a struggle--all those tubes that connected
it. I managed to get it out. it tasted delicious, far better than turtle. I ate his
liver. I cut off great pieces of his
flesh.

Note how Pi is forced
to become savage himself to survive. He later comments that the sailor was an evil man,
but that worse was the way in which he met "evil" in Pi too. By allegorically creating
Richard Parker to represent this untamed savagery in his original story, Pi symbolically
indicates his own descent into savagery in his grim battle for
survival.

Brabantio says " Look to her, moor,if thou hast eyes to see.She has deceived her father and may thee" Is this a fair comment on Desdemona ?

I am not entirely certain that this is a fair comment on
Desdemona.  One has to look at the source.  Brabantio is the father that has been done
wrong and shamed by his daughter.  He never approves of the marriage and believes that
his status as a Magnifico will persuade the Senate, his daughter, and even Othello that
this marriage should not happen.  However, he recognizes that his status as an insider
is quickly transformed to outsider by Desdemona's selection and the nature in which she
ran off with Othello.  His words are along the lines of a warning, curse,
foreshadowing.  Perhaps, Shakespeare wrote this in as a generational gap issue.  The
father warning the younger husband of what deception may lie ahead.  As the husband
becomes "older," the words of the father increasingly stick in his mind, almost becoming
a type of self- fulfilling prophecy.  Naturally, if one were to look at the quote
objectively, it is not necessarily fair because Desdemona does not "deceive" Othello. 
He is led to believe that by the skillful manipulation of Iago.  Yet, she does not
deceive him.  In the end, Othello's doubt and insecurity are only enhanced by the
father's words.

Solve the equation log3 x + 1/log3 x=5/2

We'll multiply all terms both sides by the least common
denominator.

2*log3 (x)*log3 (x) + 2 = 5*log3
(x)

2*[log3 (x)]^2 - 5*log3 (x) + 2 =
0

We'll replace log3 (x) by
t.

2t^2 - 5t + 2 = 0

We'll
apply quadratic formula:

t1 = [5+sqrt(25 -
16)]/4

t1 = (5+3)/4

t1 =
2

t2 = 1/2

But log3
(x)=t.

log3 (x)=t1 <=> log3
(x)=2

We'll take antilogarithms and we'll
get:

x = 3^2

x =
9

log3 (x)=t2

x = sqrt
3

Since both values are positive, we'll
accept them as solutions of equation: {sqrt3 ;
9}.

In what quadrant does the curve y= x^2 -5x+3 meets the curve y= 2x^2 -3x +4

Given the curve y= x^2 - 5x + 3 and the curve y= 2x^2 - 3x
+ 4

We need to find the position of the intersection
point.

First we will determine the coordinates of the
intersection points.

==> 2x^2 - 3x + 4 = x^2 - 5x +
3

==> x^2 + 2x + 1 =
0

==> We will
factor.

==> (x+1)^2 =
0

==> x= -1 ==> y=
9

Then the intersection point is (-1,
9)

The point ( -1, 9) is located into the second
quadrant.

Then the curves meet in the second
quadrant.

What is surprising about the narrative point-of-view Dickens has adopted?Great Expectations by Charles Dickens

Unlike other first person narrators that Dickens has
employed in his works such as David Copperfield, the narrator of
Great Expectations is an adult who relates the narrative in his own
voice, but he tells the story from his memory rather than as it happens.  Unique to this
novel, also, is the narrator's memory is very selective, recalling copious details of a
young boy's fear and unhappiness, but there is also the omission of other details such
as those of the beatings that Pip receives from Mrs. Joe.  Added to the selectivity of
remembrances, the narrator also makes evaluations of incidents in his life.  For
instance, after Pip talks with Joe one night, having shown him his lessons from Biddy,
Pip remarks,

I
had a new sensation of feeling conscious that I was looking up to Joe in my
heart.

And, after Pip returns
from Miss Havisham in Chapter IX, Pip assesses the events of that
day: 

That
was a memorable day to me, for it made great changes in me. But it is the same with any
life. Imagine one selected day struck out of it, and think how different its course
would have been. Pause you who read this, and think for a moment of the long chain of
iron or gold, of thorns or flowers, that would never have bound you, but for the
formation of the first link on one memorable
day.

And, later in Chapter
XIV, Pip reflects upon how his visits to Miss Havisham have changed his attitude about
himself and his home,

readability="10">

IT IS A most miserable thing to feel ashamed of
home. There may be black ingratitude in the thing, and the punishment may be retributive
and well deserved; but, that it is a miserable thing, I can
testify.

There is much of the
adult in Pip's first person narrator.  For example, the satirical portrayals of Uncle
Pumblechook and Sarah Pocket with their pompous and sycophantic attitude toward the
upperclass are open for satire as Pip describes how he acts at Christmas dinner, as well
as his behavior at the home of the Gargerys. Comic relief, too, is provided by this
mature narrator as Pip often spends time at the Wemmick's home complete with
cannon. Along with the comedic, the evaluation of various situations provides the reader
with a great insight into the man Pip as well as the other characters, an insight that a
younger Pip could not realistically provide.  Indeed, it is a reflective narrator as
well as one with a sense of comic relief that relates the story of a young boy who
matures in the course of the narrative of Great
Expectations.

In "The Story of an Hour," how is the imagery in the fifth paragraph used to develop mood?

The fifth paragraph comes after Mrs. Mallard has heard the
dreadfully upsetting news of her husband's death, and when she has ensconced herself in
her bedroom to grieve by herself. Interestingly, we are told that the "storm of grief"
that first possessed her when she first heard the news had passed, and it is clear that
what she sees as she looks out of the window and what she hears from her bedroom are
used to develop a very different mood that will come to characterise Mrs. Mallard's
emotions. Note what this paragraph says and the imagery it
contains:

She
could see in the open square before her house the tops of trees that were all aquiver
with the new spring life. The delicious breath of rain was in the air. In the street
below a peddler was crying his wares. The notes of a distant song which some one was
singing reached her faintly, and countless sparrows were twittering in the
eaves.

Of course, the imagery
of the trees being "all aquiver with the new spring life" finds its parallel in the
state of freedom that she is able to enjoy. She, now that her husband has been taken for
her, experiences "spring life." Likewise, the "delicious breath of rain" shows her
sensuous enjoyment of nature, as does the "twittering" of the sparrows. In short the
imagery employed in this paragraph shows us Mrs. Mallard's appreciation and enjoyment of
nature and how much she has to look forward to. As the story itself is set in Spring,
which is a time of re-birth and a new beginning, so Mrs. Mallard, so she believes, has
been given a new beginning and the gift of freedom. Nature and the internal thoghts and
feelings of Mrs. Mallard connect in this sense.

The function f:R-->R is given by f(x)=4x-3. Solve the equation f[f(x)]-f(1)=0

To solve the equation, we need to determine the term
f(f(x)), that is the result of composition of functions, such as: (fof)(x) =
f(f(x)).

f(f(x)) = 4*f(x) -
3

f(f(x)) = 4*(4x-3) -
3

f(f(x)) = 16x - 12 -
3

f(f(x)) = 16x - 15 (1)

Now,
we'll determine the value of the function at x = 1:

f(1) =
4*1 - 3

f(1) = 1 (2)

We'll
replace (1) and (2) in the equation that has to be
solved:

16x - 15 - 1 = 0

We'll
combine like terms:

16x - 16 =
0

We'll divide by 16 both
sides:

x - 1 = 0

x =
1

The solution of the equation f(f(x)) - f(1)
= 0 is x = 1.