CHAPTER 9: Describe the terrible event at the end of this chapter in Lord of the Flies. What happened and why is this significant?Thanks!

In Chapter Nine of Lord of the Flies,
Jack finally decides to create his own tribe, promising its members plenty of food,
fun and protection from the beast. Ralph tries to remind the boys that he is still the
duly elected chief, but Jack reminds him that he no longer holds the conch. As a
lightning storm erupts, the boys begin to dance wildly in circles, and when what they
perceive to be the beast comes from the woods, the boys furiously attack it. However, it
is not the beast: It is Simon, who has returned to tell them that the beast is only a
dead airman dangling from a parachute. Simon is brutally murdered, and his body washes
into the sea.

Simon's death is significant primarily
because it marks the end of any civilized behavior on the island. It is also symbolic
because it puts an end to the highly spiritual character whose understanding and
goodness makes him the best of the castaway boys.

In Chapter Twelve of The Egypt Game, why did the author describe the characters as being filled with helpless fuming anger?

Let us just briefly remind ourselves of what happens at
the beginning of Chapter 12, entitled "Elizabethan Diplomacy." The four friends are in
the yard and are surprised and terrified suddenly by a "shapeless inhuman figure" that
jumps over the fence and leaps into the middle of the yard. It is only when Marshall
notices a second figure climbing over the fence, dressed up in a costume that reveals
the identity of the two mysterious arrivals, that they realise what is happening, and
that they have been tricked by Toby and Ken, who have remained in their costumes to
scare the four friends. This explains the reaction that your question refers
to:

In all
four Egyptians frozen fear boiled at once into a choking mixture of anger and
relief.

They have realised
that they are not being visited by some strange monster or demon, and thus on the one
hand are intensely relieved, yet at the same time are filled with anger at how they have
been tricked and scared by the boys.

What is a famous quote by Voltaire?

Voltaire, whose birth name was Francois-Marie Arouet, is
well-known for his defense of civil liberties and his ideas about human brotherhood. 
The quote that is most often connected to him has to do with this.  That is the quote
that goes

I
disapprove of what you say, but I will defend to the death your right to say
it.

However, it is clear that
Voltaire himself never wrote or said this phrase.  It is actually a statement of his
values, but not one that he himself said.

One famous quote
that is truly from Voltaire is also on the subject of civil liberties, religious
toleration, and the universal brotherhood of human beings.  Voltaire
wrote

I say
that we should regard all men as our brothers. What? The Turk my brother? The Chinaman
my brother? The Jew? The Siam? Yes, without doubt; are we not all children of the same
father and creatures of the same
God?

This quote is not as
well-known as the one that he didn't actually say, but it is a good representation of
the sorts of things that Voltaire believed.

Where can you find the word "hegemony" in Guns, Germs, and Steel?

I do not believe that the word "hegemony" appears at any
point in this book.  I have searched for the word using the Kindle version of the book
and I have searched using the search utilities in Google Books and at Amazon.com.  In
all cases, no matches were found.

Diamond could well have
used the word if he had been so inclined.  One meaning of "hegemony" is something like
"influence" or "power" that one person or group has over others.  Diamond could have
used the word, for example, in Chapter 16.  He could have said that Chinese governments
gained "hegemony" over the entire region that is now China.  However, it appears that he
did not choose to use this word here or anywhere else in the
book.

How to verify or prove this identiy?Here is the identity I need to prove: (sin x + cos x)(tan x + cot x) = sec x + csc x Thanks to any answer!

First you need to remember that tan x is the same as sin
x/cos x,     cot x = cos x/sin x, sec x = 1/cos x, and csc x = 1/sin
x.

Then if you look at the left side of the equation and
multiple out the terms using FOIL, you'll get:

sin^2 x/cos
x + cos x + sin x + cos^2 x/sin x = sec x + csc x

Since you
have fractions on the left side, and you are adding, you need common denominators, so I
changed cos x to cos^2 x/cos x and sin x to sin^2 x/sin x.  Then you can add the two
fractions with cos x in the denominator and the two fractions with the sin x in the
denominator, this gives you:

(sin^2 x +cos^2 x)/cos x +
(sin^2 x + cos^2 x)/sin x = sec x + csc x

The last thing
you need to remember is the identity: sin^2 x + cos^2 x = 1, so you can replace both of
the numerators with one and this gives you:

1/cos x + 1/sin
x = sec x + csc x

Now, by the definitions of secant and
cosecant that I listed at the top, that proves the
identity.

Hopefully that helps.

What is the central irony of "The Story of an Hour"?

There is one central irony in Chopin's short story "The
Story of an Hour". The main character, Mrs. Mallard, is a woman who feels the stress of
being a repressed wife. As a woman, the lines of her face show her to be much older than
she really is. The stresses of her life have pre-maturely aged and overwhelmed
her.

Upon learning of the death of her husband, Mrs.
Mallard locks herself in her bedroom to think about the path her life will take. She
looks out the window and notices the renewal that nature brings and begins to embrace
herself as a free woman.

Soon after her epiphany, Mrs.
Mallard emerges from her bedroom "like a goddess of Victory." Unfortunataley, and
ironically, Mrs. Mallard's joy comes to an abrupt end. Mr. Mallard has not died in a
train accident. Instead, he was not even at the site of the accident and is
alive.

Here is where the story hits its ironic twist. After
seeing that her husband is still alive Mrs. Mallard dies- on the spot. The irony of the
story exists given that her husbands "death" allows her to find her freedom. Upon the
realization that her freedom does not really exist, Mrs. Mallard succumbs to the fact
that she is, again, a bound woman. This new epiphany kills her.

I need to write and internal dialogue for Hamlet. My character must fill a gap in the play. What would be a good character to choose from?What...

What an interesting task!  You have lots of options with a
project like this.  I think it probably makes sense to take one of the minor characters
and add a piece to the play that reveals his or her perspective to a greater degree. 
Here are a few suggestions:

1.  What is Ophelia thinking
after Hamlet's strange behavior during the play within a play?  He had told her "get
thee to a nunnery" just a scene before, but his talk was very suggestive in this scene. 
What does she make of this?

2.  How do Rosencrantz and
Guildenstern feel about their doing the king's bidding and betraying their friend
Hamlet?  Do they have any second thoughts?  What are their motivations?  Are they ever
suspicious of the King?

3.  What is the pirates version of
the story?  How did the attack go down?  Why?  Why do they believe Hamlet and do his
bidding in regards to the letters he wants delivered in Act
4?

No matter what you decide to do, it is important that
the scene starts with a connection to the actual events and language of the play.  This
will help create an interesting and logical continuity to the actual
play.