What is x if sin8x=sin5x ?

We'll recall the method of solving the elementary
trigonometric equation:

sin x = a => x =
(-1)^k*arcsin a + k*pi

Comparing, we'll
get:

8x = (-1)^k*arcsin (sin 5x) +
k*pi

But arcsin (sin 5x) =
5x

8x = (-1)^k* 5x +
k*pi

We'll discuss two
cases:

1) If k is an even integer
number:

k = 2n

8x = (-1)^2n*
5x + 2n*pi

8x = 5x + 2n*pi

8x
- 5x = 2n*pi

3x = 2n*pi

x =
2n*pi/3

2) If k is an odd integer
number:

k = 2n + 1

8x =
(-1)^(2n+1)* 5x + (2n+1)*pi

8x = -5x + 2n*pi +
pi

8x + 5x = 2n*pi + pi

13x =
2n*pi + pi

x = 2n*pi/13 +
pi/13

The solutions of the equation are
represented by the reunion of the sets: {2n*pi/3/ n is an integer number} U
{(2n+1)*pi/13 / n is an integer number}.

What was Amy Tan's whole purpose of writing The Joy Luck Club?

Whenever we consider the "purpose" of a text, we often
have to infer the reasons that the author had for writing it. However, when we think
about the life of Amy Tan and how her life experience is reflected in this excellent
novel, perhaps we can understand her reasons. Amy Tan herself, like the four younger
characters in this novel, was a person who had to struggle with two cultures: the
culture of her parents who had left China during the Communist revolution and the
culture of the country where she was born, America. Amy Tan herself said that she "grew
up with several Englishes," and just like the characters in The Joy Luck
Club, she had to struggle with the various cultures in which she lived,
especially concerning expectations of her Chinese parents and the freedom and
opportunities given to her in America. Thus we can deduce that this novel was written to
share and communicate something of the experience of Chinese immigrants and their
children and the struggles that they face.

Why might it be dangerous to have a government?

The major danger in having a government is the danger of
tyranny, the danger of having absolutism arise.

When we set
up a government, we give it many significant powers.  The government, for example, has
the power to take away our money through taxation.  It has the power to take away our
liberty by putting us in jail.  We allow it to have armed forces that we could never
resist, even if we do all own guns.

When we give the
government this much power, we risk having it abuse and tyrannize us.  We risk having it
take too much of our money.  We risk having it use its police powers to arrest us for no
good reason.  Basically, by giving it that much power, we risk having it take away the
liberties that we want it to protect.

What are some quotes that support the theme of "The Gift of the Magi"?Please explain them in detail.

With the theme of O. Henry's "The Gift of the Magi" being
that love supercedes materialism, that is, the spiritual gift of love is far more
important than any material object, much of the written narrative is directed toward
this moral.

When, for instance, Della decides to sell her
most precious possession, hair that the Queen of Sheba would have envied, in order to
purchase a platinum watch chain for her husband's handsome watch, she is delighted to be
"ransaking the stores for Jim's present."  In fact, O. Henry writes that "the next two
hours tripped by on rosy wings."

As Jim arrives home, he
stops inside the door with "a peculiar expression on his face."  When he learns why
Della has cut her hair, "[He] enfolded his Della."  Jim explains that there is nothing
that "could make me like my girl any less."  Further, he says  that if she opens the
package she will understand his perplexity.  And, when Della discovers the combs for
which she has yearned, she

readability="9">

...hugged them to her bosom, and at length she
was able to look up with dim eyes and a smile and say, 'My hair grows so fast,
Jim!'

Then, Della hurries to
give Jim his present, the watch chain.  But Jim has sold his watch in order to buy the
combs for Della.  Instead of being upset and regretting his loss, Jim tells
Della,

readability="6">

"...let's put our Christmas presents away and
keep 'em awhile.  They're too nice to use just at
present...."

Finally, the
authorial intrusion of O. Henry explicates the
theme:

...And here I have lamely related to you
the uneventful chronicle of two foolish children in a flat who most unwisely sacrificed
for each other the greatest treasure of their house.....Of all who give and receive
gifts, such as they are wisest.  Everywhere they are wisest.  They are the
Magi.

What happens to Miss Maudie's house in To Kill a Mockingbird?

Scout describes her first experience with snowfall in
Chapter 8 of To Kill a Mockingbird. She is terrified when she sees
the white particles falling from the sky, and thinks the world is ending. After a fun
day of building a "Morphodite" snowman, in part with Miss Maudie's borrowed snow, the
temperature dropped to 16 degrees that night. Everyone had their fireplaces
blazing. Scout was awakened in the middle of the night and told to hurry outside. When
she heard the "soft taffeta-like sounds and muffled scurrying sounds," she knew a house
was on fire. It was Miss Maudie's. Her neighbors managed to save some of her furniture
and personal items, but the house was a total loss. According to Maudie, she had left a
fire burning in her kitchen fireplace, and the flue must have caught fire. She later
moved in with Miss Stephanie before rebuilding.

What does the dream finally help Amir realize in The Kite Runner?

There are several dreams--and nightmares--in The
Kite Runner, but the most important one comes in Chapter 19. Amir awakes
during the night in Farid's house in Jalalabad "with a scream trapped in my throat." He
has had a nightmare, a vivid re-creation of the last moments of Hassan's life. As he
kneels in the wet street, bound and bleeding, Amir hears Hassan muttering,
"For you a thousand times over." An arm wielding a rifle puts the
barrel to Hassan's head, and the trigger is pulled. When Amir traces the barrel upward
to the bearer of the weapon, he sees his own
face.

Symbolically, in his terrible dream, Amir has caused
the death of Hassan. When he walked outside, he felt, for the first time on his journey,
that he was home. He felt a kinship for his homeland again, and he had a renewed faith
in the mission that he was about to undertake.

In the poem Marrysong, what kind of imageries and literary devices does the author use? Write a commentary on the poem and answer the question.

Dennis Scott poem narrates a poem about a man who tries
wih a great effort to understand her wife's attitude towards him. "He Charted" she went
so far that he had to chart her but when he was about to finish an idea about her
strange behaviour suddenly "She made wilderness again. Roads dissapeared. The map was
never true". He described her as a "territory without seasons" in which we see reflected
an angry woman that for moments he seems to love him and sometimes not "... her love
shortened or grew ...". One way or another he ends up not figuring out what was going on
with her but taking away his frustration "he accepted that geography". And above all her
mood swings and unpredictableness he still loved
her.

Through out all the poem he compares her
with various landscapes of nature because nature changes constantly and he is in a way
being put into that geography where he explored her but sometimes found himself lost and
he could never figure out what was going to happen next (we are always refering to her).
He could not understand how is it that her mood changes everyday and how their marriage
went from bad to better. For example he says that one day you can "see cool water
laughing where the day before there were stones in her voice", this is a good example to
show how the author conveys nature with mood.

When he
remarks, “He never learned her quite”, the speaker may be amidst an interminable sea,
trying to study it in vain. The sea may also be considered as his wife, whom he is
trying to learn. He could see “cool water laughing where the day before there had been
stones in her voice”. This means that the sea at times is rough, but later becomes calm
and cools without any reason – just like his wife. The word ‘charted’, used to describe
the actions of the speaker, reveals his embarrassment in trying to map the maze-like
heart of his wife.

The territory without seasons may also
be personified as the speaker’s spouse. It is universally agreed that the change of
seasons add colour and joy to the world. However the lady’s behavior is described as a
territory WITHOUT seasons (thus without any joy or love) Sometimes her love for
increased and sometimes it lessened –“the shadows of her love shortened or grew”.
Finally, however the unfortunate husband is forced to accept the wild geography, giving
up all hope to decipher the complex furls of the human mind.