Comment on the use of supernatural elements in Macbeth.

I have to divide the post in two parts for its
length.

Part
1:

In the play Macbeth,
the supernatural elements primarily include the “weird sisters” and their gang. These
elements are used to pave way to show Macbeth the path of his ultimate
downfall.

The three witches instigate Macbeth's inner
ambition and greed by luring him. And this they do through their so-called prophecies.
The predictions of the witches and the apparitions are nothing but equivocations in the
name of prophecies. The witches, at first, tell Macbeth that he would be the Thane of
Cawdor and the King of Scotland soon. This is not something extra-supernatural they do,
since, it is a matter of common-sense that, Macbeth, if he would have fought
courageously and shown his man-of-the-battle attitude, he would definitely get rewarded,
and if he continues to go after his ambition, would be the king possibly. Later, the
apparitions prophesy that the no human born of women can kill Macbeth ever, and he would
not be killed unless Birnam wood would come closer to his fort. The first prophecy is a
lie in a sense that, Macduff, who is born of his dead mother's body via surgery, kills
him. The second one is an equivocation also, since, though Birnam Wood does not come
closer, yet the soldiers of the opposition hide them under the leaves of the forest, and
this makes him think as if the forest itself is moving towards him, and he loses all his
hope and courage to fight further. It is clear hence that, what the prophecies told was
half-truth to destroy Macbeth. Ambiguity they create in
Macbeth's mind throughout the whole play. Ambiguity, or conflict between appearance and
reality, is one of the key themes in this tragedy. The witches just equivocate in a
dubious way; implying that, lie in a way which seems apparently true. And this they do
solely to win his trust and make him a devil like them.

The
witches know that, Macbeth is an ambitious man who just needs a spur in order to rouse
his ambition and let it develop fully to achieve his end. They show him what he wanted
to see. They tell him what he wanted to hear. Their prophecy awakens his inner demon and
instigates his voracity. Macbeth is thus deceived. He is told that no human born of
woman can kill him; neither would he be killed till the Birnam Wood come close to his
fort. Later, when he finds that the Birnam Wood does not come nearer, rather soldiers
hiding themselves under leaves come closer, and Macduff is found to be born out of
surgery probably because of his mother's illness or death, he understands clearly that,
he has been deceived by the witches' dubious prophecy. In act 5, scene
7, disillusioned Macbeth tells to Macdufff: "Accursed be
that tongue... / That palter with us in a double sense, / That keep the word of promise
to our ear/ And break it to our hope." So, it is clear that, the witches
prophesies contributes to influence and instigate him towards evil deed.

In fact, Lady Macbeth's greed and cruelty
increases more once she is aware of the witches' prophetic
statements.

Could someone please provide an analysis of "Smile, Smile, Smile" by Wilfred Owen?

With regard to Wilfred Owen's poem, "Smile, Smile, Smile,"
it refers, as do all of his poems, to World War I.

There is
an incongruity at the start of the poem: the newspapers are advertising new homes to be
ready when the war is over.

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For,' said the paper, 'when this war is
done
The men's first instinct will be making
homes.

This creates a
conflict within the speaker, as he believes the war has only just begun. And if it
should end so soon, he believes it would somehow rob the dead of the "integrity" of
their sacrifice.

The speaker goes on to say that the
greatest honor to show a fallen hero is to remember
him.

We rulers
sitting in this ancient spot
Would wrong our very selves if we
forgot
The greatest glory will be theirs who fought,
Who kept this
nation in integrity.'

Owen
then writes that those wounded, who survive, share a special, private camaraderie with
one another: the value of sacrifice, perhaps.

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The half-limbed readers did not
chafe
But smiled at one another curiously
Like secret men who know
their secret safe.

The last
several lines I find ambiguous:

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Pictures of these broad smiles appear each
week,
And people in whose voice real feeling rings
Say: How they
smile! They're happy now, poor
things.

I assume the pictures
appearing each week (in the same newspaper, perhaps, that advertises new homes...) are
of those who have died in action. Readers of the newspaper, with sincerity in their
voices, remark at the fallen soldiers' smiles—saying, "They're happy now," as if dying
for one's country would validate the smile, somehow, of their sacrifice. However, the
closing, "...poor things" might convey that the reader does not fully comprehend the
satisfaction a hero would have in making the ultimate sacrifice, for the "sincere
voices" can only sympathize with the soldier's passing.

I
think, having read other poems by Owen, that the patriotic spirit of the solider lies at
the forefront of his poems. War asks of its fighters the greatest sacrifice, and true
heroes are only to glad to answer the call. They are most honored, then, in being
remembered by a thankful nation for what they have given.

You find a puddle of a clear liquid on your drive way. it is either water, vinegar, or battery acid from the car.How can you safely test (other...

If it is a question relating to chemistry, perhaps it
assumes ready availability of some chemicals or facilities of testing. Bur if it is a
question from common everyday life, I will try to make out the substance from its smell.
While water will have no smell, vinegar will have a very distinct smell. Acid will have
some kind of acrid smell which I may not recognize very clearly. If some how or the
other I had a means of knowing that is is only one of these three options the smell test
will be good enough to identify the liquid clearly. But If I do not have these three
possible options, things will be more difficult.

But then I
will not just stop with the smell test. I will also try to find the source from which
the liquid in the puddle has come. Once possible sources have been identified, I will
match the smell of liquid in puddle with that in suspected source. If this matches, it
will be a confirmation of the original smell test.

In Flowers for Algernon, who suggested that Charlie should be a part of the experiment in the first place?

We are never actually told specifically who suggested
Charlie would be a suitable subject for the experiment that changes his life so
drastically. However, there are hints that we can pick up that suggest that Dr. Strauss
contacted the Beekman School for Retarded Adults and spoeke to Miss Kinnian to ask for a
suitable candidate. Notice how in the third progress report, Dr. Strauss tells Charlie
that Miss Kinnian had given them a report about him:

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He said Miss Kinnian tolld him I was her bestist
pupil in the Beekman School for retarded adults and I tryed the hardist becaus I reely
wanted to lern I wantid it more even then pepul who are smarter even then
me.

Thus we can infer that
Dr. Strauss and his scientific team contacted the school and asked for a potential
candidate that they could use for a suitable case study. Miss Kinnian, who is obviously
impressed with Charlie and his dedication to his studies, suggested his name, which is
how Charlie found himself the subject of this intelligence
experiment.

Please explain the circumstances surrounding the Louisiana Purchase.What events occurred that led to the Louisiana Purchase?

After the Revolutionary War, Americans began to settle in
the Ohio River valley.  The Appalachian Mountains made it very expensive and difficult
to transport goods to the east coast.  The cheapest way to ship goods to the coast was
to float them down the Ohio River, then down the Mississippi River to New Orleans, where
they could be transferred to ocean going vessels for shipment to the east coast and
Europe.  The problem was that the U.S. had no control over New Orleans and Thomas
Jefferson, president at the time of the Louisiana Purchase, feared that the U.S. would
lose its right of deposit at New Orleans.  At the time, Louisiana was controlled by
Spain, but in a secret agreement, Spain was to cede Louisiana to France in exchange for
a Spanish Kingdom in Italy.  With knowledge of this agreement, Jefferson sent Robert
Livingston, and then James Monroe, to France to negotiate the purchase of New Orleans
from Napoleon for $10 million. With the hopes of a Caribbean empire based on the sugar
trade dashed with the loss of Santo Domingo, Napoleon lost interest in controlling
Louisiana. In need of money to continue his European wars, Napoleon offered the U.S. the
entire Louisiana territory, more than 800,000 square miles, for $15 million.  One
problem confronted Jefferson.  He was a strict constructionist and did not see anything
in the Constitution which would give him the power to purchase Louisiana.  What he did
know was that he did have the power to negotiate treaties. Knowing that this deal was in
the best interest of the United States, he put the purchase of Louisiana in a treaty
which the Senate later ratified.  In 1830, the United States doubled in size with the
purchase of Louisiana from Napoleon for $15 million.

What is the theme of "Thank You, Ma'am?"

To me, the theme of this story is that people can be
transformed by love and trust more than they can be transformed by fear and
punishment.

In the story, Roger is a thief.  But when he
meets up with Mrs. Jones, his life is changed because she catches
him.

But she does not call the police or tell his parents
or anything.  Instead, she treats him well and shows that she trusts
him.

This works, in my opinion, because people often behave
the way they are expected to behave.  That is the theme of the story in my opinion --
the idea that if you trust someone and treat them well, you can change their
life.

What is tan2x if cosx=1-sinx ?

cosx=1-sinx

sinx =
1-cosx

devide the equation by
cosx

tan = secx -1

tanx = secx
- 1

we know that tan2x =
2tanx/(1-tan²x)

tan2x = 2(secx-1)/[1-
(secx-1)²]

tan2x = 2(secx-1)/[1
-(sec²x-2secx+1)]

tan2x = 2(secx-1)/[1
-sec²x+2secx-1)] 

tan2x =
2(secx-1)/[2secx-sec²x]

tan2x =
2(secx-1)/secx(2-secx)

tan2x =
2(1-cosx)/cosx.secx(2-secx)

tan2x =
2(1-cosx)/(2-secx)

tan2x =
2cos(1-cosx)/(2cosx-1)