Chicken and eggs are complements in production. If the price of chicken goes down, what happens to the supply curve of eggs?thanks

In this answer, I am assuming that you are talking about
the price that can be gotten by selling the chicken, not
the price of producing the
chicken.

If the price for which chicken can be sold goes
down, the supply curve for eggs will shift to the left.  In other words, the supply of
eggs will go down, assuming that chickens and eggs are complements in
production.

The reason for this is simple.  If the price of
chickens goes down, farmers will raise fewer chickens, all other things being equal.  If
farmers raise fewer chickens, there will also be fewer eggs laid.  When that happens,
the supply decreases and the supply curve moves to the left.

Using complete sentences, explain how to find the zeros of the function f(x) = 2x^3 – 9x + 3

To find the zeros of the function f(x) = 2x^3 - 9x + 3, we
need to equate f(x) to 0 and solve the equation we
get.

Here we have to solve 2x^3 - 9x + 3 =
0

As the highest power of x among all the the terms is 3,
we will get 3 values for x which satisfy the equation.

The
function has 3 zeros.

To find the roots of the cubic
equation that we have got, the following formula can be
used

2x^3 - 9x + 3 =
0

=> x^3 - (9/2)x + 3/2 =
0

a = -9/2 and b = 3/2

Now
substitute the values of a and b in the following to determine the three
zeros:

Let A =
cuberoot(-b/2+sqrt(b^2/4+a^3/27))

and B =
cuberoot(-b/2-sqrt(b^2/4+a^3/27))

Then the three solutions
are:

x1 = A +
B

x2 = -(A+B)/2 +
(A-B)sqrt(-3)/2

and x3=
-(A+B)/2 - (A-B)sqrt(-3)/2

In theessay "Once More to the Lake," White desribes the lake house as "a holy spot." Why is the lake sacred to him?

On a fishing trip to a lake in Maine with his young son,
as the author recalls his own childhood summers at the same lake, he inevitably begins
to see himself in his son and is jolted into awareness of his own mortality. This
evocative essay, then, deals with time: its delightful past, its pleasant present, and
its tragic future—when the author finally acknowledges its passing.  The essay,
nostalgic and affectionate in tone, is nevertheless a bit sad and peaceful, much like a
reverie, as if White somehow needs to reconnect with the lake before it’s too late,
before he, too, passes on. Some of his descriptive words for the lake, “this holy spot,”
“cool and motionless,” “sweet outdoors,” and “the stillness of the cathedral” (2), show
that White viewed the lake as a nearly sacred place, undisturbed and natural; he seems
to have respected the lake to the point of holding it in awe. In paragraph 3, the phrase
“remote and primeval” reinforces this impression, as if to say that the lake is
prehistoric, without the imprint of people, a thought that foreshadows the essay’s
ending with a shock of recognition: “suddenly my groin felt the chill of
death.”

Is the theme of Keasts' "On the Grasshopper and Cricket" the cycle of life and how to spend it?

The theme of Keats' sonnet
"On the Grasshopper and Cricket" must be derived from textual evidence.
Three things point to the theme. The
first is the title in which Keats introduces specifically
the grasshopper resplendent in summer and the cricket that endures the winter. In the
contemplations of the poem, Keats describes his awareness of, his experience of, the
grasshopper and then the cricket.

The
second thing is the opening line of the sonnet, which is repeated at the
9th volta, or turning, line: "The poetry of earth is never dead." Keats is focusing our
attention on the music, the "poetry," of nature; bear in mind that, for Romantic poets,
nature contained truth that inspired poetry, truth that poetry sought to imitate or
reproduce.

The third thing is
the final triplet of the poem (the last three lines). Keats speaks of the "Cricket's
song" and of the "drowsiness" of being half asleep and of the similarity of the
cricket's song to the grasshopper's ("And seems to one ... / ... / The Grasshopper's
[song]"). Keats also speaks of being drowsily transported to summertime and the sound of
the grasshopper singing, perhaps from under "some pleasant
weed."

When you consider these three things, the
theme begins to emerge. Keats speaks of poetry, voice,
song; he speaks of poetry never ceasing; he equates the grasshopper with the cricket by
imaging the one while hearing the other; and he equates poetry with the songs of the
cricket and grasshopper through the word "voice."

One might
be tempted to think this sonnet reflects the theme of the "cycle of life," but this
theme has no correspondence to poetry, voice, song, which is the music of nature. A more
correct analysis of theme would be that Keats is expressing the idea that the trivial,
insignificant small things of nature comprise nature's poetry and song: grasshoppers and
crickets are very trivial, small and insignificant. Yet it is the song and poetry
(remember, song and poetry are equated through "voice") of the grasshopper and cricket
that carry on when all else are done.

Keats says that after
the birds ceased their singing in the hot summer, the grasshopper could still be
heard:

When
all the birds are faint with the hot sun,
And hide in cooling trees, a voice
will run
From hedge to hedge about the new-mown
mead;

Keats also says that
"when the frost / Has wrought a silence" in winter, the cricket can still be heard on
the hearth, its "song, in warmth increasing ever." In this sonnet, Keats is putting
forth a theme that reflects the Romantic period belief in
the inspiring truth of nature by showing that even when all nature seems
overcome by heat or cold, there is still the poetry and song of nature that gives truth
and inspires:

readability="9">

The poetry of earth is ceasing never; / ...
/
The Cricket's song, in warmth increasing ever,
And seems to one in
drowsiness half lost,
The Grasshopper's among some grassy
hills.

How were the World War II POWs were treated in the USA?

There was a joke in the German military during World War
II which said, if there is ever a world war, get on the side fighting the United States
and then surrender to them, and you'll be sure to come home alive.  While this wasn't a
joke you said to the wrong people, it was generally
accurate.

While POWs in Japan's empire or in the Soviet
Union had to literally fear for their lives, and depending on country of origin,
possibly in Germany too, those captured and actually imprisoned by Britain or the US
were all but guaranteed to survive.  The worst that would happen to you is you would be
forced to do agricultural work (the US was short of farmworkers during the war), but
even then, when working on family farms, the family would be required to provide a
meal.

My Mother-in-law was a young child in Kansas dring
the war, and they had a group of five German POWs who regularly worked for their father
in planting and harvest time.  Kids were told to stay out of the room when the POWs were
eating lunch, but my Mother-in-law snuck in one time, a German saw her and immediately
burst into tears, no doubt thinking of his own daughter back home, who he was eventually
returned to once the war ended.

Why do you think Hughes entitled this poem "The Weary Blues" rather than something like "Harlem Blues" or "Piano Man Blues"? What do you...

Truthfully, the only way to know why Langston Hughes
titled his famous poem "The Weary Blues" would be to ask him. Given that we no longer
have that option, your opinion is as good as mine.  However, as you noted in the
question, there might have been good social reasons to include the word "weary" in this
particular poem.  The writers of the Harlem Renaissance, of which Hughes was a part, had
good reason to be weary. They were fighting an uphill battle, both as Americans of color
and members of a cultural movement to be taken seriously as practitioners of their
common craft.  Hughes' emphasis on weary also applies well to a blues musician, a piano
player working in a bar for a living had to play long hours for people who often did not
appreciate that fact.  One would indeed be weary by the end of the
night.

But I don't think Hughes was only being literal. I
think his use of the term "weary" is specifically meant to point out the body and soul
weariness of trying to be accepted as equals after so many generations of slavery and
maltreatment.  Plus, playing for whites, as so many of the jazz musicians of the time
did, would add another element of weariness to people who were already carrying a heavy
burden.

How is Pitty Sing (the cat) instrumental to the whole plot of "A Good Man Is Hard To Find"?

The cat in O'Connor's "A Good Man is Hard to Find" causes
the accident that leaves the family stranded in the vicinity of The Misfit and his
partners in crime. 

In this O'Connor story, the grandmother
must come into contact with The Misfit.  The spiritually fallen woman must interact with
the twisted, grotesque force that shows her the error of her ways, so to speak.  The cat
enables O'Connor to steer the grandmother toward the meeting.  This leads to the woman
understanding, perhaps and at least in part, the truth of her beliefs and behaviors.  It
also allows The Misfit to reveal the truth that he speaks of when he declares that she
would have been a good woman if someone had held a shotgun to her head everyday of her
life. 

O'Connor believed that this was the only means of
salvation for spiritually hardened or lackadaisical
Christians.

Incidentally, the cat's presence in the car
reveals characterization of the grandmother as well as adding to the plot:  it provides
still another example of her disrespect for others and her haughty
nature.