A piece of wire 24 cm long has the shape of a rectangle. Given that the width is w cm, show that the area, A cm^2....., of the rectangle is given...

If the length of the rectangle is 24 and the width is w,
then the width of the rectangle could be found from the formua of perimeter of the
rectangle.

The perimeter of a rectangle is the sum between
twice length and twice width.

P = 2*24 +
2*w

We'll factorize 2 and we'll
get:

P = 2(24+w)

The area of
the rectangle is:

A = 36 -
(6-w)^2

We'll expand the square and we'll
get:

36 - 36 + 12w - w^2

We'll
eliminate like terms and we'll get:

A = 12w -
w^2

We also know that the area of the rectangle is the
product of the length and the width.

24w = 12w -
w^2

We'll move all terms to one
side:

w^2 - 12w + 24w = 0

w^2
+ 12w = 0

We'll factorize by
w:

w(w+12)=0

Since the width
cannot be 0 or negative, the relation for area doesn't hold.

How to write a letter to your boss requesting status change from part-time to full-time position.for a job

When you write this request, make sure to use standard
English and write in complete sentences. Have a greeting (like "Dear ____,"), a body
(your request), closing ("Sincerely,") and your signature. Use your best handwriting,
or, type it out and sign your name at the end.

Regarding
the content of the body--be respectful by noting that you value your job and appreciate
your boss for considering your request. State your argument as brieflly as possible. Be
firm, though, and don't make any apologies for your request. If you are a good worker
and deserve more hours, you should be honest about that. Trying something like this: I
feel like I deserve to become a full-time employee because I have been a dedicated
worker and always show up to work on time..."

I hope all
goes well!

How should marginal costs be considered when determining prices?

The basic rule of setting prices is that a firm must
produce a quantity of goods or services that allows the marginal revenue to be equal to
the marginal cost.  This is called the profit-maximizing point.  From this point of
view, a firm should determine the optimal quantity of products to make and should then
set its price so as to sell all of those products.

However,
there are cases in which firms should vary their prices.  There are instances in which a
firm should set prices for some people higher than marginal costs and sell to other
people at a price that is lower than marginal costs.  This is called price
discrimination and should be used when it is not possible for someone to buy at a lower
price and then turn around and resell the thing they have
bought.

For example, let us say that an airline has empty
seats on a given flight on the day that the flight is scheduled to leave.  The empty
seat will cost the airline money.  Therefore, the airline should sell that seat cheaply
to anyone willing to buy it so long as the price is higher than the marginal cost of
carrying that passenger.  

What is meant by Nick's comment: "Then it had not been merely the stars to which he aspired on that June night. He came alive to me...."The quote...

In Chapter Four of The Great
Gatsby, Nick Carraway's admiration of the quest for the ideal and romantic
reaction to Jay Gatsby's purchase of the house in West Egg for the sole purpose of being
near Daisy Buchanan foreshadows the ending lines of the
novel:

Gatsby
believed in the green light, orgastic future that year by year recedes before us.  It
eluded us then, but that's no
matter...

Despite his knowing
that Jay Gatsby's personal history is fabricated, Gatsby emerges for Nick Carraway as
the Romantic Ideal.  He pursues his "holy grail" and attains mythological proportions as
his car is likened to the flight of Icarus soaring through the Valley of Ashes "with
fenders spread like wings."

This statement of Nick about
Jay Gatsby in Chapter Four underscores the themes of aspiration and the theme of
the ideal.  For him, Gatsby's car's "three-noted horn" trumpets the approach of royalty
among the decadent, materialistic crowd that frequents Gatsby's
parties.

What does Homer Barron represent? How importent is it that he is a Yankee? From "A Rose for Emily" by William Faulkner.

In "A Rose for Emily," Homer is a Northerner, as opposed
to a Southerner, and it is very important that he is a
Yankee.

The story presents a South that is still recovering
and changing following the collapse of the Southern economy during and following the
Civil War.

The townspeople represent the new South, the
South after the economy that was based on plantations has
collapsed. 

Emily represents the old South, and she does
not adjust well to the new society.  Emily's holding on to the past, to the way things
were before, is representative of the South holding on to a past that was seen as
glorious.

Homer is from the victorious North.  He is a
Yankee.  He is looked down upon by the townspeople, and Emily is criticized when she is
seen with him.  In the socially conservative South, being seen with a beau in public is
anathema, but being seen with a beau from the North is even worse.  He is seen as
"below" Emily. 

The story is a bit of a microcosm of the
South after the Civil War, and Homer is part of the invading and unwanted
North.

What is the difference between bulls and steers in Chapter 13 of The Sun Also Rises?In Jake’s group, who are bulls and who are steers? And what...

The bulls are potent, the steers, having been castrated,
are not. The bulls are center stage in the sport of bull fighting, and are seen as noble
and respected. The steers, on the other hand, exist to serve the bulls. They are put in
the corrals with the bulls to

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"...keep them from fighting, and the bulls tear
in at the steers and the steers run around like old maids trying to quiet them
down."

To be a steer is not a
good thing; sometimes the bulls "go right after them and kill them." The steers' sole
purpose is to "quiet down the bulls and keep them from breaking their horns against the
stone walls, or goring each other." As Bill sardonically
notes,

"It
must be swell being a
steer."

In Jake's group,
Jake, having been rendered impotent in the war, is the steer. He and Brett seem to have
a close tie, but because he cannot consumate their relationship, he is relegated to the
role of the steer, forever trying to calm the men who can. Mike and perhaps Robert Cohn
are the bulls, vying for the favors of the female, Brett Ashley, although I believe
Robert Cohn can also be considered a steer, because when forced to confront Mike, he is
sorely lacking in resolve and effectiveness. This relationship among Jake, Brett, Mike,
and Robert Cohn, the steer(s), the female, and the bull(s), is representative of the
values of the time among the "Lost Generation" because it illustrates that immediate
gratification and physical satisfaction are more important than love. It is Jake whom
Brett loves, or seems to love, but since he cannot have sex with her, she constantly
seeks the company of other men more potent than him. Jake, on his part, can do nothing
more than act the part of the steer, looking after Brett while others vie for and win
her favors (Chapter 13).

In The Crucible describe the sequence of events that lead to the discovery of the poppet.

We learn about the poppet and what caused it to be
discovered near the end of Act Two.  Herrick and other officials of the court come to
John's house, and immeidately start searching, asking if they keep any poppets in the
house.  Earlier that evening, Mary Warren had come home from court and given the poppet
to Elizabeth, telling her that she had sewed it for her during the court's proceedings
that day.  Unfortunately for Elizabeth, there was a needle stuck in the belly of the
poppet, which the courts took as proof of witchcraft.  We can piece together the events
as follows:

1. While Mary and Abby are in court that day,
Abby notices that Mary is sewing a doll, and that she put the needle in the doll's belly
at the end of the day.

2.  Abby, who was unable to cast any
negative light upon Elizabeth Proctor in court that day, comes up with a plan.  That
night at dinner, in front of the judges, she sticks a needle in her belly, falls to the
ground in pain, screaming out that it is Elizabeth's "familiar spirit" that put the
needle there, through means of a voodoo doll.  She says that Elizabeth made a doll, and
through witchcraft, is manipulating it to harm Abby.

3. 
The courts issue a warrant for Elizabeth's arrest, provided they can find proof of the
voodoo doll theory.  While this is going on, Mary goes home and gives Lize the
doll.

4.  The court officials show up and find the doll. 
Elizabeth denies the charges, and even Mary says that Abby saw her put the nedle in the
doll herself.

I hope that clear things up a bit.  I hope it
helped!