Thursday, February 7, 2013

what was the role of America in both the World Wars? it is really basic.

America only entered World War I in Spring, 1917 when
Germany resumed unrestricted submarine warfare. Prior to that time, the U.S. had
attempted to maintain neutrality. At the time the U.S. entered the war, both the Allied
and Central Powers were exhausted and locked in a stalemate. With fresh troops and the
strength of its economy behind it, the U.S. entry into the War played a key role in the
collapse of German lines. Primary American commander in World War I was General John J.
"Black Jack" Pershing; who presumably said upon landing in France, "Lafayette, we are
here." The war ended November, 1918; so U.S.participation was not that lengthy, but was
important.


The U.S. danced around neutrality originally in
World War II; although it was more involved than the government would like to admit. The
U.S. furnished Britain with "overaged" naval destroyers and also stopped shipments of
oil and scrap metal to Japan before it became actively involved. Japan had already
determined that war with the U.S. was inevitable and planned the attack on Pearl Harbor
to destroy the U.S. Pacific Fleet.


The U.S. entered the war
after the Japanese bombed the fleet at Pearl Harbor on December 7, 1941. This was one
day after the German advance on Stalingrad was halted on December 6. Two days after the
U.S. declared war on Japan, Germany and Italy declared war on the U.S. American role in
World War II was much more decisive than in World War I. Dwight D. Eisenhower, later
president of the United States, was Supreme Commander of the European Theater of
Operations and personally directed the D-Day invasion of Normandy. In the Pacific
Theater, General Douglas McArthur commanded ground forces and Admiral Chester Nimitz
commanded Naval forces. The war ended after an American plane dropped an Atomic bomb on
Hiroshima and later Nagasaki in August, 1945.

What is x if the numbers 2*square root(x-1), 3+square root(2x-6), 2*square root (x+4) are the terms of an arithmetical progression?

If the given numbers are the consecutive terms of an
arithmetical progression, we could use the arithmetical mean
theorem:


3 + sqrt(2x-6) =
[2sqrt(x-1)+2sqrt(x+4)]/2


3 + sqrt(2x-6) = sqrt(x-1) +
sqrt(x+4)


We'll raise to square both
sides:


9 + 6sqrt(2x-6) + 2x - 6 = x - 1 + 2sqrt[(x-1)(x+4)]
+ x + 4


We'll combine like terms both
sides:


3 + 2x + 6sqrt(2x-6) = 3 + 2x + 2sqrt(x^2 + 3x -
4)


We'll eliminate 3 + 2x both
sides:


6sqrt(2x-6) = 2sqrt(x^2 + 3x -
4)


We'll divide by
2:


3sqrt(2x-6) = sqrt(x^2 + 3x -
4)


We'll raise to square both sides to eliminate the square
root:


9(2x-6) = x^2 + 3x -
4


x^2 + 3x - 4 - 18x + 54 =
0


x^2 - 15x + 50 = 0


The roots
of the quadratic are x1 = 5 and x2 = 10.


The
given numbers are the consecutive terms of an arithmetical progression if the values of
x are: x = 5 or x = 10.

How to find the lower an upper quartile given an even set of data?Take 2, 2.5 ,4,5.5,6,7 as an example!...

Quartiles are basically measures of central tendancy in a
group of data that divide it in four subgroups by three quartiles Q1, Q2 and
Q3.


Q1 - First Quartile - seperates first 1/4th data from
remaining 3/4th data (located at 25th
precentile)


Simillarly Q2 and Q3 are located 50th and 75th
percentile.


Now, the formula for finding quartile is i =
(P/100)*n where p = percentile and n = number of terms in
data.


If we get i=whole number, we take the quartile as the
average of ith term and (i+1)th from the data, eg. if i obtained is 3, we take average
of 3rd and 4th term as quartile


If "i" obtained is not
whole number, we simply take next term as quartile, eg. if i obtained is 3.75, we take
4th term as quartile.


In your
example,


Date = 2, 2.5, 4, 5.5, 6,
7


Q1(Lower Quartile), p=25, n=
6


i = (25/100)*6 = 1.5,


Since
i obtained is not a whole number, we take 2nd number as quartile, therefore Q1 =
2.5


Simillary for Q3(Upper Quartile), p=75,
n=6


i = (75/100)*6 = 4.5


Since
i obtained is not whole number, we take 5th number as quartile, therefore Q4 =
6.


Ans.:-


1) Lower Quartile Q1
= 1.5


2) Upper Quartile Q3 = 4.5

In the context of the American Dream, discuss Lennie's own hopes in Of Mice and Men.

Lennie's own vision represents the desire for domestic
happiness which is a part of the "American Dream."  While a significant part of the
American Dream is the idea of being able to generate wealth and develop a sense of
autonomy in one's life, I think that another part resides in domestic tranquility and
happiness in the personal realm.  This component of the American Dream builds on the
idea of private happiness, or finding a realm of comfort that cannot be intruded upon by
the outside world.  Certainly, Lennie desires for this.  From the start of the novel, he
wishes to own this farm with George where he can "tend the rabbits."  The ability to
feed, pet, and take care of the rabbits becomes the representation of his own happiness
in his American Dream.  Lennie does not covet money or power, but rather the
establishment of the private realm where his happiness lies.

Wednesday, February 6, 2013

What is the definite integral of y = square root(1-x^2) if x=0 to x=1.

I'll suggest to replace the variable x by the function sin
t.


x = sin t


We'll
differentiate both sides and we'll get:


dx = cos t
dt


We'll change the limits of integration,
too:


x = 0 => t = 0


x =
1 => t = pi/2


The definite integral will be
evaluated using the Leibniz Newton formula:


Int sqrt[1 -
(sin t)^2] cos t dt = F(pi/2) - F(0)


But, from Pythagorean
identity, we'll have:


1 - (sin t)^2 = (cos
t)^2


We'll take square root both
sides:


sqrt [1 - (sin t)^2] = sqrt (cos
t)^2


sqrt [1 - (sin t)^2] = cos
t


Int sqrt[1 - (sin t)^2] cos t dt = Int (cos t)^2
dt


Int (cos t)^2 = Int (1+cos
2t)dt/2


Int (1+cos 2t)dt/2 = Int dt/2 + (1/2)*Int cos 2t
dt


Int (1+cos 2t)dt/2 = t/2 + sin
2t/4


F(pi/2) - F(0) = pi/4 + sin pi/4 - 0 + sin
0/4


sin pi = 0


F(pi/2) - F(0)
= pi/4


The definite integral of the given
function is: Int sqrt(1 - x^2) dx = pi/4

can someone tell me how to work this question out? need to know for exam. A drink stall sells small,medium and large cups of fruit drink for...

Let S, M and L stand for small, medium and
large. 


So S(1.5) + M(2) + L(2.5) = 1360.  This means each
size cup times its price, all added together equals the entire amount of
$1360.


 But you can't solve with three different variables,
so you have to get everything so you only have one variable.  Let's see what you
know:


3S=M    3 times as many medium drinks as small or,
turning it around, 1/3M=S.


L= M-140    Number of large cups
is 140 less than the number of medium


Now, plugging in: 
1/3M(1.5) + M(2) + (M-140)(2.5) = 1360.


By working out the
value of M mathematically, you will know how many medium cups were sold.  1/3 of that
number will be the number of small cups, and the number of Medium - 140 will give you
the number of large cups.

In "Dusk" by Saki, what is the meaning of "jostling ranks of those who enjoyed prosperity or struggle for it?"

In "Dusk," by Saki, the narrator shares the main
character's disposition. The reader understands what Gortsby is
thinking:



So
Gortsby's imagination pictured things as he sat on his bench in the almost deserted
walk.



Gortsby believed the
defeated came out at dusk. He is feeling defeated at the
moment:



He was
in the mood to count himself among the
defeated.



If the defeated
show up at dusk, why is Gortsby out at this time of the evening? While some people who
come out at dusk have money problems, this is not the case with Gortsby. He did not have
financial issues:


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Money troubles did not press on him; had he so
wished he could have strolled into the thoroughfares of light and noise, and taken his
place among the jostling ranks of those who enjoyed prosperity or struggled for
it.



In this passage, jostling
means to push or shove or to brush shoulders or elbows. Gortsby can fit in with the
wealthy who brush elbows in upper class events. The jostling ranks would be the upper
class people who enjoy money, those who rub elbows because of their prosperity. The
jostling ranks consist of people who attend upper class events because they are wealthy.
The jostling ranks have money through inheritance or through a struggle of hard
work.


Gortsby is thinking that he can push and shove with
the best of those who have money. He can brush shoulders or elbows with those who enjoy
money or struggle for money. In other words, money is not the issue. Gortsby can hold
his own when it comes to financial situations. Gortsby has
money.


Gortsby is sitting on the park bench for another
reason. He is preoccupied with something, but it is not a money issue. He can take his
place with those who rub elbows in high ranked positions of
society.

What accomplishments did Bill Clinton have as president?

Of course, Bill Clinton's presidency will be most clearly remembered for the fact that he was only the second president ever...