Why did the Articles of Confederation fail?

They failed because they did not manage to convince the
elites of society that their interests would be protected by the sorts of governments
that sprang up under the Articles.

During the time that the
US was under the Articles, there were various kinds of economic problems.  The state
governments' responses to the problems (spurred by the demands of the common people who
were being hurt most by the problems) hurt the interests of the elites.  They also
convinced the elites that the nation would not be able to prosper economically under the
sorts of governments that would take those steps.  (Follow the link to see what the
economic problems and the states' responses to those problems
were.)

So, the Articles failed because the elites who took
the most interest in government felt that the governments were acting in ways that were
bad for A) the interests of the elites and B) the long-term interests of the country as
a whole.

Give an example of personification in the poem "To His Exellency, General Washington," by Phillis Wheatley.

This poem by Phillis Wheatley, "To His Excellency, General
Washington," was written and sent in a letter to General Washington by the author. 
Wheatley was obviously inspired by Washington, and his return letter to her is equally
complimentary.  Wheatley uses many complex images and allusions, and this poem is no
exception.  Your question is about personification, and I found several examples in the
first few lines of this poem. 

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While freedom’s cause her anxious breast
alarms,
She flashes dreadful in refulgent arms.
See mother earth her
offspring’s fate bemoan,
And nations gaze at scenes before
unknown!

Here, freedom and
mother earth have been personified (inanimate objects given human qualities).  Freedom
here feels alarm, and she "flashes dreadful"--both human actions which a literal freedom
can not do.  Mother earth has children ("offspring") and she "bemoans" (cries out in woe
over) their fate. 

If you keep reading, there are plenty
more examples of personification in this poem.  The e-notes link below has some other
helpful information regarding Phillis Wheatley and this particular
poem. 

How is Granny Weatherall's outlook on life influenced by her actions in "The Jilting of Granny Weatherall"?

I think one element about Granny Weatherall's character
that comes across incredibly strongly is her independence and inner-strength. Part of
the reason why she is so cantankerous in her near-death state is because suddenly she
has to be dependent after years of being independent. Consider one of her memories of
her life before getting old:

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In her day she had kept a better house and had
got more work done. She wasn't too old yet for Lydia to be driving eighty miles for
advice when one of the children jumped the track, and Jimmy still dropped inand talked
things over: "Now, Mammy, you've a good business head. I want to know what you think of
this?... Old. Cornelia couldn't change the furniture around without asking. Little
things, little things!

We can
see then that Granny was considered capable, intelligent, and reliable; her grown
children came to her for advice and she is immensely proud of her homemaking skills and
her capacity for hard work. We can see then that these qualities have a massive impact
on her outlook on life as she looks at life through her "lens" of independence and
inner-strength, so that at the end of the story, she meets death with the same customary
strength as she has shown throughout the entire story.

A circular cylinder is to fit inside a sphere of radius 10 cm. Calculate the maximum possible volume of the cylinder. Use differentiation (dy/dx)It...

Let r a be the radius of the cylinder and 2h be the height
of the cylinder. and R be the radius of the sphere.

Then
the  consder  the points , O the centre of the sphere, the centre  P of the top cercular
face and a point A on the top cirular circumference .

OPA
is right angle OP= h, OA = R and PA = r.

Then R^2 =
h^2+r^2.........(1).

Volume of the cylinder  V = pir^2*2h =
pi(R^2-h^2)2h = 2pi (R^2*h-h^3)

For maximum volume, dV/dh =
0  for som h = h1 and d^2V/dh^2  = should be negative at h =
h1.

dV/dh= V'  = 0 gives: 2pi (2R^2*h-h ^3)' =
0

V' = 2pi (R^2-3h^2) = , (R^2-3h^2) = 0 , R^2 = 3h^2 , h =
(R^2/3)^(1/2) = R/sqrt3

d2V/dh^2 = 2pi(R^2-3h^2)' = - 12pih
is negative as h >0. So for h = R/sqrt3, V = 2pi(R^2-h^2)h attains the
maximum.

Therefore maximum volume V = 2pi (R^2-R^2/3)
(R/sqrt3)

= 2pi (2/3)R^2
(R/sqrt3)

=  (4/9)(sqrt3) Pi*
R^3

= 2418.4 cm^3.

In A Midsummer Night's Dream, how will the Puck change the situaton of Hermia, Lysander, Helena and Demetrius?

You might find it helpful to focus on one particular scene
rather than the whole play to answer this question. Therefore to help you out I am going
to focus on Act III scene 2 and look at the changes that occur in the lovers here. Of
course, what you need to remember is that previous to this, Lysander has been made to
fall in love with Helena instead of Hermia.

The riotous
confusion of the Athenian lovers continues in this scene, as Oberon and Puck realise
that Puck has made a mistake and has annointed the wrong Athenian youth. We see that
Lysander is now desperately in love with Helena, having abandoned his betrothed, Hermia,
and we, like Hermia, are bewildered and suspicious of the change in the affections of
the apparently steadfast Lysander as he protests his love to
Hermia:

Why
should you think that I should woo in
scorn?

Of course, this
situation is further complicated when Demetrius wakes up, having been anointed by Puck,
and sees Hermia. Again, he, like Lysander, has a complete change of character in terms
of who he loves:

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O Helen, goddess, nymph, perfect,
divine,

To what my love, shall I compare thine
eyne?

This situation seems to
escalate as Hermia enters, still trusting in the steadfastness of Lysander's affections,
and her resulting horror, rage and anger against Helena who she holds responsible for
taking Lysander away from her.

Of course, what is important
to note is how Shakespeare is using the events of this play. He is making a comment
about love and how fickle our emotions often are, but what is so masterful about what he
does is that by making us as the audience laugh at such events, we pronounce our own
judgement on ourselves for the irrational acts and words we utter when we are under the
spell of love. We are perhaps more fickle when under the spell of love than we give
ourselves credit for.

DISCUSS THE ELEMENTS OF PASTORAL ELERGY WITH REFERENCE TO MILTON'S "LYCIDAS."

Lycidas is considered to be the
archetypal pastoral elegy in English; as a result, it embodies many of the
characteristics of the pastoral.  One of the major pastoral elements of the poem is that
Milton disguises himself and Edward King (the friend for whom the poem was written) as
"swains," or shepherds.  Milton likens their life together at Cambridge to the life of
the mythical shepherds, herding sheep and playing music.  As a result, the whole poem is
told through this pastoral "lens."

Another feature of the
pastoral evident in the poem is its harmony with nature.  After Lycidas dies, nature
mourns him; the flowers all die, and the vines shrivel up.  Similarly, they are brought
forth in a beautiful catalog of flowers to decorate Lycidas's grave.  The plants and
nature seem to feel for Lycidas and the speaker, and to be active participants in the
mourning.

However, an anomalous feature in
Lycidas that doesn't fit within the traditional pastoral trope is
the easy blending of pagan and mythical thought with Christianity: Milton's reference to
"he who walks the waves" would be anachronistic for his ancient pastoral
setting.

Mark is 4 years older than his sister. What are their ages if after 3 years Mark will be twice her age.

Let mark's age be M and his sister's age is
S

Given that mark is 4 years older than his
sister:

Then M = S + 4
............(1)

Now after 3
years:

Mark's age = M + 3

His sister's
age = S + 3

But Mark's age will be twice his sister's
age:

==> M+3 = 2 (
S+3)

==> M + 3 = 2S +
6

==> M = 2S + 3

But from (1) we
know that M = S + 4

==> S + 4 = 2S +
3

==> S = 1

Then the sister's
age = 1 year old

Then Mark is 1+ 4 = 5 years old
Now

After 3 years:

Mark will be 5+3 = 8
years old

His sister's age will be 1 + 3 = 4  years
old