Could you tell me about the setting of the Women's Missionary Circle in chapter 24 of To Kill a Mockingbird?

I would confirm that the missionary circle takes place at
the Finches' home under the care of Aunt Alexandra during the end of summer before the
kids go back to school, in August.

Aunt Alexandra was
hosting this event so that the ladies of Maycomb who helped support the missionary J.
Grimes Everett would have the opportunity to learn about where their donations are going
and what the donations are doing. However, we find that through Scout's eyes, the
missionary circle is about much more than that. They gossip and participate in terrible
hypocrisy.

The significance of this event in this time and
this place is that it allows Scout to discover some disturbing information in the
kitchen about Tom Robinson. Had the meeting been at someone else's house, Scout might
not have learned the information because she likely wouldn't have gone.  Being the end
of summer, the trial is still fresh in everyone's minds and it is almost too much to
bear for the Finch family. This build great suspense.

Why was the Dual Monarchy of Austria/Hungary important in European history between 1867 and 1918?

I would say that the main importance of the Dual Monarchy
during the time that it existed was the fact that its involvement in the Balkans led to
the start of World War I.

The Dual Monarchy was, of course,
led by monarchs who were ethnically German.  However, it governed areas that had many
different ethnicities.  The most important of these (in terms of world history) were the
Slavs in the Balkans.  This was especially true after the 1908 Balkan Crisis in which
the Dual Monarchy took Bosnia-Herzegovina over the protests of the (Slavic)
Serbians.

The rising nationalism of the Slavs inside and
outside of Austria-Hungary helped cause WWI when Slavic extremists assassinated Archduke
Franz Ferdinand in 1914.

In the postscript to the story, is the "tall, dry-looking old gentleman" who demanded to know the moral of the story, really Ichabod Crane?

The only real reason to believe that this man is in fact
Ichabod Crane comes from his physical description.  We are told that he is tall and dry
looking and that he does not seem very inclined to laugh.  These things could well
describe Ichabod Crane.  However, they could just as well describe any number of other
people and are not, therefore, good grounds for concluding that the listener is in fact
Crane.

If we look at what the man says, there is little to
make us think that he is Crane.  He does not dispute the story or try to say anything
that would make the listeners think better of Crane.  Instead, he simply asks what the
moral of the story is and then says he thinks the story is somewhat extravagant.  This
hardly seems like what Crane would say if he heard the story being told.  One would
think that he would be trying to defend himself and to make himself look less like an
object of humor.

Explain how the story of Frankenstein developed into a tale of terror. The plot come to Marry Shelley in a dream.

Mary Shelley references how Frankenstein
came to be in the introductions to her novel. One of the most poignant introductions is included
in the 1831 publication of Frankenstein.

The
historical tale of how the novel came to be is renowned. Mary Shelley, accompanied by her husband
(Percy Bysshe Shelley), were vacationing with Lord Byron and John Polodori. Lord Byron decided to
pose a challenge to create a ghost story. The four agreed that it sounded like a good idea, given
they were confined to the house due to rain.

After a few days, Mary
Shelley had a dream, or more of a nightmare. She dreamed about a "student of unhallowed arts"
bent over his "hideous phantasm of a man." The student, exhausted by his labors, awakens to find
his "hideous corpse" staring at him with yellow eyes.

Upon
awakening, Mary Shelley realized that she had her ghost story. The image of the creature
frightened her so much that she realized it would frighten others as well. The story was
completed upon her husband's urging.

Given the circle center (1,1) and the point on the circle (3,5) what is the equation of the circle.

We'll write the equation of the
circle:

(x - h)^2 + (y - k)^2 =
r^2

The center of the circle has the coordinates C(h ;
k).

We know, from enunciation, that h = 1 and k =
1.

We'll substitute them into the
equation:

(x - 1)^2 + (y - 1)^2 =
r^2

 We'll determine the radius considering the constraint
from enunciation that the circle is passing through the point
(3,5).

If the circle is passing through the point (3,5),
then the coordinates of the point are verifying the equation of the
circle:

(3 - 1)^2 + (5 - 1)^2 =
r^2

2^2 + 4^2 = r^2

4 + 16 =
r^2

20 = r^2

r =
2sqrt5

Note: we'll reject th negative value of radius
-2sqrt5.

The equation of the circle
is:

(x - 1)^2 + (y - 1)^2 =
20

What is x if x^2+(1/x^2)+x+(1/x)=4 ?

x^2 + ( 1/x^2 ) + x + 1/x =
4

First we will re-write into two
parts.

==> ( x^2 + 1/x^2 ) + ( x+ 1/x) =
4

Let x + 1/x =
y..............(1)

==> (x+ 1/x)^2 =
y^2

=> x^2 + 2 + 1/x^2 =
y^2

==> x^2 + 1/x^2 = y^2 -
2............(2)

Now we will substitute ( 1) and
(2).

==> (y^2 - 2 ) + ( y) =
4

==> y^2 + y - 2 =
4

==> y^2 + y - 6  =
0

==> ( y + 3) ( y-2) =
0

==> y1=
-3 

 ==> x + 1/x  =
-3

==> x^2 + 1 =
-3x

==> x^2 + 3x + 1 =
0

==> x1 = ( -3 + sqrt(5)
/2

==> x2= (
-3-sqrt5)/2

==> y2=
2

==> x+ 1/x =
2

==> x^2 + 1 =
2x

==> x^2  -2x + 1
=0

==> ( x-1)^2 =
0

==> x= 1

Then x
values are:

x = { 1, (-3+sqrt5)/2 ,
(-3-sqrt5)/2}

What are the four exmaples of disease imagery used in Act 4 of Hamlet?

There is disease and decay imagery throughout the play,
but in Act 4 the disease imagery is primarily used by Claudius in his talking about the
problems he is having with Hamlet.  Here are three
examples:

1.  In talking with Gertrude about Hamlet in
scene 1 Claudius says that the people will think that it was their great love of Hamlet
that kept them from keeping him under control or stopping him, and therefore he was a
danger and he killed Polonius.  He compares this to a disease when he says they are
"like the owner of foul disease, to keep from it from divulging, let it feed even on the
pith of life."  They are willing to let the disease (of Hamlet) destroy them rather than
admidt there is problem.

2.  In a short soliloquy at the
start of scene 3 Claudius calls Hamlet a disease and states that, "diseases desparate
grown by desparate appliance are relieved."  He means that the only way to end the
problem of Hamlet is by some desparate means -- he plans to have him killed in England. 
The worse the disease the worse the cure (like cancer and
chemotherapy).

3.  At the end of the scene 3 Claudius again
refers to Hamlet as his disease and says he is "like the hectic in my blood (and) he
rages" and is calling on England to "cure" him.