Based on the event & details in "The Lottery," what is the argument the author seems to be making about the social contract?

I think that Jackson is making a pretty strong statement
against the social contract in the short story.  The social contract is the
understanding that the community and the government share in the general will, in the
same conception of the good.  Jackson's story reflects how this can be twisted to
suppress the rights of individuals.  In this light, Jackson seems to be arguing that
there should be some type of individual entitlements that can supersede the general will
in the event it is wrong.  The "tradition" of the people in the village is an exercise
in brutality.  Yet, the general will is evident in that community and political
structure both endorse this heinous act.  In the end, it is this point that Jackson
seems to be making in the name of the general will.  If the community and political
leadership is wrong, Jackson seems to be asking where individuals will turn to find some
level of sanctuary or relief.

In Cry, the Beloved Country, for what charge does Absalom's lawyer want him to plead guilty, and what does he ultimately plead?

Absalom, a cousin, and a friend were attempting to rob Arthur
Jarvis, and unfortunately, Absalom was carrying a gun for protection. When Jarvis returned home
unexpectedly, Absalom shot and killed him in a moment of panic and fear. It wasn't truly an
accident, but it wasn't a premeditated plan to kill the man.

The
lawyer, Mr. Carmichael, wants Absalom to plead guilty to firing the gun "because he was afraid."
Unfortunately, the cousins get a very good lawyer and completely deny even being present when the
incident occurs; they say they have no idea why Absalom is trying to bring them into this case.
It is a very challenging situation that is not likely to have a good
outcome.

At the trial, Absalom wants to plead guilty to
unintentional homicide--admitting to killing Jarvis, but not on purpose--not murder. The problem
is there is no charge of homicide, there is only a charge of murder, so Absalom pleads not
guilty. Unfortunately, the judge has no choice but to find Absalom guilty of the crime with which
he is charged, murder. The sentence for this crime is death. It is a heart breaking reality of
the South African law.

Find the circumference of a circular disk whose area is 100pi square centimeters.

The area of a circular disk with radius r is given by pi*r^2,
wher pi  is the ratio of the circumference to the diameter of the
circle.

The actual area of the disk is 100pi sq
cm

Therefore pr^2 = 100pi sq
cm

Therefore r ^2 = 100 sq cm. So r = sqrt100 = 10
cm.

So the radius of the disk is 10
cm.

The circumference c of the circular disk is given
by:

c = 2pir.

Therefore c = 2p*10 cm =
20pi.

Therefore the circumference of the disk = 20
pi.

Please explain the quote "Not so happy, yet much happier" in Macbeth.

This quote comes in Act I scene 3 and is delivered by the Second
Witch to Banquo. Having addressed Macbeth with a series of paradoxical prophecies, the Witches
turn to Banquo and deliver a typical set of paradoxical predictions. Of course, a paradox is
something that is not literally true, and overtly it is not possible to be unhappy whilst being
happy, which is what the witches are predicting for Banquo. Yet, it does foreshadow Banquo's fate
and that of his descendants. Obviously, the witches identify the way in which he will be unhappy
because of his death at the hands of Macbeth, but it also foreshadows the way in which Banquo
will ultimately be a lot happier because of the successful escape of Fleance, and the way his
descendants will take the throne of Scotland. Thus, Banquo's death by treachery is balanced
against the success of his line in gaining the crown. Macbeth will die childless, and thus
Banquo's descendants will outlive Macbeth's treachery. Such contradictory speech is typical of
the prophecies that the witches deliver and the way that they play on the secret hopes and fears
of characters.

What were the conditions behind the Glorious Revolution?

I would say that there were two main conditions that were
behind this revolution.  They were A) the fact the England had been a Protestant country
for most of the past 150 years at that point and B) the fact that Parliament had come to
have a lot of power in the country's political system.

When
King James I came to the throne in 1685, both of these conditions caused problems to
arise.  James tried to take power away from the Parliament so that he could create a
more powerful monarchy.  He also tried to make England move towards Catholicism.  When
he and his wife had a son, the succession of his dynasty seemed secure and Parliament
decided he needed to be overthrown.

Compare and Contrast Othello and Iago in Othello by Shakespeare.

There will be much out there written on this subject.  I
think that in assessing the relationship between both characters, one has to notice a
shift of weight.  At the start of the play, Othello holds a great deal of power over
Iago in terms of the latter wishing to receive the promotion from the former.  Yet, when
Cassio is favored, it is interesting to see how the relationship changes.  Rather than
become disempowered, Iago actually gains more power in terms of what he is able to do to
others with his manipulation of them.  It might even be argued that he gains more power
with his demotion than anything else.  I think that a comparison of both characters
focus in a study of insecurity.  Iago is insecure of Cassio's position and his apparent
favoring by Othello.  The decision to promote him over Iago triggers in much of this
insecurity, causing him to embark on a manipulative quest.  Othello's insecurities are
much more subtle, not really as evident until things start to work in Iago's favor.  He
is insecure of his ethnicity and age, his status as a soldier who has gained "insider"
status, and the fact that he cannot believe that someone like Desdemona is in love with
someone like him.  In the end, both Othello and Iago are haunted and fraught with
insecurities, making them more susceptible to enduring pain from deliberate and
unintentional acts of cruelty.

How could ‘Optimization of Portfolio’ be achieved?

An investor's portfolio should ideally have several asset
classes and different assets within each asset class. When an asset is added to the portfolio it
is expected to provide a certain return and there is also a certain amount of risk that is
associated with the expected return.

With time, the risk-return
profile of different assets changes. The expected return of some assets may go up with an
increase or decrease in the risk; for others the expected return may have come down with a change
in the associated risk.

This requires the assets in the portfolio to
be altered accordingly to increase returns while keeping the associated risk at an acceptable
level.

Portfolio optimization involves eliminating certain assets
and substituting them with better alternatives that may have become available. An investor or
portfolio manager has to constantly be on the lookout for such
opportunities.

For example if a company has undergone a turnaround
and turned profitable, it would make sense to acquire shares of that company while selling shares
of a company that is not doing that well. Similarly if the portfolio has bonds and interest rates
are expected to rise, the bonds could be sold.

Portfolio
optimization involves a lot of mathematical modeling and calculations to determine the best
choices among the available options. While altering a portfolio there are also several
transaction costs involved which have to be kept in mind. As the transaction costs makes frequent
changes unprofitable, all changes have to be made carefully and with a lot of
thought.