Does Lady Macbeth show any guilt or concern for her part in Duncan's murder before the "Out, damned spot!" soliloquy in Macbeth?

The last appearance of Lady Macbeth before she sleepwalks
onto the stage, in Act V, scene i, is the banquet scene and its aftermath, Act III,
scene iv.  Lady Macbeth does accept the guilt for her part in the murder up to this
point, in fact she revels in the murder and all the guilt that can be accepted.  In Act
II, scene ii, when Macbeth won't return the daggers to the crime scene, she does so
herself.  Upon her return, she says this to Macbeth:

readability="7">

My hands are of your colour; but I
shame

To wear a heart so
white.

She is implying that
any remorse or angst he feels over the murder is the sign of a coward.  Lady Macbeth
bears her part in the murder, her guilt, as a badge of honor in the first Acts of the
play.  It is her 180 degree turn in Act V that reveals the dark side of the effect of
the murder and its guilt on her sanity.

But, even though
Lady Macbeth proudly bears her part in the murder, her guilt, Shakespeare does provide
some ironic foreshadowing of what is to come in Act V for Lady Macbeth.  At the very end
of Act III, scene iv, as she attempts to sooth the rattled Macbeth, she
says:

You lack
the season of all natures,
sleep.

and Macbeth
answers:

readability="10">

Come, we'll to sleep.  My strange and
self-abuse

Is the initiate fear that wants hard
use;

We are yet but young in
deed.

The mention by Lady
Macbeth of sleep as the restorative for Macbeth's addled mind, is ironic because it will
be her lack of sleep and her restless sleepwalking that reveal how her guilt has robbed
her of her peace of mind.

And, interestingly, it is Macbeth
who realizes that he must shake off his regret and remorse in order to be in it for the
long haul.  Throughout the remainder of the play, he is the one who freely accepts his
own guilt while continuing to murder and commit evil with a free conscience.  It is,
ultimately, Lady Macbeth, who is consumed and taken down by her own feelings of remorse
and regret.

For more analysis of Lady Macbeth and guilt,
please follow the links below.

The area of square fenced field is 576 ft^2. Find the area enclosed if we use the same fence to make a circle.

Given that the area of the square field is 576
ft^2

Then, we will calculate the length of the
sides.

Let the side of the field be
x.

==> A= x^2 = 576

==> x
= 24

Now we will calculate the perimeter of the fence
.

==> P = 4*x = 4*24 = 96

Then
the circumference of the circle will be 96 ft.

Now we will calculate
the radius.

==> c = 2*pi * r =
96

==> r = 96/2pi = 15.28
ft.

Now we will calculate the
area.

==> A = r^2 * pi = 15.28^2 * pi = 733.39
ft^2

Then the area of the circular field will be
733.39 ft^2.

Simplify the ratio? 8: 3/4Show full working out and eplain the steps to how you got the answer.

The ratio given is
8:(3/4).

Normally the ratio i in the simplest form is in
lowest possible integer form.

A ratio is same if we
multiply or divide its(ratio's) ordered pair of numbers by an equal number (but
never by zero).

Therefore we
multiply , by 4 here:

8*4  :
(3/4)*4

32 : 3. The new form but still  ratio is  same or
in equivalent form. It is not different  in value from the given ratio. Only physical
form of look of the ratio  has become different.

How does Hawthorne show the major elements of antitranscendentalism in "Young Goodman Brown"?

Hawthorne belonged to a group of authors, including
Melville and Poe, who were known as anti-Transcendentalists, or Dark romantics. This is
because their views of the world were at variance with the views of the
Transcendentalists - of Emerson and Thoreau, for example. These writers placed an
emphasis on Original Sin and the inherent wickedness of human beings. Thus Dark Romantic
literature always features at least some of the following ingredients: the conflict
between good and evil, the psychological effects of guilt and sin, madness in the human
psyche. The attempt of Dark Romantics can be summarised as to strip away the acceptable
and respectable veneer of human nature and reveal the blankness, hypocrisy and evil that
lurks not too far beneath.

Considering this sketch of
anti-Transcendentalist ideas, it becomes clear that a number of these aspects fit in to
"Young Goodman Brown." This is a story that seeks to show the evil inherent in all of us
through establishing the hypocrisy of the Puritan elect in Goodman Brown's locale.
Likewise the fact that everyone needs to make the visit to the woods at least once
indicates that evil is an inherent part of the human condition. We could also say that
the impact of this experience on Goodman Brown and his inability to accept the fact of
evil in all humans illustrates how other forms of evil can operate in Puritan society,
for he ruins his own life and that of his wife through his
depression.

What conflicts are evident in Mrs. Auld's changing behavior toward Douglass in Narrative of the Life of Frederick Douglass?

In my mind, the number one element that is brought out through
Sophia Auld's character is the reality the society of the slaveowner is constructed to be
diametrically opposed to the slave's. When Sophia teaches Douglass how to read and write, it
forces a contradiction between the social orders. A slaveowner, or white society, is not meant to
do anything to benefit or empower the slaves, black society. In this construction, conflict
presents itself when Sophia teaches Douglass how to read and write because such a trait empowers
slaves to break free from their slaveowners, causing challenge to white society who benefits from
the imbalance of social and political power. Sophia's action earns rebuke from her husband, and
her kindness turns into cruelty, demonstrating that the social and political division is
intensely ingrained. This helps to bring out that it will take a great deal of commitment from
individuals to change such a social and political order, something to which Douglass devoted his
life after achieving his freedom.

In chapter seven - How does Nick react when he realizes Gatsby's innocence?

When Nick thinks Gatsby was the one who ran over Myrtle,
he has intense dislike for him.  In fact, he is disgusted with whole crew--Gatsby,
Jordan, Daisy, Tom, after the fiasco at the Plaza Hotel.  After Gatsby tells Nick that
Daisy was the one actually driving, we do not have Nick's initial response.  Chapter 7
closes with Gatsby standing outside Daisy's house watching to see if she flicks on the
light, signaling that she needs his help.  Nick had already glanced into the Buchanans'
house and knows that Daisy and Tom have moved on.  Daisy would not be needing anyone's
help.  So, he leaves Gatsby alone.

However in the following
chapter, Nick goes over to Gatsby's to say goodbye.  Upon leaving, he tells Gatsby,
"They're a rotten crowd" and that "You're worth the whole damn bunch put together!"
 Nick has at this point separated Gatsby from the others, and decided that he is their
moral superior.  After Gatsby is killed, it is Nick who stays around and takes
responsibility for notifying Gatsby's father and "friends."  This last act of Nick's is
a tribute to Gatsby who according to Nick "turned out all right in the end."  He decides
that the others are "careless people" who "smashed up things and creatures and then
retreated back into their money."

During the party at Myrtle's apartment with Tom, how do any one of the guests (or Myrtle) act as if they are something they are not?Recite a...

As part of his satire of the Jazz Age, Fitzgerald points to the
worship of affluence that all classes of people in the time illustrated. In the New York
apartment with the association of the wealthy Tom Buchanan, Myrtle Wilson somehow feels herself
elevated. Additionally, her sister,too, and the others carry on this same charade of social
place. Myrtles's sister, for example, a slender "worldly" girl who, after being called over to
the apartment, enters with what Nick calls "such a proprietary haste" and looks around at the
furniture "so possessively" that he wonders if she does not live there. When he asks her if she
does, Catherine laughs "immoderately" and repeats the question aloud to mock Nick.

In fact, Catherine finds value in being the sister of Myrtle who
has been elevated by being the mistress of such a wealthy man. In a falsely intimate manner, she
leans over to Nick and whispers in his ear about her sister and Tom, "Neither of them can stand
the person they're married to." Then, as though she is part of the society of the Buchanans and
knows them, she tells Nick,

readability="6">

"It's really his wife tha's keeping them apart. She's a
Catholic and they don't believe in divorce....When they do get married...they're going west to
live for a while until it blows
over."

Nick narrates that Daisy is not
a Catholic and he is shocked at the "elaborateness of the lie." This atmosphere of falsity is
perpetuated by Mrs. McKee, too, as she develops Catherine's declaration that she and another
"girl" traveled to Monte Carlo, saying that she almost married someone else until Chester McKee
rescued her. The entire atmosphere of the party is
artificial:

People disappeared, reappeared, made plans to
go somewhere, and then lost each other, searched for each other, found each other a few feet
away.

In The Taming of the Shrew, explain why the quote below is ironic."And place your hands below your husband's foot: In token of which duty, if he...

This quote is heavily ironic because it is Katharina that
utters these lines expressing her desire to do anything to make her husband happy. This
quote comes in a long speech of Katharina's that she is commanded to give by her
husband, Petruchio to tell them about the duty that a woman owes to her
husband:

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Katharine, I charge thee tell these headstrong
women

What duty they do owe their lords and
husbands.

This is situational
irony at its best, for throughout the play, Katharina has been described as the ultimate
"shrew" in her disrespect and sharp-tongued anger that she expresses with great alacrity
towards any potential suitor. Thus to suddenly have Katharina deliver a lecture to the
sweet and mild-mannered Biana on the duties of a wife to her husband is incredibly
ironic.

What did Frederick Douglass regularly speak to his audiences about?

Not surprisingly, the major topic on which Frederick
Douglass spoke to audiences was slavery.  In the time after he escaped from slavery,
Douglass's public life was mainly dedicated to the cause of
abolition.

In his speeches, Douglass talked about slavery
in a variety of contexts.  However, slavery was always at the heart of what he was
discussing.  So, when he talked about his attitudes towards the Constitution, he talked
about how he felt about the fact that it allowed slavery.  When he talked about the
Civil War, he did so because of the impact it would have on
slavery.

So the short answer here is that he was an
abolitionist and talked about slavery in most of his speeches.

Find the slope of the curve x^2 + xy + y^2 = 7 at (1,2)

To do this problem we first apply the product
rule:

d ( xy) / dx = y + x*dy/dx

to find the derivative of x^2 + xy + y^2 =
7.

So the derivative of x^2 + xy + y^2 = 7
is

2x + x*dy/dx +y + 2y* dy/dx
=0

Now taking dy/dx to one
side,

=> dy/dx( x +2y ) = -x^2 -xy -
y^2

=> dy/dx = (-x^2 -xy - y^2) /
(x+2y)

At (1,2)

dy/dx = (-x^2
-xy - y^2) / (x+2y)

=>( - 1^2 - 1*2 - 2^2)/ (1+
4)

=> (-2 -2 -4
)/5

=>
-8/5

Therefore the required slope is
-8/5

Discuss and describe ways that an employer can reinforce safe practices by employees.

Safety at workplace is dependent on many factors which includes
action by the management or owners as well as by the employee or workmen directly engaged in the
work. Direct action by employers includes things like provision of right equipments, facilities
and material for safe working. In addition they also play an important role in promoting safe
working practices by the employee. The action that employees can take mainly relates to the
education of the employees in the importance of safe working and in the methods of safe working.
The employees can conduct periodic training programs for such education, or the employees may be
sponsored to outside training programs. In addition, regular reminder of safe and correct work
practices may be provides by means of appropriate signboards and
posters.

It is important that the employers display their commitment
to safe working practice by not doing anything that tends to show a lack of concern for safety.
For example, an employee who rewards a employee for higher productivity achieved by ignoring
safety precautions, clearly shows disregard for safety. Employers mus take care to avoid sending
any such wrong signals to employees.

What does the idea below suggest about the ways the novel’s plot is or is not dependent on gender differences in Persuasion?In Persuasion by...

Of course, Jane Austen would not have thought in terms of plot
dependence (or lack of dependence) on gender differences; this is purely a contemporary thought
construct. On the other hand, Persuasion is an "ivory" upon which Austen
"paints" the miniature though accurate picture of the lives of men and women in her era in her
class and the classes in which she was privileged to socialize. In these classes, the needs,
requirements, and opportunities of men and women often overlapped yet were as often different. As
a result, someone from the twenty-first century might examine the text of
Persuasion from a cultural theory of criticism and discover a dependence in
the plot on gender differences.

This sort of analysis would be
supported by the conversation Anne and Harville have while standing at the window about the
constancy of men's and women's affection and devotion. Another support for it would be
Wentworth's ability to advance in a career and change his fortunes while, during the same period
of time, Anne only fades in beauty, cares for her demandingly petulant married sister, and
subsists on the expectation of a lonely life. Another support might be Louisa's happiness at
Captain Wentworth's attentions and the expectations of social and financial benefit she and her
family expect to receive as a result of a marriage between them.

What's really happening when Atticus moves backward toward the porch and the crowd draws in, what is Jem, Atticus, the crowd thinking at this...

In Chapter 15 of To Kill a
Mockingbird, Scout narrates that in Maycomb men come and stand in the yard
for only two reasons:  death and politics.  So, when the men arrive in the Finch yard,
they crowd around Atticus who has stepped out to learn their reason for coming. The
children overhear Heck Tate expresses concern that there could be "trouble."  The men
move in and contribute to the discussion.  Link Deas tells Atticus that he has
everything to lose by taking Tom Robinson's case. In short, the men seem to threaten
Atticus in an attempt to get him to give up the case.  But, with great fortitude,
Atticus Finch tells Link Deas:

readability="8">

"Link, that boy might go to the chair, but he's
not going till the truth told....And you know what the truth
is."

Watching from inside,
Jem senses the pressure being put upon his father.  When the phone rings, Jem calls to
Atticus, "...the telepone's ringing!"  This interruption breaks the tension and the men
depart.

What was some of the technology used in the Spanish American War?

The Spanish-American War was not a particularly advanced war in
terms of its technology. There were no airplanes and no machine guns. It was not a war that was
won or lost because of technology.

On the American side, there were
only two weapons that can really be seen as technologically advanced in any way. The first of
these was the Model 1896 Krag-Jorgenson Rifle. This rifle was advanced because of the fact that
it used smokeless powder (new to the US) and because it had a five shot magazine instead of being
a single shot rifle. Most American units, however, did not have this weapon because it was quite
new. Second, the US used the 1895 model of the Gatling Gun. This was not a machine gun, but it
was a weapon that could fire very rapidly. The rate of fire of this weapon was considerable and
it did help the US win the war.

How does Hermia defy her father in A Midsummer Night's Dream?

The plot of this excellent comedy is started or initiated by the
way in which Hermia defies her father. In Act I scene 1 of the play, we are introduced to the
main Athenian characters and the issue that has provoked Egeus, Hermia's father, so sorely. He
craves an audience with Theseus, the Duke of Athens, because of the way his daughter is defying
him. Hermia, although she knows that her father wants her to marry Demetrius, is refusing to
comply with his wishes, and actually wants to marry Lysander. Note what Egeus says about
Lysander:

With cunning
hast thou filched my daughter's heart,

Turned her obedience, which
is due to me,

To stubborn
harshness.

Thus Hermia is defying
Egeus in refusing to marry the man that he wants her to, and insisting on marrying the man whom
she loves. How this problem will be resolved will occupy the rest of the
play.

Where do the lines 3x + 19y =7 and x + 2y = 1 meet?

3x + 19y =
7................(1)

x + 2y =
1.....................(2)

We need to determine the
intersection points of the lines (1) and (2).

The points of
intersection are the points that verifies both equations. Then the points of
intersections are the solution of the system.

Let us solve
the system.

We will re-write equation
(2).

x+ 2y = 1

==> x=
1- 2y

Now we will use the substitution method to
solve.

Let us substitute with x= 1- 2y into
(1).

3x + 19 y = 7

==>
3( 1- 2y) + 19y = 7

==> 3 - 6y + 19 y =
7

==> 3 + 13y =
7

==> 13y =
4

==> y=
4/13

==> x= 1- 2y = 1- 2*4/13 = 1- 8/13 =
5/13

==> x =
5/13

Then, the lines intersects at the point
( 5/13, 4/13)

Comment on the representation of Hinduism in A Passage to India.

On many levels, Forster's depiction of Hinduism and its values
are to be seen through the prism of vast difference that its Western counterparts.  This is seen
in how Forster depicts Professor Godbole.  Through this character, Hinduism is seen as
"accepting" and a type of religious structure where there is total openness and one whose
structure is vastly different than its Western contemporary.  The idea of the sound emanating
from the caves, "BOUM," helps to accent this.  Such a depiction of Hinduism was unique for its
time, in that the book did not show the religion to be something of a savage and indigenous
nature.  Yet, its depiction might have actually contributed to its classification of a religion
where "anything goes."  This certainly might not have been the intent of Forster in doing so, but
his depiction, especially when seen in stark contrast to religions of the West, represents one
where individuals come to understand Hinduism as nothing more than a set of values where
"everything is accepted."  This overall, and limited view of acceptance, is combined with a
depiction that Hinduism is mystical and beyond the reach of the individual, as seen again with
Godbole.  While this might be true, it contributes to the idea that Hinduism is perceived to be a
value system where there is little in way of tradition and dictum.

In A Doll's House, describe the relationship between Torvald and Nora.

Of course, your question relates to the theme of the story
and Ibsen's original intention in writing this excellent play. In A Doll's
House, the position of females in Ibsen's time is examined and he presents
his hope for feminism and equality through the character of Nora and her realisation of
her situation and her choice to embark on a search for her own
identity.

At the beginning of the play, the relationship of
Nora and Torvald is examined. It is clear that their relationship has more in common
with a father and daughter relationship than with a husband and wife, and we discover
that Nora relates to her husband and is treated exactly the same way that she related
and was treated by her father. In response to her husband's insulting comments and
patronising remarks, Nora cajoles, begs and acts like a child (or even a "doll").
Torvald even says: "Has my little sweet tooth been indulging herself in town today by
any chance?" Nora responds using childish phrases: "Oh. Pooh!" It is clear that Torvald
possesses Nora and regards her as nothing more than a belonging to make him look
good.

Nora, too, at the beginning of the play, is caught up
in this "Doll's House", as we can see in her definition of freedom which she gives to
Mrs. Linde: "Free. To free, absolutely free. To spend time playing with the children. To
have a clean, beautiful house, the way Torvald likes it." She is unable to perceive her
situation as being caged inside her "Doll's House" and plays a part of the perfect wife
according to her husband's wishes.

Of course, the action of
the play, and in particular the realisation of Torvald that Nora has deceived him and
his response, triggers the epiphany that Nora needs to realise the truth of her
situation and give her the desire to escape this "Doll's House". In his response to this
realisation, Torvald shows himself to Nora for who he really is: a self-centred, petty
man who is concerned only about keeping up the facade of marriage: "From now on, forget
happiness. Now it is just about saving the remains, the wreckage, the appearance." It is
this unmasking that gives Nora self-understanding of her situation. She says to Torvald,
"I've been performing tricks for you Torvald. That's how I've survived. You wanted it
like that. You and Papa have done me a great wrong. It's because of you I've made
nothing of my life." By the end of the play then, she becomes a stronger, tougher more
independent individual, determined to make her own life free from the constricting
gender roles that have been imposed upon her. We see a woman who is making a bold action
against gender inequality and the position society and culture has given
her.

Find the Antiderivative of f(x)= 3x^4 - square root of 8 x^8 + 5/9x^5

The antiderivative of the given function is the indefinite
integral of f(x).

We'll calculate the antiderivative of the function
you've provided:

f(x) = 3x^4dx - sqrt8*x^8 +
5/9x^5

We'll use the property of integral to be
additive:

Int f(x)dx = Int 3x^4dx - Int sqrt8*x^8 + (5/9)*Int x^-5
dx

Int f(x)dx = 3x^5/5 - 2sqrt2*x^9/9 + (5/9)*x^-4/-4 +
C

The anitderivative is 3x^5/5 - 2sqrt2*x^9/9 +
(5/9)*x^-4/-4 + C.

Was the desire to kill Jews a primary cause of WWII?The Nazi Party had an obvious goal to commit extensive murders against the Jewish population...

No, the primary cause of WWII's Allied response to
Hitler's Germany was the other countries concerns about their borders and sovereignty.
The aftermath of the First World War had not left Europe as an entirely stable
region.

Although there were humanitarian concerns in WWII,
they were not enough to cause the Allied nations to directly confront the Axis. In fact,
the practice of appeasement, or letting Germany take over small
neighboring countries, was used until it became clear that Hitler would not, in fact, be
appeased by these smaller gains. See attached article.

Does Rudyard Kipling belong to Indian writing or British writing?

This is a very interesting question.  On one hand, I think that
a clear case can be made that Kipling belongs in the category of British writing.  It is clear
that his primary audience is British.  He writes with this audience in mind.  His writing,
itself, reflected the colonizers and the colonizer attitude towards the indigenous people.  His
desire to serve the British Empire comes out in many of his works and how it depicts those who
were colonized by the European forces.  At the same time, I think that Kipling becomes a sort of
starting point for the postcolonial writer that emerges out of nations like India.  For these
writers, they write in the shadow of  Colonialism and writers' attitudes like Kipling forms a
great deal of the backdrop of their writing.  In a bizarre twist, this helps to make Kipling a
force in Indian writing, though not through his own call.  Writers from nations as India had to
address the writings of Kipling as an example of how identity in the post- colonial world is a
hybrid one, combining elements of colonizer and colonized.  Kipling becomes a starting point in
how his attitudes ended up filtering through identity in the post- colonial world.  In this
light, Kipling becomes a part of both domains, though he might not have intended to be
so.

In "The Star-Spangled Banner," the word "O'er" means: a rowing tool; a mining product; before; over; or other?

Originally titled "The Defence of Fort McHenry" by its author,
Francis Scott Key, his poem was eventually placed to music (to the tune of a song already known
in America, "The Anacreontic Song," aka "To Anacreon in Heaven") and was adopted as the young
country's national anthem. Key used the word "o'er" as the first word of the repeating last line
of each of the four stanzas (as well as in the middle of the first stanza as well). In this case,
the word is a shortened version of the word "over." Key probably chose "o'er" because of its
single syllable, rather than "ov-er," whose two syllables did not fit as
well.

In the Great Gatsby, numbers such as 3 and 5 reoccur. What could these number motifs represent?Quotes: -Dan Cody: The arrangement lasted five...

I have found some of the occurrences of numbers you refer
to above, but also others:

Nick says that his family has
been “prominent and well-to-do” for THREE generations. Daisy’s daughter is THREE years
old. Every Friday, FIVE crates of oranges and lemons are delivered to Gatsby’s house.
Gatsby was in the THIRD division during the war. Nick often walks across 33rd Street in
New York City to go to Penn Station. Nick writes the names of people who came to
Gatsby’s party on July 5th on an old train timetable. The horn on Gatsby’s car sounds
THREE notes. Mr. Wolfsheim tells Nick and Gatsby a story about one night in New York
City when FIVE of his friends were gunned down. Jordan tells Nick that when she and
Daisy were young girls, she once came upon Daisy talking with a handsome young officer
(Gatsby) and Daisy was so engrossed in the conversation that she didn’t even notice
Jordan until she was FIVE feet away. When Gatsby has tea with Daisy at Nick’s house, he
tells them that he and Daisy have not seen each other in FIVE years. Tom shows up in a
riding party of THREE one afternoon at Gatsby’s, on horseback. A man fainted at Daisy’s
wedding and he stayed at her house for THREE weeks afterwards. Gatsby tells Tom he only
stayed at Oxford for FIVE months. At Myrtle Wilson’s funeral, at THREE o’clock her
husband George starts to figure out that it was Gatsby’s car that killed Myrtle. Nick
tries to call Meyer Wolfsheim to tell him about Gatsby’s murder and the operator tells
Nick he has rung the number THREE times. Gatsby’s father sends word to Nick THREE days
after Gatsby’s murder that he is coming to New York. Gatsby’s funeral is at THREE
o’clock. A young Gatsby had written in his journal that he would save THREE dollars each
week. At FIVE o’clock, Gatsby is buried. Nick tells Jordan that he is 30 years old, FIVE
years too old to lie to himself. At the end of the story, Nick runs into Tom walking
down FIFTH Avenue.

Although I don’t believe one can make
this statement with 100% accuracy based on the incidents of the occurrence of the number
3 and 5 as outlined above, it seems as if the number 5 is associated mostly
with negative things, and the number 3 is associated mostly
with positive things. I am not so certain that Fitzgerald intended to use
strong symbolism with these numbers, however. For example, if you do some research into
what numbers stand for, you will find that it depends greatly on your reference point.
For example in Christian-based numerology, the number 3 stands for the Father, Son and
Holy Ghost. Or, this number can stand for stability, as in the 3 sides of a triangle. It
can also represent birth, life, death. The number 5 is often associated with
instability, radical changes, chaos. Both 3 and 5 are odd numbers, so this could be
significant.

Anyway – I have given you something to think
about. So, what do YOU think?

What are the similarities between the first and last dream in "The Secret Life of Walter Mitty"?

I think the similarities seem to lie more in the kind of heroic
display of character that Walter Mitty is able to make in both daydreams rather than the actual
situation. However, we can perhaps find some similarity in the way that Walter Mitty always
chooses impossible situations for his heroic persona to face in his daydreams. In the first
daydream, Walter Mitty is the commander of a plane who has to go through a massive storm. His men
are terrified that the aircraft will be destroyed in the storm, but Walter Mitty insists they go
on through and we are shown the admiration with which he is regarded by his men because of his
bravery and leadership. The last daydream features Walter Mitty facing the firing squad and
scornfully rejecting a handkerchief to blindfold his eyes. Notice the way he is described at the
end:

Then, with that
faint, fleeting smile playing about his lips, he faced the firing squad; erect and motionless,
proud and disdainful, Walter Mitty the Undefeated, inscrutable to the
last.

Both daydreams represent escapes
from an overbearing wife, quite ironically in the last one, as it presents death as preferable to
being with her, but at the same time they show a tragic inability to confront Walter Mitty's own
problems by creating this do-or-die situations that, in his daydreams, he can
resolve.

Exactly what human characteristic is being applied to what non-human entity or concept?specific uses of personification in "To His Coy Mistress",...

I believe that the author using personification to make
his arguments more persuasive by making the objects he personifies seem alive—imbuing
them with human characteristics...as he tries to make her feel that his passion for her
is a living thing all its own, as seen with the use of active verbs in the lines of
personification:

'"My vegetable love should
grow" - giving a plant the human characteristic of
love

"An hundred years should go to
praise / Thine eyes...Two hundred to adore
each breast..." - while one might argue that there is an inferred "I would spend," these
lines could also be taken to mean that had they the time, years would praise and
adore

"Time's winged chariot hurrying
near..." - that time can ride a chariot

"...then worms
shall try / That long preserv'd virginity..." - seems to say that
the worms shall take ("try") her
virginity

"...your quaint honour turn
to dust, / And into ashes all my lust" - honour and lust are personified like dead
bodies turning to dust and ash

"While youthful hue /
Sits on thy skin" - youth is personified as "sitting" or resting on
her skin

"...though we cannot make our sun /
Stand still, yet we will make him run" - the
sun is personified, suggesting it can stand still or run

Please give quotes that show how Macbeth is ambitious and how his mind unfolds into murderous intentions towards King Duncan.

Sparklekid has the most important quote in the answer
given previous.  In Act I, scene vii comes a very famous soliloquy in the play.  I would
say that there are random quotes peppered throughout the scenes that lead up to this
soliloquy, but this is the first moment that Macbeth is onstage alone to confide his
inmost thoughts to the audience.  The whole of the speech is the "unfolding" of "his
mind" "into murderous intentions towards King Duncan."  He
says:

If it
were done when 'tis done, then 'twere well

It were done
quickly; if the assassination

Could trammel up the
consequence, and catch

With his surcease success; that, but
this blow

Might be the be-all and end-all
here,

But here, upon this bank and shoal of
time,

We'ld jump the life to
come.

In these opening lines
of the speech, Macbeth admits that, if he could murder Duncan and be assured of no
consequences for his action, he would do it without pause.  But, he knows that the world
does not work this way.  He continues:

readability="14">

. . .But in these
cases

We still have judgement here:  that we but
teach

Bloody instructions, which, being taught,
return

To plague the inventor.  This even-handed
justice

Commends the ingredients of our poison'd
chalice

To our own
lips.

So, for Macbeth, the
idea of karmic retribution, or the idea of his evil deeds coming home to roost, is a
potential reason not to go forward with the murder.  He goes on in the speech to list
other reasons, but, as good and sound and true as his reasoning is, he ignores it all in
favor of his ambition:

readability="9">

. . .I have no
spur

To prick the sides of my intent,b ut
only

Vaulting ambition, which o'erleaps
itself

And falls on the
other.

This speech is the
best single bit of text from the play that reveals the inner workings of Macbeth's mind,
rather than a simple reaction to outside circumstance or another character's words or
actions.  He speaks this soliloquy alone onstage to only the audience, and it is in this
speech that the audience sees the reasoning Macbeth undergoes in deciding to kill
Duncan.

Please follow the links below for further analysis
of this speech.

What is meant by El Nino ??

El Nino is a natural phenomenon that refers to the Pacific
Ocean warm currents near the coasts of Peru and Ecuador. The El Niño phenomenon
dramatically affects the weather in many parts of the world. The strongest El Niño
events of the 20th century occurred in 1982-'83 and in1997-'98. The effects of 1982-'83
included significant storms throughout the southwest United States and one of
Australia's worst droughts of the century.According to the World Meteorological
Organization, the 1997-'98 El Niño was a major factor in 1997s record high
temperatures

Find the equation of the tangent for y=x^2+8x+12, where x=-4.

The equation of tangent at (x1,y1)for a curve y = f(x) is given
by ;

y - y1 = f'(x1) (x-x1).

The given
function is f(x) = x^2+8x+13.

At x1= -4 ,  y1 = (-4)^2+8*(-4)+12 = 
16 -32+12 = -4.

f(x) = (x^2+8x+12) =
2x+8.

f'(x1) = f(-4) = 2(-4) +8 =
0.

Therefore the equation of the
tangent.

Therefore the tanget at (-4, -4) is given
by:

y - 4 = 0(x--(4)).

Or y -4 = 0. Or
y = 4 is the tangent at x= -4.

What are some easy essay topics for the novel Oryx and Crake by Margaret Atwood?

I assume that from your question you need to choose an essay
topic yourself based on this novel. With any dystopian fiction, an excellent essay topic would be
to take one of the aspects of the speculative future that we are presented with and to use that
as an essay topic, looking at the extent to which it is true now in our society or to what extent
is it occurring now.

There are many such topics that you could
select from this novel. An excellent one would be the blurring of the boundary line between
reality and fantasy through media. Note the number of internet sites that Jimmy and Crake look at
during their teenage years, including porn sites, sites of beheading and assisted suicides. Crake
believes that they are all staged but it is clear that the effect of this media onslaught is to
muddy the waters between the states of fantasy and fiction. To what extent is this happening now
in our society?

Another topic you might want to think about is the
potential for a disease to wipe out humanity. Is this a possible scenario? Could mankind we wiped
out that easily?

Hope these ideas help!

How many grams of ammonium sulfate are needed to make a 0.25 L solution at a concentration of 6 M?

Moles = mass of solute/ gram molecular mass.
Solute is the 'stuff being disolved.
Solution is a homogeneous mixture of a solute in a solven. G.M.M. is
gram molecular mass

. moles of solute

Molarity
is defined as: ___________________________________

. liters of
solution

.
[g
(NH4)2SO4/G.M.M]

6
M = ______________________________

. L
(NH4)2SO4(aq)

.
? g
/
132g/mol

6 M = __________________

.
0.25 L

g
(NH4)2SO4
= 6 mol/L * 0.25 L * 132 g/mol = 198
g(NH4)2SO4

Since
6M is only 1 significant figure the answer to 1 significant figure
would be 200 g
(NH4)2SO4.
6.0M solution would also use 200 (with the bold numbers representing
the significant figures)

If the solution were 6.00M (3 sig figs)
then you would need 198
g(NH4)2SO4

If y = (2x- 1 / x+7 )^3. What is y' ?

y= (2x-1)/(x+7)^3

Let y=
(u/v)^3

==> y' = 3*(u/v)'
(u/v)^2

But (u/v)' =
(u'v-uv')/v^2

==> y' = 3*[(u'v-uv')/v^2]
*(u/v^2)

             = 3*[uu'v -
u^2*v]/v^4

u= 2x-1 ==> u' =
2

v= x+7 ==> v' = 1

Now
substitute:

==> y' = 3[2(2x-1)(x+7) - (2x-1)^2
]/(x+7)^4

          = 6(2x^2+13x -7) - (4x^2 -4x +
1)]/(x+7)^4

           = (12x^2 + 78x - 42 - 4x^2 + 4x
-1)/(x+7)^4

            =  (8x^2 +82x -
43)/(x+7)^4

 ==> y' = (8x^2 + 82x -
43)/(x+7)^4

Analyse and explain the theme of marriage in Seamus Heaney's Glanmore Sonnets, specifically, sonnet I:Vowels ploughed into other: opened ground....

The theme of marriage does not seem to be especially prominent
in the very first of Seamus Heaney’s Glanmore Sonnets. The sonnets were
written in response to a move, by Heaney, his wife, and their children, from violent Northern
Ireland to a much more peaceful, rural life in an area south of Dublin in the Irish Republic. The
poet’s wife, however, is nowhere explicitly mentioned in the opening sonnet of the sequence, nor
is marriage as an institution. Instead, the twin focuses of the poem seem to be on farming and on
art – two forms of creativity.

Heaney opens the poem with a splendid
example of a description whose very sounds illustrate the thing described: “Vowels ploughed into
other” (1). Here the jamming together of the “ow” sounds of the first two words forces the reader
to speak the very idea the phrasing presents. (Similarly skillful use of assonance (and also
alliteration) occurs in the first two words of line 3: “Is mist.”) The next two lines celebrate
the peaceful beauty of the weather and the earth:

readability="5">

The mildest February for twenty years
Is mist
bands over furrows . . . (2-3)

The
imagery of line 3 is particularly memorable and beautiful, as is the striking reference, later in
that line, to a “deep no sound” – a wonderful way of mentioning silence without using the
over-used word “silence.” But Heaney is careful to guard against any facile,
simple-minded romanticism. Thus, in the next line he makes sure to mention that this “no sound”
is “Vulnerable to distant gargling tractors” (4). The idyllic rural landscape is not entirely
free, or distant from, the rumblings of machines, and indeed it is probably these very machines
that have created the appealing “furrows.” The poem presents no easy opposition between the land
and industry; industry helps farmers till the land and prepare for the coming of the crops: “the
turned-up acres breathe” (5).

The speaker, as artist and poet, is
inspired by the beauty of the ploughed earth:

readability="5">

I am quickened with a redolence
Of farmland as a
dark unblown rose. (10-11).

Like the
rose that has not yet fully opened, the true beauty of the tilled land will not be fully apparent
until it blooms. In the poem’s final lines, the speaker anticipates the bounty of the harvest –
both literal and (figuratively) artistic – that is yet to
come.

Although marriage is not an explicit theme in this poem,
images of the ploughing of fields have long been associated with human sexuality and human
fertility (as in Shakespeare’s 3rd sonnet), and certainly the speaker of this poem seems alive to
twin ideals of sowing seeds and watching them develop.

What are some of the cons of plea bargaining?

The only real motivation the accused has to enter into a
plea bargain arrangement with a prosecutor is that it almost always means a lesser
charge will be applied, or more lenient sentencing will take
place.

For that reason, someone who commits a gruesome
murder or otherwise violent attack might be charged with manslaughter, or indecent
liberties as opposed to murder or rape, and with a much lighter sentence for those
crimes, one could argue that justice is not being
served.

What's more, many who enter into plea bargains are
minorities or the poor, who, on advice of a public defender or the attorney they can
afford, plead guilty even if they are innocent because they believe, rightly or wrongly,
that they will be convicted nmo matter what, so they might as well get the best deal
possible.  This isn't justice either.

Why should scientists consider the impact their work will have on human before proceeding with any new experiment?

I would think that scientists are bound by an ethical code
of conduct to consider the impact of their work before proceeding with it.  I think of
the scientists who helped develop the atomic bomb as an example.  The standard telling
of this narrative is that they were completely zealous in the development of this device
towards many ends.  They saw it as a means to end the war, or to end war, in general, as
a source of limitless power, as well as a means to engage in a scientific impossibility
of splitting the atom.  Yet, I think that all of the scientists involved understood that
there was a need to talk, to discuss realities that would arise from their experiments
and discoveries.  Such a moment demonstrated that while science is a boon in so many
ways, it also involves a level of ethical and personal responsibility that requires
discussion and discourse before proceeding with any new
endeavor.

At Gatsby's Party in The Great Gatsby, Jordon says to Nick about Gatsby's parties, At Gatsby's Party, Jordon says to Nick about Gatsby's parties,...

This quote brings up an interesting paradox about parties.
Jordan says something that doesn't seem like it could be true -- it seems that the opposite would
be true -- and yet with some thought the quote makes perfect sense. That is the definition of a
paradox: a seemingly contradictory statement that is actually
true.

In this case, Jordan is talking about parties. She claims that
large parties are more intimate. At a first thought that makes no sense: how can you have
intimate conversations or interactions with people at a large party? There are so many people
around it would seem that it would be hard to get into deep conversations with people. You could
spend your whole night just making a superficial attempt to meet and greet fellow party
attendees. She extends her thought by adding that at a small party there isn't any privacy, when
in actuality, small parties are very private: only a select few are in attendance. So the
question is, "how can Jordan be right?"

Jordan is right because at a
large party there are so many people present that each individual can actually have a sense of
anonymity and be "lost in the crowd." If two people are lost in the sea of other people, they
have an intimacy that could block out all the behavior and conversations of those around them.
There is no intense scrutiny of them. You have the opportunity to have an intimate conversation
if there are lots of other people having lots of other conversations with everyone else. One the
other hand, when you are at a small party, there is no escape. Your absence is noticeable. You
can't have a private chat because the small group in the room is listening and observing the few
people around them. Perhaps there is only one conversation happening at a time. There would
certainly be no privacy in that circumstance -- whatever you say is said to the whole group.
There can be no asides without drawing everyone's attention to the
side-conversation.

Gatsby wants to attract Daisy's attention, and he
knows that she may attend one of his grand affairs for the express reason that she could remain
somewhat private and aloof amoungst a throng of party-goers. She would have the privacy to blend
into the background and merely observe -- to see for herself what Gatsby has
become.

Find x and y: log 4 (x+y) = 2 log 3 x + log 3 y = 2 + log 3 7

We'll impose the constraints of existence of
logarithms:

x>0

y>0

Now,
we'll take anti-logarithm for the first equation:

x+y =
4^2

x+y = 16 (1)

We'll apply
the product rule of logarithms in the second equation:

log
3 x + log 3 y = log 3 (x*y)

We'll re-write the sum from the
right side of the second equation:

2 + log 3 7 =2*1 + log 3
7

2*1 + log 3 7 = 2*log 3 3 + log 3
7

We'll apply the power rule of
logarithms:

2*log 3 3 = log 3 3^2 = log 3
9

We'll re-write the second
equation:

log 3 (x*y) = log 3 9 + log 3
7

log 3 (x*y) = log 3
(9*7)

log 3 (x*y) = log 3
(63)

Since the bases are matching, we'll apply one to one
rule:

x*y = 63 (2)

We'll write
x with respect to y, from (1) and we'll substitute in
(2):

x = 16 - y

(16 - y)*y =
63

We'll remove the
brackets:

16y - y^2 - 63 =
0

We'll re-arrange the terms and we'll multiply by
-1:

y^2 - 16y + 63 = 0

We'll
apply the quadratic formula:

y1 = [16+sqrt(256 -
252)]/2

y1 = (16+2)/2

y1 =
9

y2 = 7

x1 = 16 -
y1

x1 = 16-9

x1 =
7

x2 = 16-7

x2 =
9

The solutions of the symmetric system
are:

{9 ; 7} and {7 ;
9}

What weakness does Godfrey display in Silas Marner?

Godfrey is a push-over, basically. He got involved with a
woman for a brief instance and ended up getting her pregnant, marrying her, and hence
destroying his possibilities with the person whom he is wished to marry,
Nancy.

He lets his brother Dunsley toy him around and
actually pays the consequences for his brother's actions just as long as Dunsley doesn't
tell his Dad about his bad marriage choice.

He also lacks
initiative. He would like to be in charge of his father's property and manage it, but he
lacks the discipline and the courage. He also is very easily led, as he is following
Dunsley's bad habits of drinking and gambling to the point of hurting the family
finances.

This is basically the problem with Godfrey: Lack
of gumption and tremendous co-dependence.

A man wants to construct a rectangular enclosure around his model railroad. Only three sides must be fenced, since his garage wall will...

We want to have the rectangular enclosure with a maximum
area and with three sided fencing of 24 meters.

We assume
that the two parallel sides of the rectangular eclosure measure x meters each and the
remaining third side is 24-2x meters, as the sum of all 3 sides is 24
meters.

Therefore, the area A(x) =  product of two adjacent
sides of the rectangle.

So A(x) = x*(24-2x) , Or A(x) =
24x-2x^2.

A(x) is maximum for some x = c , if A'(c) = 0
and  A" (c) < 0.

Therefore, we differentiate A(x) =
24x-2x^2:

A'(x) = (24x-2x^2)' = 24-4x.  A'(x) = 0 gives 24
-4x = 0 which gives x = c = 24/4 = 6.

Therefore x = c =
6.

A"(x) = (24-4x)' = -4.  So A"(6) = -4 which is <
0.

Therefore A(x) is maximum for  x = c=
6.

So the rectangular enclosure has the maximum area for
the rectangle of width = 6 meters and length = 24-2*6 = 12 meters. Therefore, area =
6*12 = 72 sq meter.

Are we meant to find the incident of the whiskey and the pigs amusing in Animal Farm?

This incident is found towards the end of Chapter
8.

I would have to say that we are meant to find this
amusing just based on the way that Orwell talks about the pigs and how they act.  If he
didn't want it to be funny, he would not have needed to put in all the
details.

When I mention details, I am talking about things
like:

• How Napoleon comes out wearing the hat and
  runs around the farmyard.


• How Squealer has "dull" eyes
  and how his tail is hanging limply.


• How Squealer
  announces that Napoleon is ill and about to
  die.

To me, a lot of these details could be
left out if Orwell didn't want to make it funny.  He could just have had the pigs get
drunk and change the Commandment and it still would have showed that they are changing
and becoming more like people.  It would have had the same message without being
funny.

Determine f'(3) from first principles if f(x)=-5x^2.

We have to find f'(3) for f(x)=-5x^2, using the first
principle.

Now from the first
principle,

f'(3) = lim [f(x) - f(3)]/(x-3), for
x->3

=> f'(3) = lim (-5x^2 + 45)/(x - 3), for
x->3

=> f'(3) = lim [(-5)(x^2 - 9)]/(x-3),
for x->3

=> f'(3) = lim [(-5)(x-3)(x
+3)/(x-3), for x->3

=> f'(3) = (-5)*lim
(x+3), for x->3

=> f'(3) = -5*(3
+3)

=> f'(3) =
-5*6

=> f'(3) =
-30

The required value of f'(3) is
-30

Prove sin^2 (pi/4 + x/2)/sin^2(pi/4 - x/2) = (1+ sin x)/(1 - sin x)

The identity to be proved is [sin (pi/4 + x/2)]^2/[sin(pi/4 -
x/2)]^2 = (1+ sin x)/(1 - sin x)

We know that cos 2x = 1 – 2*(sin
x)^2

=> (sin x)^2 = (1 – cos
2x)/2

Let’s start with the left hand side of the given
identity

[sin(pi/4 + x/2)]^2/[sin(pi/4 -
x/2)]^2

=> [(1 – cos(pi/2 + x))/2]/[ (1 – cos(pi/2 -
x))/2]

use cos (pi/2 - x) = sin
x

=> ( 1 – (-sin x))/(1 - sin
x)

=> (1 + sin x)/(1 – sin
x)

which is the right hand
side.

This proves the identity sin^2 (pi/4 +
x/2)/sin^2(pi/4 - x/2) = (1+ sin x)/(1 - sin x)

What is the purpose of deer in our ecosystem besides hunting them? How do they help the earth?

Deer are part of  food chains and webs in nature. They are
herbivores or primary consumers. These ruminants graze on a variety of plants and digest this
material in their four chambered stomach. Carnivores are consumers that eat animal flesh. A deer
is a prey animal that is hunted by carnivores. Wolves can eat deer. However, many wolves have
been driven to almost extinction in most states in the United States. However, it has been shown
that wolves help keep the deer population in check by hunting and feeding on deer, usually older,
younger, weak or sick ones that they can catch. This keeps the population at levels the ecosystem
can support in terms of resources and space. When predators like wolves are removed from the
ecosystem, deer experience a population explosion due to lack of predation. Then, due to
competition for limited resources, the deer experience a die- off due to starvation.  Deer are an
important part of nature. Deer are used for transportation, food(venison) and
clothing.

Is 2x^2-1 a Linear Function or not? Why?

The general form of a linear function
is:

f(x) = ax + b

If the equation can
be placed into this form, then it is linear. Otherwise, it is
not.

2x^2 is a quadratic (order 2) polynomial. Thus, 2x^2-1 is not
linear.

A linear function has the shape of a line. Higher order
polynomials have curves. This is another way to tell that the equation is not
linear.

Linear equations are special because it is easy to
interpolate the exact answer if you know two points on a line, and want to find a third point.
Because linear equations do not have variables that are products of one another, they are often
easy to solve. This makes them very useful in math and science.

In A Separate Peace Leper says "only the people who've been evolving the right way survive"war. How does that apply to Leper, Gene, and Finny?

If you look at the characters of Leper, Gene and Finny, in the
end, it is only Gene that actually makes it through the war with sound health and mind. Leper
cracks under the pressure of training, and his mind becomes the victim to the rigorous schedule
and lifestyle of a soldier. Finny, because he can't be on the front lines participating in the
war, is torn apart by it and copes by making up stories about it. Also, Finny was so good-natured
that Gene accurately concludes of him that he would be no good at fighting. He doesn't have the
nature to be any good at war.

To "evolve the right way," you must
steel yourself to the harsh realities of war; Leper was unable to do that, and Finny was caught
off guard by the cruelty of war himself. In the book, Gene symbolically declares war on Finny
through is declaration of it at the tree; his jealousy and insecurity led him to an act of
thoughtless cruelty; in the end, that cost Finny his life. Finny was too nice to recognize that
cruelty in Gene; when he finally was forced to confront it, he couldn't handle it, and it broke
him. He didn't evolve with the proper amount of perspective and hardness to handle war. Leper did
not evolve with the proper amount of hardness and resolve to survive it. Gene, however, did. He
knew what cruelty was--he had seen it in his own heart. He knew the war was hard--he had seen it
break Leper. He developed the attributes that needed to survive the
war.

I hope that those thoughs helped a bit; good
luck!

What's a passage thats shows the theme in "To Build a Fire"?

There are several recurring themes that run through Jack
London's "To Build a Fire." All of them relate in some manner to the chechaquo's battle against
the elements and the way in which he eventually confronts death at the end. The newcomer makes
many mistakes during his fateful final journey, the most important being his refusal to follow
the advice given to him by the "old-timer on Sulphur Creek."

readability="9">

The old-timer on Sulphur Creek was right, he thought, in
the moment of controlled despair that ensued: after fifty below, a man should travel with a
partner.

The newcomer failed to
recognize that what seemed to him like friendly advice was really information that would protect
him the cruelest situations that Mother Nature may present.

readability="7">

It did not lead him to meditate upon his frailty... and
upon man's frailty in general... and from there on it did not lead him to the conjectural field
of immortality and man's place in the
universe.

In the following list, where is the second statement the negation of the first?I. The Canucks won last year.The Canucks lost last year. II. A...

The   negation  of a proposition p
is notp.

So if the propsition p is true
, then  the propoitio notp is not true.

If the proposition p is not
true ,then notp is true.

The truth table of P and not is as
folows:

p      
notp

T        F

F       T.

Therefore
applying this to the pairs of staments given we easily determinne:

 
I. The Canucks won last year.
The Canucks lost last
year.

The second stement is negation of the first , as it
negates the truth (or false ) of the
first.

II. A rhombus is a trapezoid.
A trapezoid is not a
rhombus.

 The first statement value is F. The  second
statement is true. But it  is not the negation of the first , but
the negation of  the proposition a trapezoid is a rhombus.

III. A
square is a rectangle.
A square is not a
rectangle.

P is true , p is not true form.
So this a
negation.

Answer:

 e)
I and III is correct choice.

How did Hinduism change from the Aryans to the Gupta?

By this I assume you mean the period from roughly 1500
BCE, which signals the end of the Indus Valley Civilization, until the rise of the Gupta
Empire in the 4rd-6th centuries CE. This is a span of time that covers roughly 2000
years and contains some of the most important formative moments in Hindu
history.

First, the Vedas were developed in the period
1500BCE-800BCE. These collections of hymns and mythology were intended to accompany
complex rituals. The brahman priests performed these rituals,
chanting the Vedas to the gods, thus maintaining the cosmic
harmony.

But the Vedic rituals were complex, expensive, and
difficult. Commentaries on the Vedas began to teach that one should worship the gods
within, through meditation, fasting, and prayer. The Upanishads mark this change in
orientation. These texts taught that one's true Self, the immortal
atman, was divine in nature and that through yoga and meditation
one could lose oneself in divine union.

A third major
religious movement developed in this period in Hinduism. Many of these teachings (of
Vedic rituals, of sacrifice, of losing oneself in God) were often reserved for upper
classes and/or people who left society on a spiritual quest. But in the period
200BCE-200CE the great epics, the Ramayana and the
Mahabharata presented many of these ideas in a popular format with
stories of heroes. In particular, the Bhagavad-Gita that all people
should act selflessly, performing their caste duties, and live in virtuous devotion to
God. So this third movement may be described as a popular movement, a way of making
these earlier teachings more publicly available.

By the
way, it used to be thought that India was subject to invasions by people called the
Aryans. In recent decades, this idea has been largely abandoned. Although a few scholars
current in the field still believe the Indus Valley Civilization fell to some Aryan
invasion, there is little evidence to substantiate this idea.

In The Kite Runner, could it be said that by telling Amir about her affair with the Afghan man, Soraya is taking responsibility for her...

This would be a very good example of someone taking
responsibility for their actions. This section of the novel comes in Chapter Twelve,
when after the engagement has been arranged by Baba, Soraya calls up Amir and tells him
about her past. What is important about this phone call is that this comes at the
beginning of their formal relationship, and, as Soraya says, she doesn't want their
relationship to "start with secrets." The revelation that follows - that Amir had
actually heard about from Baba - shows Soraya's remorse at what she has done, but also
the way that now she is able to thank her father for what he did in rescuing her from
that situation.

Of course, what you need to be aware of is
how the author uses Soraya as a foil for Amir here. The last paragraph of this chapter
makes this clear:

readability="6">

I envied her. Her secret was out. Spoken. Dealt
with... I suspected there were many ways in which Soraya Taheri was a better person than
me. Courage was just one of
them.

So, yes, this example
shows Soraya taking responsibility for her actions, in a way that Amir has yet to
do.

How does Eugene Ionesco's "Rhinoceros" demonstrate qualities of existentialism?Existentialism itself is hard for me to grasp, if anyone could...

I think that you have a couple of challenging elements
here.  The philosophy is a bit complex and that is only matched by the Ionesco work. 
Between both of them, one can get lost in the realm of inquiry.  To break things down, I
would suggest that one can think of existentialism as an  actor being thrust on stage,
in front of an audience, spotlight blaring, without a script or without a director with
the order "to act."  In this light, the individual is forlorn, without any sort of
relief, and is isolated from all others in their lack of totality and explanation as to
why things are the way they are.  All the individual can do is "act."  In the end, this
is how existentialists see the world and the human being's place in it.  This might
connect to Ionesco's play in a couple of ways.  Berenger's stand against the rhinoceros
reflects how he stands alone against a social order and can "only act" or use his
freedom.  The alienated and isolated nature of human beings with only the agony of
choice to accompany them is something that we see Berenger embody when all of his world
turns against him and he is the only one left.  In his resistance as being "the last
man," he has only his freedom and this is what might make Berenger an ultimate
"existentialist" hero.

In "The Cask of Amontillado", can you think of any other villains that share some of Montresor's villainous characteristics?

You know, for some reason, what comes to mind is a series
of James Bond villains, who are ferociously intelligent, agile and quick with their
brains, but hideously unaware of their motivations and what drives them. For me, the key
to Montresor's character is the fact that he is unaware of what drives him - he is an
archetypal unreliable narrator in that we come to suspect his words when he talks about
his anger and desire for revenge against Fortunato. Thus it would need to be a villain
that shows themselves to be exceptionally devious in terms of their planning and quick
thinking and use of their enemy's weaknesses against them, but also one that is mentally
disturbed or challenged. Any James Bond villain will do - or you might want to think of
a Batman villain such as the Joker or someone like that.

Given M1(1,-2,3), M2(-3,5,-2) write the vector form and parametric form of the equation of the line M1M2.

We'll write the vector form of the equation of the line
M1M2.

r = r1 + t(r2 - r1)
(*),

where r1 and r2 are the vectors of position of the
points M1 and M2.

r1 = xM1*i + yM1*j +
zM1*k

We'll substitute the coordinates of
M1:

r1 = 1*i + (-2)*j + 3*k

r1
= i - 2j + 3k (1)

We'll write the equation of the vector
r2:

r2 = xM2*i + yM2*j +
zM2*k

r2 =  -3*i + 5*j +
(-2)*k

r2 =  -3i + 5j - 2k
(2)

We'll compute the
difference:

r2 - r1 = (-3-1)i + (5+2)j +
(-2-3)k

r2 - r1 = -4i + 7j - 5k
(3)

We'll substitute (1), (2), (3) in
(*):

r = i - 2j + 3k + t( -4i + 7j -
5k)

The vector form of the equation of the line that passes
through M1 and M2 is:

r = i - 2j + 3k +
t( -4i + 7j - 5k)

Knowing the vector form of
the equation, we'll write the parametric
form:

x = 1 -
4t

y = -2 +
7t

z = 3 -
5t

From Polonius' conversation with Laertes in Act 1 Scene 3 what kind of a life philosophy does Polonius seem to have?

If you look at the totality of Polonius's advice to
Laertes, it is pretty clear that Polonius is very concerned with outward appearances and
maintaining one's reputation.  Most of his advice is in reference to the appropriate
actions a man must take to keep himself from damaging his
reputation. 

1.The first few pieces of advice are
specifically about behavior.  He tells Laertes to "give thy thoughts no tongue."  He is
telling Laertes to keep his opinions and thoughts to himself so as not to offend anyone
or be misinterpreted by anyone.  He follows that up with, "nor any unproportion'd
thought his act."  He is telling him not to overreact to what others say. He follows
this theme a few lines later when he counsels Laertes to listen to everyone, but
reserve his comments and judgements.   He wants Leartes to be friendly, but not overly
so, until Laertes knows for sure they can be trusted -- only then should hold them "with
hoops of steel."

2. He warns him not be hot-headed and then
enter into quarrels, and be careful of what he might reveal if he is in
a fight. 

3. He next goes on about Laertes' outward
physical appearance, telling him to look nice, but not gaudy -- afterall, the clothes
are a first impression.

4. His last piece of advice is to
be careful with money -- lending to others often comes with more strife than it is worth
-- thus could create conflict.

Polonius sums up all of this
advice with a final thought: "This above all to thine own self be true."  If you only
look at that one line, then it could be regarded as a contradiction to everything he
says before it, but if you consider the complete sentence, he makes a logical point. 
The rest of thought is "And it must follow, as the night the day, thou canst not then be
false to any man."  What he means is that if you keep in mind all of the advice, and
think about your actions first, then you will not likely offend anyone else in the
process -- therefore you will be able to maintain you yourself and you
reputation.

In the end, the speech reveals a bit of
Polonius's skepticism about the nature of humanity -- assuming the negative about other
people's natures and motives, but Polonius has his position in the court by playing the
game correctly, so he is probably speaking from some truth of
experience.

How is "divine vengeance" manifested in The Case For The Defence? In detail, please. :)

Excellent question
krayola....

Divine vengeance is the main essence of the
uncanny classic, "The Case for the Defence", by Graham
Greene.

Initially, in the story, Greene presents forth
that at least one of the Adams are certainly the murderers. This
can be understood clearly by the number of evidences (witnesses), and the manner of
writing of Greene. The scene yet plays loopholes and ultimately both the Adams escape
without any of them held guilty. This is certainly against the “DIVINE
JUSTICE”. It is obvious that when things get beyond the hands of we
mortals, the spiritual Lord does justice. After the twins escape human
justice, one of them ends up being killed by a bus. This is not elaborate to any great
extent as it gives the story a sinister appeal. Hence, to answer your question, this is
a clear cut example of divine vengeance.

Hope sum of it is
applied to our politicians :)

Which major organs make up the digestive tract of a frog?

In order to ingest food, frogs use their tongue as an
appendage to capture and bring in to their mouth flies and other prey. They have
vomerine teeth in the roof of the mouth to aid in holding their prey and maxillary teeth
which help chew the food. Once swallowed, it passes through the espophagus and to the
stomach. In the stomach, chemical digestion occurs. The food next passes through the
small intestine, where further hydrolysis occurs. They have a pancreas which secretes
digestive enzymes as well as the liver which produces bile. Bile can emulsify fat and is
stored in the tiny gall bladder until it is needed. The large intestine collects
undigested material and it then eventually reaches the cloaca. This is a common duct for
the removal of undigested matter or feces and can also be used for excretion of urea and
for the exit of sperm and eggs during reproduction.

How do you describe Sarah's actual physical description to your students in order to create the most impact on them?This is with regard to Staying...

One way you can make the most of the description is to
have students draw Sarah, from the description.  First, give every student a copy and
have them circle the descriptive words.  Then, have them draw her based on the
description. 

This way, students can focus on specific
details and really pay attention to them.  Then, you can ask students to write a short
paragraph about the drawing and what it makes them think of.  For example, they might
feel sorry for Sarah.  They might talk about Sarah's pride or feelings.  Use the drawing
to kick-off a conversation about Sarah and the way we related to obesity in our
society.

This can lead to conversations on empathy, how we
react to an obese person, reasons why people are obese and so
on 

One way you can make the most of the description is to
have students draw Sarah, from the description.  First, give every student a copy and
have them circle the descriptive words.  Then, have them draw her based on the
description. 

This way, students can focus on specific
details and really pay attention to them.  Then, you can ask students to write a short
paragraph about the drawing and what it makes them think of.  For example, they might
feel sorry for Sarah.  They might talk about Sarah's pride or feelings.  Use the drawing
to kick-off a conversation about Sarah and the way we related to obesity in our
society.

This can lead to conversations on empathy, how we
react to an obese person, reasons why people are obese and so on

What level of government or government agency is responsible for dealing with racism? Why?

I'm assuming you mean the American government and, well, there
really isn't a level of government or a specific agency that deals with racism, per se.  We have
a court system and a Justice Department that deal with issues of racial discrimination and hate
crimes based on race, but these are actions as opposed to social
beliefs.

It is impossible for government to control a person's
racism, they can only seek to influence it through education.  What's more, racism is not
illegal.

Depending on the type of crime and the state in which it
happens, some murders and assaults can be considered hate crimes if they can prove the motivation
for the crime was race.  In that case, we have a judicial system and sometimes US Attorneys will
investigate on behalf of the Justice Department, and in other cases, such as during the Civil
Rights Era of the 1950s and 1960s, the FBI has been used because states were not acting in
accordance with court rulings.

Act 4 scene 5, how does Lord Capulet show regret for this daughter's death?explore the way in which he personifies death during this episode of...

If you recall, the last time Capulet spoke to his daugher,
it was with great anger and he pretty much told her to get out if she wasn't going to
marry Paris, so when he speaks the lines:

readability="14">

Ready to go, but never to return.
O
son! the night before thy wedding-day
Hath Death lain with thy wife. There she
lies,
Flower as she was, deflowered by him.
Death is my son-in-law,
Death is my heir;
My daughter he hath wedded: I will die,
And leave
him all; life, living, all is
Death's.

He is demonstrating
great regret and compassion as now he refers to her again as his daughter which includes
her in their family. He speaks with great emotion.

This
passage also personifies death as the new suitor which has claimed Juliet as his wife.
This passage demonstrates Juliet was important to him and now she is gone in the arms of
Death.

What is (cos 15) ^ 2 – (sin 15)^2

We could also solve this problem as a difference of
squares:

a^2 - b^2 =
(a-b)(a+b)

a = cos 15 and b = sin
15

(a-b)(a+b) = (cos15 - sin15)(cos15 + sin
15)

We could also consider 15 degrees as the half of 30
degrees.

cos 15 = cos
30/2

(cos 15)^2 = (cos
30/2)^2

(cos 30/2)^2 =
(1+cos30)/2

(cos 30/2)^2 =
(2+sqrt3)/4

(sin 30/2)^2 =
(2-sqrt3)/4

(cos 15)^2 - (sin 15)^2 = (cos 30/2)^2 - (sin
30/2)^2

(cos 30/2)^2 - (sin 30/2)^2 =
(2+sqrt3-2+sqrt3)/4

We'll eliminate and combine like
terms:

(cos 15)^2 - (sin 15)^2 =
2sqrt3/4

(cos 15)^2 - (sin 15)^2 =
sqrt3/2

Why does the first scene in act one does not include Othello?

The play is about judgment and misjudgment.  In the first scene,
Iago and Roderigo discuss their feelings toward Othello.  Iago characterizes Othello as a pompous
man "loving his own pride and purposes."  We learn that he passed over Iago who has field
experience for a promotion and instead chose Cassio, a much less experienced man, for his
lieutenant. We understand Iago's indignation.  We learn that Othello has eloped with Desdemona
and that Iago, Roderigo, and Brabantio disprove of this marriage.  This first scene creates a
negative image of Othello.  We are not sure whose side we are on at the beginning of the
play.

In the next scene, we find out that the negative view of
Othello presented earlier in the play is wrong.  Othello is an honorable and dignified general.
 He is not prone to fight, and would rather handle disputes calmly.  He is genuinely in love with
Desdemona, and is not afraid of defending his love.  He did not kidnap her, but won her love
through honorable means.

In a wonderful twist, Shakespeare shows us
how even the audience can misjudge the hero and the villain, which leads nicely into Othello's
misjudgment of Desdemona's faithfulness later on in the play.

What are some of the visual images in the poem "The Slave's dream"?

The visual images in any story or poem cam be only
perceived through apt expression by the poet and H.W. Longfellow has certainly succeeded
in doing so.

The heart moving poem, “The Slave’s Dream”,
melts the lachrymal glands of many. It begins with the image of a destitute slave,
working under poor conditions. His lack of potency and recreation made all the more
worn-out and he went on to sleep, where he saw his former Native Land, which Longfellow
pictures in front of us.

readability="7">

Again, in the mist and shadow of
sleep,

He saw his Native
Land.

Next, we are brought to
the vigorous lands of Africa where the slave resided previously, as a king. The Niger
passed by where he lived with his “dark – eyed”(black) wife. He also had his children
by, and all of them were embracing each other. The scenario intensifies as a tear falls
down from the slave’s eye. Along the Niger he travelled on
horse-back.

Longfellow then appreciates Nature of her
Divine creations as he mentions flamingoes and tamarinds and caffre
huts.

The
bright red flamingoes flew.

At night he heard the lion
roar,

And the hyena
scream.

The forests, with their myriad
tongues,

Shouted
Liberty.

The above quoted
lines signify an immense deal of liberty, equality and independence. These images come
across the slave’s mind because of his underprivileged condition, which makes these
things even more striking for him.

Then we are again
brought back to the original setting. The immortal part(soul) had left his mortal
portion(body) as he breathed no more.

Find the integral of f(x)= 12/(x^2-4x-12)

f(x) = 12/(x^2 -4x -12)

We need to
find the integral.

First we will use partial fraction to
simplify.

==> x^2 - 4x -12 =
(x-6)(x+2)

==> 12/(x^2-4x-12) = A/(x-6) +
A/(x+2)

Now we will multiply by x^2 -4x
-12

==> 12 = A(x+2) +
B(x-6).

==> 12 = (A+B)x +
(2A-6B)

==> A+B = 0 ==> A=
-B

==> 2a-6B = 12

==>
-8B= 12 ==> B= -12/8 = -3/2

==> A =
3/2

==> 12/(x^2 -4x-12) = 3/2(x-6) -
3/2(x+2)

Now we will find the
integral.

==> Int 12/(x^2-4x-12) = (3/2)[ Int (1/(x-6) dx -
Int 1/(x+2) dx ]

= (3/2)[ ln l x-6l - ln (x+2) ] +
C

= (3/2) *ln (x-6)/(x+2) +
C

==> Int 12/(x^2-4x-12) = (3/2)*ln (x-6)/(x+2)
+ C

How is Theseus convinced by Phaedra to take revenge against Hippolytus?

In Euripides' Hippolytus, Phaedra,
the wife of Theseus, is in love with her stepson Hippolytus. For a long time, Phaedra
had tried to hide her love, but eventually her nurse convinces her to reveal her secret
to her. When the nurse learns of Phaedra's love for her stepson, the nurse convinces
Phaedra to allow her to approach Hippolytus.

Hippolytus,
however, is devoted to preserving his chastity and therefore he rejects the "indecent
proposal" that the nurse makes on Phaedra's
behalf.

Phaedra, in an effort to preserve some semblance of
self-respect, hangs herself; but before she does so, she writes a letter accusing
Hippolytus of sexually assaulting her.

When Theseus
discovers this letter, he believes that Hippolytus is guilty of this crime. Given this
belief, Theseus curses Hippolytus, a curse which results in Hippolytus having a chariot
accident and being dragged to death by his own horses.

Identify the significance of the setting, including the major shifts in locale that take place, and when they occur in A Midsummer Night's Dream.

In A Midsummer Night's Dream by
William Shakespeare, the settings of the different scenes reflect the "realities" of the
world the characters inhabit during the play. The Elizabethans believed that the world
of the fairies came to light after dark, when these mystical creatures inhabited the
woods.

The audiences of Shakespeare's time, therefore,
would know that no wise person would ever venture into the woods once the sun went down.
Shakespeare is perhaps the one author most responsible for presenting fairies in an
entirely different light than had been done so before his time. Up until this point,
people believed that fairies could be more than mischievous, but also malicious and
nasty. For instance, at one time they believed that fairies would steal their children,
leaving a changeling in their baby's place.

However,
Shakespeare presents the fairies in this play as playful sprites who would entertain
themselves at the expense of humans, but make things right by the end of the evening.
The audience would have had no doubt that what transpired in the play would actually
happen to them if they were in the woods after
dark.

With this in mind, the world of the fairies existed
for man to see during the night in the forest. The woods during the day belonged to
human beings. And if an unsuspecting human trespassed into the fairy realm after dark,
mischief was afoot and strange occurrences would be
witnessed.

When the Nick Bottom and his fellow thesbians go
into the woods to practice the play they want to perform at the Duke's wedding, they
take the risk of being the evening's entertainment for the fairies. In fact, a good deal
of the play's humor revolves around the spell Puck puts on Nick to turn him into an
"ass."

When the young lovers (Lysander and Hermia) plan to
run away together, and others (Demetrius and Helena) come to "stop" them, Oberon (King
of the Fairies) and Puck (his faithful "henchman") also get involved: Oberon wants the
lovers to end up in "happily-ever-after" with the right person, and so he plays the
matchmaker with Puck's assistance.

Major shifts of locale
take place between the human world (the woods during the daytime where the lovers first
plan to elope) and when the lovers leave the civilized world to travel through the
forest (the fairy realm) at night. "Sanity" returns when the young people leave the
woods at daybreak, thus making their experiences feel like a
"dream."

When the sun is up, the world reverts to the
control of the humans, and all is "right with the world."

Why did Johnny Cade want to read Gone With the Wind at the hospital?

In The Outsiders by S. E. Hinton, Johnny Cade and Ponyboy
are in major trouble and they have to leave town.  While they are hiding out they begin
reading Gone With The Wind.  When Johnny was injured and in the
hospital he wanted a copy of the novel because he liked how all of the men in the novel
sounded like gentlemen and heroes.  He wanted to be a hero.  He enjoyed that the
characters in Gone With The Wind always seemed to save people and are
genteel. 

Johnny came from a poor background where no one
really cared about him.  Yet, he wanted to amount to so much more.  He wanted to make a
difference in his life and the life of others.  The men in Gone With The
Wind were very different than the people he was used to so he enjoyed reading
about them.

Discuss filial ingratitude in King Lear.

There is a sense in which the whole play is dogged by Lear's
incredible lack of understanding of his daughters. Cordelia's truthful response of "I love your
Majesty / According to my bond, no more nor less" is noteworthy in comparison with the flowery,
exaggerated and completely insincere declarations of love from Regan and Goneril, and yet Lear
wants his pride flattered and the love his daughters have for him to be overt and public. The way
in which he turns on the one true daughter who loves on him and surrenders himself into the hands
of Regan and Goneril indicates his own foolishness.

However, having
given away his authority to Regan and Goneril, he then goes on to see how his daughters only
squander that power and bring his kingdom into a state of chaos. Appearance and reality have been
confused by Lear, but it is only towards the end of the play that he is able to recognise how
true Cordelia has been towards him, raising an army to save him from her sisters. Note Cordelia's
words as she is finally reunited with her father in Act IV scene
7:

Restoration
hang

Thy medicine on my lips, and let this
kiss

Repair those violent harms that my two
sisters

Have in thy reverence
made!

Cordelia is a character who is
explicitly linked therefore with reconciliation and restoration. Just as with her sisters, her
true attitudes expose themselves during the course of the play and Lear comes to realise which of
his daughters he can really trust.

How is Maria from the Twelfth Night a stock character?In your answer, be sure to define stock character.

A stock character can be considered a stereotype, and in
drama, a playwright employs stock characters to further the complications of the story. 
Stock characters are used especially often in Comedies, as it is the recognizably
stereotypical human foibles that make for good comic characters and situations --
foibles like craftiness, dimwittedness, miserliness, and  being crazy-in-love or a
braggart.

Maria is an embodiment of the "crafty servant"
stock character.  This character was found in Comedies of ancient Rome, but more
contemporaneously to Shakespeare, the Commedia dell' Arte of Italy.  This comic and
improvisational theatre form allowed both male and female performers onstage and might
have been a very strong influence on Shakespeare's theatrical sensibilities.  The comic
servant from Commedia who can be associated with Maria is Colombina, the crafty servant
of the female lead of a play, a servant who also often had a love
interest.

For more on stock characters, Commedia, and
Maria, please follow the links below.

In All My Sons, what has really happened on the day the defective parts were sent from Keller's point of view?

We find out the answer to your question at the end of Act I when
Joe Keller tells "his" story to Ann Deever, Steve Deever's daughter and Joe's former partner on
whom Joe has conveniently blamed the defective parts. Joe's life is built around the fiction that
he did not know that the parts were defective and it was all Steve's fault, however at the end of
the play he is forced to confront his self-made fiction and admit that the 21 pilots that died
were "all his sons" and face his own guilt in the matter. However, at this stage in the play he
reveals to us how he views what happened:

readability="19">

Every half hour the Major callin' for cylinder heads,
they were whippin' us with the telephone. the trucks were hauling them away hot, damn near. I
mean just try to see it human, see it human. All of a sudden a batch comes out with a crack. That
happens, that's the business. A fine, hairline crack. All right, so - so he's a little man, your
father, always scared of loud voices. What'll the Major say? - Half a day's production shot...
What'll I say? You know what I mean? Human. So he takes out his tools and he - covers over the
cracks. All right - that's bad, it's wrong, but that's what a little man does... That's a
mistake, but it ain't murder.

Note how
in this dialogue Joe does his best to make Steve look better than he actually does, emphasising
the pressure they were under during war time and the way that Steve was a "little man" who
wouldn't be able to face up to either the General or Joe for the faulty cylinders. This is how
Joe presents the "truth" of what happened, and it is only gradually that the real truth is
exposed.

Two numbers are such that the first is half as large as the other. If the sum of the two numbers is 720, what are the numbers?

Let the first number be x and the second number be
y.

Given that x is half y

==> x
= y/2 .............(1)

Also, given that the sum of the numbers is
720.

==> x + y =
720.............(2)

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

==> (y/2) + y = 720

We will
multiply by 2.

==> y+ 2y =
1440

==> 3y = 1440

Now we will
divide by 3.

==> y= 1440/3 =
480

==> y= 480

==> x=
480/2 = 240

Then the numbers are 480 and
240.

In Fahrenheit 451, why does Bradbury describe the books as "pigeon-winged"?

You are of course referring to the opening chapter of this
classic dystopian novel that refers to Montag's penchant for fire and in particular the curious
way that the books themselves are described as Montag and his colleagues burn them. Note how the
books are given the qualities of living animals that are
slaughtered:

...while
the flapping, pigeon-winged books died on the porch and lawn of the
house.

The books are given life, but
this life is only to be extinguished when the firemen arrive and burn them. Likewise too when
they raid the woman who burns herself and her book collection, this imagery is repeated as "books
fell like slaughtered birds" and a book falls into Montag's
hands:

A book lit,
almost obediently, like a white pigeon, in his hands, wings fluttering. In the dim, wavering
light, a page hung open and it was like a snowy feather, the words delicately painted
thereon.

This imagery is used
throughout the novel to make the crime of burning books and the destruction and loss of all the
ideas, culture and thought that they represent worse. By depicting the books as birds, killing
them is a much more heinous crime, as it helps us to see how books are not just inanimate objects
but real life beings.

Find the angle a if 2cos^2a+1=3cosa

The first step is to move all terms to the left
side:

2(cos a)^2- 3cos a + 1 =
0

Now, we'll use substitution technique to solve the
equation.

We'll note cos a = t and we'll re-write the
equation in t:

2t^2 - 3t + 1 =
0

Since it is a quadratic, we'll apply the quadratic
formula:

t1 = {-(-3) + sqrt[(-3)^2 -
4*2*1]}/2*2

t1 =
[3+sqrt(9-8)]/4

t1 =
(3+1)/4

t1 = 1

t2 =
(3-1)/4

t2 = 1/2

Now, we'll
put cos a = t1.

cos a= 1

Since
it is an elementary equation, we'll apply the formula:

cos
a = y

a = +/- arccos y +
2k*pi

In our case, y = 1:

a
=  +/-arccos 1 + 2k*pi

a = 0 +
2k*pi

a = 2k*pi

Now, we'll
put cos a = t2

cos a = 1/2

a =
+/- arccos 1/2 + 2k*pi

a = +/- (pi/3) +
2k*pi

a = 2k*pi + pi/3

a =
2k*pi - pi/3

The solutions of the equation
are:{  2k*pi}U{2k*pi - pi/3}U{2k*pi + pi/3}.