y' + 2xy = 10x Solve the first-order differential equation

y'+2xy =10x
To solve, re-write the derivative as dy/dx .
dy/dx + 2xy = 10x
Then, bring together same variables on one side of the equation.
dy/dx = 10x - 2xy
dy/dx = 2x(5 - y)
dy/(5-y) = 2x dx
Next, take the integral of both sides.
int dy/(5-y) = int 2xdx
-ln |5-y| +C_1= (2x^2)/2 + C_2
Then, isolate the y.
-ln|5-y| = x^2+C_2-C_1
ln|5-y|=-x^2- C_2 +C_1
Since C1 and C2 represent any number, express it as a single constant C.
ln|5-y| = -x^2+ C
e^(ln|5-y|) = e^(-x^2+C)
|5-y| = e^(-x^2+C)
5-y = +-e^(-x^2+C)
Applying the exponent rule a^m*a^n = a^(m+n) ,
the right side becomes
5-y = +- e^(-x^2)*e^C
5-y = +-e^C*e^(-x^2)
-y = +-e^C*e^(-x^2) - 5
y = +-e^C*e^(-x^2)+5
Since+-e^C is a constant, it can be replaced by a constant C.
y = Ce^(-x^2) + 5
 
Therefore, the general solution is  y = Ce^(-x^2) + 5 .

How does James Baldwin develop the theme of the individual in Notes of a Native Son?

Baldwin develops the theme of the individual in several ways. First, he uses illustrative characters to reinforce the idea of aloneness. Through a delineation of his father's character (and his own), Baldwin shows how an individual is marginalized by the larger community.
Baldwin distinguishes himself from his father. They are both individuals, but each experiences "aloneness" differently. Ironically, each is also alienated from the other, reinforcing the precarious position of the individual, the maverick. Baldwin also uses details, imagery, symbols, and events to highlight the theme of the individual.
He provides facts about his father, who was said to be the "first generation of free men" who came to the North after 1919. Baldwin describes his father as "handsome, proud, and ingrown." He emphasizes his father's "blackness," which was both immensely beautiful and alienating. This "blackness" is a symbol of aloneness and menace; it disguises the deep bitterness Baldwin's father harbored. Here, the individual is set apart through an overpowering emotion, one that repels others. Baldwin presents the image of his father "sitting at the window, locked up in his terrors; hating and fearing every living soul."
Baldwin realizes that he has inherited his father's "bitterness" and that it could kill him. During his childhood, Baldwin's family moved from church to church because his father's abrasive style failed to endear him to congregations. Here, the individual is set apart, one by choice and the other by compulsion. Baldwin maintains that his father's overpowering intensity kept society at bay. As a result, Baldwin experienced overwhelming loneliness as a child. The only white people that stepped foot in the family home were welfare workers and bill collectors. Baldwin's father treated them with contempt and vindictive indifference.
Baldwin continues to develop the theme of the individual through a recounting of events, replete with colorful details and imagery. He relates his experiences in New Jersey, where he is treated with undisguised resentment.

It was the same story all over New Jersey, in bars, bowling alleys, diners, places to live. I was always being forced to leave, silently, or with mutual imprecations.

In the North, Baldwin is surprised to experience the effects of Jim Crow laws. White waitresses refuse to serve him, and others spit out varied strains of "we don't serve Negroes here." Baldwin details racial tensions in Harlem. The story begins when an African American soldier quarrels with a white policeman over a girl. The conflict eventually leads to widespread riots. Baldwin maintains that the facts tell a different story. In this, he is set apart, an individual who calls no man his master.

The soldier had not been shot in the back, and was not dead, and the girl seems to have been as dubious a symbol of womanhood as her white counterpart in Georgia usually is, but no one was interested in the facts. They preferred the invention because this invention expressed and corroborated their hates and fears so perfectly.

Baldwin ends his book by again reinforcing the theme of the individual. Alone, he must fight to ensure that his heart is untainted by "hatred and despair."

Discuss the tensions that have arisen between family members due to the poverty that they face. How have their dreams been affected?

Like most families, the Youngers have hopes and dreams for their lives. However, their lack of money has forced them to make changes and sacrifices in these dreams. As the play unfolds, we watch the family decide what to do with Big Walter's $10,000 insurance check.
Leana Younger, Walter's mother, is the matriarch of the family. Her dream is that the family can move up in the world. She believes they can achieve this by buying a bigger house in a different neighborhood. She sees her husband's insurance money as a vehicle for achieving this dream.
Walter Lee Younger is a chauffeur who wants to be wealthy instead of driving around other wealthy people. As he discusses his plan to go into the liquor store business with his friend Bobo, it is clear that he's had several plans to get rich quickly before. Now that there is the possibility of using his father's insurance money for the store, he believes his dreams will come true. As he tells his mother, " I want so many things that they are driving me kind of crazy…Mama – look at me." Walter wants to be able to make a name for himself and to be able to take care of his family's financial needs.
Ruth Younger, Walter's wife and mother to Travis, tries to be a strong woman for Walter. She's described as being only 30 but looking so much older. She spends her time worrying about the other members of the family. There is no mention in the text about her family, so the Youngers are her only family now and so they are who she cares the most about in the world. Poverty has affected her when she realizes that she's pregnant. She knows they barely have enough money to take care of each other, and so she worries about how to take care of a baby. She considers abortion as an option to alleviate any burden a new person in the house may cause.
Beneatha is Walter's sister. At just twenty years old, she often disagrees with her mother's older generation viewpoints. Bennie is in college and dreams of becoming a doctor. Poverty impacts her as she cannot achieve her goals without the insurance check to fund her tuition.
Travis is Ruth and Walter's son. They've tried to protect him from the world, but since the boy doesn't even have his own bedroom, he is well aware of their situation. He tries to help out by carrying groceries after school for extra money when his parents can't give him any extra money.

Discuss the significance of animals in Celtic folklore and mythology.

Since the Celts were an agrarian people, animals were central to Celtic life. Thus, animals such as the wild boar, deer, wolf, and raven figured prominently in Celtic mythology and folklore.
For example, the raven was said to be a symbol for Morrigan, the goddess of war. It was believed that she often frequented the fields of battle disguised in the form of a raven. In Celtic lore, the raven was a symbol of death and destruction; it was considered a bad omen to see a flock of ravens fly across the sky on the eve of a battle.
In the aftermath of battle, however, ravens or carrion birds were a familiar sight to warriors; indeed, the Celts were a war-like people. They also practiced what was called ornithomancy, where ravens were used by priests to divine the future. So, the raven figured prominently in Celtic folklore and mythology because it was central to the warrior culture of the Celts.
Another animal that figured prominently in this war-like culture was the boar, a symbol of physical strength, courage, and prowess in battle. In fact, boar meat was preferred by Celtic warriors during celebratory feasts. The symbol of the boar was engraved onto helmets, vests, shields, and swords. In all, the boar was the Celtic emblem of warfare. It was also connected to legends of the Otherworld or Spiritworld, where it was associated with Druid worship. According to Druid beliefs, humans could connect with animals (like the boar) in the Spiritworld through the medium of their dreams and their unconscious.
Within that unconscious realm, Druids also believed that they could connect with the salmon, the repository of wisdom. As the oldest animal in the Celtic tradition, salmons were said to be central to the pursuit of knowledge.
Meanwhile, the wolf was another revered creature in Celtic lore. Known for its resilience, the wolf was said to rule over the winter months. It presided in ceremonies from Samhain (Halloween) to Imbolc (the festival of Saint Brigid and of purification). The Celts knew February as Faoilleach, the month of the wolf, and February was a time of rebirth, purification, and renewal. Interestingly, the goddess Morrigan was said to have taken the form of the red-furred wolf when she pursued Cu-Chulainn, the legendary Celtic hero.
http://www.celticheritage.co.uk/articles_animals.cfm

https://exemplore.com/spirit-animals/Call-Of-The-Wild-The-Wolf-In-Mythology-Power-Animal

https://www.druidry.org//druid-way/teaching-and-practice/druid-animal-lore

Discuss how the Columbian Exchange between the Old and New Worlds affected both societies.

The Colombian Exchange was very beneficial for Europeans. Europeans gained many new vegetables from the New World such as squash, tomatoes, and potatoes. This new influx of vitamins increased European birth rates as well as longevity. The downside to this was an increase in the European population that led to overcrowding, poverty, and wars as nations competed over dwindling resources.
The Colombian Exchange had mainly bad effects for the Native Americans. Many died due to smallpox and other diseases. The small number of Spanish conquistadors who arrived in Central and South America could have never defeated the native empires there without the spread of disease. European pigs also rooted through Native American fields, destroying crops and causing unrest between Europeans and natives. The Colombian Exchange brought the horse to the New World—the horse allowed the Plains tribes to become more mobile in their buffalo hunts. Horses would eventually be considered a wealth symbol for the Plains tribes.

The Old World—that is, Europe—derived enormous benefits from the Columbian Exchange. In the short-to-medium term new crops were introduced to Europe, such as potatoes and tomatoes, that would radically diversify agriculture on the continent. This made it possible for more farmers to produce more food, thus minimizing the ever-present threat of famine. As a result, European society became more stable, less prone to the destabilizing effects of chronic food shortages.
As for the indigenous society of the New World, the effects of the Columbian Exchange were generally negative. As well as introducing diseases to which the natives had no natural immunity, the Europeans introduced a number of animals into the New World, which had a negative impact on the delicate eco-system. In societal terms, these factors had a catastrophic effect on the indigenous people, leading to the eventual dispersement of native tribes away from their traditional hunting grounds, which in turn made it easier for European settlers to steal their land.

The Columbian Exchange was the exchange of crops, livestock, and disease from the "Old World," which consisted of Europe, Africa, and Asia, to the "New World" of the Americas.
Some of the new goods that benefited the "Old World" were agricultural staples like tomatoes, potatoes, corn, cassava (which became the staple African "manioc"), beans, and sweet potatoes. As a result of the new foods transported to the "Old World," population increased; this was possible because the variety of new foods and nutrition allowed people to live longer. The Columbian Exchange also encouraged other explorers to make their way to the "New World" in search of land and new treasures; it was like a doorway to new riches that Europeans took advantage of in the form of forced labor and mercantilism.
The "New World" also got new crops, like sugar and citrus fruits, but the impact of the Columbian Exchange was remarkably worse on the native inhabitants. Afroeurasians (that is, people who lived in Africa-Europe-Asia) had been communicating and exchanging for centuries, but the native inhabitants of the Americas were isolated. One of the biggest problems with a new contact with the "Old World" was the transmission of disease. Smallpox, carried with "Old World" explorers, wiped out large portions of American populations; historians estimate anywhere between fifty and eighty percent of total populations. Entire civilizations crashed, like the Aztec in central Mexico and the Inca in South America. Europeans took advantage of the "New World" lands and people by setting up plantations, where indigenous Americans or African slaves worked to grow crops like tobacco, sugarcane, coffee, indigo, and cotton.

What false promises is Beatty referring to?

In Part Two of Fahrenheit 451, Montag shows Mildred his stolen copy of the Bible and she tells him that he must hand it over to his boss, Captain Beatty. Montag doesn't want to, prompting Mildred to shriek that he must make a choice between her and the Bible. It is in this melee that Montag hears the voice of Captain Beatty, encouraging him to relinquish his collection of books:

"All the silly things the words mean, all the false promises, all the secondhand notions and time-worn philosophies."

In other words, Beatty wants Montag to stop believing in the power of books and to accept that books will not make him happy or satisfied with his life. To convince Montag of this, Beatty tells him that books contain "silly things" and "false promises." In Montag's thoughts, Beatty says this while "perspiring gently" which suggests that Beatty is nervous because he is lying. In truth, Beatty knows that books contain the answers which Montag seeks and that there is little he can do to stop him from reading.

In Gods Go Begging, how does time change in war and prison? Make sure to quote the text and closely analyze the metaphors and symbols, the tone and/or feeling of each scene, demonstrating their connection to your claims and arguments.

Time slows down in the prison scenes of the novel, and while the body is inert, the mind travels. Véa writes of men in prison:

Their beds were geared for long distances, for trips to Alpha Centauri and the Sombrero Galaxy. Everyone doing time knew you had to sleep away the years in a state of suspended animation in order to reach your destination alive. (53)

Véa uses a metaphor comparing time in prison to time spent suspended in the darkness of space. The prisoners' beds are compared to space ships, and prisoners who hope to get out of jail spend their time in a state of inert waiting for their dark journey to end. While they are in jail, they spend time dreaming and sleeping. Véa writes:

For most prisoners, the bed, powered by a decent pillow, would merely calculate your good time credits automatically and wake you up when your time in the stir was done. (53)

This passage also uses a metaphor in which the bed is compared to an alarm clock that will wake up the men after they have spent their prison time dreaming. The mood of these passages is one of dread and waiting. 
In war, however, time speeds up so that all of life can be compressed into one second. The protagonist, Jesse Pasadoble, fought in Vietnam. He recalls how fear can make one moment seem like an eternity. Véa writes:

A year and a half of incredible fear in the highlands of Vietnam had been transformed into an almost anguished love of the living, intact moment, the moment that can never be possessed. (45)

In other words, from living with constant fear while fighting in Vietnam, Jesse comes to regard each moment of life as a precious eternity. Véa implies that fear makes Jesse treasure each moment as if it held all the mystery and majesty of life. In war, time is sped up so that the soldier tries to experience all of life in one moment. 

What does the poet refer to as "that voice from the world of men"?

The voice in "that voice from the world of men" refers to the voice of the traveler who is seeking admittance to the house (" 'Is there anybody there?' he said"), and it is from "the world of men" in contrast to the world not of men, or beyond men that exists inside the house, and which is inhabited by "only a host of phantom listeners." The impression is that those listeners inside of the house are perhaps ghosts or spirits of some kind. This is implied most of all by the word "phantom" in the quotation above but also by the reference to "their strangeness" which the traveler "felt" and by the description of them "thronging the faint moonbeams on the dark stair." This last quotation suggests that these "listeners" exist in the air, illuminated only by the shafts of moonlight that penetrate the windows. They are ethereal, and immaterial. Nonetheless, they may be real, meaning that they might really exist outside of the traveler's mind. Or, as the word phantom sometimes suggests, they might be illusory, a projection of the traveler's imagination, existing only inside his mind.
Either way, the traveler's voice, calling repeatedly, "Is anybody there," goes unanswered. The real mystery of this poem is why the listeners choose not to respond to his voice, the only voice from "the world of men." They certainly seem to hear him ("Stood listening...they heard his foot upon the stirrup"), and he has been asked to call on the house ("Tell them I came...that I kept my word"), but still they do not respond. The fact that the traveler's voice is described as "that voice from the world of men" could suggest that it is not so much the individual traveler but the "world of men" that they will not, or cannot, respond to. Perhaps they are ghosts or spirits from the afterlife that are unable or unwilling to make themselves heard across the divide between their world of spirits and the corporeal world of the traveler.
It is reputed that near the end of his life, the poet, Walter De La Mere, told a friend that this poem was "about a man encountering a universe." If this is so, then perhaps the traveler seeking admittance, waiting for an answer or response from inside the house, represents mankind, and the "phantom listeners" inside the house, listening but not responding, represent the universe, whether this be spirits, God/s, or the cosmos in a broader sense. We have all, like the traveler, tried to find a greater meaning to life and sought answers from the world in which we exist. And it is likely too that we have all felt that deafening, indifferent, and infuriating silence in response ("their stillness answering his cry"). That "voice from the world of men" is then the voice of us all, sometimes lonely ("the lonely Traveler's call"), sometimes desperate ("he suddenly smote on the door"), and often seeking answers that do not come but which leave only our questions "echoing through the shadowiness of the still house."
https://www.scottishpoetrylibrary.org.uk/2012/05/there-anybody-there-century-listeners/

Line 16 of Walter De La Mare's "The Listeners" contains that particular phrase. It does make more sense with a few of the lines preceding it because the preceding lines allow the "voice from the world of men" to be part of an entire thought.

But only a host of phantom listeners
That dwelt in the lone house then
Stood listening in the quiet of the moonlight
To that voice from the world of men:

The phantom listeners in the house are listening to a voice from the world of men. The voice is coming from an actual man that is in the house. The opening line of the poem introduces readers to "the Traveller." We don't know much about him, but we do know that he expects somebody to be at the house. He knocks on the door and is met with silence. He then knocks on the door a second time and verbally calls out.


And he smote upon the door again a second time;
‘Is there anybody there?’ he said.


His inquiring call is the voice from the world of men that the phantom listeners hear.

College Algebra, Chapter 5, 5.5, Section 5.5, Problem 10

There are 400 bacteria's after 2 hours and 25,600 after 6 hours in a culture.

a.) Identify the relative growth rate of the bacteria population? Express your answer in percentage.

b.) Determine the initial size of the culture?

c.) Find a function that will model the number of bacteria n(t) after t hours.

d.) What will be the number of bacteria after 4.5hours?

e.) When will the number of bacteria be 50,000?



a.) Recall the formula for growth rate

$n(t) = n_0 e^{rt}$

where

$n(t)$ = population at time $t$

$n_0$ = initial size of the population

$r$ = relative rate of growth

$t$ = time



$
\begin{equation}
\begin{aligned}

\text{if } n(2) =& 400, \text{ then}
&& \text{and}&
\text{if } n(6) =& 25600 \text{ then}
\\
\\
400 =& n_0 e^{r(2)}
&& &
25600 =& n_0 e^{r(6)}
\\
\\
n_0 =& \frac{400}{e^{2r}} \qquad \text{Equation 1}
&& &
n_0 =& \frac{25600}{e^{6r}} \qquad \text{Equation 2}

\end{aligned}
\end{equation}
$


By using equations 1 and 2,


$
\begin{equation}
\begin{aligned}

\frac{400}{e^{2r}} =& \frac{25600}{e^{6r}}
&& \text{Multiply both sides by $e^{6r}$ and divide each side by } 400
\\
\\
\frac{e^{6r}}{e^{2r}} =& \frac{25600}{400}
&& \text{Apply Property of Exponents}
\\
\\
e^{4r} =& 64
&& \text{Take $\ln$ of each sides}
\\
\\
4r =& \ln (64)
&& \text{Recall } \ln e = 1
\\
\\
r =& \frac{\ln (64)}{4}
&& \text{Solve for } r
\\
\\
r =& 1.0397 \times 100 \%
&& \text{Express as a percentage}
\\
\\
r =& 103.97 \%
&&

\end{aligned}
\end{equation}
$


b.) By using equation 1


$
\begin{equation}
\begin{aligned}

n_0 =& \frac{400}{e^{2(1.0397)}}
\\
\\
n_0 =& 50

\end{aligned}
\end{equation}
$


c.) By substituting all the acquired information in the general equation, we have

$n(t) = 50e^{1.0397 t}$

d.)


$
\begin{equation}
\begin{aligned}

\text{if } t =& 4.5 \text{ hours, then}
\\
\\
n(4.5) =& 50 e^{1.0397 (4.5)}
\\
\\
n(4.5) =& 5381.23 \text{ or } 5381

\end{aligned}
\end{equation}
$


e.)


$
\begin{equation}
\begin{aligned}

\text{if } n(t) = 50,000 \text{ then}
&&
\\
\\
50,000 =& 50 e^{1.0397 (t)}
&& \text{Divide each side by } 50
\\
\\
1000 =& e^{1.0397(t)}
&& \text{Take $\ln$ of each side}
\\
\\
\ln (1000) =& 1.0397 t
&& \text{Recall } \ln e = 1
\\
\\
t =& \frac{\ln (1000)}{1.0397}
&& \text{Solve for } t
\\
\\
t =& 6.64 \text{ hours}

\end{aligned}
\end{equation}
$

What does Hamlet do to catch Claudius

Hamlet does not completely trust the ghost and needs to confirm that Claudius was responsible for the king's death before seeking revenge. At the end of act two, scene 2, Hamlet describes his plan to catch Claudius and prove that Claudius assassinated his father. After everyone leaves the scene, Hamlet laments about his inability to act on his powerful emotions, in a moving soliloquy. At the end of Hamlet's soliloquy, he says that he plans on having the players reenact King Hamlet's assassination on stage during the play The Murder of Gonzago. While the actors are portraying King Hamlet's murder, Prince Hamlet plans on analyzing Claudius's reaction to the scene on stage. Hamlet ends the scene by saying,

"The play’s the thing /Wherein I’ll catch the conscience of the king" (Shakespeare, 2.2.566-567).

In act three, scene 2, the players reenact King Hamlet's murder on stage, and Prince Hamlet witnesses Claudius stand up and exit the theater. Claudius's reaction indicates that he committed regicide and gives Hamlet the proof that he is looking for to enact revenge. Unfortunately, Hamlet continues to hesitate and make excuses for not murdering Claudius.

Why does Monsieur Loisel advise his wife not to tell her friend about the lost necklace?

Monsieur Loisel doesn't want to tell Madame Forestier about losing the necklace because it would mean a loss of face. Though not a crashing snob like his wife, he's doubtless aware that his recent invitation to the Education Ministry ball could've been the start of big things for him both professionally and socially. So the last thing he wants to do is to damage his chances of advancement by admitting to having lost what he and Mathilde believe to be a valuable diamond necklace. Instead, he gets Mathilde to spin a yarn about breaking the necklace's clasp and needing to get it fixed as a way of buying time so that he and his wife can see if they can find the lost necklace.

Monsieur Loisel advises his wife to tell Madame Forestier that she has broken the clasp on the necklace she has borrowed from her, and that it will take some time to get it repaired at a jewelry shop. Loisel comes up with this lie this so that they have some time to retrace their steps on the night of the gala to see if they can find the necklace that Madame Loisel has lost.  When they do not find it, Loisel goes to "the police station, to the newspapers, to offer a reward, to the cab companies..." to see if the necklace will surface. When no one steps up after a week has gone by, he combines his inheritance from his father's estate with borrowed money to come up with sufficient funds to purchase a diamond necklace that looks very much like the one that Madame Loisel has lost.   

What is the value of the following commutator containing the spin 1/2 operators; [[S_x*S_y,S_y],S_z]?

Remember the definition of the commutation relation
[a,b]=ab-ba
Preform this operation on [S_x*S_y,S_y]
[[S_x*S_y,S_y],S_z]=[[S_x*S_y*S_y-S_y*S_x*S_y,S_z]
The following is the commutation relation for spin 1/2 systems.
[S_x,S_y]=i barh S_z
For cyclic permutations of x , y , and z . barh is represents the reduced planks constant here.
=[[S_x,S_y]S_y,S_z]
=[i barh S_z*S_y,S_z]
=i barh S_z[S_y,S_z]
=-barh^2S_z*S_x
http://easyspin.org/documentation/spinoperators.html

Describe the spaceship.

Chapter 4 is probably the best location for a description of what the spaceship looks and sounds like. At this point, Billy knows that he is about to be taken by the spacecraft, so he goes out in the yard in order to wait for it. The first thing that he notices about the flying saucer is that it sounds like a hooting owl. The flying saucer is capable of navigating both space and time, and it is most likely perfectly circular. The reason for that is that the narrator tells readers that the ship's diameter is 100 feet, so the flying saucer isn't exactly that big. By comparison a modern day semitruck and trailer are roughly 75 feet in length. The flying saucer has portholes around its outer rim, and purple light pulses from the windows. In the bottom of the flying saucer, there is an airtight hatch through which a ladder can extend out of. The ladder leads into an airlock that has two "peepholes" for somebody to look into the airlock. The airlock also has a speaker inside of it. There are several rooms inside the flying saucer, and readers are told that Billy's room is complete with a "Barca-Lounger." There is also a cargo hold aboard.

The hold of the saucer was crammed with other stolen merchandise, which would be used to furnish Billy's artificial habitat in a zoo on Tralfamadore.

What are differences and similarities between Tom Robinson’s trial in To Kill A Mockingbird and the Scottboros trials?

The two cases are extraordinarily similar. In fact, many scholars who studied the work assumed that the Tom Robinson trial was largely based on the case of the Scottboro Boys, though Harper Lee herself said that she was going for something "less sensational." Both trials include black men on trial for a crime that they did not commit and being convicted despite overwhelming evidence in their favor. Due to overwhelming prejudice, the defendants in both cases were written off before they even went to trial. Both cases even feature a pre-trial lynch mob. In regard to differences, they are not many. The first is that one of the accusers of the Scottsboro boys actually admitted to the fabrication of the story before the trial was over, though it did not help their case. Also, unlike Robinson, the Scottsboro boys had very poor legal representation.

The Scottsboro Boys were a group of young African American males wrongly convicted of the rape of two white women. The case took place in Alabama, the setting for To Kill a Mockingbird. Clearly, Tom Robinson's case is very similar to that of the Scottsboro Boys. In both cases, the prosecution had no hard evidence of guilt, relying instead upon blatantly fabricated stories. Tom Robinson and the Scottsboro defendants were effectively found guilty before they even appeared in court. At that time in the South, an accusation of rape by a white woman against an African American male was almost tantamount to a death sentence, irrespective of any actual evidence of guilt.
The Scottsboro case, unlike that of Tom Robinson, was recognized as a blatant miscarriage of justice, achieving wide resonance throughout the United States. Another difference is that Tom Robinson was convicted despite having such an outstanding, conscientious lawyer representing him at his trial in the shape of Atticus Finch. However, the Scottsboro Boys, initially at least, were severely hampered by inadequate legal representation, a common occurrence for African Americans at that time.
http://www.encyclopediaofalabama.org/article/h-1456

Examine the character of Beowulf. What can we infer about the Anglo-Saxon, masculine ideal/stereotype? Are these ideals still present in our culture? Give examples. How does violence fit into this?

Beowulf is a traditional, stereotypical heroic man. In history and literature, there is an archetype of the masculine hero, and this is the type we observe in his story. The traits that it illuminates for the Anglo-Saxon idea of masculinity is primarily physical strength and the ability to conquer. Like Hercules or Oedipus, he is a very strong man who can take down mighty beasts and engage in impressive feats of strength. He is also a leader of his people and can conquer his enemy.
Violence is a common thread in the stereotype of masculinity, which is why young Spartan boys were sent to military school from the time they were five years old. Beowulf is not only physically strong, he shows his strength through his violent conflicts with Grendel and the dragon.
To an extent, these traits are still lauded. With strength competitions and a heavy emphasis on physical fitness for men in the media and entertainment industries, it is clear that strength is still important. The archetype may not be explicitly encouraged, and there is a tendency to discourage violence, but the same traits are encouraged and found desirable.

The character of Beowulf is typical of heroic epic. He is, in many ways, the ideal hero, evolving from a modest young warrior with great potential to one who does great deeds and finally to a wise and powerful king. His first and most obvious characteristic is martial prowess which he demonstrates by engaging in athletic contests as a youth (the swimming challenge) and then by killing monsters as an adult. As well as being strong and skilled in the arts of war, he is also of good moral character, acknowledging and fulfilling debts and obligations, and willing to risk or even sacrifice his own life when needed for the greater good (e.g. the fight against the dragon). He exists within a strongly hierarchical society and one that respects the bonds of kinship and hospitality, and he demonstrates the important value of loyalty.
This tradition of admiration of physical prowess, tribalism, and hierarchy is still present in the military and in team sports although technological advances do mean that the skilled engineer is now more valuable to the military than someone who can just lift heavy weights or shoot a bow accurately. Similarly, the loyalty to a small group defined by kinship and hospitality exchange is one that is admirable in some ways but in other ways can lead to narrow-mindedness and hostility to outsiders, not traits that are admirable or productive in a globalized and multicultural world. 

What are the reasons for inflation in a democracy?

There are various reasons why inflation may occur. One factor would be an increase in the demand for products. If people have more money or more access to money, they will generally spend it. Federal Reserve Board policies may impact the money supply. If the Federal Reserve Board lowers interest rates, it makes it easier for people and businesses to borrow money. If businesses borrow money to expand their operations, this should create more jobs, increasing employment and giving people more money to spend. Likewise, if interests rates drop, people may take out loans in order to buy products. In these situations, the demand for products should rise, and if supply doesn’t increase, prices will also rise.
The government may also be responsible for inflation. If government spending increases, this will also increase the demand for products and services. With more money in the economy and with an increased demand for products, inflation would occur.
Another factor that might lead to inflation would be an increased cost of doing business. If businesses have to pay more for their supplies and for their labor costs, they will likely pass these additional costs on to consumers. When the price of gasoline rose to over $4.00 per gallon in the United States, many businesses passed their increased transportation costs on to consumers, resulting in higher prices.
https://fee.org/articles/the-causes-of-inflation/?gclid=CjwKCAjwwPfVBRBiEiwAdkM0HTyNu3PWvW0rpYuwAjWgwhozYuV1P923cL_2eP6mRssrI9QVBMuMghoCWJEQAvD_BwE

https://www.frbsf.org/education/publications/doctor-econ/2002/october/inflation-factors-rise/

"Inflation" is a term which refers to an overall increase in the prices of things across all markets. There are two main reasons inflation happens:
1. Demand for goods and services grows too quickly for the economy to keep up. If there is a sudden increase in demand for a particular item, and the economy is unable to produce more of the item so that supply meets demand, the price of the item will rise. If demand grows across multiple sectors, causing multiple price rises, this drives inflation. This type of inflation can also be driven by an increased supply of money to the economy from the banks, making the money itself worth less.
2. The actual cost of production increases, because the raw material used to produce goods gets higher, or the minimum wage is lifted so that the cost of employing people is higher. This can lead to an increase in the overall prices of goods that make it to the consumer.

How is a scientific name written?

I am going to assume that this question refers to the final part of the scientific name. That would be the genus and species name. The rules regarding how to write these names are very specific.
Fortunately, they are also very simple: The genus name always precedes the species name. The first letter of the genus name is always capitalized. The first letter of the species name is never capitalized. The entire name is always underlined or italicized.
For example, the gray wolf's genus and species name would be written as follows: Canis lupus. It is possible to abbreviate the scientific name. In order to do this, the first letter of the genus name is used and the species name is used in full. The italics or underline rule is still present. Canis lupus = C. lupus.
http://generalhorticulture.tamu.edu/h202/labs/lab3/sciname.html

Why does Cassius want Antony killed, and why does Brutus wish to spare his life?

Cassius is a better judge of human character than Brutus, as the events in the play reveal. Brutus is an idealist. He has an honest, generous character and expects other men to be the same. When he takes over the titulary leadership, he wants the conspiracy to appear to the public to be a patriotic and necessary deed. Cassius is a selfish, greedy man who expects other people to be like himself. When he suggests Mark Antony should be killed along with Julius Caesar, he foresees, correctly, that Antony could be extremely dangerous. Brutus and Cassius both state their opinions of Antony in Act II, Scene 1.

CASSIUS: I think it is not meetMark Antony, so well beloved of Caesar,Should outlive Caesar. We shall find of himA shrewd contriver; and you know his means,If he improve them, may well stretch so farAs to annoy us all, which to prevent,Let Antony and Caesar fall together.

Antony does in fact prove to be a shrewd contriver. He knows how to manipulate Brutus, and then shows he knows how to manipulate a whole crowd of lower-class Roman citizens who all listen to Brutus's funeral speech, support Brutus, and favor the assassination of Julius Caesar.
When Cassius suggests killing Antony in Act II, Scene 1, Brutus dismisses the proposal. Brutus is a good and wise man in many respects, but he has his faults. He is a bookish, solitary man wrapped up in his own ideas. He assumes he knows more than any other man in Rome. He has a reputation for integrity and patriotism, largely because of his family background, and this is of great importance to him. He wants the masses to think of him as a hero after the assassination. In reply to Cassius's proposal to kill Antony, he says,

Our course will seem too bloody, Caius Cassius,To cut the head off and then hack the limbsLike wrath in death and envy afterwards;For Antony is but a limb of Caesar.Let us be sacrificers, but not butchers, Caius.We all stand up against the spirit of Caesar,And in the spirit of men there is no blood.O, that we then could come by Caesar's spirit,And not dismember Caesar! But, alas,Caesar must bleed for it! And, gentle friends,Let's kill him boldly, but not wrathfully;Let's carve him as a dish fit for the gods,Not hew him as a carcass fit for hounds;And let our hearts, as subtle masters do,Stir up their servants to an act of rageAnd after seem to chide 'em. This shall makeOur purpose necessary and not envious,Which so appearing to the common eyes,We shall be call'd purgers, not murderers.And for Mark Antony, think not of him,For he can do no more than Caesar's armWhen Caesar's head is off.

When Brutus speaks to the mob in Act III, Scene 2, he tries to make them think he and all the conspirators were public-spirited "sacrificers." When Antony displays Caesar's shredded, bloody cloak and mangled body, they serve as evidence that most of the conspirators were "butchers, not sacrificers" and that they "hewed Caesar as a carcass fit for hounds." In truth, most of the thirty or more assassins were motivated by hatred, rage, fear, and panic, not the noble motives Brutus attributes to them.

Which statement BEST describes Rousseau’s view of the relationship between governments and the rights of the people? A. If governments are to remain in power, they must protect the rights of at least some of their citizens. B. When governments are created with the consent of the people, the people are more likely to retain their natural rights. C. Governments should act as a paternal, or father figure, whose sole responsibility is to protect society from chaos. D. Governments should only protect the rights of the majority, since it is the majority of citizens that give the government its power and authority.

Statement B best describes Rousseau's views.
In The Social Contract, Rousseau posited that people, when they remained in the state of nature, were not corrupt. Instead, it was society that corrupted them, particularly the competition for material wealth. In his view, society created inequalities that were unnatural. Prior to the French Revolution, France was a very unequal society with an increasingly desperate working-class and a willfully blind aristocracy. For Rousseau and other Enlightenment figures, this situation was untenable. 
Rousseau believed that a government formed by popular sovereignty, or with the consent of the people, would be most sustainable in the long-term.
Rousseau had a positive view of human nature. On the other hand, Thomas Hobbes had a negative view. Statement C best reflects Hobbes's view as explained in Leviathan. He believed that, without a strong monarch, citizens would give in to their worst instincts. 
However, neither Hobbes nor Rousseau favored the abandonment of minorities. It was a government's responsibility, whether it be a popular sovereignty or a monarchy, to protect the interests of all citizens.

What roles have international institutions played in helping developing countries curb various challenges? How have some challenges not been resolved and some risen due to the involvement of these institutions?

International institutions are non-governmental institutions created in developed countries to provide various kinds of aid and development assistance to developing countries. Non-governmental organizations (NGOs) are funded by their country of origin's government, but are not overseen or regulated by those governments. Clear examples of these international institutions are the International Monetary Fund, the International Red Cross, and the World Health Organization.
Some of the roles played by NGOs (or international institutions) and some of the challenges faced by developing countries that NGOs address are described in the United Nation's Millennium Development Goals (MDGs), which include "combating HIV/AIDS," eliminating "extreme poverty and hunger," empowering women and promoting gender equality, and achieving "universal primary education" (UN Millennium Project). NGOs work in developing countries on challenges such as poverty, economic inequality, trade barriers, sustainable industry, education, human rights, health and disease, child mortality, agriculture, and economic growth.
The history of NGOs, such as the IMF and World Bank, shows NGOs, while interested in improving challenges in developing countries, are also interested in profits. Many NGOs have received a lot of criticism on their philosophies, plans, and actions, and this criticism has led to attempts to improve the focus and methods of NGOs. A significant point of criticism has been that NGO development projects give rise to new challenges that are detrimental to the growth of health, economies, human rights, and sustainable ecological development. Ecological degradation is one of the newly arising challenges caused by NGOs. The history of the Mobil oil pipeline (now Exxon Mobil) in Nigeria is a good illustration of how development projects funded by NGOs—in this case the World Bank—can result in serious new challenges.
NGO-funded development of cash crops, such as cotton, which are intended to increase a developing country's national income by exporting the crop to developed nations, illustrates how some challenges addressed by NGOs have not been resolved, while simultaneously giving rise to new challenges. Cash crop emphasis was a strategy to address the hunger associated with extreme poverty. Planting cash crops did increase national income and reduce poverty, but emphasizing cash crops monopolized limited agricultural lands. The cumulative result of the cash crop strategy is to trap the poorest people in continued hunger because the cash crop of the small, poor farmer displaces the sustenance food crops that would otherwise feed the farmers, their families, and their neighbors. In this way, the challenge of hunger was left unresolved while raising the new challenge of land degradation.
https://www.un.org/un70/en/content/70ways/

A process strategy is an organization’s approach to transforming resources into goods and services. Which process strategy would a hospital choose and why?

Process strategy involves figuring out the most efficient way to produce a good or deliver a service so that processes do not need to be outsourced and so that quality assurance is maximized. There are four types of process strategies: process focus; repetitive focus; product focus; and mass customization.
A hospital needs to implement the process strategy of process focus, which involves producing low-volume services that involve a high degree of variety. This type of process strategy permits a business to use flexible strategies to produce different kinds of services and to concentrate on the processes that are essential to a business. For example, a hospital would concentrate on the processes of patient care and patient outcomes, as these processes and everything that goes into them (including nursing, physician care, pharmacy care, nutrition, etc.) are essential to the core business of the hospital. 
Repetitive focus involves the mass production of goods and services through repetitive processes. A hospital uses these types of functions, such as in food production, but they are not as essential to the hospital as the special functions it provides in giving medical care. 
Product focus involves producing high volumes of a particular product without a great deal of variety or flexibility. This is not usually the focus of a hospital, unless it is a specialized hospital that focuses on one area, such as surgery, as most hospitals offer a variety of types of medical care.
Mass customization, which is the most complicated type of process strategy, involves using up the resources of the organization to suit the needs of its customers on a constantly changing basis. A hospital must also use this strategy at times, as the hospital must deliver what the patient wants when he or she wants it. For example, different patients will require different types of medical or other interventions depending on their needs. One person in a community hospital might need diabetes care, while another might need a knee replacement surgery. The hospital must customize its services for each patient. 

In the Herdelin cemetery, what do Mathilde and Sylvain notice on the tomb of Ange Bassignano?

Mathilde is with her uncle Sylvain at the Herdelin cemetery, visiting the grave where Manech is supposed be buried. She recalls the first time she visited the place, and saw the graves of Manech's co-condemned. She remembers seeing the little white crosses marking the final resting places of Jean Echevery and Kleber Bouquet. Finally, a few rows away, she saw the grave of Ange Bassignano. On his grave was a vase of flowers made of colored beads, which spelled the name "Tina." This was Tina Lombardi, his prostitute girlfriend.
Mathilde remembers being rather annoyed to see a tribute left on the grave of such a disreputable character, this notorious pimp otherwise known as "Common Law." While she was still searching high and low for Marech, Tina, someone Mathilde dismisses as "a tart from the mean streets of Belle de Mai," had managed to track down her departed lover and adorn his grave with an appropriate memorial. The implication is that a tribute such as this is wasted on an unsavory character like Ange Bassignano.

Elaborately explain the theme of morality in Tess of the d'Urbervilles.

The subtitle of Tess is "A Pure Woman Faithfully Presented." From the title onward, Hardy is attacking Victorian sexual morality. 
Tess, a naive 15-year-old, is not well protected by her parents, who put her in harm's way when they send her to work for a supposed cousin, Alec. Alec, an older man, rapes and impregnates Tess, who is now shamed as a "fallen" woman. Hardy shows, however, that what happened to her is not her fault. He portrays her as a good young woman.
Later, at the dairy, Tess experiences living in a place where conventional morality doesn't press so strongly. She starts to believe that Angel Clare could love her despite her past. After they marry, he tells her that his past hasn't been "pure," but when she confesses what happened to her with Alec, he reacts in horror and recoils from her. He responds according to the hypocrisy of the Victorian moral code, which allows a man, but not a woman, to have sexual experiences before marriage.
While today Alec would be in prison as a pedophile rapist and Tess not blamed, Victorian audiences objected strongly to Hardy's subtitle labelling Tess a "pure" woman. To them, she was a fallen, impure woman. The public missed Hardy's point entirely. Hardy was trying to point out that Victorian sexual morality was twisted, hypocritical, and wrong in blaming women for the things men did to them. But his readers were not ready to accept that. Today, we more clearly see that it was the moral code, not Tess, that was at fault.

How would Sylvia’s and her grandmother’s lives have changed if they had the ten dollars from the stranger?

The hunter, in an attempt to persuade Sylvia to reveal the location of the white heron's nest, says that he would give ten dollars to any person who could help him find it. For Sylvia, "No amount of thought, that night, could decide how many wished-for treasures the ten dollars, so lightly spoken of, would buy." The little family of Sylvia and her grandmother is described as "poor" in the third-to-last paragraph of the story, so I would imagine that the ten dollars would help, for a time, to put food on the table and in their bellies. It might help pay for some new clothes and shoes for the two of them. I would think that they'd be able to pay for some necessary items with this money, and so it might not really be used for the "wished-for treasures" Sylvia imagines if they truly are so very poor.

Using one piece of evidence, explain the purpose for Ferdinand and Isabella’s religious policies during their rule in Spain.

The Spanish "reconquista", or reconquering was all about bringing the then Muslim owned Iberian Peninsula under Catholicism. Ferdinand and Isabella's marriage was political in its own right, and their ambitions were to unite the different provinces of Castile and Aragon and create a more united, Catholic Iberian nation--which would later be known as the Kingdom of Spain.
The reconquista itself took over 700 years to complete, as conquering the land back from the Moors kingdoms was a long and arduous process. Both Ferdinand and Isabella believed that the reconquista was a holy war, and that taking Spain back was a mission from God: therefore, this helped to shape their religious decrees. Views of Islam inspired xenophobia in the natives of the different Spanish territories. In "Muslim-Christian Relations: Historical and Contemporary Realities", Jane Smith writes:

Within the Islamic community early attitudes of seeming tolerance and even appreciation of Christians and Jews soon gave way to more narrow interpretations of the Qur’an and Islamic law, resulting in growing intolerance. From the beginning Christians were nervous about the growth of a new religion that they saw as a Christian heresy and which invaded and took over many of their lands.

To make a long story short, the Spaniards were intolerant of the growth of the Moors, who were not only different, but somewhat kinder to their colonists, too. They were considered heretics according to hundreds of years of Christian historical doctrine before them. Each small kingdom of Spain had to be painstakingly reconquered, and Isabela and Ferdinand's shaky hold needed to be strengthened. Therefore, The show of strength the nation made with the Alhambra Decree (which forced all Jews and Muslims to be removed from Spain or forcibly converted to Christianity) united Spain underneath the Catholic mantle, and allowed for the Spaniards to create a religiously "pure" nation--truly one nation, under God.
Tl;dr (the summary): The Catholics had always believed the Muslims, being different than them, were heretical and bad, so Isabella and Ferdinand were able to use that fear to unite their kingdoms and eventual country under Catholicism.
Check out https://www.h2g2.com/edited_entry/A30498979 for a little more information!

The main aim of King Ferdinand and Queen Isabella's religious policy was to ensure that their kingdoms in the Iberian Peninsula were entirely Catholic. They did this formally with the Alhambra Decree on March 31, 1492.
For over seven hundred years, much of Spain had been under the control of Muslim Moors. The Moors tolerated different religions in their domains, and consequently, during their rule, Spain had a diverse population of Christians, Muslims, and Jews. After the Moors were expelled, Ferdinand and Isabella set about strengthening the Catholic presence in Spain. Besides being deeply religious, they felt that they could use Catholicism to maintain a more powerful hold on their newly won kingdoms.
With the aid of the Pope, the Catholic monarchs had already extended the Spanish Inquisition to investigate and prosecute converted Muslims and Jews (conversos) who were secretly practicing their former faith. Partially out of concern that the remaining non-Catholic population would influence more conversos to revert to their old faith, the monarchs decided to expel any remaining Jews and Muslims form their domains.
The Alhambra Decree gave non-Catholics four months to leave Spain. About 200,000 Jews and a lesser number of Muslims had already converted to the Catholic faith. With the Alhambra Decree, the remaining population of non-Catholics, mostly Jews, faced the choice of converting or leaving. As many as 100,000 Jews chose to leave Spain for other areas around the Mediterranean. Many found an unwelcome reception in the lands they fled to and returned to Spain, whereupon they accepted baptism. Others settled in North Africa, Italy, and the Ottoman Empire.
With the passage and implementation of the Alhambra Decree, the dominions of King Ferdinand and Queen Isabella legally became one hundred percent Catholic. As such, the Spanish monarchs had completed the Catholic reconquest of Spain. Heresy was strictly enforced under the Spanish Inquisition and Spain remained, at least officially, completely Catholic until Spanish citizenship was restored to Jews in 1924. The Alhambra Decree was not revoked until 1968; although, it had not been enforced for some time prior.

How do a barn owl's hunting habits help it to survive?

A barn owl typically preys on small mammals such as field voles, common shrews, wood mice, etc. The barn owl is highly adapted to hunt these mammals and is a very effective predator.
The barn owl is capable of flying very slowly and hovering, giving itself ample time to find its prey. It has the most sensitive hearing out of all the animals tested and has asymmetrically placed ears that help it determine the exact location of its prey. 
It generally hunts at dusk and dawn and determines the location of its prey by sound only. It typically hovers over the location before pouncing on its prey. When it gets ready to strike, it starts with a head-first dive and then pulls back the head to use its outstretched talons to grab its prey. Given these physiological adaptations, the barn owl is very successful at hunting its favored prey.
During the winter season, the barn owl hunts by dropping down from a perch, thus saving the crucial energy that would have (otherwise) been used in movement and also for keeping the body warm during the cold flight. 
Thus, hunting habits and physiological adaptations (such as hearing, wings, etc.) enable the barn owl to survive by hunting successfully.
Hope this helps.

What is an analysis of the character of Brick and the social issues he faces?

Brick (also known as Jamie) is one of the central characters in Heidi W. Durrow's 2010 novel The Girl Who Fell From the Sky. There's a lot to talk about with respect to his character and the social issues around him. Here, we'll go over a few specific examples of moments in the novel that reveal elements of his personality and/or the social milieu he lives in.
The story opens with a major event. Young Brick is looking out the window when he sees what appears to be a large bird flying by. Shortly, he realizes it wasn't a bird but a human being (several, in fact: a neighbor family has leapt from the heights of the building). Brick is scarred by the sight of the dead mother and child splayed across the sidewalk outside the building.
Right off the bat, we learn a lot about Brick and his setting. He's a bird enthusiast, for starters, and he's sensitive: he's deeply affected by the sight of the family. We also get a sense for the kind of world Brick lives in. He lives with his drug-addicted mother in a poor area of Chicago. The woman who jumped from the building, we'll learn, was also addicted to drugs. Both families have mixed-race children, which will turn out to be a major theme in the book. Brick and Rachel (the only survivor of the family's jump from the building) will both struggle with their identities and whether to identify as black or white.
Let's look at an example of this kind of racial self-identification. Later in the story, after Rachel and Brick have become acquainted, she asks him about his racial background:

“What are you? Like black, or—like me?” Rachel asks.
“Oh, I’m black. Regular,” is his answer.

Unlike Rachel, who doesn't know where she belongs (she has light brown skin and her Danish mother's blue eyes, so she feels like she doesn't fit in with either the black or white girls at school), Brick is relatively untroubled by his racial background. In fact, he points out to Rachel that she would be more comfortable identifying as black if she didn't have blue eyes:

“Do you think people would ask you that if you didn’t have your mother’s eyes?” 

Let's look at a third example in the novel that helps us to understand Brick's character and the social issues he faces. When the story opens, Brick is not called Brick: he is Jamie. He decides to start going by the name "Brick" because he likes the strong sound of it, especially as a young boy. 
But later in the book, when Brick has grown taller and bigger (and is living on the streets, as he's run away from home), he finds that he doesn't need to look or sound any stronger than he is. As an adult black man, he needs to downplay his potentially threatening image in order to survive. This detail speaks to the social setting that he lives in and that, unfortunately, is still very much the case today: being a young black man can be dangerous, regardless of what you do, merely because of the way that other people might perceive you.

What are objective intent and subjective intent mens rea?

Mens rea is determined by the defendant’s state of mind or intention. It is coupled with the actual act to constitute a crime. During criminal trials, proof of mens rea will be required to make a determination. Cases that fall within strict and absolute liability will not require proof of mens rea.
Mens rea can be determined through subjective or objective procedures. A subjective intent is determined based on the defendant's perspective. The defendant’s thoughts, desires, plans, and level of awareness are considered.
An objective intent is determined based on the quality of the defendant’s state of mind. The quality of the defendant’s behavior is determined based on established standards of a reasonable individual. Thus, the judge and jury will rely on the perspective of a reasonable person.
http://e-lawresources.co.uk/Mens-rea-intention.php

Precalculus, Chapter 9, 9.5, Section 9.5, Problem 78

You need to use the binomial formula, such that:
(x+y)^n = sum_(k=0)^n ((n),(k)) x^(n-k) y^k
You need to replace 5 for x, sqrt3*i for y and 4 for n, such that:
(5 - sqrt3*i)^4 = 4C0 (5)^4+4C1 (5)^3*(-sqrt3*i)^1+4C2 (5)^2*(-sqrt3*i)^2+4C3 (5)^1*(-sqrt3*i)^3 + 4C4 3a*(-sqrt3*i)^4
By definition, nC0 = nCn = 1, hence 4C0 = 4C4 = 1.
By definition nC1 = nC(n-1) = n, hence 4C1 = 4C3 = 4.
By definition nC2 = (n(n-1))/2, hence 4C2 = 6.
(5 - sqrt3*i)^4 = 625 - 500sqrt3*i+450*i^2- 60sqrt3*i^3 + 9*i^4
Using the powers of i yields:
i = i; i^2 = -1, i^3 = -i, i^4 = 1
(5 - sqrt3*i)^4 = 184 - 440sqrt3*i
Hence, expanding the complex number using binomial theorem yields the simplified result (5 - sqrt3*i)^4 = 184 - 440sqrt3*i

What are some of the traditional ways to celebrate Kwanzaa?

Kwanzaa is traditionally celebrated after Christmas; it lasts from December 26 to January 1. Created by Maulana Karenga, a black activist, Kwanzaa is a festival derived from the civil rights movement, and it pays homage to the global African community. Kwanzaa is a composite of several African harvest traditions, and it celebrates seven principles (or Nguzo Saba): Umoja (Unity), Kuji-chagulia (Self-determination), Ujima (Collective Work and Responsibility), Ujamaa (Cooperative Economics), Nia (Purpose), Kuumba (Creativity), and Imani (Faith).
The above principles are celebrated in order during the seven-day festival. On each day, one of seven candles or Mishumaa Saba is lighted. Mishumaa Saba consists of three green candles, three red candles, and one black candle. On the first day of Kwanzaa (December 26), the black candle (symbolizing Umoja or unity) is lighted. As a rule, the Mishumaa Saba (seven candles) are placed in the kinara (candle holder), and the kinara is then placed on a mkeka (mat) that rests on top of an African tablecloth. The black candle is always placed in the center of the kinara.
On the right of the black candle, three green candles representing Ujima, Nia, and Imani are placed. On the left of the black candle, three red candles representing Kujichagulia, Ujamaa, and Kuumba are placed. The three colors are derived from the black nationalist flag that Marcus Garvey created. The kinara symbolizes the deep respect African families have for their ancestors. During Kwanzaa, some people visit nursing homes, elderly family members, or elderly friends to show their appreciation for the aged. Ears of corn or mihindi are also placed on the mkeka to represent fertility and the number of children in the family.
On the sixth day of Kwanzaa, many celebrants enjoy a karamu or feast. Many wear traditional African clothing to attend the karamu. During the feast, a Unity cup or kikombe cha umoja is used to perform a libation ritual. The libation (or tambiko) is usually juice, water, or wine; each person drinks from the cup as a sign of unity. After everyone has drunk, the last portion of the tambiko is poured out in the direction of the four winds to honor the ancestors. The dishes that are shared during the feast varies. Some families choose to enjoy Caribbean, South American, or traditional African diaspora dishes.
Menus can include Jollof rice, collard greens, Yassa chicken, beef and groundnut stew, and sweet potato biscuits. Here's an example of a Kwanzaa karamu menu: Kwanzaa feast.
On the seventh and last day of Kwanzaa, celebrants traditionally give gifts or zawadi to their friends and family members. Some gifts are homemade, in honor of the Kwanzaa principles of creativity, accomplishment, and self-determinism. Children are also given gifts to reward accomplishments and to promote future successes. In all, these are some of the traditional ways to celebrate Kwanzaa.
http://www.officialkwanzaawebsite.org/celeb-procedures.shtml

https://www.bhg.com/holidays/kwanzaa/traditions/kwanzaa-history-traditions/

https://www.history.com/topics/holidays/kwanzaa-history

College Algebra, Chapter 8, 8.3, Section 8.3, Problem 40

Find an equation for the hyperbola with foci $(\pm 3, 0)$ and passes through $(4,1)$.
The hyperbola $\displaystyle \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ has foci $(\pm c,0)$. So, the value of
$c$ is $3$. Thus, the first equation gives us $a^2 + b^2 = 9$. Also, if the hyperbola passes through the given point, then the point is a
solution to the equation,

$
\begin{equation}
\begin{aligned}
\frac{(4)^2}{a^2} - \frac{(1)^2}{b^2} &= 1 && \text{Substitute the given}\\
\\
\frac{16}{a^2} - \frac{1}{b^2} &= 1 && \text{Evaluate}\\
\\
\frac{16}{a^2} &= \frac{1}{b^2} + 1 && \text{Add } \frac{1}{b^2}\\
\\
16b^2 &= a^2 + a^2 b^2 && \text{Multiply } a^2 b^2\\
\\
a^2 &= \frac{16b^2}{1 + b^2} && \text{Simplify, thus gives us the second equation}
\end{aligned}
\end{equation}
$

By substituting the second equation to the first equation, we get

$
\begin{equation}
\begin{aligned}
\frac{16b^2}{1+b^2} + b^2 &=9 && \text{Multiply } (1 + b^2)\\
\\
16b^2 + b^2 + b^4 &= 9 + 9b^2 && \text{Simplify and combine like terms}\\
\\
b^4 + 8b^2 &= 9 && \text{Subtract 9}\\
\\
b^4 + 8b^2 - 9 &= 0 && \text{Factor}\\
\\
(b^2+9)(b^2-1) &= 0 && \text{Zero Product Property}\\
\\
b^2 + 9 &= 0 \text{ and } b^2 - 1 = 0 && \text{Choose the value of $b$ that will give real roots}\\
\\
b^2 -1 &= 0 && \text{Solve for } b^2\\
\\
b^2 &= 1
\end{aligned}
\end{equation}
$

We back substitute $b^2$to the Equation, we have

$
\begin{equation}
\begin{aligned}
a^2 + 1 &= 9 && \text{Solve for } a^2\\
\\
a^2 &= 8
\end{aligned}
\end{equation}
$

Therefore, the equation is
$\displaystyle \frac{x^2}{8} - y^2 = 1$

How could I start writing a thesis for a macro-level critical analysis on Macbeth centered around the prompt, "'The central issue of the play is the conflict between duty and desire.’ To what extent does this reflect your understanding of the play?"

Although a thesis is the main point of an essay or analysis, most people don't know, when they being writing, what their thesis will be. Their main point usually emerges to them after they have written for a while.
To come up with a good, strong thesis, I suggest you write a "discovery draft." This means you spend some time writing freely about different aspects of the question, not worrying yet about whether what you are producing is coherent or would make a good final product. This discovery draft is for your eyes only, but it will help you discover your thesis.
First of all, I suggest you spend about 15 or 20 minutes—more if inspiration strikes you—writing about your reaction to the play. What scenes stood out most to you? Which characters did you most resonate with—or recoil from? What felt powerful, what felt unfinished? Did anything bother you about the play? These are the types of questions that will help you determine what your reaction was to the play. By the end of this exercise, you should have an emerging sense of "your understanding of the play."
After you do your discovery draft, set it aside and take a break. Then come back and do a second discovery draft. This one should be about the sentence, "The central issue of the play is the conflict between duty and desire." In this discovery draft, try to prove that this is true. Does Macbeth represent desire, and someone else (MacDuff?  Banquo?) represent duty? Or is Macbeth duty, Lady Macbeth desire? Or do you find duty and desire both at war within the various characters? Once again, spend about 15 or 20 minutes writing about this. Don't worry if you don't reach a firm conclusion.
After this, set both discovery drafts aside and take a break again, ideally overnight.
It's possible that, because you have spent some time thinking about your own reaction to the play and about duty/desire, your mind will spontaneously start to answer the assigned question and come up with a thesis statement. If so, that's great. Jot it down while it's hot; then you'll have it on hand when you buckle down to writing your paper.
If that doesn't happen, don't worry, as you still have your discovery drafts. After taking your break, get them both out and look at them. Now you know your reaction to the play, and you have some thoughts on duty/desire. From these, you can form a thesis that answers the question.
It might be along these lines:
"The conflict between duty and desire is very close to my understanding of the play, because [insert insights from duty/desire writing, combined with your reaction]." OR...
"I have a very different understanding of what the play is about. It's not about the conflict between duty and desire so much as it is about [insert material from your reactions to the play, planning to show why this is more important than duty vs. desire]." OR...
"While duty and desire are certainly strong themes in Macbeth, I had trouble seeing them as the main theme because they were overshadowed by [insert overwhelming thing from your reaction discovery draft]."
Once you have done this, you will end up with a thesis statement that really reflects what you think and feel about the play. Once you have that statement, it will be much easier to write the rest of the analysis. The thesis statement, and the prewriting that you've already done, will guide you. You will probably end up using ideas from your discovery drafts, though you probably will not use the very same sentences.
Writing a discovery draft might seem to take more time up front, but it saves time in the long run because it makes the writing process much easier.

What concept does each of the characters in "The Birthmark" stand for?

Nathaniel Hawthorne's story "The Birthmark" uses allegory, a literary device where the characters represent specific elements of a story's social or political message. To figure out what each character signifies, we first need to look at the main theme of this story: man's desire to conquer and tame nature. Alymer is obsessed with science and using his intellect to, in Hawthorne's words, "lay his hand on the secret of creative force and perhaps make new worlds for himself." In other words, he wants to bring order to the chaos found in the natural world. The situation gets dangerous, though, when he transfers his obsession with natural perfection to his wife, Georgiana, and the hand-shaped birthmark on her face. In using his scientific abilities to eliminate the birthmark, he achieves his goal, but Georgiana dies in the process. In short, the story shows the dangers that arise when people try to alter the natural imperfections of the world.
Now that we've established the theme, let's look at each of the three characters in the story and see how they illustrate this idea:
Alymer: As both a protagonist and antagonist in the story, Alymer represents the intellectual and spiritual nature of humans. Hawthorne directly states this in the second half of the story: "Aylmer's slender figure, and pale, intellectual face, were no less apt a type of the spiritual element." Alymer's quest to create perfection through science and his overall belief that the natural world can be made better fit both of these characteristics.
Georgiana: Georgiana represents the finite, imperfect nature of humanity. This can be seen chiefly through Hawthorne's description of the birthmark itself: "It was the fatal flaw of humanity which Nature, in one shape or another, stamps ineffaceably on all her productions, either to imply that they are temporary and finite, or that their perfection must be wrought by toil and pain." We are also told that Alymer sees the birthmark as "the symbol of his wife's liability to sin, sorrow, decay, and death." Thus, Alymer's quest for perfection and enlightenment via science is directly at odds with the fact that his wife, despite her beauty, is fallible to human error and mortality.
Aminidab: Alymer's quirky assistant is set up as a direct foil to Alymer's intellectualism by representing the physical, earthly nature of people. Hawthorne describes Aminidab as almost caveman-like: "With his vast strength, his shaggy hair, his smoky aspect, and the indescribable earthiness that incrusted him, he seemed to represent man's physical nature." Beyond this description, it is also important to look at his reaction to Georgiana's death. His response of laughter suggests that he is mocking Alymer's efforts to overcome the reality of the physical world that imperfection cannot be tamed.
As a result, the allegorical representations of each character perfectly fit within the overall thematic scope of the story. Try reading through the story again with these ideas in mind and looking for quotes of your own that illustrate each of these three concepts.

Why are the Lilliputians able to tie up Gulliver?

Gulliver's ship is dashed against a rock, and he, along with five other members of the crew, escape in a lifeboat and get clear of the sinking ship and the rocks. They row for a while but become exhausted and are obliged to allow themselves to drift on the waves. Suddenly, a storm comes upon them, and Gulliver swims for his life. He does not know what becomes of his crewmen, either on the ship or from the lifeboat; he assumes they did not survive. Eventually, he finds himself in water in which he can stand, and he continues to walk through the water until he makes it to shore. With night quickly approaching, Gulliver cannot find any inhabitants of the land, and he "was in so weak a condition" that he finds himself "much inclined to sleep." Gulliver says that the "heat" and the "half a pint of brandy" he drank before leaving the ship have made him especially sleepy. He lies down and falls into a "sounder" sleep than any he can recollect. Because of his total exhaustion, resulting from the experiences I've related, the Lilliputians are able to tie him without his noticing.

Discuss the founding and early years of the Jamestown settlement. What factors made its early years extremely difficult? What factors led to its survival and growth?

The Jamestown settlement was first founded in 1607. From the very beginning, it faced significant challenges. To start off with, the settlers had no idea how to farm in this new land. Even the local Powhatans considered the land where Jamestown was built to be ill-suited for farming. It was too swampy, and it was prone to flooding. Mosquito-borne diseases were a constant problem. When the settlers first arrived, they were too late to plant crops for that year. To make matters worse, there was very little potable water available at the site of the colony, and the area was undergoing a severe drought. Nevertheless, the native peoples initially helped them by providing food and agricultural knowledge.
The original settlers never really did get the hang of farming. Many were from the upper classes of English society and were unaccustomed to the hard physical labor required to live in the wilderness of seventeenth-century Virginia. When the colony's investors in England started to demand results, the colonists had nothing to show them. This threatened to end the necessary lifeline the settlement had to the resources of England.
Things got worse when relations with their Native American neighbors soured. Fighting with the Paspahegh diverted a lot of resources and energy from the affairs of maintaining the settlement.
The worst disaster in the early years of the Jamestown colony occurred in 1609–1610. When resupply ships from England were prevented from arriving due to bad weather, much-needed supplies failed to reach the settlement. That winter about 80% of the colonists died of starvation, bringing Jamestown's population of 214 down to just 60.
After supply ships successfully arrived in 1610, the fortunes of the colony began to turn around. More settlers arrived and started farming land that had once belonged to the local Native Americans. By 1620, enough colonists had arrived to manage a self-sustaining colony of farmers.
https://www.nps.gov/jame/index.htm

Where does the rapping come from the second time?

In the sixth stanza of "The Raven," the speaker observes that he again hears a rapping. In the first stanza he heard it as a tapping at his chamber door, but the second time the sound is concentrated at his "window lattice." A latticed window features strips of metal that function to hold small pieces of glass in place, as in a multi-paned or stained glass window. The tapping or rapping is louder this time, either because it is closer to the speaker or because the entity seeking entry is more insistent than the first time. The speaker goes to the window and opens the shutter; and, into his chamber steps a "stately Raven," a large black bird that ranges over the majority of the world's northern hemisphere.

The first time the narrator hears the rapping at the door, he answers it to find that there is no one there. He whispers his dead lover's name, Lenore, hears it echo back to him, and then he turns back into his room, feeling upset anew. He then hears "a tapping somewhat louder than before" (line 32). He hears that something is tapping at his window, and he assumes it is the result of the wind blowing and nothing more. He opens up the shutters, and a strange raven steps into the room via the now open window. The raven does not seem at all afraid or wary of the narrator; in fact, the narrator describes the bird as acting as though it were a lord or lady. The raven perches on a bust of Athena that the speaker has standing above the door to the room.

"The wife of a man who is, of his own accord, submissive is altogether out of employment. All those weapons which she has inherited from her grandmothers of untold centuries are useless in her hands: the force of her tears, the fire of her anger, and the snare of her glances lie idle." Please explain this passage from the story, "The Lost Jewels" by Rabindranath Tagore.

This passage, when read in the full context of the story, references the author's perspective on marriage and the benefits and challenges it poses to men and women. Here, the author is referring to Bhusan and his wife, Mani. Bhusan is a quiet, virtuous, and placid man who is described as "absolutely faultless." Meanwhile, his wife is a shrewd and often callous woman who finds her husband's perceived perfection to be evidence of weakness. The author further states that, due to his agreeable nature, Bhusan "was therefore neither successful in business nor in his own home." This harsh statement is a reflection of the author's belief that the purpose of marriage is to allow a woman, by virtue of her charms and feminine nature passed down through her ancestors, to civilize her husband and make him into something great. This can be seen as Tagore's take on the old saying, "Behind every great man is a great woman."
Earlier in the passage, Tagore notes, "From the very moment that man and woman became separate sexes, woman has been exercising all her faculties in trying by various devices to fascinate and bring man under her control." Here, he is referring to what he believes is the desire of all wives to "tame" or subordinate the barbaric nature of their husbands into something more agreeable to civilized society. Tagore argues that, because Bhusan is already in possession of a civilized nature before he married Mani, he presents no challenge for his wife. As a result, Mani's charms have no practical impact on her husband and she is without "employment." In other words, Tagore believes that she has no role to fill in their marriage because the "work" has already been done for her.
https://archive.org/stream/TheLostJewels/The%20Lost%20Jewels_djvu.txt

What are some similarities between igneous and metamorphic rocks?

Igneous, sedimentary, and metamorphic are the three types of rocks. Among these, igneous and metamorphic rocks share the following similarities:
Both of them are types of rocks.
Temperature is a key factor in the formation of both types of rocks. Igneous rocks are formed from the cooling of magma, which is formed as a result of high temperatures causing rocks to melt. Metamorphic rocks are formed as a result of temperature and/or pressure action on existing rocks causing changes in the composition and resulting in the appearance of minerals in rocks. This process is known as metamorphism and results in the formation of metamorphic rocks.
Both igneous and metamorphic rocks are part of the rock cycle and can transform into other types of rocks over time.
Hope this helps.

What are 5 examples of gothic elements in "The Fall of the House of Usher"?

One element that characterizes American Gothic literature is the intersection of the rational and the irrational. The story's narrator is the voice of reason; he comes to the House of Usher because his old acquaintance has indicated that he's having some difficulties, and the narrator believes it is his duty to help. The narrator realizes that Roderick looks very weak and sickly, and he soon recognizes that events within the house are hard to reconcile with rational behavior. One is the return of Madeline Usher from what seems to him to be death, since he helps to entomb her.
Another element of gothicism is the confrontation of guilt. Roderick Usher knows that the incest that his family has long engaged in is problematic, yet it is apparent that he and his sister Madeline are heir to the behavior. It is possible that he entombs her to bring to an end the family's curse of inbreeding over which he apparently feels immense guilt.
Madness is a theme often explored in gothic literature, and Roderick Usher's mental state suggests that he has become seriously destabilized. It may be the genetic result of his ancestors' incest, it may be a result of the isolation in which he and his sister have been living, or it may be those things and other causes. Regardless, he suffers distorted thinking and sensations that he describes to the narrator. His senses, for example, are hyper-attuned to the point of pain.
Writers of Gothic narratives often employ the setting of the forbidding-looking or haunted house, and the physical structure of the House of Usher aligns with that idea. The narrator describes it as being surrounded by vegetation that he imagines to be sentient, and its windows are described as eyelike.
A final element of gothicism often involves death. The narrator assists Roderick in entombing his sister because he believes that she has died. She eventually claws her way out of the crypt and, in doing so, causes her brother's and her own death when she confronts him.

Edgar Allan Poe is one of the most accomplished and best known Gothic writers. Gothic texts typically involve the supernatural, mystery, and strange characters and settings. Poe is excellent at creating the dark, foreboding mood that often characterizes Gothic literature. In one of his most famous stories, "The Fall of the House of Usher," Poe incorporates several of the qualities we expect to see in Gothic literature.
1. Death and decay: The setting of "The Fall of the House of Usher" is epitomized by its death and decay. The old Usher house and the surrounding environs are "dull, dark," "bleak," "shadowy," and "insufferable." The speaker calls the house a "mansion of gloom." The Usher siblings themselves are also subject to decay, especially Madeline, who is afflicted with an illness and is presumed dead at one point in the story. The house eventually crumbles and the siblings are killed in the midst of the house's demise. 
2. Strange and mysterious characters: Roderick and Madeline Usher are an odd pair. The story heavily implies that they, as is there entire family line, are products of insect, which may explain their physical problems and personality quirks. Roderick is described as excessively nervous and superstitious. Madeline has a disease that features "a gradual wasting away of the person" and symptoms that mimic death. Their relationship is also quite strange, as they seem to have a psychic connection. Roderick ends up burying Madeline prematurely, and the scene when she emerges from the grave and walks toward Roderick is one of the most horrific in all of Poe's tales.
3. Isolation: The Usher home itself is isolated, and its inhabitants do not interact with the outside world at all. It is unusual that Roderick invites the narrator to the home at all. The isolation seems to exacerbate the eccentricity and subsequent decay of the family name and home. 
4. Intense emotional reactions and/or madness: We see in Gothic literature and especially in Poe's stories the psychological deterioration of characters. Often narrators or other characters descend into madness. In this story it is not the narrator but his old friend Roderick who goes insane. As I said previously, Roderick is already nervous and superstitious, but Madeline's declining health seems to put him over the edge. His actions become increasingly erratic, until he eventually buries his sister alive. 
5. The supernatural: In many Gothic works, writers scare their characters and readers with supposedly supernatural phenomena only to later reveal the actual, reasonable explanations for seemingly strange events. "The Fall of the House of Usher" includes the premature burial of Madeline. However, at first, she appears to be actually dead. So when the narrator hears strange noises in the night and she emerges at the end of the story, it may seem like she is a ghost and then later that she has returned from the dead. It turns out that she was not dead and was merely trying to get out of the tomb. 
Again, Poe's stories are usually Gothic in style, and "The Fall of the House of Usher" is no exception. The strange story of the Usher siblings and their demise includes many of the elements typical of the Gothic genre. 

Where is Matt from in Gathering Blue by Lois Lowry?

Matt lives in an area known as the Fen, which is a lower-class area equivalent to a slum in our culture. Kira lives in the village, and those who live in the Fen are closely associated with village people in that they are part of the same large community. The villagers live in cotts (small homes) in a central area near the marketplace and not far from the Edifice. The Fen is farther removed from that area.
When Kira and Thomas venture to the Fen, they first come to an area on the outskirts of their village where the huts are closer together. They then cross a makeshift bridge over a "foul-smelling stream," presumably flowing with human waste and refuse. "Poisonous oleander bushes" border the stream on the Fen side. Kira and Thomas then see a cluster of small cotts. Although the cotts are not that different from the one Kira grew up in, the area in which they are situated is shaded because of the tall trees, and the entire setting is damp and dirty, a breeding ground for disease. The half-clothed children run around with runny noses; the parents seem even more vicious toward their offspring there than in the village.
Kira and Thomas find Matt's cott next to a gnarled, dying, rotted tree, which mirrors the type of home life he has. The cott is in disrepair, and the interior is dark and filthy. The Fen is a place of squalor. Matt's cheerful, buoyant personality stands in stark contrast to his surroundings, making Kira appreciate him even more.

Will nitrogen molecules form strong induced dipole-induced dipole bonds with one another? Why or why not?

”Strong” is a relative term. The induced dipole-induced dipole forces between nitrogen molecules are weaker than the attractions between permanent dipoles or hydrogen bonding interactions. Comparing only with other species whose strongest intermolecular attractions are induced dipole-induced dipole, we still find that the attractions in nitrogen are relatively weak.
Strength of induced dipole-induced dipole attractions increases as the number of electrons increases. Number of electrons increases as molecular weight increases, whether we move to more massive atoms in the formula or to a formula containing more atoms, so we often look at molecular weight to predict the strength of induced dipole-induced dipole interactions. The halogens provide an instructive example. All of them form diatomic molecules, like nitrogen. The two lightest, fluorine and chlorine, are gases at room temperature. Bromine, with a molar mass close to 160 g, is a liquid at room temperature, while iodine, with a molar mass of about 254 g, is solid at room temperature.
The molar mass of molecular nitrogen is 28 g. A few gases, including hydrogen, helium, methane, and neon, have lower molar masses, while those of diatomic oxygen and fluorine and of argon are a little more. Most molecules that feature only induced dipole-induced dipole interactions are more massive, so on this basis we can state that the induced dipole-induced dipole attractions are not very strong.

Calculus of a Single Variable, Chapter 6, 6.4, Section 6.4, Problem 55

Given (2y-e^x)dx + xdy = 0
=> 2y-e^x+xdy/dx =0
=> 2y/x -e^x/x +dy/dx=0
=> 2y/x +y'=e^x/x
=> y'+(2/x)y=(e^x)/x
when the first order linear ordinary Differentian equation has the form of
y'+p(x)y=q(x)
then the general solution is ,
y(x)=((int e^(int p(x) dx) *q(x)) dx +c)/e^(int p(x) dx)
so,
y'+(2/x)y=(e^x)/x--------(1)
y'+p(x)y=q(x)---------(2)
on comparing both we get,
p(x) = (2/x) and q(x)=(e^x)/x
so on solving with the above general solution we get:
y(x)=((int e^(int p(x) dx) *q(x)) dx +c)/e^(int p(x) dx)
=((int e^(int (2/x) dx) *((e^x)/x)) dx +c)/e^(int (2/x) dx)
first we shall solve
e^(int (2/x) dx)=e^(ln(x^2))=x^2
So proceeding further, we get
y(x) =((int e^(int (2/x) dx) *((e^x)/x)) dx +c)/ e^(int (2/x) dx)
=(int (x^2 *e^x/x dx) +c)/x^2
=(int xe^xdx +c)/x^2
=(xe^x -e^x +c)/x^2
=(e^x (x- 1) +c)/x^2
y(x) =(e^x (x- 1) +c)/x^2

I need help describing the musical elements of the song "TiK ToK" by Kesha.

We can break down the musical elements of Kesha’s “TiK ToK” into its sonic and lyrical characteristics.
Sonically, this piece represents a combination of dance-pop and electropop, with the addition of synthesized noises so commonly found in bitpop beats. Kesha’s vocals themselves are a style of spoken word rap blended around a sung chorus. Unfortunately, due to her frequent usage of auto-tune, Kesha has often faced criticism for her lack of singing ability; however, as an answer to that criticism, Kesha returned to the musical world with the single “Praying” from her 2017 album Rainbow, which strips away the auto-tune to reveal an impressive vocal range in the young singer. In addition to Dr. Luke and Benny Blanco’s production, “TiK ToK” also features guest vocals from Diddy.
According to Musicnotes.com by Kobalt Music Publishing, “TiK ToK” is set in common time with 120 beats per minute (BPM) and in the key of D minor. Its chord progression is B♭–C–Dm, and Kesha’s vocals range from D3 to the note of D5. She frequently draws comparisons with Lady Gaga and Fergie for their particular vocal and digital effects.
Lyrically, “TiK ToK” captures the narrative of a young woman who enjoys partying and who occasionally stumbles home from parties half-drunk. It extolls the excesses of drinking in lines like “Before I leave, brush my teeth with a bottle of Jack [Daniel’s],” while also touching on moral responsibility and issues of consent in the lines like “Boys tried to touch my junk, junk / Gonna smack him if he getting to drunk, drunk.” Dr. Luke and Benny Blanco co-wrote the song with Kesha, who claimed a great deal of autobiographical ownership of song’s content.
Structurally, verse 1 presents an AABB end rhyme scheme ("Diddy"/"city," "Jack"/"back"). Pre-chorus 1 follows the end rhyme scheme CC, a slant rhyme D, EE, and a partial rhyme F ("toes"/"clothes," "phones," "CDs"/"parties," "tipsy"). The chorus, however, contains internal rhyme schemes FFGHIIJIKKLMMMMM ("stop"/"pop," "up," "tonight"/"fight," "see," "sunlight," "tock"/"clock," "party," "no"/"oh"/"woah"/"oh").
The line “Oh, woah, woah, oh” is a palindromic phrase, meaning that it can be read the same way forwards and backwards. It is also repeated twice in the refrain. Verse 2 follows the end rhyme scheme NNOO ("beer"/"here," "swagger"/"Jagger"). Pre-chorus 2 follows the end rhyme scheme PPPQRRS ("crunk"/"junk"/"drunk," "out," "down"/"down," "us"). The bridge follows the end rhyme scheme TUVUTUWW ("down," "me," "now," "me," "down," "me," "up"/"up"). And the break is a simple end rhyme scheme Z ("in"). Combined, you have quite a dynamic array of lyrics and meter.
Additional Reference:
https://play.google.com/music/preview/Thxk4nd4j6yqdq3zr6p2c46g34m?lyrics=1&utm_source=google&utm_medium=search&utm_campaign=lyrics&pcampaignid=kp-lyrics&u=0#
https://en.wikipedia.org/wiki/Tik_Tok

https://www.musicnotes.com/sheetmusic/mtd.asp?ppn=MN0080585

In "The Discourse on the Love of Country, 1789" What is the point of view of the author?

In this pamphlet, Richard Price expresses an interesting point of view in support of the French Revolution, which was taking place at the time of his writing. He states that patriotism should mean the love of one's country in its ideal form—that is, love of one's own communities and ideals. If a citizen believes that his country is being oppressed by a tyrannical government, or one whose beliefs and laws are immoral and out of step with the nation's "natural" beliefs and ideals, it is in fact the duty of that citizen to educate his fellows and encourage them to rise up and rebel. In Price's view, it would in fact be unpatriotic to allow an immoral government to oppress one's people. Therefore, he feels that the French Revolution is justified precisely because the actions of the French monarchy were unjustified, and that those driving the revolution are true patriots.

Single Variable Calculus, Chapter 3, 3.5, Section 3.5, Problem 18

Determine the derivative of the function $h(t) = (t^4-1)^3(t^3+1)^4$


$
\begin{equation}
\begin{aligned}
h'(t) &= \left[ (t^4-1)^3 \cdot \frac{d}{dt} (t^3+1)^4 \right] + \left[ (t^3+1)^4 \cdot \frac{d}{dt} (t^4 - 1)^3 \right]\\
\\
h'(t) &= \left[ (t^4-1)^3 \cdot 4(t^3+1)^3 \frac{d}{dt} (t^3 + 1) \right] + \left[ (t^3+1)^4 \cdot 3(t^4 - 1)^2 \frac{d}{dt} (t^4-1)\right]\\
\\
h'(t) &= \left[ (t^4 - 1)^3 \cdot 4(t^3+1)^3)(3t^2) \right] + \left[ (t^3+1)^4 \cdot 3(t^4-1)^2(4t^3)\right]\\
\\
h'(t) &= \left[ (t^4 - 1)^3 (t^3+1)^3(12t^2)\right] + \left[ (t^3+1)^4(t^4-1)^2(12t^3)\right]\\
\\
h'(t) &= (t^4-1)^2(t^3+1)^2(12t^2) \left[ (t^4-1)+(t^3+1)(t) \right]\\
\\
h'(t) &= (t^4-1)^2(t^3+1)^3(12t^2)(t^4-1+t^4+t)\\
\\
h'(t) &= (t^4-1)^2(t^3+1)^3(12t^2) (2t^4+t-1)
\end{aligned}
\end{equation}
$

what does the shepherd reveal to Oedipus?

A messenger brings what appear to be glad tidings to Oedipus. His father, King Polybus, has died of old age. There is an air of relief around the court. It would seem that Tiresias's prophecy now cannot be fulfilled; Oedipus has assuredly not killed his father. But that still leaves the matter of the other important part of the prophecy: that Oedipus will marry his mother, Merope, who is still very much alive.
The messenger, sensing Oedipus's uneasiness, tries to be helpful and says that Polybus and Merope are not Oedipus's real parents after all. He then tells the story of how he gave the baby Oedipus, abandoned by a shepherd, to the royal couple. Oedipus is determined to hear the shepherd's side of the story, so he decides to track him down. Jocasta, Oedipus's wife, is terrified of what will be revealed.
And she is right to be terrified. For the shepherd reveals the truth about Oedipus's true parentage. Tiresias's prophecy has indeed come true: Oedipus has killed his father and married his mother. The consequences will be devastating for all concerned.

How does the butterfly that Eckels steps on contribute to the theme of the short story?

This Bradbury story is a cautionary tale about the importance of handling technology carefully. The story's theme is that if we use technology carelessly, we risk paying a heavy price.
In the story, Eckels pays a large sum of money, $10,000, to take a safari trip back to the time of the dinosaurs so that he can hunt a T-Rex. Although he is warned to stay on a specially constructed path and to not touch anything from the past, he panics when he sees the T-Rex. As a result, he runs off the path and kills a butterfly.
This seemingly insignificant act has immense consequences, as he and the others find out when they return to the present day. History has changed, and a dictatorial, brutal man has been elected to the US presidency.
Bradbury is advising us not to use powerful technologies for frivolous purposes. It was dangerous to send a group of rich people back in time so they could indulge the whim of a dinosaur hunt. Instead, we should treat technology with greater respect.

The main themes of the short story examine the relationship between the past, present, and future, and explore how a seemingly insignificant action in the past can dramatically impact the future world. In the short story, Eckels is warned numerous times to stay on the path and follow every direction in order to not alter the future during their time traveling safari. Travis explains how something as insignificant as accidentally killing an insect can upset the delicate ecosystem and dramatically impact the future in unforeseen ways. Unfortunately, Eckels is terrified at the sight of the Tyrannosaurus Rex and ends up running off the path, where he accidentally steps on a butterfly and completely changes the future. Upon their return, the group discovers that Deutscher has become president and the United States has changed for the worse. Eckels's seemingly insignificant mistake dramatically impacts the course of human history. The butterfly symbolically represents any small or insignificant aspect of the past and the dramatic results of its death emphasize the close relationship between the past, present, and future.

Travis, the safari leader, tells Eckels that he has to be very careful with what he does in the “land of the past.” He must stay on the path carved out by the Time Safari, and he must only shoot those animals allowed him by the safari leaders. He has to take care not to “kill an important animal, a small bird, an insect, a flower even” as doing this “could destroy an important link in a growing species.” Unfortunately, Eckels does not follow the instructions that Travis gives him. Immediately he sees the giant Tyrannosaurus rex, panics, and decides that he cannot shoot it. He says that it is too big to be killed with a mere riffle. His cowardice puts the whole safari at a risk. His colleagues, noticing his behavior, command him to hide in the time machine. However, he veers off the metal path and steps on a “brightly colored butterfly” as he struggles to make his way to the machine.
When the hunters get back home, in the year 2055, they discover big changes. For one, the president of the United States is the horrible Deutscher—before they left for the “land of the past,” the president had been Keith. Even the sign at the safari company has changed. To make matters worse, Eckels, in his carelessness, has carried back to the present the dead butterfly. The extent of the damage caused by Eckels’s actions cannot be estimated, though the impact on their present is immediately seen in these astonishing instances. Eckels wishes that he could be able to reverse his actions, but it is too late. His actions cost him his life. The writer uses the butterfly to contribute to the theme that all actions, big or small, have consequences. The butterfly’s death causes far-reaching changes over time—changes that cannot be reversed.

What were at least two of the major controversies that arose during Jackson's presidency?

Andrew Jackson's legacy has become more and more controversial in recent years. In fact, there has been a movement to remove him from the $20 bill.
There are at least two major controversies regarding Jackson. His stance on slavery and the impact that he had on Native Americans would be the major two.
Jackson, like many southerners of his time, owned slaves. He was known to be a particularly cruel slave owner and vocal proponent of slavery. Jackson also disapproved of efforts to outlaw slavery in the new Western territories.
Jackson's philosophy of "Indian removal" was ultimately responsible for the displacement of tens of thousands of Native Americans. Jackson wanted to expand parts of the Southeastern United States for white settlement and sought to remove Native Americans from the land. Many tribes negotiated an unfair deal to move and some tribes refused to go. One of these refusals ended in the "Trail of Tears," the forced removal thousands of Cherokee off of their lands, resulting in the deaths of at least 4,000.
http://www.americaslibrary.gov/aa/jackson/aa_jackson_subj.html

In Pirandello's "War," what are the different views that passengers articulate regarding war?

In Pirandello's "War," the different attitudes that the passengers articulate about war reflect the challenge of enduring it.
When the man and wife enter the train, they sit amongst the other passengers. The wife does not want to interact with anyone. As a result, the husband feels it is his responsibility to explain to the other passengers the source of her dejection. The other passengers do not express solidarity or support. One passenger talks about his son, who has been on the front since "the first day of the war." His view towards war is that it creates an unending sense of loss in the people who must see their loved ones sacrifice for it. This prevents him from fully identifying with the couple's predicament.
When the fat traveller enters the train, he speaks of another view towards war. He talks about how "good boys" willingly sacrifice for their country.  The fat man talks about how love of parents is secondary when a country calls for a young soldier.  He uses his own son as an example to prove his point:  

Everyone should stop crying; everyone should laugh, as I do. . . or at least thank God—as I do—because my son, before dying, sent me a message saying that he was dying satisfied at having ended his life in the best way he could have wished.

This reveals another view towards war.
The passengers espouse different views towards war. Hurt exists alongside valor and sacrifice. These reactions reflect how people react in different ways towards the war experience.

What do you think was Montresor's motivation for killing Fortunato?

While the story contains no explicit mention of a motive, it may be gleaned somewhat from the narrator's choice of words and the dialogue. Montresor's motivation is complicated. It has to do not so much with murdering Fortunato specifically as somehow avenging the decline of his family name and prestige. Our narrator is a deeply insecure man. These insecurities manifest themselves as a desperate need for decisive, bold action, namely murdering Fortunato.
As to the catalytic insult which triggered this whole thing? It most likely was something similar to the conversation the two characters had on their way through the wine vaults:

"The Montresors," I replied, "were a great and numerous family."
"I forget your arms."

Note that Montresor says they were "a great and numerous family." This implies the family has since dwindled and become less important. Montresor may logically feel ashamed or insecure about this, and thus he feels stung by Fortunato's lack of knowledge (or respect for) his family's importance. Fortunato does not know the family's arms or motto and does not seem to revere the Montresor name as Montresor thinks he should. Montresor resents Fortunato's arrogance and reads it as an insult to his entire existence—his name and family history. 

In Edgar Allan Poe's short story "The Cask of Amontillado," Montresor wants to kill Fortunato in order to seek vengeance for the "insult" that Fortunato has dealt him. What exactly this insult entails, we do not know; Poe never tells us the specifics of the grievance; we only know that it comes after a "thousand injuries" dealt by Fortunato. 
Montresor then decides that he must punish Fortunato "with impunity." He lures Fortunato to his family's cellar with the promise of letting him taste his pipe of Amontillado. The already drunk Fortunato agrees, and, when they arrive, Montresor supplies Fortunato with more alcohol. At this point, he paves the inebriated man into an alcove, effectively sealing him into a suffocating, tiny tomb and leaving him there to die.