How does Celie describe her daughter in The Color Purple?

In Celie's tenth letter to God, she describes seeing her daughter in a store with a woman. She had not seen her daughter since the night that she gave birth. Her father (and the father of the baby) had taken the little girl from her right after she was born. Celie thought that her father had killed the baby out in the woods. Really, he had given or sold the baby to a reverend and his wife, who happened to be shopping near Celie at the time that she describes in her tenth letter.
She saw the baby and knew right away that it was her child. She writes, "She look just like me and my daddy. Like more us then us is ourself." She spoke to them and examined the girl. "She got my eyes just like they is today. Like everything I seen, she seen, and she pondering it."
There is not much more description of Olivia from Celie's perspective, as she does not get to raise her daughter. Later on in the novel, letters reveal more of what Olivia is like, but Celie is not the one describing her.

What is the main summary and theory of this journal article? Primary Care Screening for and Treatment of Depression in Pregnant and Postpartum Women Evidence Report and Systematic Review for the US Preventive Services Task Force

The purpose of the study was to review the efficacy of depression screening and treatment for pregnant and postpartum women and to access the accuracy of specific screening instruments.
To realize the objectives of the study, two independent investigators reviewed fair and high quality studies from sources such as government websites, MEDLINE, PubMed, PsycINFO, and the Cochrane Collaboration Registry of Controlled Trials through January 20, 2015. Investigators also assessed the benefits of cognitive behavioral therapy (CBT) for depressed pregnant and postpartum women.
The investigators created summary tables to document key questions (KQ) and their conclusions.
For the advantages and disadvantages of depression screening (KQ1, KQ3), the investigators studied randomized or non-randomized clinical trials conducted in primary care settings. For diagnostic accuracy (KQ2), they examined studies of the Patient Health Questionnaire (PHQ) or Edinburgh Postnatal Depression Scale (EPDS) compared to structured or semi-structured diagnostic interviews with a trained interviewer or mental health clinician.
For the benefits of antidepressants and behavioral-based treatments (KQ4), the investigators included trials that had a minimum of six weeks of follow-up. For the harms of treatment (KQ5 and KQ5b), they examined randomized or non-randomized clinical trials, large comparative observational studies, and systematic reviews.
Here are the study results:
1) 6 trials showed 18% to 59% relative reductions with screening programs and 2.1% to 9.1% absolute reductions in the risk of depression at follow-up (3-5 months). Thus, screening programs (with additional treatment supports such as those provided by specially trained depression care clinicians) were seen to reduce symptoms of depression in pregnant and postpartum women.
2) 23 studies showed sensitivity ranging from 0.67 (95% CI, 0.18-0.96) to 1.00 (95% CI, 0.67-1.00), and specificity was consistently 0.87 or higher on the Edinburgh Postnatal Depression Scale. The screening instruments used were the Patient Health Questionnaire (PHQ) or Edinburgh Postnatal Depression Scale (EPDS). Both were shown to be effective in identifying pregnant and postpartum women who required further evaluation and treatment for depression.
3) Gestational second-generation antidepressant use may result in a slightly increased risk for potentially serious maternal and infant harms. Maternal harms included preeclampsia, suicidality, seizures, bleeding, and miscarriage. Infant harms included major malformations, low birth weight, neonatal respiratory distress, seizures, and neonatal death.
4) Clinically-depressed pregnant and postpartum women who were treated with CBT showed an increase in the likelihood of remission.

What is the narrative mode?

A narrative is a work which communicates a story, a series of connected events and details. For a work to be delivered in the narrative mode means that the characters, settings, and events are not merely recited as facts, but presented within the context of their interlocking relationships. In short, a story is told. The narrative mode of writing can be fiction or nonfiction, and told from a number of different points of view.
In the case of "A New England Nun," the story unfolds through a third person narration, or a person who is an entity not directly involved in the story. The writer chooses this form and point of view for several important reasons.
The crux of the short story is to elucidate Louisa's struggle for independence and a coherent sense of self in the context of an unwanted marriage. Louisa's identity is expressed and affirmed extensively through domestic chores and projects. The narrative mode lends itself to detailed descriptions which illuminate the actions and events of characters. In this case, the narrative style does well to communicate the daily minutiae of Louisa's life and give the reader an idea of how domesticity enriches Louisa's sense of purpose and self.
The narrative mode is also very much about weaving together many elements to form one cohesive whole. The narrative aptly captures Louisa's journey, as she too weaves together a life, an identity, from many discrete objects, feelings, tasks, and events.

Who is Rasheed in A Thousand Splendid Suns by Khaled Hosseini most like in the Kite Runner? Amir Or Assef?

In Khaled Hosseini's A Thousand Splendid Suns, Rasheed is the abusive husband of both Mariam and Laila. Rasheed operates as an extremely conservative character who believes in the subservience of women and treats the failure of Mariam to bear his children as a disgrace. In order to carry on his line, Rasheed tricks Laila into marrying him; this marriage produces a son, Zalmai, and a daughter, Aziza. Although the birth of Zalmai brings out some of Rasheed's softer qualities, he still remains unbearably cruel and sadistic toward Mariam, Laila, and Aziza. Despite his traumatic past and the death of his first wife, he is a definitively unlikeable character--a product of the misogynistic society he lives in who meets an untimely end due to his own violent actions.
Thus, we could easily argue that Rasheed is most like Assef in The Kite Runner, Hosseini's first book. In this novel, Assef is a complete bully--an older boy who is sociopathic in his cruelty and serves as the driving force behind the book's tragedy. Assef is a racist who views Hassan, a Hazara boy and the son of a servant, as inferior. In order to get revenge when Hassan protects his friend Amir from an attack, Assef corners Hassan in an alleyway and beats and rapes him. This act of cowardice and terrible violence becomes the wedge that drives Hassan and Amir apart. As an adult, Assef sexually abuses Sohrab, the son of Hassan. Clearly, Rasheed and Assef are very similar in their lust for blood and desire to see others horrifically punished. 
While Amir does act out of cruelty in The Kite Runner, he is a much more dimensional and redeemable character. Yes, Amir witnesses the rape of Hassan and chooses not to intervene; he also frames Hassan for theft in order to get rid of the boy so that he no longer has to feel guilt over what he witnessed. However, Amir eventually grows out of this and attempts to make amends by rescuing Hassan's son from Assef's clutches. His is not a straightforwardly even character in the way that both Rasheed and Assef are. 

College Algebra, Chapter 4, 4.6, Section 4.6, Problem 84

The equation $\displaystyle C(t) = \frac{30t}{t^2 + 2}$ represents the concentration of a certain drug in the blood stream. At time $t \geq 0$ (in minutes since the injection) where the concentration is measured in mg/L.

a.) Draw the graph of the drug concentration.

b.) What eventually happens to the concentration of drug in the bloodstream.







It shows from the graph that after injecting the drug in the bloodstream, it will only take at approximately $1.50$ minutes for the drug to start taking effect and eventually decrease until the concentration has been consumed.

What would be a resistant/alternate reading of the character Friar Laurence in Romeo and Juliet?

Friar Laurence is usually seen as a kindly character who advises Romeo and Juliet, helps them get married, and tries unsuccessfully to avert their tragic fates at the end of the play. There's plenty of textual evidence for this interpretation, and such a reading would not be wrong. However, it's possible to view Friar Laurence in an alternate light. Indeed, the Friar could be blamed, at least in part, for much of the play's tragic happenings. First of all, he's the one who agrees to marry Romeo and Juliet secretly in the first place, and one of the reasons he does so is because he wants to help ease the tension between the warring Montague and Capulet families. Second, he convinces Juliet to drink the potion that makes her appear as if she's dead. As we all know, this potion works, but it also leads to the tragic deaths of the play's protagonists. As such, Friar Laurence might not be as helpful as he seems. 
There are two alternate readings here: first, we could hypothesize that Laurence actively wanted to sabotage Romeo and Juliet's love. While this idea is possible, it's also pretty unlikely; it's hard to read Laurence as entirely evil, no matter how you interpret the text. A more likely interpretation is that Laurence is not a helpful counselor, but is actually an inept character whose attempts to "help" Romeo and Juliet do more harm than good. In this alternate reading, Friar Laurence becomes less of a valuable counselor and more of a misguided fool who is responsible for most of the play's final catastrophe.  

How has vampirism changed?

Your mention of Bram Stoker and vampirism lead me to conclude that you are looking for changes in the depiction of vampires since the publication of Dracula.
Perhaps the greatest degree of change that occurred in the history of the depiction of vampires came in the form of Bram Stoker’s 1897 work, Dracula. Up until that point, vampires were regarded as repulsive undead monsters. Conversely, Stoker depicted the vampire Dracula as a suave aristocrat. The subsequent Universal films further solidified this sultry yet dangerous demeanor. Vampires thus began to be largely defined by film, with their various powers and weaknesses being adjusted from movie to movie. But what is perhaps most surprising is how the core elements remain the same—fangs, the sucking of blood, aversion to daylight, and so on.
When one or more of these elements is adjusted, however, the author or filmmaker seems obligated to make a justification for it; we can see this with the “sparkly” quality of vampires in sunlight according to Stephenie Meyer’s Twilight series. Vampires since Dracula have been consistently depicted as generally charismatic, with some minor yet significant changing of their abilities.

In "The Rape of the Lock," what quote references the upper class as petty?

It's not just one or two specific quotes, but the whole atmosphere of the narrative in "The Rape of the Lock" that portrays the upper class as petty. Pope does so in a subtle enough way, however, that the impression is a light-hearted one. It's not the kind of slashing, bitter satire in which Pope's contemporary Swift specialized. I would select the opening lines of Canto 3 as representative of the general attitude of Pope toward the men and women he deals with:

Close by those meads, for ever crown'd with flow'rs,
Where Thames with pride surveys his rising tow'rs,
There stands a structure of majestic frame,
Which from the neighb'ring Hampton takes its name.
Here Britain's statesmen oft the fall foredoom
Of foreign tyrants and of nymphs at home;
Here thou, great Anna! whom three realms obey,
Dost sometimes counsel take—and sometimes tea.

It's typical of the heroic couplet to present ideas that function both as opposites and likenesses. Britain's statesmen seem equally interested in the "fall" of young women on the one hand and foreign tyrants on the other. The effect is to ridicule or trivialize matters of state. Similarly, Queen Anne takes counsel and tea, and which of the two does Pope imply is more important to her?
Remember that Pope's literary talent had granted him an entry into the highest levels of society, but he was an outsider still for two main reasons: his Roman Catholic religion and his unattractive appearance. One can imagine that, understandably, he is somewhat motivated by envy in his put-downs of the British gentry. These people do not seem to embody the height of intellectualism or profound emotion:

In various talk th' instructive hours they pass'd,
Who gave the ball, or paid the visit last;
One speaks the glory of the British queen,
And one describes a charming Indian screen;

The one moment in which this crowd seems to come to its senses and to get serious is when Clarissa asks "Say, why are beauties praised and honoured most?"
This is the core of Pope's theme: the falseness and inadequacy of "appearances" in life, especially in relations between men and women. Despite Clarissa, both the comic tone and the overall mock-heroic approach are a facade that prevents us from seeing just how deep Pope's criticism is of the pettiness and superficiality of these people. His final message seems to be that it is only his own art that redeems them, especially Belinda. The theme of art immortalizing temporal beauty is one that extends far back in literary history. Spenser in Amoretti wrote his beloved's name in the sand on the beach, and Pope writes Belinda's in the sky:

This lock, the Muse shall consecrate to fame,
And midst the stars inscribe Belinda's name!

This satirical poem is a pastiche of the traditional heroic epic, focusing on the upper class of London at the time it was written. In criticizing contemporary society, the poet's general attitude is that the upper class behaves in petty ways as a matter of course. We might point specifically to comments such as "At ev'ry word a Reputation dies" as indication of how focused were Pope's upper echelons of society on the sport of tearing down each other's reputations. This comment suggests that a great deal of time was spent on gossiping about others for the entertainment of those assembled. Their conversation revolves around such facile subjects as "who gave the Ball, or paid the Visit last." Canto 3 in particular presents the so-called high society of the land as vacuous in their conversation and habits. Pope depicts these people as having little to do other than sing, laugh, "ogle," and pass comment upon the behavior of others.

Calculus of a Single Variable, Chapter 8, 8.6, Section 8.6, Problem 32

Indefinite integral follows the formula: int f(x) dx = F(x)+C
where:
f(x) as the integrand function
F(x) as the antiderivative of f(x)
C as constant of integration.
To evaluate the given integral problem: int (e^x)/(1-e^(2x))^(3/2) dx or int (e^xdx)/(1^2-(e^x)^2)^(3/2) , we may apply u-substitution by letting:
u =e^x then du = e^x dx .
Plug-in the values, the integral becomes:
int (e^xdx)/(1^2-(e^x)^2)^(3/2) =int (du)/(1^2-(u)^2)^(3/2)
In that form, it resembles one of the formulas from the integration table. It follows the integration formula for function with roots:
int dx/(a^2-x^2)^(3/2)= x/(a^2sqrt(a^2-x^2))+C
By comparing a^2 -x^2 and 1^2 -u^2 , we determine the corresponding values as: a=1 and x=u . Applying the integration formula, we get:
int (du)/(1^2-u^2)^(3/2) =u/(1^2sqrt(1^2-u^2))+C
=u/(1sqrt(1-u^2))+C
=u/sqrt(1-u^2)+C
Plug-in u =e^x on u/sqrt(1-u^2)+C , we get the indefinite integral as:
int (e^x)/(1-e^(2x))^(3/2) dx =(e^x)/sqrt(1-(e^x)^2)+C or (e^x)/sqrt(1-e^(2x))+C

How would you write an analytical essay about the importance of dialouge in Top/Dog UnderDog

This is a good question. There are several ways I think you could go with this, and several things you could possibly focus on. Topdog/Underdog is a play by Suzan-Lori Parks about two brothers, Lincoln and Booth (named for Abraham Lincoln and John Wilkes Booth as a joke). The way they speak to each other throughout the play is very telling of their relationship, so perhaps your paper could analyze the way that the brothers speak to each other, and what each one's individual voice says about that character and how he feels about his brother.
Another way you could come at this is perhaps to think about the fact that the two brothers were named after two historical enemies, one who was ultimately killed at the hands of the other. Does the dialogue in the story foreshadow its violent end?
You could also discuss the dialect used by the characters. It is very heavy and pronounced, so maybe you could take a look at how this dialect is used to create the characters and how it relates to their upbringing, way of life, etc. What does their dialogue and way of speaking tell us about where they came from? Does it help to develop and individualize their characters or to make them seem more realistic?
Even aside from all this, dialogue is arguably the most important part of the play, because it is just that: a play. In a play, dialogue is the thing that tells the story and moves the play forward (along with the actions of the actors on stage). So on the most basic of levels, you could also argue that without dialogue, this particular play wouldn't even really exist.

What is SWOT analysis in education?

A SWOT analysis is a planning tool useful in any field and typically associated with business. However, its versatility lends itself to any number of practical disciplines, including education.
SWOT is an acronym that stands Strengths, Weaknesses, Opportunities, and Threats. During a SWOT analysis of a program or initiative, one lists each of the strengths, weaknesses, opportunities, and threats which face that program or initiative. These are typically, though not always, represented on a Cartesian plane in which each quadrant is used to list one of the four dimensions of analysis. By looking at the results of the SWOT analysis, a decision maker can determine if a strategic objective is attainable given the extant environment.
Three examples of a SWOT analysis used in educational practice are contained in the links section of this answer.
https://files.eric.ed.gov/fulltext/ED543801.pdf

https://www.fisd.us/apps/pages/index.jsp?uREC_ID=1246631&type=d&pREC_ID=1473226

https://www.stcloudstate.edu/strategicplan/analysis.aspx

In general, a SWOT analysis is used to analyze any group, entity, organization, or idea, by identifying four aspects that represent one letter in the SWOT acrostic: strengths, weaknesses, opportunities, and threats. In terms of education, the SWOT analysis can be effective in identifying what is and is not effective procedure for staff, faculty, and management in school systems. A SWOT is often implemented in an educational environment in anticipation of some change in policy, or in done simply in preparation for a quality check. The primary goal of a SWOT analysis is identifying barriers that can be overcome by playing to individual strengths in order to achieve to goals of the institutions, as well as identifying any risks and reducing them as much as possible.

Generally speaking, a SWOT analysis is applied to an organization, although it can certainly be applied to various units of the organization, too.  Within the context of education, there is no reason such an analysis could not be done upon an entire school district.
A strength of a school district might be magnet schools with great reputations, or it could be the kinds of labs and equipment the district makes available to its students. A weakness might be too many inexperienced teachers or insufficiencies in art and music education. An opportunity could an increase in state funding or the ability to compete for some great grants.  One real and significant threat to public schools is the competition, which is charter schools and private schools, all of which can drain off students and state funding. 
I would imagine that a SWOT analysis would be helpful to any number of school districts or even to individual schools, if anyone took the time and trouble to perform one.  I refuse to think of public education as a business, but this is one business concept that might actually be useful!

SWOT analysis refers to a way of evaluating a situation. This strategy involves looking at the Strengths, Weaknesses, Opportunities, and Threats surrounding a certain person or situation. While this strategy is applicable to many situations, it can be used in education to evaluate students, teachers, or even institutions. By using this type of evaluation in education, a targeted strategy tailored to the particular student or teacher in question can be formed.
On a student level, SWOT analysis can paint a picture about the strengths and needs of a particular student, as well as environmental factors that can provide support or could thwart learning objectives. This can include areas in which the child excels, where he or she needs extra help, support services available, and problems beyond the student's control that need to be overcome. The same can be said of a teacher. SWOT analysis can find teachers' strengths and weaknesses and identify what can aid or reduce their efficacy in the classroom.
http://halifaxcc.edu/Depts/IE/G&O/2009internalswot.pdf

Identify the leaps in the story? Which ones are literal? Which ones are figurative?

In Louise Erdrich's short story, the daughter's account of her mother is categorized by the woman's leaps throughout her life.
Anna Avalon has two literal, physical leaps:
When she was part of the trapeze act The Flying Avalons, a deadly tornado struck while she and her husband Harold Avalon were in midair under a circus tent. As Anna and Harry reached out for each other's hands, lightning struck a main pole of the circus tent, toppling Harry forward. As he swept past Anna in the air, she decided not to fall with him. Instead, she twisted herself around and grabbed the metal pole, which was still hot from the lightning charge. Her hands were severely burned and her arm broken.
During the narrator's youth, her parents were out for the evening one night. A fire started in the kitchen, and it traveled up the stairs toward the narrator's bedroom, preventing the babysitter from being able to reach the girl. But, when the mother returned home, she quickly assessed the situation. Anna took off her dress and climbed a ladder onto a tree whose limb hung over the roof of the house. The mother then leaped through the night air onto the roof. After tapping on the window, the mother instructed her child how to open it. She swung down and crawled through the opening. Then, she and her daughter "flew out the window, toward earth, [her daughter] in her lap, her toes pointed. [They] break through the cold air to the fireman's net."
The other leap was an figurative, intellectual leap. While Anna was in the hospital with her burns and a broken arm, she and the attending doctor fell in love. While she described to him exciting details about all the places she had been, he taught her how to read, and new worlds opened for her.

An analysis of mcm14 pls

The greatest clue to what this poem is all about is its title — "MCMXIV." These are the Roman numerals for the number 1914. The year 1914 was the start of World War I in Europe. Additionally, it is important to know that Philip Larkin was English and a renowned post-war poet. That background knowledge is central to any interpretation of the poem.
Knowing that the poem is set in England prior to WWI, we can begin to draw conclusions based on the speaker's descriptions. The first stanza depicts lines of men waiting to enlist, "Grinning as if it were all / An August Bank Holiday lark." The men are excited, as if they are on vacation or going to a sporting event, as they sign up to enter one of the bloodiest and deadliest wars in recorded history.
The picture shifts, with "shut shops" and "dust behind limousines." The country has been abandoned as the men have gone off to war, and the tone has changed to one of loss. What exactly has been lost is identified in the last stanza of the poem, echoed both in the first and last line of that stanza: "Never such innocence again." The fact that this poem is all one sentence further suggests that it is a single thought — that the transition from naive enthusiasm to jaded cynicism occurs in a single moment as fleeting as the time it takes to utter just one sentence.

looking for a thesis statement for The Secret life of Walter Mitty and The Glass Menagerie

A simple and accurate thesis statement involving The Glass Menagerie and "The Secret Life of Walter Mitty" would convey that we are ultimately responsible for finding our true identity using determination, rather than fantasizing about being different. This is true, even when we are forced to exist in a world that overbears us.
In both short stories, we find characters who have fallen short of the expectations society bestows upon them. However, rather than summoning determination and taking responsibility for changing their lives, these characters resort to fantasizing and deflecting their problems, thus perpetuating their fantasy lives.
Walter Mitty spends his life daydreaming about being a socially, physically, financially, and intellectually superior version of himself. The presence of his pushy wife makes things worse for him; he seems to be helpless and less motivated by her in his desire to be better. However, his tragic flaw is that he lacks the determination to change. Even at the end of the story, we see no redeeming qualities in him. He remains a very flat character. Even something as mundane as having to face his wife would make him break into a daydream.

He took one last drag on his cigarette and snapped it away. Then, with a faint, fleeting smile playing about his slips, he faced the firing squad . . . Walter Mitty the Undefeated, inscrutable to the last.

In The Glass Menagerie, several characters lack the will to change. Amanda is unable to move away from her past, and she consistently brings up memories of the better years she spent as a young woman. Jim, a former high school jock, is still living up to his past as a “popular kid” and has unrealistic dreams for the future.
Laura, her daughter, has been so overprotected by Amanda that social anxiety has taken the best of her. Moreover, Laura allows a physical handicap that makes her limp to define who she is as a person. As such, she acts more like a dependent “cripple” than like what she truly is: a young woman with every chance to be independent and make it in the world, if she truly wanted to.
Instead, Laura spends her time listening to the phonograph and tending to her glass menagerie. In doing this, she is deflecting attention from where it should be placed. She prefers to take the easy way out and make up a world of her own, much like Walter Mitty.
Tom is also lost in identity. Even though he manages to escape his overbearing life, it does not seem as if he has entirely found himself. In both works, all characters lack an anchor of identity.

How were these writings influenced by Augustine's own personal experience and the historical context?

Augustine of Hippo is thought to have completed this work in 426 AD. In order to understand how his own experiences and context drove him to write this book, we must first appreciate what a radical change had just taken place in the balance of power in Europe.
The eponymous "City of God" refers to the heavenly kingdom of New Jerusalem to which good Christians look forward, but Augustine's work is also very much concerned with the Earthly City, or the City of Man, as personified by Rome. For centuries, Rome had dominated the Western world; its empire had stretched far beyond Europe; the Roman way of life had been imposed upon countries from Africa to Britain, and the Empire had begun to seem indefatigable. In 410 AD, however—sixteen years before Augustine completed this book—the unthinkable happened: Rome fell to the Vandals. The rest of its Empire, too, was being eroded over the decade just before Augustine wrote this text, as the Franks took Gaul and the Anglo-Saxons took Britain. The days of Rome were over, a fact which seemed so incredible that it prompted the Romans to wonder which God or gods were responsible and what they had done to offend them.
Rome in the early fifth century was divided by religion; although Constantine in the early fourth century had decriminalized Christianity and the religion had begun to dominate, there were many in Rome who still adhered to the old ways. Following the fall of Rome, traditional Roman pagans accused the nascent Christian religion of destroying their city, angering the Roman gods, and eliciting the destruction of the empire. They also asked how, if the Christian God was so powerful, he had failed to protect the city. It was in response to this argument that Augustine wrote The City of God: it directly addresses the accusations from Roman pagans that the spread of Christianity across the Empire had occasioned it to fall.
Augustine's ultimate thesis is that although what had happened to Rome was terrible, to say it was caused by Christianity was to ignore the fact that bad things had happened to Rome in the past during the days of the pagan gods. He says that the lengthy endurance of Rome is evidence of the true God at work, rewarding ancient Romans for their faith and good behavior even when they were not aware of Him. (This question of achieving the City of God through "works" rather than "faith" is one that would be discussed many times and cause much splintering in the Christian religion in the centuries to follow, but Augustine makes clear that paganism itself could be condoned so long as the people were virtuous—implying that contemporary Roman pagans were not.)
Effectively, Augustine's text provides a rebuttal to the Roman pagans who blamed Christianity for the fall of Rome while also presenting them with an alternative to the Eternal City in the form of the City of God, which promises eternity of a better kind to those who might be willing to become Christians.

How can I write an essay on Maya Angelou in MLA format?

Maya Angelou was a very prolific writer who also did many things outside of literature. She started her public career as a dancer, then became a Calypso singer. She acted on stage, notably in Jean Genet's "The Blacks," and she was a Civil Rights activist who developed friendships with Malcolm X and James Baldwin.
If you are interested in writing an essay about her adult life, her memoirs are rich places to start. She writes about her singing career in Singin' and Swingin' and Gettin' Merry Like Christmas. She writes about her life during the Civil Rights Movement and her personal experience of the 1966 Watts riot / uprising in A Song Flung Up to Heaven. Most notably, she writes about her childhood, particularly her self-imposed silence after being raped, in I Know Why the Caged Bird Sings. It would be useful to examine Angelou's use of figurative language and how she weaved life lessons into her narration.
It is also possible to examine Angelou's poetry. One possible topic would be how Angelou's poetry fits into the Black Arts Movement of which she was a part. 
When using the MLA (Modern Language Association) format, remember to cite sources that are directly quoted, –– both entire quotes and portions of quotes –– as well as sources that are paraphrased, which would be cited within parentheses at the end of the paraphrased sentence. If citing a page number in a book of prose or non-fiction writing, the citation would look as follows: (Angelou 122). If quoting lines of poetry, you would cite them in the following way in text: (l. 4-6). Please also be sure to include a works cited page, which should list your sources –– both direct and secondary –– alphabetically.
https://owl.purdue.edu/owl/research_and_citation/mla_style/mla_formatting_and_style_guide/mla_formatting_and_style_guide.html

Are there any examples of logos appearing in Into The Wild?

If by logos you mean argument by logic or the use of facts to prove a point, then there are plenty of examples in the book. Take, for instance, Krakauer’s argument about how Chris died in Chapter 18. He spends several pages and interviews two experts on the poisonous properties of wild potato seeds and how eating them could have caused Chris’s death. Krakauer’s argument is persuasive to the extent that it provides a credible theory about what happened to Chris. Much of Krakauer’s book is based on reporting he has done—specifically, interviews with people who knew Chris and the McCandless family. This kind of primary source work can also be thought of as a kind of fact-based form of argumentation. While Jim Gallien’s impressions of Chris in chapter 1 are purely subjective, the fact is that these are his impressions as told to Krakauer. It’s important to understand, however, that using facts in argumentation doesn’t automatically make it an example of logos. Krakauer’s account of his ascent of the Devil’s Thumb is factual, but the purpose of the story is to argue that his own experience might give him some insight into Chris and to suggest that his own wilderness credentials make him someone his reader can trust when it comes to writing about the wilderness. In this sense, the use of facts has an emotional element (empathy with Chris) and works to establish Krakauer’s credibility.

The author uses several examples of logos, or an appeal to logic, to show how woefully unprepared Chris McCandless was for his trek into the interior of Alaska. For example, the author cites Jim Gallien, an experienced woodsman and hunter, who reports that McCandless was carrying far less food and gear than what was needed for the kind of trip he was going on (page 4). This is also an appeal to ethos, or credibility, because Gallien is an outdoors expert. On the next page, the author includes more logical details to show that McCandless was headed for disaster and to illustrate the cause of McCandless's demise. The author writes that the only food McCandless had in his pack was a ten-pound bag of rice, and he also writes that McCandless's cheap hiking boots were not insulated or waterproof.
The author uses a series of logical facts to show that McCandless's preparations for his trip into the bush were almost farcically inadequate. For example, Krakauer writes on page 45 that McCandless was doing calisthenics each morning to get ready for his trip (hardly the right preparation for his trip). This compilation of logical facts shows that McCandless was not prepared for his journey into the wild and that he was very naive about the conditions in Alaska.

The way that I interpret this question is that it is asking if any company logos appear in the book.  I can provide two specific times when Krakauer comments on a specific logo within Into the Wild.
The first described logo is the logo found on Chris McCandless when he was discovered dead in the bus.  When McCandless was found, the Alaska State Troopers could not identify who he was.  McCandless didn't travel with any kind of identification.  McCandless happened to be wearing a shirt that had the logo of a towing company in Santa Barbara.  The law enforcement officers then contacted the towing company in hopes that they knew McCandless.  
The second specific logo mentioned in the book appears on a jacket being worn by Walt McCandless.  The jacket's logo is for the Jet Propulsion Laboratory.  
If by "logos," you mean logic, then the best example from the book would be chapters 8 and 9.  In those chapters, Krakauer tries to convince readers that McCandless is not some singular crazy guy.  Chapter 8 focuses on Gene Rossellini, John Waterman, and Carl McGunn, and chapter 9 focuses on Everett Ruess.  During these chapters, Krakauer attempts to establish similarities between McCandless and the four men.  The arguments are presented in a logical format with supporting evidence, and those chapters did quite a bit to change my opinion of McCandless himself. 

"Violence of temper approaching to mania has been hereditary in the men of the family," Miss Stoner says of her stepfather's family. Do you think Dr. Roylott gave evidence of having inherited this trait?

Dr. Roylott certainly gives plenty of evidence of possessing violence of temper approaching to mania, but the only evidence that it might be inherited is Helen Stoner's assertion. She must know a lot more about Roylott and his ancestors than she tells Holmes and Watson in her back story. A modern reader might feel skeptical about her belief that her stepfather could have inherited his violence of temper from the men of his family. But we must remember that people in the Victorian era knew less about such matters than is known today. There were undoubtedly a lot of false theories about human psychology and genetics in vogue at the time which have since been discredited. Sir Arthur Conan Doyle's purpose in having Helen offer this diagnosis of her stepfather's violent temper is most likely to offer some explanation for it, however speculative. It tends to make his character more credible. Helen's explanation of Roylott's near-mania sounds somewhat "Victorian"--but this is a Victorian tale written in 1892 and set in Victorian England.

int 1/sqrt(16-x^2) dx Find the indefinite integral

Given to solve ,
int 1/sqrt(16-x^2) dx
using the Trig substitutions
for sqrt(a-bx^2)
x= sqrt(a/b) sin(u)
so for ,
int 1/sqrt(16-x^2) dx --------(1)
so , x can be
x= sqrt(16/1) sin(u)
 = 4sin(u)
=> dx = 4cos(u) du
so,for (1) we get
int 1/sqrt(16-(4sin(u))^2) (4cos(u) du)
=int (4cos(u))/sqrt(16-16(sin(u))^2) du
= int (4cos(u))/(4sqrt(1-sin^2(u))) du
= int (4cos(u))/(4sqrt(cos^2(u))) du
=  int (4cos(u))/(4cos(u)) du
= int (1) du
= u+c
but x= 4sin(u)
=> x/4 = sin(u)
=> u = arcsin(x/4)
so ,
=> u+c
= arcsin(x/4)+c
so ,
int 1/sqrt(16-x^2) dx = arcsin(x/4)+c
 

Precalculus, Chapter 9, 9.4, Section 9.4, Problem 18

You need to use mathematical induction to prove the formula for every positive integer n, hence, you need to perform the two steps of the method, such that:
Step 1: Basis: Show that the statement P(n) hold for n = 1, such that:
1^3 = 1^2(1+1)^2/4 => 1 = 1*4/4 => 1=1
Step 2: Inductive step: Show that if P(k) holds, then also P(k + 1) holds:
P(k): 1^3 + 2^3 + .. + k^3 = (k^2(k+1)^2)/4 holds
P(k+1): 1^3 + 2^3 + .. + k^3 + (k+1)^3 = ((k+1)^2(k+2)^2)/4
You need to use induction hypothesis that P(k) holds, hence, you need to re-write the left side, such that:
(k^2(k+1)^2)/4 + (k+1)^3 = ((k+1)^2(k+2)^2)/4
k^2(k+1)^2 + 4(k+1)^3 = (k+1)^2(k+2)^2
Factor out (k+1)^2 to the left side:
(k+1)^2(k^2 + 4k + 4) = (k+1)^2(k+2)^2
Notice that k^2 + 4k + 4 is a perfect square, such that:
k^2 + 4k + 4 = (k+2)^2
(k+1)^2(k+2)^2 = (k+1)^2(k+2)^2
Notice that P(k+1) holds.
Hence, since both the basis and the inductive step have been verified, by mathematical induction, the statement P(n):1^3 +2^3 +3^3 + ... + n^3 = (n^2(n+1)^2)/4 holds for all positive integers n.

What personal tragedy did Shakespeare endure as a parent?

The greatest tragedy that William Shakespeare endured as a parent was the death of his only son Hamnet at the age of eleven. Other than this, very little is known about young Hamnet's short life. It is likely that he died of the bubonic plague as there were many outbreaks of this deadly disease at the time. Children were especially susceptible to the plague. Whether or not the plague was the cause of Hamnet's death, it was not uncommon for children to die young during the Elizabethan period. Hamnet probably spent his time in Stratford-Upon-Avon at his grandfather's home while his father was away in London employed as a playwright. Consequently, William Shakespeare would not have had the chance to spend much time with his son.
https://www.representingchildhood.pitt.edu/medieval_child.htm

William Shakespeare married Anne Hathaway in 1582, and they had three children together.  The eldest was Susanna, born just six months after the wedding ceremony.  Their twins, one boy, Hamnet, and one girl, Judith, were born in January of 1585.  They were actually named after two good friends of Shakespeare's, Hamnet and Judith Sadler; Sadler, apparently, was a baker in Stratford-upon-Avon.  Sadly, when the young Hamnet was only eleven years old, he died of an unknown illness.  We have no records of his life other than when he was born and baptized and when he passed away.  
It sounds as though the Shakespeares' older daughter, Susanna, lived a prosperous and fulfilling life. She was married to a Stratford doctor named John Hall.  Their younger daughter, Judith, on the other hand, lived a somewhat sad life.  Her husband, a vintner named Thomas Quiney, was irresponsible and unfaithful to her.  

Who is the antagonist in "A&P"?

The antagonist of John Updike's short story "A&P" is the store's manager, Lengel. Lengel is also a Sunday school teacher and is described as being "pretty dreary." When the three young ladies wearing revealing bathing suits enter the grocery store to buy Kingfish Fancy Herring Snacks in Pure Sour Cream for Queenie's mother, Sammy's boss, Lengel, reprimands the girls for their attire. Sammy, the store's nineteen-year-old cashier, listens as Lengel embarrasses the three girls by telling them that "this isn't the beach." After Queenie innocently responds to Lengel's comment, he repeats himself and tells the three girls that the next time they enter the store they need to be decently dressed. Sammy, who harbors romantic ideas and wishes to be the girls' "unsuspected hero," tells Lengel that he quits as the girls leave the store. When Sammy tells his manager that he embarrassed the girls, Lengel replies by saying, "it was they who were embarrassing us" (Updike, 4). Lengel is clearly a strict, callous man, who is authoritative and inflexible. Lengel proceeds to warn Sammy about his decision to quit, but Sammy remains obstinate and heads to the parking lot in hopes of seeing the girls he stood up for.

The antagonist in "A&P" is Lengel, the manager of the store. The narrator describes Lengel as a "dreary" Sunday School teacher. Lengel intervenes when Sammy, the protagonist and narrator, begins to ring up the purchase of the three girls he has been watching. The girls enter the store barefoot and in their bathing suits. They seem to attract a great deal of attention as they walk the aisles because, as the narrator shares, women "generally put on a shirt or shorts or something" before entering the store. As they bring the item they wish to purchase to Sammy's register, Lengel approaches and reprimands the girls for the way they are dressed. Lengel says, "We want you decently dressed when you come in here." Sammy rings up the purchase and takes the money from the girl he refers to as "Queenie." Realizing the girls are embarrassed, he hopes to be their "unsuspected hero" and informs Lengel that he quits.

How important is it to understand the Diagnostic and Statistical Manual?

Understanding the Diagnostic and Statistical Manual of Mental Disorders (DSM) is crucial in any career that functions in a social environment. The teaching of the DSM is no longer exclusive to mental health professionals like psychiatrists or psychologists. Most degrees and courses, regardless of the major, will include basic psychology (including the DSM).
The DSM is important because everyone will deal with it sometime in their career, whether at entry or senior level. The DSM is a guideline, inexhaustive, meaning that diagnosing people with it will never be as straightforward as 1+1=2. But it's the most reliable and accredited manual concerning mental disorders to date. Whether you apply for a job, hire someone for a job, or deal with people on a day to day basis, the DSM will be relevant in your life.
The studying of the human mind and psychology is a relatively new field of science. Thus, the DSM changes regularly when new information comes to light from research. The workforce of the western world and most companies within are equipping pro-mental health policies, which means that frequent psychological diagnosis' of their employees' is being undertaken. In other areas of employment being evaluated by a professional, who will make use of DSM, is mandatory in order to be hired. This includes government employees like the police force, military, special services, security and correctional facility security. Apart from the high-risk jobs, there has been a recent increase in requiring an evaluation when working in sensitive fields of service, like working with children, the disabled, or the elderly.
However, DSM evaluations and profiling will never be 100% accurate, nothing that has to do with people will ever be perfect. But the DSM aids in identifying certain risk factors in individuals who might pose a risk to society, and/or identifying individuals who might be at risk of a psychiatric disorder. By using the DSM guidelines it provides companies insight into whether or not someone is fit for a certain job, or if the requirements of the job might pose a risk to mentally strain the particular individual. Companies are responsible to assure their employees don't pose a risk to others, while at the same time assuring the health of their employees.

Understanding the Diagnostic and Statistical Manual is the foundation of a social science such as psychology. It is important to understand the defining characteristics of each mental disorder and the criteria for diagnosing before one can be applied to a particular person or situation. The DSM is a reference tool meant to be used in conjunction with other reasearch and personal experience. Therapists learn with practice that because of new studies and findings, the DSM requires updating that it does not always receive right away. As with any discipline, it is important to “learn the manual“ or basics well before being able to stray away from it. The Diagnostic and Statistics Manual must be understood because it is used as a guide for diagnosis, therapy, and treatment. If the guide was not understood, there would be no frame of reference for practice.

How important it is to understand the Diagnostic and Statistical Manual of Mental Disorders (DSM) is really a matter of what discipline of social science you follow. The field of social science includes a wide range of subdisciplines, including archaeology, economics, history, law, geography, linguistics, anthropology, politics, sociology, and the most relevant for this discussion: psychology.

Given the focus of the DSM on mental disorders, you might understand how it serves as a foundational reference text for psychology and sociology disciplines. Asking whether the manual is important is like asking whether the dictionary or an encyclopedia is important. The answer would be very much so; however, important for particular applications.

Let’s say you’re putting together a paper on the historical development of disorders based upon contemporary attitudes; one source could be the DSMs of yesteryear, which would reveal a range of attitudes that were accepted at the time of publication. An example of this would be the classification of homosexuality as a mental disorder, which persisted until 1987 in the DSM and until 1992 in the World Health Organization’s International Classification of Diseases (ICD-10) publication.

That’s one very specific application of the DSM and not exactly what you might expect its primary function to be. In reality, the DSM characterizes a range of disorders in a rather prototypical fashion. It establishes baseline categories for a variety of manifestations of human behavior and thought. If you look on any clinician’s bookshelf, you’re bound to find a DSM or at least a reference to the DSM from a secondary text. However, the tradition a clinician belongs to and their experience in the field will dictate how much or how little they will reference the manual.

Novice therapists may find themselves routinely revisiting the text, whereas more seasoned professionals may employ it only for its insurance codes. Like instruction, therapy is a skill that develops over time through a steady stream of client interaction, self-reflection, and ongoing training and education. The DSM is merely a starting point.
https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&ved=0ahUKEwjozJ3-96PbAhUDtlkKHYYbCBEQFggpMAA&url=https%3A%2F%2Fwww.psychiatry.org%2FFile%2520Library%2FPsychiatrists%2FPractice%2FDSM%2FAPA_DSM_Insurance-Implications-of-DSM-5.pdf&usg=AOvVaw3

https://www.psychologytoday.com/us/blog/sacramento-street-psychiatry/201608/is-the-dsm-clinically-useful

What was the second prophecy in Macbeth?

The witches’ second prophecy is that Macbeth will be Thane of Cawdor. 
After the battle, Macbeth and Banquo hear prophecies from three mysterious witches. They are women with beards and are known as the “weird sisters.” The witches tell Macbeth three prophecies in Act I, Scene 3:

First Witch
All hail, Macbeth! hail to thee, thane of Glamis!
Second Witch
All hail, Macbeth, hail to thee, thane of Cawdor!
Third Witch
All hail, Macbeth, thou shalt be king hereafter!

Macbeth is currently the Thane of Glamis, and becoming Thane of Cawdor would be a promotion. Macbeth will get this promotion because he defeated and killed the last person to hold that title in the battle. When Macbeth finds out the witches were right about the promotion, he is surprised.
ROSS
And, for an earnest of a greater honour,He bade me, from him, call thee thane of Cawdor:In which addition, hail, most worthy thane!For it is thine.
BANQUO
What, can the devil speak true?
MACBETH
The thane of Cawdor lives: why do you dress meIn borrow'd robes? (Act I, Scene 3)
The Thane of Cawdor promotion is not enough for Macbeth. He wants to be the king. That was the third prophecy, and Macbeth now wants it to come true like the others have. This seems less likely when King Duncan announces his son, Malcolm, will succeed him on the throne. This prompts the beginning of Macbeth's path to destruction.
Before the witches' intervention, Macbeth seems to have been a loyal soldier. The prophecies make him greedy. When one came true and the other seemingly did not, Macbeth became upset. He decided he was going to become king, one way or another. He would have to kill in order to make it happen, but that didn't matter to him.

Calculus and Its Applications, Chapter 1, 1.6, Section 1.6, Problem 126

Illustrate the $f$ and $f'$ of the function $f(x) = x^2 (x - 2) (x + 2)$.
Then, estimate points at which the tangent line to $f$ is horizontal. If no such points exists, state that fact.


$
\begin{equation}
\begin{aligned}
f(x) &= x^2 (x - 2)(x + 2)\\
\\
f(x) &= x^2 (x^2 - 4)
\end{aligned}
\end{equation}
$


Then, by using product rule,

$
\begin{equation}
\begin{aligned}
f'(x) &= x^2 \cdot \frac{d}{dx} (x^2 - 4) + (x^2 - 4) \cdot \frac{d}{dx} (x^2)\\
\\
&= x^2(2x) + (x^2 - 4)(2x)\\
\\
&= 2x^3 + 2x^3 - 8x\\
\\
&= 4x^3 - 8x
\end{aligned}
\end{equation}
$




Based from the graph, the points at which the tangent line to $f$ is horizontal (slope = 0) are
at $x \approx -1.40, x= 0$ and $x \approx 1.40$

Where and when did the poet hear a thousand blended notes in "Lines Written in Early Spring"?

"I heard a thousand blended notes" is the opening line of William Wordsworth's "Lines Written in Early Spring." The title reveals the time of its composition, and the second line, "While in a grove I sate reclined," confirms the poet's location.
It's among the poems included in Wordsworth's "Lyrical Ballads," the volume in which he unfurled the romantic revolution in English poetry. The lines

To her fair works did Nature link
The human soul that through me ran;

embody the poet's belief in the sacral quality of the bond between man and nature, which would become a central feature of this literary movement. In conclusion, the poet contrasts his pantheistic vision, in which the playing birds and budding twigs on a spring day express a pleasure that are part of "Nature's holy plan," with a melancholy reflection on "what man has made of man."

The poet hears the thousand blended notes as he sits reclined—relaxing—in a grove in the early spring. He is out in nature, and he is most enjoying the scene in front of him: the periwinkle and primrose in bloom, the song of the birds, and the sight of the birds hopping and playing, the buds bursting on the tree limbs, the breezes, and the green of the earth emerging as winter ends. It puts him into a "sweet mood." He thinks of all he sees as part of God's plan. The beauty of nature is holy to him.
The sweet mood he experiences watching the natural world also brings, however, sad thoughts. What has civilization done to this beautiful natural world that God has created? The narrator thinks, in contrast to all this, of what "man has made of man," sorrowing over the cruelties people visit on one another.

What two boys tried to convince Ralph to stay chief?

Piggy and Simon both encourage Ralph to remain chief.
Toward the end of chapter 5, Jack says, "Bollocks to the rules!" as his group of hunters exit the assembly meeting (Golding, 130). Ralph immediately becomes upset and depressed at the entire situation. Ralph is well aware that Jack is slowly gaining power, and he cannot stop him. Ralph then says that he should give up being chief. However, Piggy and Simon disagree with Ralph's assessment of himself, and both encourage him to remain chief. Piggy tells Ralph that if he relinquishes his authority, Jack will become chief and ruin the boys' chances of rescue. Piggy also mentions that he is scared of what Jack would do if he were to become chief. Simon also encourages Ralph to remain chief by saying,

Go on being chief (Golding, 132).

Piggy then tells Ralph that Jack cannot hurt him and will hurt the next thing, which is him. Simon once again displays his support for Ralph by saying,

Piggy’s right, Ralph. There’s you and Jack. Go on being chief (Golding, 133).

Out of all the boys on the island, Piggy and Simon are Ralph's biggest supporters and refuse to follow Jack and his tribe of savages. 

The setting of "The Most Dangerous Game" is essential to the story. Without this specific setting, we would not have the same story. Explain why. How does the setting affect the story? Additionally, why is the setting perfect for General Zaroff's game? Be specific and use at least one citation.

It is correct that with a different setting the story would not be exactly the same. However, I do not think that the setting is entirely what makes this story work so well. The 1994 movie Surviving the Game is essentially a movie of "The Most Dangerous Game." A few things have been changed here and there, like setting and character backstory, but the core remains the same. It is a movie about skilled hunters pitted against each other in a hunt to the death.
What the movie and the story both do similarly about setting is place events of the story in remote locations. This works incredibly well for "The Most Dangerous Game" because Zaroff needs a place to hunt humans that is far from prying and curious eyes. He cannot just have anybody wandering onto his hunting grounds. Additionally, Zaroff's island essentially makes it impossible for any man to escape him.

The smile on the general's face widened. "To date I have not lost," he said. Then he added, hastily: "I don't wish you to think me a braggart, Mr. Rainsford. Many of them afford only the most elementary sort of problem. Occasionally I strike a tartar. One almost did win. I eventually had to use the dogs."

If the hunt was on the mainland and the hunted was fit enough and fast enough, the hunted could essentially just keep running away. Zaroff would eventually be taken so far from his home that continuing the pursuit would be too much trouble. Setting the story and Zaroff's home on an island contains his prey. He has his own confined battle arena in which to go to work. The Hunger Games has a similar setup. Additionally, the island gives Zaroff access to prey that will not be missed. Sailors go missing for various reasons. They can fall overboard, ships can get lost, or they can run aground. The sailors' death is more or less expected in those cases, so when Zaroff captures and kills them, nobody cares enough to investigate. Zaroff says the following:

If I wish to hunt, why should I not? I hunt the scum of the earth: sailors from tramp ships—lassars, blacks, Chinese, whites, mongrels—a thoroughbred horse or hound is worth more than a score of them.

Precalculus, Chapter 6, 6.1, Section 6.1, Problem 12

Using law of sines
sinA/a = sinB/b = sinC/c
A,B and C are angles and a,b and c are opposite lengths of a triangle as in the image.
According to the question we have following data.
A = 5^040' = 5.667
B = 8^015' = 8.25
b = 4.8

sinA/a = sinB/b
a = sinAxxb/sinB
a = (sin5.667)xx4.8/sin8.25 = 3.30

The addition of angles in a triangle is 180^0 .
A+B+C = 180
C = 180-5.67-8.25 = 166.08

sinA/a = sinC/c
c = asinC/sinA
c = 3.3xxsin166.08/sin5.667 = 8.04

So the answers are
Angle C = 166.08 deg
Length a = 3.3 units
Length c = 8.04 units

What does Miss Maudie have to say about Atticus?

According to Miss Maudie, Atticus' courage and integrity makes him an admirable man. She tells Jem that Atticus has taken on the mantle of a true Christian: he is defending an innocent black man from being convicted for a crime he didn't commit.
In Miss Maudie's conversation with Jem, she tells him what she most admires about Atticus: his belief in equality for everyone. Atticus' principles can be summed up in the following quote:

“But there is one way in this country in which all men are created equal—there is one human institution that makes a pauper the equal of a Rockefeller, the stupid man the equal of an Einstein, and the ignorant man the equal of any college president. That institution, gentlemen, is a court...Our courts have their faults, as does any human institution, but in this country our courts are the great levelers, and in our courts all men are created equal."

During her conversation with Jem, Miss Maudie tells Jem that Atticus has more supporters than most people realize. She maintains that Judge Taylor's naming of Atticus as Tom Robinson's court-appointed lawyer was no accident. By right, Tom's case should have gone to Maxwell Green, Maycomb's newest lawyer. However, Judge Taylor named Atticus because he knew that Atticus was the only lawyer who could come close to saving Tom.
Most importantly, Judge Taylor knew that Atticus was the only lawyer who could tweak the public's conscience about the travesty of justice Tom has suffered.
Later, Miss Maudie tells Aunt Alexandra that, by letting Atticus represent Tom, Maycomb was paying the highest tribute they could pay to a man. Essentially, the public trusted Atticus to do what was right in the eyes of the law. Miss Maudie also maintains that Atticus has his supporters: people who believe that fair play is for everyone.

Following the Tom Robinson trial, Miss Maudie reveals her support for Atticus and his family by baking the children cakes. When Jem, Scout, and Dill visit Maudie's home to eat their cakes, Miss Maudie encourages Jem not to fret. She then says,

I simply want to tell you that there are some men in this world who were born to do our unpleasant jobs for us. Your father’s one of them (Lee, 219).

Miss Maudie understands the difficult task that Atticus faces while defending Tom Robinson in front of a prejudiced jury. Unlike the racist majority of Maycomb's citizens, Miss Maudie does not attend the trial and simply wishes Atticus the best.
Maudie then proceeds to tell Jem that the community of Maycomb is fortunate to have a brave, morally upright man like his father to represent them when they are called to be Christians. Maudie finishes her conversation by elaborating on the numerous people in the community who supported Atticus's efforts defending Tom Robinson.

Three resources Europeans wanted from Africa.

This question depends on when those Europeans arrived in Africa. Early in Africa's discovery, Europeans wanted slaves from Africa. These slaves were especially valuable in the New World and this created a triangular trade that allowed for the economic expansion of the New World and Europe but effectively drained Africa of its human resources.
Gold made South Africa especially valuable and was one of the key reasons that Britain came to covet the territory and minimize Dutch presence there. Diamonds would also be found in South Africa. The discovery of gold in the 1880s came at a time when Europeans were colonizing large portions of Africa. The idea was not to transplant a large number of Europeans there but rather to harvest the natural resources in the region. The riches of the region did not go to the Africans but instead to the colonizing Europeans.  
Finally, African ivory would prove to be quite valuable. This ivory could be used to make trinkets to trade to other groups or sell as home furnishings. The ivory trade led to market hunting that depleted the wildlife of the region. Even today poachers continue to attack the endangered animals of Africa.

The story lines of Shakespeare’s plays have been the basis for many works in the modern era—from plays to movies to TV shows. Think about the various storylines or plots in A Midsummer Night’s Dream and write about how you see a similar plot or plot device at work in a contemporary work that you have read or seen. For instance, can you think of another instance of star-crossed lovers and misplaced affections? Or, couples who plot to get the upper hand in a relationship, like Oberon and Titania do? Or, instances of comedy of manners like those we get with Bottom and his crew of mechanicals? (Please answer the question 300 words.)

What a great question! You are correct. Shakespeare's works have inspired a lot of remakes of his plays or retreads of story lines and characters that Shakespeare first created.
I'll start with the movie Get Over It starring Kirsten Dunst. The film is about a high school musical production of A Midsummer Night's Dream, and it comes complete with a love quadrangle motif. The film also includes some daydream sequences in magical forests which directly allude to the setting found in Shakespeare's original play. Nick Bottom's character is also reimagined in Martin Short's character. His character is a super untalented theater director with a huge ego about how great he is.
The question specifically gives an example of couples trying to get the upper hand in a relationship like Titania and Oberon. This concept brings to mind the film How to Lose a Guy in 10 Days. While the exact interactions between Andie and Ben do not exactly mirror Titania and Oberon, the two people are clearly trying to manipulate the other person's feelings.
A Midsummer Night's Dream brings up the concept of a love potion. Oberon wants Titania to be given a potion that will make her fall desperately in love with the first person that she sees. The concept of a love potion appears all over the place in modern-day media. In 1963, The Searchers released a song titled "Love Potion No. 9." The song is about a man that struggles with dating, and he is given a magical love potion to fix his problems.

I told her that I was a flop with chicsI've been this way since 1956She looked at my palm and she made a magic signShe said "What you need is love potion number nine"

The song and love potion concept was turned into a film by the same title of this song in 1992 with Sandra Bullock and Tate Donovan. The story revolves around two scientists that are hopeless when it comes to the opposite sex. They invent a substance that makes them irresistible to any person that hears them speak.
Finally, the short story "The Chaser" by John Collier includes a love potion as well. Alan Austen is the main character, who is frustrated that the girl of his dreams doesn't reciprocate his feelings. He consults a potion dealer, and the salesman sells him a potion that will make Diana fall madly in love with him.

"She will want to know all you do," said the old man. "All that has happened to you during the day. Every word of it. She will want to know what you are thinking about, why you smile suddenly, why your are looking sad."
"That is love!" cried Alan.

What is Juliet suggesting when she says that she has “bought the mansion of a love, / But not possessed it; and though I am sold, / Not yet enjoyed”?

This line comes from Juliet's opening monologue in Act III, scene 2. In the timeline, Juliet has just married Romeo a few hours earlier and is waiting for him to come to her room after dark so that they can consummate their marriage. "The mansion of a love" is Romeo and his physical form and "But not possessed it" means that she has not yet slept with him as is customary after a wedding. She has been "sold" this state of marriage but "not yet enjoyed". Essentially, Juliet is eager to begin her life as Romeo's wife and wants him to come soon so that she can begin to love him as his wife and not just in her dreams.

Juliet suggests that she has purchased a love but not really taken ownership of it yet. She has married Romeo, the man she loves, and tied her life to his, but she has had no opportunity to live or act as a wife yet (beyond the wedding itself). She compares it to buying a home but not having moved into the home yet; it is hers but she has not really lived in it, so to speak. Next, she says that she is "sold" but "Not yet enjoyed," and this seems to suggest that she is thinking of one particular marital duty specifically: the wedding night. By the customs of her times, she now belongs to Romeo, as his wife, but he has not "enjoyed" her as a groom typically would enjoy his bride on the night of their wedding.

What are some revealing portions of Pride and Prejudice from a psychoanalytical perspective?

Darcy's first proposal to Elizabeth (in chapter 34) reveals his subconscious motives and feelings. While he speaks of his ardent love for Elizabeth, he does so in a manner that presupposes her agreement to marry him and her acceptance of her lower social position. In short, he proposes to Elizabeth with the idea in mind that she is inferior in many ways and that she will be thankful to him for the proposal. While he is clearly aware of his feelings of superiority to some degree, he is clearly not aware of how arrogant he appears and how much he believes in his own superiority.
Elizabeth, however, is acutely aware of the way in which Darcy (subconsciously to some degree) feels repulsed and disgusted by his admiration and love for her. She says to him, "You chose to tell me that you liked me against your will, against your reason, and even against your character?" In other words, Darcy himself has not grasped how much his mind and soul have tried not to like Elizabeth, as she is not the right choice for him socially. However, his sense of superiority and his disdain for her family and position are revealed in the way he makes the proposal. From a psychoanalytic perspective, his proposal reveals a great deal of his class snobbery and his somewhat subconscious sense of revulsion at Elizabeth's class status.
Later, in chapter 43, Elizabeth's reactions to visiting Pemberley are revelatory of her inner motivations and desires. When she is touring the grounds of Darcy's magnificent estate, Elizabeth and the estate are described as follows:

It was a large, handsome stone building, standing well on rising ground, and backed by a ridge of high woody hills; and in front a stream of some natural importance was swelled into greater, but without any artificial appearance. Its banks were neither formal nor falsely adorned. Elizabeth was delighted. She had never seen a place for which nature had done more, or where natural beauty had been so little counteracted by an awkward taste. They were all of them warm in their admiration; and at that moment she felt that to be mistress of Pemberley might be something!

Looking at the grounds makes her think, somewhat subconsciously, of Darcy. While she admires the tasteful hills and landscape, she is actually thinking of how understated and tasteful Darcy is. She contrasts the natural quality of the surroundings with the false adornments of other great houses, and she unconsciously shows that she is warming to Darcy because of his superior taste. The last line of this passage is particularly revelatory because she admits that she would like to marry him, though she only thinks about being the mistress of his estate rather than about being his wife. Therefore, in this passage, Elizabeth reveals some of her unconscious desires—desires that she is not even totally aware of until later.

How many present-day states must ratify an amendment to make it part of the Constitution?

Article V of the U.S. Constitution lays out the requirements for the amendment process. There are two ways the states can ratify an amendment. The first is by having 3/4 of the 50 state legislatures ratify the amendmendment. Since this number is 37.5 you would round the required number of states up to 38. The second ratification method involves 3/4 of the 50 states to hold a special convention where voting would occur for ratification to be finalized.

The procedure for ratifying a constitutional amendment is vested in Article V of the United States Constitution. Here it is stipulated that amendments can be proposed either by Congress or by a constitutional convention, but to date the latter process has never been used. Instead, all twenty seven of the Constitution's amendments have been proposed by a two-thirds majority in both the United States Senate and House of Representatives. Once this initial hurdle has been overcome, then the proposed amendment is sent to the states for ratification. If three-fourths of the states duly ratify the proposed amendment then it becomes part of the Constitution. As there are currently fifty states in America, ratification is required by thirty eight states. Technically, three-fourths of fifty is thirty seven and a half, but the number is rounded up for the sake of convenience.
https://www.archives.gov/federal-register/constitution

Why did the US want the Philippines?

The decision to take control of the Philippines was very controversial in the U.S., and there were several different reasons for why the U.S. wanted to gain control of this nation. First of all, it comes back to the idea of Manifest Destiny—the U.S. believed in expanding their land in order to have control as well as economic opportunities, and the Philippines were seen as a way to do this. Additionally, the U.S. felt that Filipinos were incapable of self-government, and felt that if they didn't take control of this nation, then another nation like Germany or Japan would. This was concerning to the U.S., not only because they felt that these nations would control the Philippines in a way that would be harmful to the people of the Philippines, but also because this would further threaten the U.S.'s control in international affairs. Finally, having control over the Philippines would allow the U.S. to enter the Asian market, and be exposed to more economic opportunities.
https://history.state.gov/milestones/1899-1913/war

https://thediplomat.com/2017/11/why-the-us-seized-the-philippines-at-the-end-of-the-19th-century/

The US wanted the Philippines because the islands would serve as valuable resupply stations for steamships going to and from China. The United States wanted desperately to get into the lucrative Chinese markets; this partially explains the US's expansion into the Pacific. The United States also wanted to ensure that a growing Japan did not exert too much power in the region. What's more, the United States wanted to take over the island to fill the vacuum left when the Spanish were ousted by the US-Filipino forces. Christian missionaries also wanted the islands as American territories in order to add a new mission field for American Protestants. The archipelago was annexed at a time when the United States was trying to take up the "White Man's Burden," and this meant forcing Western-style commerce and civilization on the developing world—whether they wanted it or not.

How was Gulliver treated by the farmer's daughter?

Gulliver is treated quite well by the farmer's young daughter, a girl he calls his "Glumdalclitch," which means little nurse. He says, in fact, that he would

be guilty of great ingratitude, if [he] omitted this honourable mention of her care and affection towards [him], which [he] heartily wish[es] it being in [his] power to requite as she deserves . . . .

When the farmer trots Gulliver around, showing him off and having him perform tricks, Glumdalclitch actually makes him a little box that she's fitted up with the softest cloth she could find, including her own doll baby's bed, so that Gulliver does not get injured from being jostled around too much. She would also complain of her own tiredness so that they'd have to stop, and this would give Gulliver much needed breaks. Glumdalclitch also uses a little religious book that she keeps in her pocket to teach Gulliver how to read and understand their language. She even goes with him to the royal court when the farmer turns Gulliver over to the king and queen; Glumdalclitch continues to take great care of him for a long time.

On Brobdingnag, Gulliver is captured by a farmer. As Gulliver is now tiny in respect to the inhabitants of Brobdingnag, the farmer appears to him as a giant. The farmer is fascinated by this strange little creature and thinks that it would be a perfect plaything for his 9-year-old daughter. Glumdalclitch, as Gulliver calls her, is deeply enamored of her new toy, treating him like her own little pet. But as well as making clothes for little Gulliver, Glumdalclitch is fiercely protective towards her living doll. Her father wants to take Gulliver out on the road as part of a freak show; he thinks—rightly, as it turns out—that he can make a lot of money out of his novelty act. Gulliver enjoys performing for the sake of Glumdalclitch, but all that touring inevitably takes it toll, and he becomes exhausted with the constant traveling. Glumdalclitch realizes this, and she gets her father to travel slowly to make things a little easier for her favorite toy. Gulliver never forgets Glumdalclitch for her loving kindness and fondly remembers her after he's returned to England.

How does Ulysses regard his son's approach to life? Which character would you consider the most effective ruler: Ulysses or Telemachus?

In Tennyson's "Ulysses," the second stanza is devoted to Ulysses' description of his son, Telemachus. To get an idea of what the king thinks of his son, it helps to look at the second stanza in full:

This is my son, mine own Telemachus, 
To whom I leave the sceptre and the isle,— 
Well-loved of me, discerning to fulfil 
This labour, by slow prudence to make mild 
A rugged people, and thro' soft degrees 
Subdue them to the useful and the good. 
Most blameless is he, centred in the sphere 
Of common duties, decent not to fail 
In offices of tenderness, and pay 
Meet adoration to my household gods, 
When I am gone. He works his work, I mine. (33-43)

By reading this stanza, it's possible to ascertain that Ulysses regards his son's approach to life with a great deal of respect. Ulysses obviously loves his son, and he assumes that Telemachus will be able to effectively rule (and potentially improve) the subjects and citizens of Ithaca with wisdom. As such, Ulysses sees Telemachus' approach to life as wise and just, as he has faith that his son will be able to rule well in his place.
 
Since Telemachus appears to be such an ideal leader, it would also appear that he is a more effective ruler than Ulysses. While Ulysses is undoubtedly a great hero and an adventurous soul, he also shows himself to be an irresponsible ruler. He regards his kingly duties as a burden and seems eager to run away from them. Telemachus, on the other hand, appears to be a wise ruler, one who is determined to faithfully serve his subjects. Based on this comparison, it seems fair to say that Telemachus is a more effective leader than his father. 
https://www.poetryfoundation.org/poems/45392/ulysses

What happens at the end of "The Story of an Hour"?

In "The Story of an Hour," Mrs. Mallard receives news that her husband has died in a tragic "railroad disaster." She immediately accepts the knowledge and weeps immediately "with sudden, wild abandonment." And then a shift occurs.
Mrs. Mallard retreats to her room in solitude to process the significance of the news. She reflects that "she had loved him—sometimes. Often she had not." And she sees this change in her situation as a move toward freedom.
Indeed, she repeats this phrase to herself several times: "Free, free, free!"
Finally, she has a chance to live for herself. She will be able to make her own decisions and not be forced to submit to her husband's whims and desires.
Then, a surprising twist occurs. She emerges from her bedroom, and her husband suddenly appears at the door, "a little travel-stained, composedly carrying his grip-sack and umbrella. He had been far from the scene of the accident, and did not even know that there had been one."
Mrs. Mallard's heart, already looking toward her new future with great excitement and anticipation, cannot take this shift back to her old life. The shock and disappointment that her husband is very much alive stops her heart and kills her.

At the end of "The Story of an Hour," Louise suddenly realizes that what she thought was her new-found freedom was just a mirage. Upon hearing of the news of her husband's death, Louise was ecstatic; for the first time in her adult life she felt as free as a bird. All of a sudden, new vistas of opportunity appeared before her eyes, giving her a glimpse into a bright future of personal freedom and self-fulfillment.
But all that is cruelly snatched away from Louise when she discovers that her husband didn't die after all and that she is destined to remain trapped in a stultifying, loveless marriage for the foreseeable future. Her weak heart cannot handle the stress of seeing her husband walk through the door and so she drops down dead on the spot.

Throughout "The Story of an Hour," Louise Mallard believes that her husband Brently has been killed that day in a railroad accident. In the hour after receiving this information, Louise cries and thinks about her husband, believing him to be a kindly but, at the same time, oppressive force in her life.
Louise reflects on the hold that people in relationships have on each other, and it occurs to her that it seems a "crime" when men or women "believe they have a right to impose a private will upon a fellow-creature." Louise begins to process the fact that Brently's death means that she will be able to think and make decisions for herself, and she allows herself to feel some joy at her impending freedom.
What happens at the end of the story is that Louise's husband Brently walks in the front door; he had not been the victim of a railroad accident. Though her husband's friend Richards tries to screen Brently from Louise's view, she sees him, and she literally drops dead. The doctors who come attribute her death to "joy that kills," meaning that they believe that she is overjoyed to see Brently return and her heart gives out. However, the feminist reading that Kate Chopin may have intended suggests that Louise dies of a broken heart because her freedom is abruptly snatched away before she can begin living her own life.

Who has integrity and dignity?

Although the story is set in a time and a place rife with racial injustice, with basic humanity often lacking in characters such as the Ewells, who perjure themselves and knowingly condemn an innocent man, to the men of the town who gather and demand the accused be turned over to them for a lynching, there are notable examples of dignity and integrity throughout the tale.
Atticus Finch, a brave man, willing to take a stand for his principles, knowing they are unpopular and even pose a danger to himself and his young children, is willing to advocate for those who have no voice, in a justice system that is rigged against people of color. The African-Americans who witness the trial, behave with dignity, despite the travesty they have witnessed. They honor Mr. Finch by standing for him as he leaves the courthouse, admonishing his daughter to stand as well.
Boo Radley emerges as a hero, saving the lives of the Finch children, in his self-appointed role as their quiet and dignified protector.

There are several characters throughout the novel To Kill a Mockingbird that have integrity and dignity. Atticus Finch embodies both character traits and demonstrates his integrity and dignity numerous times throughout the story. Atticus valiantly defends Tom Robinson in front of a prejudiced jury knowing that his chances of winning are impossible. Despite pressure from the community, Atticus does not compromise his morals and displays his integrity by defending Tom Robinson. Atticus also expresses his tolerant attitude and controls his emotions during conversations with prejudiced community members.
Both Sheriff Tate and Miss Maudie also have integrity and dignity throughout the novel. Sheriff Tate is an honest man, who supports Atticus throughout the story. Sheriff Tate does not subscribe to the prejudiced views of the other Maycomb citizens and does his best to maintain order in the small town. He tells the truth on the witness stand and also protects Boo Radley from the community's limelight towards the end of the story. Miss Maudie is a sympathetic, morally-upright woman, who also supports Atticus and is friendly towards his children. She refuses to gossip or conform to Maycomb's prejudiced ideologies and is a positive role model for Scout to follow. Miss Maudie does not believe the rumors Miss Stephanie spreads throughout the community and also challenges Maycomb's religious fanatics when they criticize her.

College Algebra, Chapter 1, 1.3, Section 1.3, Problem 42

Find all real solutions of $\displaystyle 2y^2 - y - \frac{1}{2} = 0$.


$
\begin{equation}
\begin{aligned}

2y^2 - y - \frac{1}{2} =& 0
&& \text{Given}
\\
\\
2y^2 - y =& \frac{1}{2}
&& \text{Add } \frac{1}{2}
\\
\\
y^2 - \frac{y}{2} =& \frac{1}{4}
&& \text{Divide both sides by 2 to make the coefficient of $x^2$ equal to 1}
\\
\\
y^2 - \frac{y}{2} + \frac{1}{16} =& \frac{1}{4} + \frac{1}{16}
&& \text{Complete the square: add } \left( \frac{\displaystyle \frac{-1}{2}}{2} \right)^2 = \frac{1}{16}
\\
\\
\left( y - \frac{1}{4} \right)^2 =& \frac{5}{16}
&& \text{Perfect square, get the LCD of the right side of the equation}
\\
\\
y - \frac{1}{4} =& \pm \sqrt{\frac{5}{16}}
&& \text{Take the square root}
\\
\\
y =& \frac{1}{4} \pm \sqrt{\frac{5}{16}}
&& \text{Add } \frac{1}{4}
\\
\\
y =& \frac{1}{4} + \frac{\sqrt{5}}{4} \text{ and } y = \frac{1}{4} - \frac{\sqrt{5}}{4}
&& \text{Solve for } y
\\
\\
y =& \frac{1 + \sqrt{5}}{4} \text{ and } y = \frac{1 - \sqrt{5}}{4}
&& \text{Simplify}

\end{aligned}
\end{equation}
$

x^2=-36y Graph the equation. Identify the focus, directrix, and axis of symmetry of the parabola.

Let x^2=4py be equation of parabola. Then equation of directrix is y=-p coordinates of focus are (0,p) and axis of symmetry is y-axis.
In this case the equation of parabola is
x^2=-36y
Therefore,
4p=-36
p=-9
Using the facts stated above we can write equation of directrix and coordinates of focus.
Directrix is line with equation y=9, focus is the point with coordinates (0,-9) and axis of symmetry is y-axis.                         
https://en.wikipedia.org/wiki/Parabola

What is Lucinda Matlock's occupation?

The poem "Lucinda Matlock" comes from early twentieth-century American poet Edgar Lee Masters's collection called Spoon River Anthology. Each of the poems in Masters's work is spoken by a person who lies buried in the town cemetery of Spoon River, Illinois. Because she is situated at the back of the cemetery, Lucinda's poem is number 207 out of 246 individual poems in the collection. One of the points of her poem is to criticize the others who have already told gloomy stories of sacrifice and bitterness. She labels them as "Degenerate sons and daughters."
During the course of the poem she elaborates on her long life, implying that she was simply a wife, mother, and homemaker like many of the women of her time. She may have also been a healer because she refers to "medicinal weed" which she may have used to aid the sick. She says,

And then I found Davis.
We were married and lived together for seventy years,
Enjoying, working, raising the twelve children,
Eight of whom we lost
Ere I had reached the age of sixty.
I spun, I wove, I kept the house, I nursed the sick,
I made the garden, and for holiday
Rambled over the fields where sang the larks,
And by Spoon River gathering many a shell,
And many a flower and medicinal weed

At the close of the poem she chastises the others in the cemetery for not enjoying the lives they were given. She also calls death a "sweet repose," suggesting she views it as a peaceful rest.

Whom do you think the characters represent?

Tom and Daisy Buchanan seem to represent those who were considered to be old money: this means that they were born into money, that they have inherited their fortunes and do not have to work to earn them. Gatsby can be interpreted as representing those who were considered new money: this means that he, and others like him, have had to work for their fortunes themselves. Although new-moneyed individuals could earn as much or even more money than old-moneyed individuals inherited, they were somewhat lower on the social ladder because their fortunes were earned rather than passed down. We see this represented in the differences between East Egg, where the old money live, and West Egg, the "less fashionable of the two," according to Nick, because it is where the new money live.
George Wilson seems to represent those sympathetic individuals who are still trying to reach the American Dream, which the book presents as fantastic rather than realistic. He works hard, doing good honest work, but he simply cannot get ahead because other corrupt men seem to pull the strings of society.

The Great Gatsby, is known as a classic tale of money, power, love, betrayal, and loyalty. The characters throughout this story represent certain traits at given times, while still staying true to who they are at their core.
Jay Gatsby, the main character, represents the American Dream. Gatsby is determined to win back the love of his life, whom he met while he was a soldier, by becoming one within her social status. His humble beginnings eventually lead to a life of fortune, eventually turning him into a prominent host of outrageous parties for the elite. It seems as though each decision he makes, is driven by the hope of getting Daisy to notice him. Daisy comes across as a fairly shallow, naïve, yet somewhat charming socialite who enjoys her life of money, parties and status. She reunites with Gatsby, with the help of her cousin, and falls back in love with him. Nick Carraway, Daisy’s cousin, a salt of the earth type of guy, maintains his loyalty to his family and friends throughout the story. He preserves a somewhat hopeful outlook but grows more aware of his surroundings as the story unfolds. Daisy is actually married when she reunites with Gatsby. Her husband, Tom, is the antagonist of the novel. He’s vulgar, unfaithful, filthy rich, and unforgiving.
Each character brings their own unique story to The Great Gatsby, and it’s their ties with one another that lead to a devastating ending, resulting in betrayal and lies.

In thinking about what the characters in The Great Gatsby might "represent," it is important to remember that they are not mere symbols without any kind of human agency. That said, several characters are certainly representative of various themes or trends.
For example, both Tom and Daisy Buchanan can be seen as representative of old American wealth, as a portrait of the wasteful upper classes that come from money and that people like Jay Gatsby want to emulate. Alternatively, Gatsby is in many ways representative of the American Dream, in that he believes he can obtain the wealth and status of people like the Buchanans simply by working hard (he does, of course, break the law as well, which isn't necessarily a component of the American Dream). Thus, even if the characters cannot be reduced to mere symbols, they definitely represent trends and themes that are integral to Fitzgerald's story.
Ultimately, it is the collision of these themes, of the new wealth of Gatsby and the old wealth of the Buchanans, that acts as one catalyst for the disastrous events at the end of the book.

If you were a member of the British Parliament tasked to write a response to the Declaration of Independence at the time it was written, what counterpoints would you write in reply?

The Declaration was essentially an assertion of the right of revolution, and its rationale was based on the idea that the American colonies had borne such a "long train of abuses" by the British that they could no longer remain British subjects. Of course, most politicians in Britain denied that their colonists could do such a thing. It should also come as no surprise that members of Parliament and King George III himself issued public responses to the Declaration, as did countless editorialists in British newspapers. In a speech to Parliament on October 31st, 1776, the king described the "daring" and "desperate spirit of those leaders [of the Revolution] whose object has always been dominion and power." So your essay might, as King George did, question the motives of the revolutionary leaders in an effort to discredit their cause. Another possibility would be to observe, as the famous writer Samuel Johnson did, that the supposed idealism of the colonists was meaningless when one considered the existence of slavery in their midst. Johnson asked rhetorically: "How is it that we hear the loudest yelps for liberty among the drivers of Negroes?" The Americans, one might suggest, forfeited any claims to be a bastion of liberty by their ownership of enslaved people. Finally, a member of Parliament might have pointed out that the colonists were among the wealthiest people in the world, and that they owed their prosperity in no small part to the protection of the British Empire. If this protection were withdrawn, the Americans would be at the mercy of Spain, possibly France, and various Native American peoples on their borders. Each of these arguments either were made or could have been made in response to the Declaration of Independence.
https://www.americanantiquarian.org/proceedings/44498108.pdf

https://www.history.com/this-day-in-history/king-speaks-for-first-time-since-independence-declared

What are the critical thinkings of the poem "The Ballad of the Landlord" by Langston Hughes?

Langston Hughes's poem "The Ballad of the Landlord" is a poem told in song form about a tenant (or tenants) complaining about the unfair housing practices suffered at the hands of the tenant's landlord.
This poem is interesting for many reasons, but particularly in its use of irony to demonstrate the injustices African Americans faced even in the Northern cities, where this poem seems to take place. First of all, the title "The Ballad of the Landlord" ironically paints this landlord as a victim (a ballad is a sad song and this is the landlord's ballad), even though the first five stanzas recount the tenant's struggle living in a unit where "the roof has sprung a leak" and the "steps is broken down." 
Despite the clear injustices the tenant faces, the landlord comes off as victim in the public's eye when the frustrated black tenant threatens to "land his fist" on the landlord. The poem ends with three newspaper headlines that clearly paint the tenant as villain: 

MAN THREATENS LANDLORD
TENANT HELD NO BAIL
JUDGE GIVES NEGRO 90 DAYS IN COUNTY JAIL!

There are many ways to look at this poem critically; perhaps the best way is from a social justice perspective. What is the best way for a black man without power to react? What responsibilities do those with power have? What about the media? What about the police?

Calculus of a Single Variable, Chapter 9, 9.3, Section 9.3, Problem 14

The integral test is applicable if f is positive and decreasing function on infinite interval [k, oo) where kgt= 1 and a_n=f(x) . Then the series sum_(n=k)^oo a_n converges if and only if the improper integral int_k^oo f(x) dx converges. If the integral diverges then the series also diverges.
For the given series sum_(n=2)^oo ln(n)/n^3 , a_n =ln(n)/n^3 .
Then applying a_n=f(x) , we consider:
f(x) =ln(x)/x^3
The graph of f(x) is:

As shown on the graph, f is positive on the infinite interval [1,oo) . To verify of the function will eventually decreases on the given interval, we may consider the derivative of the function.
Apply Quotient rule for the derivative: d/dx(u/v) = (u'* v- v'*u)/v^2 .
Let u = ln(x) then u' = 1/x
v = x^3 then v' = 3x^2
Applying the formula,we get:
f'(x) = (1/x*x^3- 3x^2*ln(x))/(x^3)^2
= (x^2-3x^2ln(x))/x^6
=(1-3ln(x))/x^4
Note that 1-3ln(x) lt0 for larger values of x which means f'(x) lt0 .Based on the first derivative test, if f'(x) lt0 then f(x) is decreasing for a given interval I. This confirms that the function is ultimately decreasing as x-> oo. Therefore, we may apply the Integral test to confirm the convergence or divergence of the given series.
We may determine the convergence or divergence of the improper integral as:
int_2^ooln(x)/x^3dx= lim_(t-gtoo)int_2^tln(x)/x^3dx
To determine the indefinite integral of int_2^tln(x)/x^3dx , we may apply integration by parts: int u dv = uv - int v du
u = ln(x) then du = 1/x dx.
dv = 1/x^3dx then v= int 1/x^3dx = -1/(2x^2)
Note: To determine v , apply Power rule for integration int x^n dx = x^(n+1)/(n+1)
int 1/x^3dx =int x^(-3)dx
=x^(-3+1)/(-3+1)
= x^(-2)/(-2)
= -1/(2x^2)
The integral becomes:
int ln(x)/x^3dx=ln(x) (-1/(2x^2)) - int -1/(2x^2)*1/xdx
= -ln(x)/(2x^2) - int -1/(2x^3)dx
=-ln(x)/(2x^2) + 1/2 int 1/x^3dx
=-ln(x)/(2x^2) + 1/2*(-1/(2x^2))
= -ln(x)/(2x^2) -1/(4x^2)
Apply definite integral formula: F(x)|_a^b = F(b) - F(a) .
-ln(x)/(2x^2) -1/(4x^2)|_2^t=[-ln(t)/(2t^2) -1/(4t^2)] -[-ln(2)/(2*2^2) -1/(4*2^2)]
= [-ln(t)/(2t^2) -1/(4t^2)]-[-ln(2)/8 -1/16]
=-ln(t)/(2t^2) -1/(4t^2) + ln(2)/8 + 1/16
=-ln(t)/(2t^2) -1/(4t^2) +1/16 (ln(4) +1)
Note:ln(2)/8 + 1/16 = 1/16 (2ln(2) +1)
=1/16 (ln(2^2) +1)
=1/16 (ln(4) +1)
Apply int_2^tln(x)/x^3dx=-ln(t)/(2t^2) -1/(4t^2) +1/16 (ln(4) +1) , we get:
lim_(t-gtoo)int_2^tln(x)/x^3dx=lim_(t-gtoo) [ -ln(t)/(2t^2) -1/(4t^2) + 1/16(ln(4)+1)]
= -0 -0+1/16(ln(4)+1)
=1/16(ln(4)+1)
Note: lim_(t-gtoo) 1/16(ln(4)+1)=1/16(ln(4)+1)
lim_(t-gtoo) 1/(4t^2)= 1/oo or 0
lim_(t-gtoo) ln(t)/(2t^2)=[lim_(t-gtoo) -ln(t)]/[lim_(t-gtoo) 2t^2]=-oo/oo
Apply L' Hospitals rule:
lim_(t-gtoo) ln(t)/(2t^2) =lim_(t-gtoo) (1/t)/(4t)
=lim_(t-gtoo) 1/(4t^2)
= 1/oo or 0
The lim_(t-gtoo)int_2^tln(x)/x^3dx=1/16 (ln(4) +1) implies that the integral converges.
Conclusion: The integral int_2^ooln(x)/x^3dx is convergent therefore the series sum_(n=2)^ooln(n)/n^3 must also be convergent.

How is Belinda representative of eighteenth-century women?

Belinda represents not so much eighteenth-century women as she does an ideal of glamor and womanhood that was typical of the upper-class mentality of the time. In this sense, she's not much different from celebrities of our own age who are celebrated primarily for beauty and style, rather than the "deeper" qualities people see and admire in others.
Pope views the attitudes of his time with irony and, I would argue, with a large degree of empathy for women. It's interesting that he includes the young men attending the party in his focus upon appearances and the less-than-"profound" qualities of people, as he does Belinda and other women:

Fair nymphs, and well-dress'd youths around her shone,But ev'ry eye was fix'd on her alone.

If superficiality is attributed to Belinda, Pope makes the same point about her admirer:

For this, ere Phoebus rose, he had implor'dPropitious Heav'n, and every power adored,But chiefly love—to love an altar built,Of twelve vast French romances, neatly gilt.There lay three garters, half a pair of gloves;And all the former trophies of his loves.

The Baron, then, is a ladies' man, having had previous conquests and now intending to add Belinda to his list. Though one might think its satiric object is the heroic poetry of Homer and Virgil, the mock-heroic diction is actually spoofing the manners of Pope's own age and the trivialities that are made into important things in the upper-class mentality. Belinda, in her vanity, is no better or worse than the whole culture that surrounds her. Also, the vanity itself in her case might simply be a facade:

Her lively looks a sprightly mind disclose,Quick as her eyes, and as unfix'd as those.

Belinda is not vapid or empty-headed, as some readers might assume. The following lines can be understood in multiple ways:

Yet graceful ease, and sweetness void of pride,Might hide her faults, if belles had faults to hide:If to her share some female errors fall,Look on her face, and you'll forget 'em all.

My interpretation is that Pope is parodying his own era's superficial view of women and the belief that young women must be faultless and that their good looks are the only factor canceling whatever faults they do, in fact, have. Belinda is therefore a symbol of the unfair expectations men have of women in Pope's time—and by extension, throughout all time.
One might say I'm stretching things to attribute feminist attitudes to Pope. However, Pope himself was a kind of outsider in society, for several reasons, and probably had more understanding of gender roles and more sympathy for the position of women in the world than most men of his time did. He was hunchbacked and a little person. As a Roman Catholic, he was at an additional social disadvantage. Yet his talent and his intellectual powers gave him an entry into the elite world, from which he was able to view, and ironically report on, the unfair and stereotyped attitudes of the eighteenth-century world, which unfortunately have persisted in some ways up through our own time.

Calculus of a Single Variable, Chapter 9, 9.10, Section 9.10, Problem 7

Taylor series is an example of infinite series derived from the expansion of f(x) about a single point. It is represented by infinite sum of f^n(x) centered at x=c . The general formula for Taylor series is:
f(x) = sum_(n=0)^oo (f^n(c))/(n!) (x-c)^n
or
f(x) =f(c)+f'(c)(x-c) +(f^2(c))/(2!)(x-c)^2 +(f^3(c))/(3!)(x-c)^3 +(f^4(c))/(4!)(x-c)^4 +...
To apply the definition of Taylor series for the given function f(x) = ln(x) , we list f^n(x) as:
f(x) = ln(x)
f'(x) = d/(dx)ln(x) =1/x
Apply Power rule for derivative: d/(dx) x^n= n *x^(n-1)
f^2(x) = d/(dx) 1/x
= d/(dx) x^(-1)
=-1 *x^(-1-1)
=-x^(-2) or -1/x^2
f^3(x) = d/(dx) -x^(-2)
=-1 *d/(dx) x^(-2)
=-1 *(-2x^(-2-1))
=2x^(-3) or 2/x^3
f^4(x)= d/(dx) 2x^(-3)
=2 *d/(dx) x^(-3)
=2 *(-3x^(-3-1))
=-6x^(-4) or -6/x^4
Plug-in x=1 , we get:
f(1) =ln(1) =0
f'(1)=1/1 =1
f^2(1)=-1/1^2 = -1
f^3(1)=2/1^3 =2
f^4(1)=-6/1^4 = -6
Plug-in the values on the formula for Taylor series, we get:
ln(x) =sum_(n=0)^oo (f^n(1))/(n!) (x-1)^n
=f(1)+f'(1)(x-1) +(f^2(1))/(2!)(x-1)^2 +(f^3(1))/(3!)(x-1)^3 +(f^4(1))/(4!)(x-1)^4 +...
=0+1*(x-1) +(-1)/(2!)(x-1)^2 +2/(3!)(x-1)^3 +(-6)/(4!)(x-1)^4 +...
=x-1 -1/2(x-1)^2 +1/3(x-1)^3 -1/4(x-1)^4 +...
The Taylor series for the given function f(x)=ln(x) centered at c=1 will be:
ln(x) =x-1 -1/2(x-1)^2 +1/3(x-1)^3 -1/4(x-1)^4 +...
or
ln(x) = sum_(n=1)^oo (-1)^(n+1)(x-1)^n/n

What is considered the most important change coming from the Progressive Era and why?

The answer to this question depends on whom you ask, since a lot happened during that time period.  Women received the right to vote.  The Food and Drug Act was passed, giving people access to safer food and medicine.  Government acted to break up monopolies with the Sherman Anti-Trust Act.  Thanks to the efforts of John Muir and Theodore Roosevelt, the nation gained many national parks and public lands.  The United States also passed the Volstead Act; while this act would ultimately be a failure due to a lack of popularity and enforcement, it still demonstrated that the federal government was willing to intervene at an individual level.  
To me, the most important change from the Progressive Era came at the individual level.  People became more active in politics and they expected government to fix social and economic issues.  Before this, large businesses could do whatever they wanted.  With Progressivism, government moved to rein in big business.  In the case of suffragists, people learned that they could lobby the government for the right to vote.  By making the government more accountable and personal to the people, ordinary citizens learned that they could make a national difference at the grassroots level.