Notes

`6, -2, 2/3, -2/9` To determine the next two terms, identify if it is an arithmetic or geometric sequence. Take note that an arithmetic sequence has a common difference. While a geometric sequence have a common ratio. To find the common difference, subtract the successive terms. `-2-6=-8` `2/3-(-2)=8/3` `-2/9-2/3=-8/9` Since the three pairs of consecutive terms do not have the same result, the given sequence is not an arithmetic sequence. To find the common ratio, divide the consecutive terms. `-2/6=-1/3` `(2/3)/(-2) = -1/3` `(-2/9)/(2/3)=-1/3` Since the result are the same, the given sequence is geometric. Its common ratio is `-1/3` . So the 5th term of the geometric sequence is: `-2/9*(-1/3) = 2/27` And its 6th term is: `2/27*(-1/3)=-2/81` Therefore, the next two terms of the given sequence are `2/27` and `-2/81`.

The narrator says it is surprising that, with all the busybodies and impertinent people in the congregation, not a single one of them could bring himself or herself to come right out and ask Mr. Hooper why he has begun to wear the mysterious black veil.  Further, despite the fact that Mr. Hooper has, in the past, been somewhat prone to self-doubt and a willingness to follow the advice of his advisors, no one dares to approach him to make a friendly comment about the effect the new veil has on the people in the parish.  Instead, everyone remains totally mum on the subject of the veil, and people begin to avoid him as much as possible.  He is still called on, of course, to preside over funerals and weddings, but there are no more invitations to Sunday dinner.

"Emote" means which emotions the actors would display on stage when exploring the characters.  There are a lot of complex things going on in this play, and it is extremely emotional.  We are talking about the most complicated, stressful, and tragic time of these two characters’ lives, right before they die.  First of all, you will notice that Antony and Cleopatra are varied in their emotions.  They are sometimes fierce, sometimes sentimental, and sometimes loving.  They have vicious fights, but also sometimes show each other great tenderness.  Their dealings with others also vary.  For example, Cleopatra does not treat messengers very well.  If you want to tell her something, it better be something she wants to hear!  The emotions the characters show demonstrate their fading grasp on reality.  Antony is strong and virile in the beginning of the play, but as the play goes on he seems less sure of himself and even insane.  Consider that he handles the meeting with Lepidus and C...

`x=4cost` `y=2sint` First, take the derivative of x and y with respect to t. `dx/dt=-4sint` `dy/dt=2cost` Then, determine the first derivative `dy/dx` . Take note that in parametric equation, the formula of `dy/dx` is: `dy/dx= (dy/dt)/(dx/dt)` Applying this formula, the first derivative is: `dy/dx= (2cost)/(-4sint)` `dy/dx=-1/2cott` Then, determine the second derivative of the parametric equation. To do so, apply the formula: `(d^2y)/(dx^2)= (d/dt (dy/dx))/(dx/dt)` So the second derivative is: `(d^2y)/(dx^2) = (d/dt(-1/2cott))/(-4sint)` `(d^2y)/(dx^2) = (1/2csc^2t)/(-4sint)` `(d^2y)/(dx^2)=-1/8csc^3t` Take note that the concavity of the curve changes when the second derivative is zero or does not exist. `(d^2y)/(dx^2)= 0`   or   `(d^2y)/(dx^2)= DNE` Setting the second derivative equal to zero result to no solution. `-1/8csc^3t = 0` `t={O/}` Since there are no angles in which cosecant will be zero. However, on the interval 0<t<2pi, cosecant does not exist at angle pi. `-1/8csc^3t=...

On a typical evening, Erik and Arthur are likely recovering from a football game. Since Erik is the star kicker and Arthur, who’s much less talented than Erik, at least plays on the team and practices with them, he'd also be a part of the game, even if just a benchwarmer. However, of course, football  is their one productive activity. They’re usually up to more nefarious deeds. In the evening, Erik and Arthur are probably planning how to rob the homes in their neighborhood. Since many of the Lake Windsor Downs homes are tented because of a termite infestation, no one is around to guard their valuables. Consequently, Erik and Arthur have the opportunity to steal thousands of dollars of valuables, mostly jewelry. They are also planning how to most cruelly bully those around them. Erik and Arthur enjoy making others feel uncomfortable. They may be planning how to best scare Paul or how to mess with the other stars on the Lake Windsor Downs football team.

The most important interest group involved in the negotiations that led to the Torrijos-Carter Treaties was of course the government of Panama. But there were also three other interest groups, different parts of the US government: The Department of Defense, which considered the Panama Canal an essential strategic asset that must remain under US military control, the President and Department of State, who wanted the people of Panama to achieve self-determination and become a free and independent country; and the US Congress, which was responsible for ratifying the treaty and was divided between the two extremes, with some in Congress supporting independence for Panama and others insisting on the strategic interest in retaining US control. An important undertone in all of this was the ongoing Cold War; the President of Panama, Omar Torrijos, had attained power through a military coup and had some socialist leanings that frightened many American policymakers. Also important was the fact t...

Before World War I broke out in 1914, Italy had been allied with Germany and Austria-Hungary, so, at first, it seemed likely that Italy would join the Triple Alliance. Mussolini, then the editor of a socialist newspaper, was eager to keep Italy out of the war, as he saw the war as an effort by capitalist bosses to use the proletariat as cannon fodder. By 1915, though, Mussolini's views had changed, as he saw the war as what he called "a great drama." At first, many socialists in Italy sided with Mussolini in staying out of the war, but, like him, they began to gravitate towards intervention (even as he was kicked out of the Socialist Party in Italy). The Italian government began to see the war as a way to gain more territory. In the Treaty of London of 1915, Britain agreed to grant Italy territory in the Adriatic if they became involved in the war, so Italy joined in April of 1915, entering the war on the side of the Triple Entente—Britain, France, and Russia. Britain and...

From the Middle Ages onward, much of Europe operated under the feudal system. In feudalism, the king owns all of the land in his kingdom but gives large parcels of it to nobles to rule in exchange for military service. The nobles then designate smaller portions of land to be lived on and worked by the peasantry, who are in turn protected by the nobles. The kings and nobles, along with the peasants, represent two parts of the Three Orders of society:  bellatores  (those who fight, the nobles) and  laboratores  (the working peasantry.) The third Order was  oratores  (those who pray,) including all of the religious monastics and clergymen in society. These Three Orders were considered to be the natural forms and functions of a society, and as long as everyone fulfilled their role, everything was perfect... right? Not so much! The feudal system became increasingly complex and troubled as nobles might break up their land among lesser nobles, often resulting in an individual being obliged to...

After Caesar is assassinated, Antony flees to his own home. But he must realize that he has no safety anywhere in Rome if the conspirators decide to kill him too. He sends a servant to meet with Brutus and deliver a verbal message which includes the following. If Brutus will vouchsafe that Antony May safely come to him and be resolved How Caesar hath deserved to lie in death, Mark Antony shall not love Caesar dead So well as Brutus living, but will follow The fortunes and affairs of noble Brutus Thorough the hazards of this untrod state With all true faith.     (III.1) Antony addresses Brutus as the leader of the faction. He knows that Brutus will be easier to manipulate than any of the others. Brutus is a man of honor, and as such he tends to believe that other men are like himself. He believes everything Antony tells him. Antony shows precisely what he is afraid of, and why he is using all his cunning to save his own life, when he says: I know not, gentlemen, what you intend, Who els...

Mr. Sawicki runs the film club at Steve Harmon's high school and testifies on Steve's behalf during the trial. When O'Brien questions Mr. Sawicki about Steve's character, Mr. Sawicki says that he thinks Steve is an outstanding young man. He also mentions that Steve is a compassionate, honest individual. When Petrocelli cross-examines Mr. Sawicki, she asks him if he is from Steve's neighborhood. Petrocelli then asks Mr. Sawicki if it is fair to say that he doesn't know what Steve does in his neighborhood after school. Mr. Sawicki replies by saying that it would not be fair to make that statement because Steve's films give an accurate depiction of his life outside of school. Petrocelli then asks Mr. Sawicki if he knows what Steve was doing on December 22nd, and Mr. Sawicki comments that Steve did not show him film from that day. When Petrocelli asks Mr. Sawicki if he feels that the ability to make films means that a person is honest, Mr. Sawicki says, "It...

World War I started in 1914, when a nineteen-year-old Serbian nationalist killed Archduke Franz Ferdinand, heir to the throne of the Hapsburg empire. The eventual result was that the Austro-Hungarian empire declared war on Serbia, Serbia sought and achieved an alliance with Russia, and Germany joined with Austria-Hungary. Most of the major countries of Europe were drawn into the war. Woodrow Wilson, the American President, had tried to keep the U.S. out of World War I, and he had campaigned on that promise during his re-election bid in 1916. However, events in 1917 made it hard for him to keep his promise, including unrestricted submarine warfare conducted by the Germans (Laskin, 118) and the Zimmermann telegram, sent by Germay's foreign secretary to the German ambassador stationed in Mexico with the proposal to start an alliance with Mexico against the U.S. One soldier who Laskin portrays in Max Cieminski, who was born in Wisconsin and grew up speaking Kaszubian and German. His fa...

In chapter 7 of  The Great Gatsby , F. Scott Fitzgerald emphasizes the heat wafting over the city, pointing out repeatedly that conditions are both boiling and scorching. Fitzgerald emphasizes the heat in order to symbolize the heated emotions (passion, anger, etc.) that the characters are secretly harboring and which eventually break out in a heated debate. At this point in the novel, Tom has been involved in an adulterous relationship with Myrtle Wilson for some time, while Daisy has been having an affair with Gatsby. As such, there's quite a lot of tension lurking below the surface. When Daisy, Tom, Gatsby, Nick, and Jordan travel to a hotel room in the city, this tension escalates, as Tom confronts Gatsby about his affair with Daisy, and a general argument breaks loose. This argument is a key turning point in the novel, as it sets up Gatsby's loss of Daisy and his coming downfall. Additionally, it mirrors the scalding weather, as the characters' heated emotions get the ...

Climate change is a direct result of the "greenhouse effect," or the global warming that has occurred due to the trapping of heat within Earth's atmosphere. Gases such as nitrous oxide, carbon dioxide, methane, and water vapor (as well as chlorofluorocarbons) are all contributors to the greenhouse effect; many have concentratedly risen in recent years due to fossil fuel burning, industrial production, the clearing of land, and other human behaviors. This warming has already had drastic effects on our planet. Melting glaciers and polar ice sheets have caused rapid rises in sea levels (and sea temperatures) and the diminishing of certain animal populations (such as polar bears, which are now considered endangered species); these changes mean that the ocean is almost 40% more acidic than before. Extreme weather events--such as hurricanes, tornadoes, and wildfires--are growing increasingly more likely and intense, posing major threats to human habitations and life. Food secur...

The Agricultural Revolution, which coincided with the climate change at the conclusion of the last ice age, had a dramatic impact on humanity. Farming allowed humans to form permanent settlements and abandon their nomadic ways.  Humans shifted from hunting and gathering models to fixed farming villages.  As populations increased due to the increased surplus of food, urban areas surfaced.  The surplus of food also led to developments that spawned civilization .  As an example, the increased populations and surplus of food required governments to organize the surplus and protect property.  It is also thought that religions became more sophisticated .  The surplus of food also led to the development of social classes .  Trade and a merchant class were born due to farming.  Since all people were not needed for food acquisition in farming civilizations, specialized and artistic jobs or professions were developed.  Two negative results of the Agricultural Revolution were warfare and in...

The author never explicitly says this story takes place in South Africa. But Gordimer has written about her native South Africa in other works. She also mentions Chopi and Tsonga miners in the beginning frame story. These would be workers from the neighboring country of Mozambique. So, overall, this story does allude to the political and racial tensions in South Africa during this time. (The story was published in 1989.) From 1948 to 1994, South Africa was ruled by a system of racial segregation and oppression called the "apartheid." A white (British) minority ruled (and oppressed) the black majority in this country. From 1989 to 1994, there were riots and this civil unrest led to the fear described in the story.  In the "bedtime story," the family is afraid of the riots, crime, and home intrusions that occur as a result of these political and racial tensions. The housemaid shares those fears. But her fears increase when she hears a story about an attack on another ...

Believers in Stoicism, a philosophy that developed in ancient Athens, believed that by living a virtuous life, people could achieve happiness. Adherents of this doctrine believed that virtue is sufficient and necessary to achieve happiness and that other worldly pursuits, including the pursuit of fame, achievement, or wealth, can not bring about the happiness that is conferred on us by practicing reason and virtue. Stoics also believed that we should live in harmony with nature and accept the idea that what we experience is the product of a larger cosmos over which we have no control. Our attempts to control what we can't actually control will only result in anger and disappointment. Stoicism is a relevant doctrine for today's world in many ways. While pursuing fame or fortune can bring some good, this pursuit in and of itself, even if successful, clearly does not confer happiness on people. The news is filled with wealthy and successful people who are deeply troubled. Instead,...

A substance can be classified as either an element, a compound or as a mixture. An element is the purest form of matter and is composed of identical atoms (assuming no isotopes are there). Atoms are the smallest unit of matter that still retain their properties. A compound is made up of 2 or more elements in a certain fixed ratio. Thus, atoms form elements, and elements form compounds. An atom retains the properties of a substance. An element retains the properties of its constituents, that is, atoms. A compound however, has properties that differ from its constituents. For example, water (chemical formula: H2O) is a compound and is made up of two elements- hydrogen (H) and oxygen (O) in a fixed 2:1 ratio. Note that hydrogen contains atoms of hydrogen and oxygen contains atoms of oxygen. Now, hydrogen is combustible and oxygen aids combustion, however, their combination- water, is used for fire extinguishing. Hope this helps. 

By the end of the novel, the one who best understands Gatsby is Nick. Daisy loves Gatsby, but she does not know much about who he is or where he comes from. Nor does she realize, when they are reunited, that he thinks she will now divorce Tom and pick up her romance with Gatsby where it left off. When Tom brutally reveals to her that Gatsby is not who he claims to be, she is shaken and confused. Tom "understands" Gatsby in the sense that he realizes Gatsby is not what he seems. He doesn't trust Gatsby's word, and does some research on where his money is coming from. Tom understands Gatsby's economic and social status better than anybody, but he does not understand Gatsby's thinking or motivations.   Nick does not start out understanding Gatsby well. At the beginning of the novel, he has never met him. Then, attending a party of Gatsby's, he hears rumors about him, but still doesn't know what he looks like or how old he is. He talks with Gatsby for seve...

We learn most about the Druids from Julius Caesar who, being a warrior, statesman, and priest, was very eager to learn about the Druids during Rome's conquest of Britain. It is known Caesar was friends with an historically proven Druid named Diviciacus, who supported Roman conquest, and Caesar probably learned much about Druid customs, beliefs, and practices from him. One strength of Caesar's account of the Druids in his book The Gallic Wars is that, though he is describing superstitions and practices he is not likely to agree with, his tone remains objective . He writes with the same tone an anthropologist might use in giving an account of the ways of an unknown people. In his book The Gallic Wars , Caesar describes the Druids as priests in charge of answering questions of theological importance, resolving conflicts, leading private and public sacrifices, and doling out punishments for crimes. They were considered to be even higher in social status than kings. He spends a g...

In a sense, the major characteristic is that there was no such thing as "the" ancient Greek law code. The area that is now modern Greece in antiquity consisted of independent city-states inhabited by people who spoke Greek. Greece was not unified until it was conquered by Macedonia. Each Greek city had its own code of laws and there were major differences in legal and political systems among the city states. There were a few commonalities among the laws and societies of these city-states. Slavery was ubiquitous and slaves were legally treated as property, not as people. Greek city-states were patriarchal, with women subordinated first to their fathers and then to their husbands. Women, slaves, and children were all part of a male dominated household. Women generally could not represent themselves in legal cases but male guardians acted on their behalf. The legal statutes of most city-states incorporated a concept of private property and had penalties for theft or destruction ...

In Beverly Cleary's Dear Mr. Henshaw , we learn Leigh's mother is a very hard worker with a lot of integrity , which means she is very dedicated to doing what's right. We know Leigh's mother is a hard worker because, in the letter dated November 23rd, Leigh tells Mr. Henshaw that his "mom works part time for Catering by Katy," a catering business his mother's friend runs. His mother has known Katy since they were kids. His mom only works part time because she also takes a "couple of courses at the community college" to become a Licensed Vocational Nurse (LVN); Leigh explains LVNs work as assistants to "real nurses." His mother takes these courses to  provide a better life for her son and herself, wanting to be able to afford more than a mobile home or a small cottage that is "sort of falling apart" ("November 24"). One reason she divorced her husband is because she felt he was not using his money wisely enough to...

I feel that there are two specific lines in this poem that point readers toward the fact that Annabel Lee has died.  The first line is in the third stanza.   So that her highborn kinsmen came     And bore her away from me,  To shut her up in a sepulchre     In this kingdom by the sea.  The narrator of the poem tells readers that Annabel Lee was taken away from him by some of her relatives.  They took her to a sepulchre.  A sepulchre is a tomb, and tombs hold dead people.  Annabel Lee must be dead if her relatives put her in a tomb.  Although, Poe does have a tendency to write about people being buried alive, so I suppose that she could be alive at this point.   The following lines clearly explain that Annabel Lee is dead.   That the wind came out of the cloud by night,     Chilling and killing my Annabel Lee.  The above lines are in stanza four, and they explain why stanza three's cold wind is an important detail.   The final two lines of the poem also tell readers that Annabel Le...

The nutrient you are referring to is vitamin D. By being exposed to the sun, the body can produce this important nutrient. A ten-minute exposure is all that is required to manufacture vitamin D. The skin is where vitamin D is produced by the body. Vitamin D can help the body absorb the mineral calcium from food and is involved in the regulation of the levels of calcium and phosphorus found in the bloodstream. This is important for maintaining muscle and bone health. People lacking sufficient vitamin D risk developing weak bones. Vitamin D can be consumed by eating foods like eggs and certain oils. Milk usually has vitamin D added to it. Vitamin D can also be found in cheese, liver, and fatty fish. Many foods that are fortified contain vitamin D. I have included a link which explains the importance of vitamin D and where it can be obtained in the diet.

In Shirley Jackson's short story "Charles," the title character's strongest trait is his audacity. From the Merriam-Webster online dictionary, audacity is defined as: "A confident and daring quality often seen as shocking or rude."  In this story, a boy named Laurie invents a boy named Charles to explain his behavior at school. His parents are baffled by the stories of Charles, and concerned. They often overlook the behavior that Laurie displays at home that is mirroring that of his alter ego. While telling his parents that Charles is responsible, Laurie commits many heinous acts at school. Some of his most audacious acts are: hitting the teacher, yelling so loudly he disturbs other classes, bouncing a see-saw off the head of a classmate, causing her to bleed, punching a boy in the stomach, and convincing a classmate to speak an obscene word, then saying it himself.   While all these acts are being committed, Laurie's mother and father seem oblivious to ...

To solve the equation: `10^(3x-8)=2^(5-x)` , we may take "ln" on both sides. `ln(10^(3x-8))=ln(2^(5-x))` Apply natural logarithm property: `ln(x^n) = n*ln(x)` . `(3x-8)ln(10)=(5-x)ln(2)` Let `10=2*5` . `(3x-8)ln(2*5)=(5-x)ln(2)` Apply natural logarithm property: `ln(x*y) = ln(x)+ln(y)` . `(3x-8)(ln(2) +ln(5))=(5-x)ln(2)` Distribute to expand each side. `3xln(2) +3xln(5)-8ln(2) -8ln(5)=5ln(2)-xln(2)` Isolate all terms with x's on one side. `3xln(2) +3xln(5)-8ln(2) -8ln(5) =5ln(2)-xln(2)`                                   `+8ln(2) +8ln(5) `     `+8ln(2) `        ` +8ln(5)`   ------------------------------------------------------------------------------------------ `3xln(2)+3xln(5)+0 +0 =13ln(2)-xln(2) +8ln(5)` `3xln(2)+3xln(5) =13ln(2)-xln(2) +8ln(5)` `+xln(2) `                      ` +xln(2)` -------------------------------------------------------------------------- `4xln(2) +3xln(5) =13ln(2)-0+8ln(5)` `4xln(2) +3xln(5) =13ln(2)+8ln(5)` Factor out common factor `x` on the ...

In the late 14th century, the Ottoman Empire began to use slaves as part of the janissary corps, or infantry units that made up the sultan's bodyguards and the troops that served in his house. These soldiers served the sultan directly under leaders such as Bayezid I, Mehmed I, Murad II, and Mehmed II. Janissaries were taken away from their cultures and became loyal to the sultans. They helped, as Goffman writes, "domestically to neutralize the Turkoman cavalry and internationally to neutralize European innovations in military technology" (page 65). Therefore, the janissaries were important in helping the sultan consolidate power at home and abroad. The janissaries formed one part of the kapikulu , or slave military corps that composed a great deal of the Ottoman bureaucracy. Following Mehmed II, nearly every grand vizier was from this class. By the time Suleyman was in power, one had to be part of this class to even be considered for advancement. Membership in what Goffma...

In Dave Eggers' nonfiction book  Zeitoun,  Kathy is an American who converts from Christianity to Islam. Her conversion to the Islamic faith is for both spiritual and intellectual reasons, and occurs before she meets her husband, Abdulrahman Zeitoun. As Kathy immerses herself in the tradition, she discovers that in many ways, Islam is quite similar to Christianity. Her conversion is largely a learning process in which she realizes that many of the things she thought about the Islamic faith were incorrect assumptions. As Kathy further immerses herself in Islam, she does so with curiosity and open-mindedness. Those attitudes serve her well throughout the trying times of Hurricane Katrina and the unfounded, brutal detention of her husband Zeitoun.   Before Hurricane Katrina made landfall, Kathy and her children went to Phoenix, Arizona for safety. There, they stayed with Yuko, another American convert to Islam. Yuko supports Kathy and the children throughout the hurricane and Zeitoun...

That depends on the assignment.   Have you been given an assignment that involves a specific question about the book, or that points you in the direction of certain themes? Since you don't mention anything like that in your question, I'm going to assume you haven't been given any such thing, and have just been asked to write an essay or a paper about Dr. Jekyll and Mr. Hyde , with the topic left wide open.  A thesis statement should be brief and clear, and it should make a claim about the book that it will take you the rest of the essay to prove. Here are a few suggestions of possible thesis statements to get you started: "The process of disintegration that Dr. Jekyll goes through over the course of the novel resembles the process of drug addiction." "Although Utterson is a good person and a very good friend to Dr. Jekyll, he is unable to save Dr. Jekyll from himself." "The novel would have a very different effect on readers who do not know from the...

Cotton was an important crop in India.  This cotton was turned into spun thread and woven by hand.  The cloth created by woven Indian cotton was cool and lightweight.  This made it especially popular in England.  Often it was dyed beautiful colors.   In India, all of the harvesting, spinning of the thread, weaving of the cloth, and dying of the finished product was done meticulously by hand.  The workers who did these processes were skilled.  With the arrival Industrial Revolution, it became cheaper to make cotton cloth using large factory machinery instead of by hand.  This had a negative impact on the people who wove cotton cloth by hand in India.  On top of this, the United States had already become the main center for cotton production in the world.  England had already begun purchasing cotton from the United States instead of India. Before cotton could even be produced into cloth and other goods, the seeds needed to be removed.  With the invention of the cotton gin, speeds could b...

Steve mentions several times throughout the novel that he wanted to be tough like James King, Richard "Bobo" Evans, and Osvaldo Cruz. He alludes to the idea that bravado and being respected as a tough individual are why he chose to participate in the conspiracy to rob the store. During one of the flashback scenes, Osvaldo Cruz makes fun of Steve by calling him a faggot. Another neighborhood boy mentions that Steve hangs out with some bad dudes. Osvaldo then says, " He don’t hang with nobody. He’s just a lame looking for a name. Ain’t that right, Steve? Ain’t that right? " (Myers 86). Osvaldo's comments upset Steve, and the reader acknowledges the fact that an attack on Steve's masculinity bothers him. On Thursday, July 9th, James King is seated next to Steve before they enter the courtroom and attempts to scare Steve by giving him an intimidating look. Steve mentions, " All the times I had looked at him and wanted to be tough like him , and now I saw hi...

There were disagreements over the meaning of the Constitution. People like Thomas Jefferson believed in a strict interpretation of the Constitution. He believed that you can do only what is specifically mentioned in the Constitution. John Adams believed in a loose view of the Constitution. This meant that it is acceptable to interpret the meaning of the Constitution. With this view, it is acceptable to do anything unless the Constitution specifically says it can’t be done. A strict view could limit the power of the federal government while a loose view could increase its power. One example to use to highlight these differences was the discussion about having a national bank. John Adams supported this idea while Thomas Jefferson opposed it. Jefferson felt it was not acceptable to create a national bank because the Constitution said nothing about having a national bank. John Adams believed it was acceptable to have a national bank because it wasn’t prohibited by the Constitution.

In the early twentieth century, progressive education reform entailed the reconstruction of teaching methods, curricula and academic standards to reflect stronger democratic ideals; the ultimate goal was to turn American citizens into more engaged participants in democracy by creating greater access to education that promoted intellectual, creative, and psychological growth. The roots of progressive reform theory lie in the works of European thinkers such as Rousseau and Locke, but were expanded on by later proponents in both America and Europe, including John Dewey, Helen Pankhurst, Rudolf Steiner, and Maria Montessori. By far the most influential of these was Dewey, who prioritized the needs and individuality of the student over the sanctity of a school as a domineering institutional voice. Dewey considered it the responsibility of the education system to consider a student's psychological as well as intellectual development by nurturing children's instincts, curiosity, and i...

To determine the convergence or divergence of a series `sum a_n` using Root test , we evaluate a limit as: `lim_(n-gtoo) root(n)(|a_n|)= L` or `lim_(n-gtoo) |a_n|^(1/n)= L` Then, we follow the conditions: a) `Llt1` then the series is  absolutely convergent . b) `Lgt1` then the series is  divergent . c) `L=1` or  does not exist   then the  test is inconclusive . The series may be divergent, conditionally convergent, or absolutely convergent. We may apply Root test on the given series `sum_(n=1)^oo 5^n/n^4` when we let:  `a_n =5^n/n^4` . Applying the Root test, we set-up the limit as:  `lim_(n-gtoo) |5^n/n^4|^(1/n) =lim_(n-gtoo) (5^n/n^4)^(1/n)` Apply Law of Exponent: `(x/y)^n = x^n/y^n` and `(x^n)^m= x^(n*m)` . `lim_(n-gtoo) (5^n/n^4)^(1/n) =lim_(n-gtoo) (5^n)^(1/n)/(n^4)^(1/n)`                        ` =lim_(n-gtoo)5^(n*1/n)/n^(4*1/n)`                        ` =lim_(n-gtoo)5^(n/n)/n^(4/n)`                        ` =lim_(n-gtoo)5^1/n^(4/n)`                        ` =lim_(n-gtoo)5/n^(4/...

The picaresque novel is a first-hand account of an adventurer, generally of the lower class, as he travels about. It is composed of a series of adventures and subplots in which the hero interacts with people from different social classes and tries to outwit them through lying, cheating, and stealing. The novel satirizes the values of upper-crust society as the hero constantly tries to subvert these values and lives by the codes of the lower class. This type of literature came from Spain in the 1500s, and the most famous example is Don Quixote in the 1600s. By the 18th century, the picaresque novel was on the decline, to be replaced by novels with a deeper sense of character. However, the picaresque lived on in the 18th century in novels such as Tom Jones by Henry Fielding (1749), in which Tom, an orphan, grows to adulthood and witnesses the debauched nature of London at the time. The 18th century picaresque novel, like Tom Jones , combined elements of the picaresque novel with elemen...

This question is useful. It is useful to be reminded that King isn't just a horror writer, or just out to shock readers and gross them out, but also uses a wide range of literary techniques, such as irony. Turning to the question, there are several examples of irony in King's famous novel. The first is a major element of the plot. Jack Torrance's life is a mess. He takes this position at the hotel because it is supposed to be easy. It is supposed to give him a chance to focus on his writing and rebuild his life. However, in a massive example of situational irony, Jack's time at the hotel is not easier, and his life doesn't pull together. Instead, it is far harder, and his life gets shredded. A related irony is Jack's relationship to drinking. Before he came to the hotel, Jack was having trouble with alcohol, and one reason he took this position was to dry out. However, the hotel itself provides him with alcohol, and sets up situations where he'll drink. His ...

A writer named Rowan Jacobsen recently wrote and posted an obituary for the Great Barrier Reef on a website known as Outside Online. Most experts agree that the Great Barrier Reef is not dead, but it is facing damage and there is great cause for concern. Here is an excerpt from Jacobsen's Great Barrier Reef obituary:  "The Great Barrier Reef of Australia passed away in 2016 after a long illness. It was 25 million years old. For most of its life, the reef was the world’s largest living structure, and the only one visible from space. It was 1,400 miles long, with 2,900 individual reefs and 1,050 islands. In total area, it was larger than the United Kingdom, and it contained more biodiversity than all of Europe combined. It harbored 1,625 species of fish, 3,000 species of mollusk, 450 species of coral, 220 species of birds, and 30 species of whales and dolphins. Among its many other achievements, the reef was home to one of the world’s largest populations of dugong and the larges...

The Declaration of Independence contains the claim that "all men are created equal [and] endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty, and the pursuit of Happiness." The existence of slavery, which legally allowed for slaves to be the property of slaveowners, showed how unequally these rights were applied. Slaves lacked liberty and personal autonomy and experienced violent abuse in order to enforce the will of slaveowners. The slave code, or set of laws governing relationships between slaves and slaveowners, even conceded that the definition of "slave" is "a human being, who is by law deprived of his or her liberty for life, and is the property of another." The United States, a nation established to protect liberty and human rights, was proved hypocritical through the existence of slavery. The rights claimed in the Declaration of Independence and Constitution were deprived to slaves on the basis of race.

`7^(3x+4)=49^(2x+1)` To solve, factor the 49. `7^(3x+4)=(7^2)^(2x+1)` To simplify the right side, apply the exponent property `(a^m)^n=a^(m*n)` . `7^(3x+4)=7^(4x+2)` Since the two sides have the same base, to solve for the value of x, set the exponent at the left equal to the exponent at the right side. `3x + 4= 4x + 2` `3x - 4x = 2 - 4` `-x=-2` `x=2` Therefore, the solution is `x = 2` .

Okonkwo is driven in everything he does to not be identified with his father. Okonkwo believes that his father's gentleness was really weakness, and his idleness was failure. From the time he was very young, a rage has boiled within him, and though it makes him harsh with his family, it has earned him a reputation as a fierce warrior. In battle, he has taken a number of trophies in the form of human skulls. To do so, in any case, but perhaps especially for Okonkwo, is an act of dominance. Not only has the person been overcome in battle, but now their corpse is desecrated, and the primary identifying feature (the head and face) is taken by their killer. It is truly a symbol of one person dominating another, even after death. Okonkwo has kept these head-trophies as evidence of his prowess in battle, and on special occasions, he drinks wine from the first skull. We've already addressed the head-trophies as a form of dominance, but the act of drinking from the skull really lends de...

Integrated `int10/[(x-1)(x^2+9)]dx` Solve for the variables A, B, and, C using the method of partial fractions. `10/[(x-1)(x^2+9)]=A/(x-1)+(Bx+C)/(x^2+9)` `10=A(x^2+9)+(Bx+C)(x-1)` `10=Ax^2+9A+Bx^2+Cx-Bx-C` `10=(A+B)x^2+(C-B)x+(9A-C)` Equate coefficients and solve for A, B, and C. `0=A+B` `A=-B` `0=C-B` `0=C+A` `10=9A-C` `0=A+C` `10=10A` `A=1` `C=-1` `B=-1` `int10/[(x-1)(x^2+9)]dx=int[1/(x-1)+(-1x-1)/(x^2+9)]dx` `=int1/(x-1)dx-intx/(x^2+9)dx-int1/(x^2+9)dx` The first integral matches the form`int(du)/u=ln|u|+C` `int1/(x-1)=ln|x-1|+C` Integrate the second integral using u-substitution. Let `u=x^2+9` `(du)/dx=2x` `dx=(du)/(2x)` `-intx/(x^2+1)dx=-x/u*(du)/(2x)=-1/2ln|u|+C=-1/2ln|x^2+9|+C` The third integral matches the form `int(dx)/(x^2+a^2)=1/atan^-1(x/a)+C` `=-int1/(x^2+9)dx=-1/3tan^-1(x/3)+C` `=int1/(x-1)dx-intx/(x^2+9)dx-int1/(x^2+9)dx ` `=ln|x-1|-1/2ln(x^2+9)-1/3tan^-1(x/3)+C` The final answer is:   `=ln|x-1|-1/2ln(x^2+9)-1/3tan^-1(x/3)+C `

If you woke up one day to discover that the government and everyone in society were burning books, which ones would you save? Of course, most people would save their favorite books. However, for the intellectuals that Montag meets after escaping from such a society, they choose the following books to save through memorization: "I am Plato's  Republic . Like to read Marcus Aurelius? Mr. Simmons is Marcus . . . I want you to meet Jonathan Swift, the author of that evil political book,  Gulliver's Travels!  And this other fellow is Charles Darwin, and this one is Schopenhauer, and this one is Einstein, and this one here at my elbow is Mr. Alber Schweitzer, a very kind philosopher indeed. Here we all are, Montag. Aristophanes and Mahatma Gandhi and Gautama Buddha and Confucius and Thomas Love Peacock and Thomas Jefferson and Mr. Lincoln if you please. We are also Matthew, Mark, Luke, and John" (151). Within the above list are some of the greatest writers, philosophers, po...

Harper Lee’s To Kill a Mockingbird is set in Depression era rural Alabama. For the white and African American residents, segregation and racism are accepted parts of life. Even so, Atticus Finch, in his role as defense attorney, strives that every individual charged with a crime receive a fair trial. When Atticus is appointed to the position of Tom Robinson’s attorney, he accepts. For him, there is much on the line. He is a respected attorney defending an African American man accused of beating and raping a white woman. In the eyes of many of Maycomb’s residents, Atticus taking the case is nothing less than betraying the white race he represents. Yet for Atticus, his view of equal justice extends further than the courtroom. When he hears rumors that some residents plan to kidnap Tom from his jail cell and lynch him, Atticus decides to guard the cell knowing that the mob might harm or kill him in its attempt to get to Tom.

Although readers dispute whether or not the Weird Sisters actually know the future, or if they simply manipulate Macbeth into believing that they do and, in this way, coerce him to commit unscrupulous behaviors, it is clear that the witches do have at least some real supernatural ability.  After they confront Macbeth and Banquo, and Macbeth commands them, "Speak, I charge you," they do vanish (1.3.81).  Certainly, their ability to vanish indicates that they are, truly, witches who are capable of some measure of witchcraft.  Further, later, in Act Four, they do conjure (with Hecate's help) some apparitions which do provide some information about Macbeth's future.  This information is confusingly worded and designed to make him feel secure, but it does contain some truth: Birnam Wood will come to Dunsinane, Macbeth should beware of Macduff, Banquo's issue will reign in Scotland, and so forth.  Then, afterward, the witches vanish; they should move past Lennox to leav...

After the Bipartisan Campaign Reform Act of 2002 (also known as McCain-Feingold) was passed, which banned soft money donations to political parties, many critics felt that it only succeeded in shifting money through what is often figuratively called a hydraulic process to other cracks. According to Raymond J. La Raja and Brian F. Schaffner, authors of  Campaign Finance and Political Polarization: When Purists Prevail  (please see the link below),   there is no way to stop this flow of money. The authors state, When well-intentioned reformers pass laws that limit contributions, the amount of money in politics does not change significantly, but its flow migrates. In other words, the rules do not necessarily create effective 'dams' that block money from entering politics, but instead expand or carve new 'canals' that channel its flow in other directions." Therefore, experts often feel there is no way to stop the hydraulic "money-shift" tendencies that accomp...

In chapter five, Isabel is sent to the Tea Water Pump to get "special" water for the Locktons.  She doesn't know how to get there, so Curzon volunteers to show Isabel the way.  Chapter six then begins with Curzon leading Isabel to the Tea Water Pump.  Curzon moves very quickly, and Isabel can barely keep up.  Curzon eventually slows down once he realizes that Isabel is struggling to stay with him.  Curzon explains that the Tea Water Pump is where all of the rich people get their water from, because it supposedly tastes better.  He also explains that he must pick up a package along the way. He picks up the package and some rolls for Isabel to eat.  She is deeply grateful.  While Isabel eats, Curzon asks her if Ruth is Isabel's sister.  Isabel confirms that fact, and Curzon then understands why Isabel willingly took the slap from Madam Lockton even though Ruth was guilty.   Curzon sees that Isabel doesn't have a deep loyalty to Madam Lockton, so he asks Isabel if sh...

The most prominent and well-known mention of eating in the Book of Revelation is found in Chapter 19, which describes the “marriage supper of the Lamb.” The writer (who identifies himself as John) describes a scene in which he hears the sounds of a “great multitude.” He compares the sound to rushing water or thunder, and hears the voices praising God and celebrating the marriage of the Lamb and his Bride. John is instructed by an angel to write Blessed are those who are invited to the marriage supper of the Lamb. In typical Christian metaphors, the Lamb is Christ and the Bride is the Church. In this passage, the Lamb dresses his Bride in fine, clean clothing, possibly representing Christ purifying the Church. In this celebration, Christ and the Church are united in heavenly glory, with the joy of this event compared to a great wedding reception. There are other mentions of eating in Revelation, though none as prominent as the marriage supper. In chapter 2, John addresses the church in ...

Earthquakes emit two types of body waves: primary waves (p-waves) and secondary waves (s-waves). Both waves originate at the epicenter of an earthquake. Primary waves, so named because they are the first wave to be emitted during en earthquake, travel through rock and liquid. These waves are the first to reach seismic stations, which alert seismologists of tectonic activity. Following the primary waves are s-waves, which travel through rock like p-waves, but cannot travel through liquid. The speeds of p-waves and s-waves depend on many factors, but most importantly depend on Earth's surface material. The speed of an s-wave ranges from 1 km/sec to 8 km/sec and is mostly determined by Earth's surface material. In loose, unconsolidated sediments, an s-wave may only travel 1 km/sec, whereas deeper beneath the surface, s-waves can move as fast as 8 km/sec. Because the speeds of p-waves and s-waves are dependent on their environment, it is impossible to assign an exact speed to p-w...

Betrayal drives the plot of the play. First, Macbeth betrays his king, friend, guest, and kinsman when he murders Duncan. Macbeth has always been loyal to the king, and he recently fought valiantly on two different fronts in order to secure Scotland against traitorous rebels and foreign invaders. However, once the Weird Sisters tell him that he'll become Thane of Cawdor and king, and then he actually learns that he's been named the Thane of Cawdor, his ambition consumes him and he eventually betrays his king and country. Later, Macbeth betrays his former best friend, Banquo, ordering his murder as well as the murder of Banquo's son, Fleance, because the Weird Sisters told Banquo that his descendants would be kings. Macbeth regretted Duncan's murder, but by the time he betrays his best friend, his conscience is basically dead. Betrayal of those by whom one is trusted seems to be a sure way to become utterly morally corrupt.

There are several ways the story offers relevance to day-to-day life, an idea for which Ray Kinsella's discussions of Holden Caulfield provide a metaphor. One instance in W. P. Kinsella's "build it, he will come" fantasy that provides day-to-day life relevance is the idea that nothing is finished until the metaphoric last man is out. The metaphoric "last man" can be anything any person is facing in life: it can be the needed effort, the needed bit of patience, the last interview, the last assignment, the last story written, or the last man on base. In daily life, no metaphoric street is crossed, no bridge burned, no gain made, and no loss recorded until every chance is taken and every opportunity fulfilled. Within the baselines [of a baseball field] anything can happen. Tides can reverse; oceans can open. That’s why they say, “The game is never over until the last man is out.” Colors can change, lives can alter, anything is possible. Ray's epiphany is re...

Indefinite integral are written in the form of `int f(x) dx = F(x) +C`  where: `f(x)` as the integrand            `F(x)` as the anti-derivative function             `C`  as the arbitrary constant known as constant of integration For the given problem `int xarcsec(x^2+1) dx,` it has a integrand in a form of  inverse secant function. The integral resembles one of the formulas from the integration as :  `int arcsec (u/a)du = u*arcsin(u/a) +-aln(u+sqrt(u^2-a^2))+C` . where we use: `(+)`  if `0ltarcsec (u/a)ltpi/2`                     `(-)` if `pi/2ltarcsec(u/a)ltpi` Selecting the sign between `(+)` and` (-) ` will be crucial when solving for definite integral with given boundary values `[a,b]` .  For easier comparison, we may apply u-substitution by letting: `u =x^2+1` then `du = 2x dx ` or `(du)/2` Plug-in the values `int xarcsec(x^2+1) dx` , we get: `int xarcsec(x^2+1) dx=int arcsec(x^2+1) * xdx`                                         `= int arcsec(u) * (du)/2` Apply the basic propertie...

I think the answer here is mudcracks. Mudcracks are where soil that is high in clay content, such as that found in sedimentary zones like lakes, cracks due to heat. The clay in these soils is very absorbent, much like a sponge. When the soil absorbs large amounts of water and swells, it will look like gooey mud. When the soil drys out, however, like during extended droughts and dry spells or during heat waves, the water in the soil evaporates and the mud shrinks, causing stress fractures in the mud. In deserts, these are common in wadis, or dry riverbeds, and at the basses of foothills and mountains where clay can accumulate. The slower the drying time, the more regular the crack pattern will be, with strict polygonal cracks forming in the shade. 

The given two points of the exponential function are (1,40) and (3,640). To determine the exponential function  `y=ab^x` plug-in the given x and y values. For the first point (1,40), plug-in x=1 and y=40. `40=ab^1` `40=ab`        (Let this be EQ1.) For the second point (3,640), plug-in x=3 and y=640. `640=ab^3`      (Let this be EQ2.) To solve for the values of a and b, apply the substitution method of system of equations. To do so, isolate the a in EQ1. `40=ab` `40/b=a` Plug-in this to EQ2. `640=ab^3` `640=(40/b)b^3` And, solve for b. `640=40b^2` `640/40=b^2` `16=b^2` `+-sqrt16=b` `+-4=b` Take note that in exponential function `y=ab^x` , the b should be greater than zero `(bgt0)` . When `blt=0` , it is no longer an exponential function. So, consider on the positive value of b which is 4. Now that the value of b is known, plug-in it to EQ1. `40=ab` `40=a(4)` And, solve for a. `40/4=a` `10=a` Then, plug-in the values of a and b to the exponential function `y=ab^x` So this becomes: `y= 1...

Advantage 1: Federalism allows countries to stay together if they have regions that are very different from one another.  If a country has very different regions and does not have federalism, all of the regions have to obey the same laws and many regions will be unhappy.  With federalism, the people of different regions can have much more autonomy and will be more likely to coexist peacefully. Advantage 2: Federalism allows states or provinces to be “laboratories of democracy.”  What this means is that the various states can experiment with different approaches to problems.  Let us say that various states of the US want to try to improve education in different ways.  It would be possible to take many different approaches and see which ones work and which do not.  If there is no federalism, the whole country will have to try the same approach to education and we can only test out one approach at a time. Disadvantage 1: With federalism, not all people have the same rights.  In the United...