Notes

"Progressivism" is a term often used to refer to the reform movements of the late 19th and early 20th centuries. Self-identified progressives were interested in improving the conditions of the poor, particularly the urban poor whose lives had been worsened by the rise of industrialization. Some of the specific problems that caused or fueled the movement were unsafe and unfair working conditions; big business monopolies; disease among the poor; social discrimination; and the lack of autonomy of workers. The progressive education movement reflected a desire by reformers to improve the plight of the poor by making quality schooling available to everyone; changing the student-teacher relationship in ways that increased student autonomy; and attempting to address the student's social and psychological needs. Here are the details. What specific problems inspired or caused the movement? Some of the most important include those below. Poor working conditions in factories, mines, ...

We are asked to graph the following function: `y=log_4(x)` The domain is x>0 and the range is all real numbers. The graph increases on its domain and is concave down on its domain. Some points on the graph: (1/64,-3),(1/16,-2),(1/4,-1),(1,0),(4,1),(16,2) The graph:

John Mansfield’s poem “Sea Fever” describes the feeling a mariner gets when the seafaring way of life calls to him. The seafarer in the poem says, “And all I ask is a tall ship and a star to steer her by.” Tall ships were, and are, known for their sea worthiness. Their sturdy build, with oaken masts, and a variety of sails made to catch the wind, is meant for enduring long voyages in rough seas. In John Mansfield’s seafaring days, tall ships facilitated trade across the Atlantic Ocean.   Before the use of sonar and radar to chart the course of a ship, mariners used celestial or astronavigation to find their way.  Using the location of the sun, the moon and stars in relation to the horizon, mariners were able to calculate and chart their travels. Therefore, the narrator in Mansfield’s poem is asking for clear evening skies so that he see a star to chart his course. The ship and the star are all he needs.

`sum_(n=1)^oo(4n+1)/(3n-1)`  For the given series `a_n=(4n+1)/(3n-1)` `a_n=(4+1/n)/(3-1/n)` `lim_(n->oo)a_n=lim_(n->oo)(4+1/n)/(3-1/n)` `=4/3!=0` As per the n'th term test for divergence, If `lim_(n->oo)a_n!=0` , then `sum_(n=1)^ooa_n` diverges, So, for the given series `lim_(n->oo)a_n=4/3!=0` Hence the series diverges .

Early on, in Act Two, John and Elizabeth Proctor do not do a great job at listening to one another.  Both seem still have a guard up as a result of John's extramarital affair with Abigail Williams seven months prior.  He feels that his wife continues to distrust him unnecessarily, and this angers him and makes it difficult for him to really listen to her concerns.  She feels that he continues to be untrustworthy -- saying at one time that he was never alone with Abigail, and, at another, that he was alone with her for just a few minutes -- and so she is somewhat suspicious of him and defensive of her own pride; this makes it difficult for her to really listen to his explanations.  Other characters seem to have selective hearing.  For example, in Act Two, when Ezekiel Cheever arrives at the Proctors' home to arrest Elizabeth, he reveals that Abigail has charged Elizabeth with witchcraft.  He doesn't seem to listen to Mary Warren's statements that she made the doll and in...

To evaluate the given equation `1/3log_5(12x)=2` , we may apply logarithm property: `n* log_b(x) = log_b(x^n)` . `log_5((12x)^(1/3))=2` Take the "log" on both sides to be able to apply the logarithm property: `a^(log_a(x))=x` . `5^(log_5((12x)^(1/3)))=5^(2)` `(12x)^(1/3)= 25` Cubed both sides to cancel out the fractional exponent. `((12x)^(1/3))^3= (25)^3` `(12x)^(1/3*3)=15625` `(12x)^(3/3)=15625` `12x =15625` Divide both sides by `12` . `(12x)/12 =(15625)/12` `x =(15625)/12` Checking: Plug-in `x=(15625)/12` on `1/3log_5(12x)=2`  `1/3log_5(12*(15625)/12)=?2` `1/3log_5(15625)=?2` `log_5(15625^(1/3))=?2` `log_5(root(3)(15625))=?2` `log_5(25)=?2` `log_5(5^2)=?2` `2log_5(5)=?2` `2*1=?2` `2=2 `   TRUE There is no extraneous solution. The `x=(15625)/12` is a real solution for the given equation `1/3log_5(12x)=2` .

The word "existential" refers to anything that concerns, relates to, or affirms existence.  This entire text addresses the nature of human existence, namely, the fact that human beings are inherently complacent and fundamentally disposed to stop striving once they feel "satisfied".  Essentially, most of us become metaphorical "sticks" during our lives: as the Man from Hell says, "In short, the stick is the root and source of all tools."  The majority of us -- "98.4 percent" to be precise -- are, at best, tools in the hands of others.  We are used, made to perform in some capacity, scuffed up and scarred by our experiences, sometimes "suffer[ing] rather harsh treatment" that impacts what kind of literal stick we become when we die.  Those 98 out of every 100 of us who become sticks have no "aims," just like the Hippie Girl and Boy; she explains, "Aims are out-of-date."  Our lack of personal goals, our satisf...

For the series: `ln(2)/sqrt(2) + ln(3)/sqrt(3)+ ln(4)/sqrt(4)+ ln(5)/sqrt(5)+ ln(6)/sqrt(6) +...`, it follows the formula `sum_(n=2)^oo ln(n)/sqrt(n)` where `a_n = ln(n)/sqrt(n)` . To confirm if the Integral test will be applicable, we let `f(x) = ln(x)/sqrt(x)` . Graph of the function `f(x)` :   Maximize view:  As shown on the graphs, `f` is positive and continuous on the finite interval `[1,oo)` . To verify if the function will eventually decreases on the given interval, we may consider derivative of the function. Apply Quotient rule for derivative: `d/dx(u/v) = (u'* v- v'*u)/v^2` . Let `u = ln(x)` then `u' = 1/x`       `v = sqrt(x)` or `x^(1/2)` then `v' = 1/(2sqrt(x))` Applying the Quotient rule, we get: `f'(x) = (1/x*sqrt(x)-1/(2sqrt(x))*ln(x))/(sqrt(x))^2`            `= (1/sqrt(x) - ln(x)/(2sqrt(x)))/x`            `= ((2-ln(x))/sqrt(x))/x`           ` =((2-ln(x))/sqrt(x))* 1/x`           `=(2-ln(x))/(xsqrt(x)) `  or `(2-ln(x))/x^(3/2)` Note that `2-ln(x) lt0` ...

T. becomes leader when he suggests destroying Old Misery’s house and the group votes to do it.   The story takes place after World War II, where a group of misfit teenagers meet in a carpark to make trouble. Their leader is a boy named Blackie. The gang is joined by Trevor, who is called T. He should be ostracized because his parents come from money, but he has an air of mystery. They boys do not tease him.  T.’s rise to power comes with the information he has about Old Misery. Old Misery is a grumpy old man with a big house that needs repair from the war. Old Misery is trying to do it himself. The house doesn’t even have operational plumbing. On the day the group is voting what to do, T. is late and it turns out he was looking at the house. He tells them it is beautiful, and proposes they destroy it for their next project.  Blackie is opposed to the plan. He doesn't think it is possible for a dozen boys to do. T. disagrees, and suggests it be put to a vote. It is voted on, and T. ...

The scorpion’s significance is clear, because it sets the story moving.  The baby is threatened, and the family wants money to go to a doctor.  Soon after, Kino finds a pearl.  However, the scorpion also symbolizes evil.  It represents all of the threats to the family that lurk for Kino.  Consider Kino’s reaction to the sting. He threw it down and beat it into the earth floor with his fist, and Coyotito screamed with pain in his box. But Kino beat and stamped the enemy until it was only a fragment and a moist place in the dirt. His teeth were bared and fury flared in his eyes and the Song of the Enemy roared in his ears. (Ch. 1)  While Juana has the presence of mind to treat the scorpion’s sing with home remedies, Kino keeps beating the scorpion into the dust even after it is dead and no longer poses a threat.  It represents all of his fears, and demonstrates how little control he has over his temper.  The canoe is a significant symbol because it is Kino’s heritage and also his livelih...

Contemporary art should, one might argue, continue to be influenced by the classical past while experimenting with the new. To draw a distinction between ancient and modern forms is in fact impossible, as modern forms are inspired by classical forms.  For example, as the Ted-Ed talk whose link is below explains, the pioneers of the modern art movement drew on ancient art for inspiration. Both Picasso and Matisse were inspired by an ancient African mask from the Ivory Coast. Picasso went on to explore African masks and to copy ancient forms in his art. For example, his painting of five nude women, Demoiselles d'Avignon (1907), included two women whose faces were modeled on ancient African masks. Its sense of space and shapes were primitive, and yet the painting was celebrated as one of the first masterpieces of the 20th century. Modigliani was another artist who was inspired by ancient African art, and British sculptor Henry Moore drew on ancient Toltec forms to craft his modernist...

The proper name for seed cone is megastrobilus (plural form is megastrobili), but it is also known as a female cone. The proper name for pollen cone is microstrobilus, but it is also known as a male cone. Pollen cones tend to be located on the lower branches. They survive just long enough to release pollen. Since they wither, there is little evidence of their existence after pollination. They also tend to display less structural variation than seed cones among different species. When people imagine conifer cones, they are most likely thinking of seed cones. Seed cones are both larger and longer lived than pollen cones. After pollination, megastrobilus scales will both harden and darken. They are the ones you find on the ground around conifers. Due to their structural variation, they are often used to identify different species.

According to Karl Marx, commodity fetishism occurs when an object holds significance or social power beyond its utility. An object becomes a commodity when it carries some social significance beyond its use-value, and the fetishism of these commodities is a reflection of the social relations surrounding the production and consumption of that object. The term fetishism is borrowed from anthropology and describes an otherwise mundane object which is perceived to have some special, even supernatural, quality about it. Through commodity fetishism, members of an economic unit (the producers and consumers) come to understand each other in relation to the money and goods exchanged.  Consider the following: many people in modern society define themselves in relation to the goods they interact with, or use goods to assert their identity. Consumers aren't just purchasing a table, a pair of shoes, or a set of dinner plates. Through their purchase, they are engaging in self-narrative; they bec...

The French, British, and Spanish encountered the Native Americans when they established colonies in the Americas. However, only the French had a good relationship with the Native Americans. The French treated the Native Americans well. They traded with them. They made it clear they didn’t want to take away their land. They also learned the languages of the Native American tribes. In addition, they married the Native Americans. There was respect between the French and the Native Americans. The British and Spanish didn’t have a very good relationship with them. These countries wanted to take away the land of the Native Americans. The Spanish enslaved them and exploited their land for minerals. They also tried to convert them to Christianity. The Native Americans resented these actions. The British viewed the Native Americans as inferior. The British tried to impose their laws upon them. This also led to poor a relationship with them. The French had a good relationship with the Native Ame...

George Hadley bought an expensive Happylife Home that is fully automated, to the point where his wife feels the house is raising her children more than she is. The feature that concerns them most is the nursery, because it is telepathic in addition to being automated.  The children can control the nursery, and the parents do not like what they see. The nursery has dangerous animals from Africa. George also finds his old wallet in there, covered with lion drool, and doesn’t know how it got there.  "I don't know anything," he said, "except that I'm beginning to be sorry we bought that room for the children. If children are neurotic at all, a room like that—" "It's supposed to help them work off their neuroses in a healthful way."  George isn’t convinced. He brings in a psychologist to evaluate his children, who tells him the children are seriously damaged and he should tear the room down and bring them in every day for treatment. This surprises G...

Prejudice is a negative opinion about a person or group of people that is not based on actual experience. Discrimination occurs when a person acts on their prejudice. The development of prejudice can occur in many different ways. Research has shown that individuals may develop prejudice as an attempt to build self-value when a person's self-esteem is threatened. This can occur in two ways. Individuals may ally themselves with a winning/ dominant group against a losing/ minority group. Alternatively, individuals may act on their prejudice on a person-to-person basis as an active manifestation of their belief that they are inherently better than the other person, discriminating to boost their self-esteem. When people experience an event that causes a drop in their self-esteem, they become more likely to act on prejudice in order to rebuild their self-esteem. For example, in the 1980s, Detroit autoworkers discriminated heavily against Japanese people after suffering widespread job los...

Juana trusts the doctor when she shouldn't. Juana’s greatest weakness is that she is too trusting.  She tries to get the doctor for her baby.  When Coyotito is attacked by the scorpion.  Kino panics, grinding the scorpion into dust instead of helping the baby.  Juana, on the other hand, takes action.  She sucks the poison out of the wound. It never occurs to most people in their village to call for a doctor, but Juana does.  The word was passed out among the neighbors where they stood close-packed in the little yard behind the brush fence. And they repeated among themselves, "Juana wants the doctor." A wonderful thing, a memorable thing, to want the doctor. To get him would be a remarkable thing. (Ch. 1)  This is a mistake because the doctor does not have the best interests of the people at heart.  He considers them animals, not people.  When he learns that Kino has no money, he pretends to not be home.  Then, when he learns that Kino has found a gigantic pearl, he sudden...

Helen Stoner is a typical young middle-class Victorian woman. She has always led a sheltered, protected, domestic life. She comes to Sherlock Holmes because she wants guidance. The fact that she is so frightened and helpless appeals to the compassionate side of Holmes' nature. He will help her even though she can't afford to pay him. Her stepfather, Dr. Grimesby Roylott, controls most of her resources. Helen Stoner might be termed "a maiden in distress." Holmes often gets involved with young women who are in need of help. His desire to help them provides his motivation which drives the story. Other examples of maidens in distress in Sherlock Holmes stories can be found in: "The Adventure of the Solitary Cyclist," "The Adventure of the Copper Beeches," and "A Case of Identity." Helen Stoner is not a particularly well-rounded character. She serves mainly to involve the great detective in a perplexing case. She also gives Holmes a great deal...

A trade discount is offered in a business setting and facilitates a reduction in the cost of goods and services purchased by a company. Trade discounts are typically offered within a specified timeframe, for example, two weeks or six months depending on the size of the outstanding balance. If this timeframe passes without payment, the company is expected to pay the undiscounted, outstanding balance. One of the main reasons why firms offer trade discounts is to encourage debtors to clear their outstanding balances quickly. When debtors owe sums for extended periods of time, the likelihood of bad debts (debt that is uncollectible) increases significantly. Therefore, creditors incentivize debtors with trade discounts in order to ensure debtors pay off their outstanding balances quickly after receiving the goods and services. Another reason why firms offer trade discounts is to foster brand loyalty. Trade discounts increase the purchasing power of the debtor—that is, the debtor is able to ...

The primary goal of the Crusades was to recapture the Holy Land from the Muslims. The Holy Land referred to Palestine (the region of Western Asia where Israel had been located), and Christians believed it was holy because Jesus had lived and been crucified there. Moreover, the Church held that Jerusalem was the birthplace of Christianity. Consequently, the Holy Land contained many important religious sites; for instance, Helena--Emperor Constantine's mother--had built a church at the location she believed Christ had been crucified. However, Muslims had invaded Palestine during the 7th and 8th centuries and had taken over all the holy sites. By the time of the First Crusade, the Muslims were also threatening the Byzantine Empire and Constantinople--the headquarters of the Eastern Church. The Crusades were meant to reverse the Muslim advance, preserve Christendom, and reclaim the Holy Land.

It is established early on in John Steinbeck's novella Of Mice and Men that Lennie has a fixation with petting soft things. Throughout the novel he incessantly refers to the rabbits he will "tend" when he and George get their farm. In Chapter One he is carrying a dead mouse in his pocket. He tells George that he didn't kill it and "found it lyin' right beside the road" but George claims that Lennie "broke it pettin' it." Unfortunately, Lennie doesn't know his own strength and is usually lethal to any animal he gets his hands on. The incident with the mouse proves to foreshadow the events in Chapter Five when Lennie is seen with a dead puppy. Like the mouse, Lennie has basically killed it with affection. He tells Curley's wife, "I was jus' playin' with him...an' he made like he's gonna bite me...an' I made like I was gonna smack him...an'...an' I done it. An' then he was dead." When Curley...

The idea of reawakening the artistry and culture of the past and giving new energy to the creative and inquisitive spirit of people is, indeed, one that inspires many. The Renaissance imagery and philosophy of cultivating man's interest and talents as a viable measure of culture and scientific advancement brought human beings out of the stagnation of the Middle Ages and revived the creative spirit, a spirit that is intrinsic to progress. A representative of the new thinking of the Renaissance, Giovanni Pica della Mirandola declared that God made man and woman to know the laws of the universe, to appreciate its beauty, and to be in awe of its greatness. In addition, God gave human beings the freedom of will and the ability to love. Mirandola further declared, ...the Creator [said] "I created thee a being neither heavenly nor earthly, neither mortal nor immortal only that thou mightest be free to shape and to overcome thyself. Thou mayest sink into a beast or be born anew to the...

In Chapter 15, Atticus travels to the Maycomb jailhouse and sits outside of Tom Robinson's cell just in case an angry mob attempts lynch Tom before the trial. Sure enough, several dusty old cars arrive from the Meridian Highway, and a group of men get out of each car. Scout, Jem, and Dill secretly watch as the Old Sarum bunch surrounds Atticus. Walter Cunningham, the leader of the mob, tells Atticus to step aside. Atticus refuses to move because he knows that group of men want to harm Tom Robinson before the trial. In an attempt to hear their conversation, Scout runs out into the group of strangers and feels embarrassed. Unaware of the serious situation she has entered, Scout looks for a familiar face. She eventually gets the attention of Walter Cunningham, who realizes the error in his decision to intimidate Atticus in order to harm Tom Robinson. Walter then tells the rest of the Old Sarum bunch that it's time to go home, and Tom Robinson remains unharmed. 

First, while Macbeth is offstage murdering Duncan, Lady Macbeth speaks to herself alone on stage, saying, "Had he not resembled / My father as he slept, I had done 't" (2.2.16-17).  Lady Macbeth had prayed to become ruthless and remorseless, and yet, she still seems to retain some compunction: she could not murder Duncan herself because he looked too much like her father.  In this way, then, she seems to retain some sympathy in her person, some respect for human life, because she finds that she is unable to take it when the chips are down. Later, in her sleepwalking scene, we see Lady Macbeth's guilt for the lives she and her husband have taken on full display because she is asleep and cannot control her behavior or speech.  She seems to relive, in part, the night of Duncan's murder, crying, "who would have thought the old man / to have had so much blood in him?" (5.1.41-42).  She believes that his blood still lingers on her hand, a symbol of her terribl...

In Viola’s soliloquy when Malvolio gives her the ring, she reflects on the concept of appearance versus reality.  There are a lot of deceptions and confusions going on here.  Viola realizes that Olivia has fallen in love with her male character, Cesario.  She is kind of surprised at this, and a little impressed.  It means that she has done well disguising herself as a man, but has failed at her task of wooing Olivia for her boss, Orsino.  That’s fine for her because she is secretly in love with him. Viola feels bad about Olivia being in love with her, when she is actually a woman.  Olivia’s reality is so far different from the real reality, and it is all because of the appearance that Viola is perpetrating. She loves me, sure; the cunning of her passion Invites me in this churlish messenger. None of my lord's ring! why, he sent her none. I am the man: if it be so, as 'tis, Poor lady, she were better love a dream. Disguise, I see, thou art a wickedness, Wherein the pregnant enem...

Shakespeare's most famous tragedy enjoys the rare distinction of sustained popularity. While the play owes its consistent relevance to several factors, I'd like to highlight a few specific ones. First of all, the play's plot and characters wrestle with universal questions and problems that remain relevant across generational divides. Hamlet proves to be a particularly enigmatic figure, as he struggles to come to terms with his mother's marriage to his uncle, his vow to avenge his father's murder, and his increasingly distressing suicidal impulses. Furthermore, readers continue to debate whether or not Hamlet is crazy, and so the protagonist's questionable sanity lends an intriguingly ambiguous and complex layer to not only the character, but to the plot of the play. It helps that Shakespeare renders all of these components in rich poetry, as the musicality of the language makes the already compelling material even more memorable. The famous "To be or not to...

(A) Momentum must be conserved in the collision, so the final total momentum of both carts must be the same as the initial momentum of the first cart: `m_1 v_{1i} + m_2 v_{2i} = m_1 v_{1f} + m_2 v_{2f}` `(45 kg)(24 m/s) + (0) = (45 kg)(12 m/s) + (28 kg) v_{2f}` One equation, one unknown, so we can solve. `540 kg*m/s = (28 kg) v_{2f}` `v_{2f} = 19.29 m/s` Everything is given in two significant figures, so this is our final answer for the velocity: `v_{2f} = 19 m/s` (B) The impulse delivered to the second cart is just the difference between its initial momentum (zero) and its final momentum, so it is just the final momentum, which is 540.12 kg*m/s, or 540 kg*m/s in two significant figures.

Atticus' decision to defend Tom Robinson affects his family, friends, and community. Scout and Jem are ridiculed for their father's decision to defend an African American and are continually made fun of by their community members throughout the novel. Mrs. Dubose, Cecil Jacobs, and Francis Hancock all make derogatory remarks to Scout about her father defending Tom. Scout and Jem have to learn to maintain their composure and exercise tolerance towards their ignorant community members. Aunt Alexandra comments to her grandson that Atticus is ruining the family and is even subjected to criticism on Atticus' behalf during her missionary circle. Calpurnia is also affected by Atticus' decision to defend Tom and becomes directly involved with the case because she is part of the African American community. She acts as the intermediary between the black and white communities throughout the novel. Miss Maudie is forced to keep her opinions to herself and silently supports At...

In Chapter 27 of Red Harvest, Reno Starkey confesses to the murder of Dinah Brand. Accordingly, the story is set in a small town, Personville, which has been overrun by rival groups of gangsters. Donald Willsson, a newspaper publisher, had originally hired The Continental Op, a private detective, to take down the four rival crooks who were running the town. However, Donald is murdered before he gets to meet with The Continental Op. Determined to discover the identity of Donald's murderer, The Continental Op sets to work. He discovers that Personville is actually under the control of four rival factions, each headed by an unscrupulous leader: Lew Yard, Pete the Finn, Max Whisper Thaler, and Noonan. While Pete the Finn is a bootlegger, Thaler owns a gambling joint, Noonan is the police chief of Personville, and Lew Yard owns a business dealing in stolen goods. All four turn Personville into a killing zone riddled with dead bodies. Basically, the Continental Op takes advantage of the...

Londoners faced terror and devastation from the Blitz.  For weeks straight and over a period of years, bombs were dropped by German planes over London.  Many people fled to the countryside.  The constant fear of hearing air raid sirens and low planes flying overhead caused psychological damage in some people.  People developed anxieties. Mrs. Drover and her family left their London home because of the Blitz.  She returned one day to her abandoned house to fetch a few items.  Once there, she found a strange letter.  It was supposedly from her former lover, a man who was presumed dead long ago.  He had been an ominous fellow.  He had cut her hand many years before, and she still bore the scar.  Mrs. Drover instinctively looked for the weal left by the button on the palm of her hand ("The Demon Lover"). In the letter, her former lover promised to meet Mrs. Drover on that day, and she dreaded such a meeting.  She quickly left her house.  She found a taxi cab and got into it.  It ...

The four components of GDP (Gross Domestic Product) are personal consumption (C); investment (I); net exports (NX); and government expenditures (G). During the recession of 2007 to 2009, the component of AD (aggregate demand) that declined the most was private investment (see Google doc in the links below).  Government expenditures rose during the recession, as Obama spent government money on stimulus plans and on unemployment payments. Personal consumption also stayed relatively stable (though orders of durable goods fell as the recession went on). Net exports actually stayed stable or rose in 2007 and did not fall until the fourth quarter of 2008 and into 2009. Since the Great Recession, as the recession of 2007-2009 is called, net investment as a proportion of the GDP has declined to its lowest levels since the 1930s. Experts believe that the decline in investment demand is because of excess capacity, weak expectations of sales in the future, and shifting investment overseas (see th...

`(ds)/(d alpha) = sin^2(alpha/2)cos^2(alpha/2)` To solve, express the differential equation in the form N(y)dy = M(x)dx . So bringing together same variables on one side, the equation becomes `ds =sin^2(alpha/2)cos^2(alpha/2) d alpha` To simplify the right side, apply the exponent rule `(ab)^m=a^mb^m` . `ds =(sin(alpha/2)cos(alpha/2))^2 d alpha` Then, apply the sine double angle identity `sin(2 theta)=2sin(theta)cos(theta)` . `sin (2*alpha/2)=2sin(alpha/2)cos(alpha/2)` `sin(alpha)=2sin(alpha/2)cos(alpha/2)` `sin(alpha)=2sin(alpha/2)cos(alpha/2)` `(sin(alpha))/2=sin(alpha/2)cos(alpha/2)` Substituting this to the right side, the differential equation becomes `ds = ((sin (alpha))/2)^2 d alpha` `ds = (sin^2 (alpha))/4 d alpha` Then, apply the cosine double angle identity  `cos(2 theta)=1-2sin^2(theta)` . `cos (2alpha) = 1 - 2sin^2(alpha)` `2sin^2(alpha) = 1-cos(2 alpha)` `sin^2(alpha) = (1-cos(2 alpha))/2` Plugging this to the right side, the differential equation becomes `ds = ((1-cos(2 a...

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...

There isn't a definitive number of years that it would take for the environment to return to "normal" if all usage of fossil fuels stopped immediately.  There are too many variables at work to give a specific number of years.  What is definite is that it would take a long time  for the environment to return to pre-Industrial Revolution levels.   The reason is that even if we completely stopped fossil fuel usage, the carbon emissions that have already been released stay in the atmosphere, oceans, plants, and animals for  thousands  of years.  It would take many millennia for that carbon to make its way back into Earth's rocks, minerals, etc.   But what about rising temperatures?  Would the temperature stabilize if all fossil fuel emissions ceased?  The short answer is no.  Scientists believe that there is a 40 year delay between current carbon emissions and the related temperature increase.  This delay is called "climate lag."  The lag is present because of E...

Algernon and Charlie undergo the same operation to enhance their intelligence. Charlie is the first human subject of this experiment and by watching the changes in Algernon's intelligence and behavior he is better able to understand his own progress after the operation.  Sadly, once Charlie figures out that the operation will eventually self-reverse, Algernon's mental capacity begins to deteriorate before his own, providing Charlie with a grim preview of what is in store for him.  Algernon's behavior, along with Charlie's, becomes more and more erratic.  Eventually Algernon dies, while Charlie fully regresses back into his original mental retardation.  However, Charlie is still able to remember what happened.  Unable to bear the emotional pain this causes him, he checks himself into a state facility where no one knows about the experiment.  In a final letter to Alice he asks her to put flowers on Algernon's grave.

The seemingly utopian society that Lois Lowry creates in  The Giver is based upon the principle of Sameness. The Committee of Elders controls every aspect of a person's life, including everything from what they wear to how many children they are permitted to have. Citizens in Jonas' community have every aspect of their lives planned out for them; choice does not exist in their lives. The function of Sameness in the novel invites readers to examine their own thoughts and opinions about what would happen in their lives if choice was removed.  The idea of not having to make choices in life does seem rather appealing, especially in the lives of young adults and college students, as many important choices and decisions occur during this point in a person's life. It would certainly seem convenient to have a person act as a guide down each path without having to worry about a thing. However, the absence of choice most certainly has its downfalls. It is up to each reader to examin...

In poetry, a "foot" is a measure of syllabic meter and stress that includes two syllables. Let's do as you requested and separate the feet within this excerpt from the poem with bold vertical lines: Him STILL   |  must SERVE,   |  him STILL  |  oBEY, And NO-   |  thing ACT   |  and NO-   |  thing SAY, But WHAT   |  her HAUGH-   |  ty LORD   |  thinks FIT, Who WITH   |  the POWER   |  has ALL   |  the WIT. You will also notice that I have placed some words (or parts of words) in all caps while leaving other words without this emphasis. I did this to help you note the pattern of stresses within these four lines. Normally we would "scan" a poem with the use of markings--a small "u" over syllables that are unstressed and an accent or slash ("/") over syllables that are stressed. However, since we are typing this out rather than handwriting the scansion, this is the easiest way to convey the stresses. Unstressed syllables have been lef...

`inttan^3(pix/2)sec^2(pix/2)dx` apply integral substitution: `u=(pix)/2` `=>du=(pi/2)dx` `=>dx=(2/pi)du` `inttan^3(pix/2)sec^2(pix/2)dx=inttan^3(u)sec^2(u)(2/pi)du` Take the constant out, `=(2/pi)inttan^3(u)sec^2(u)du` Again apply integral substitution: `v=tan(u)` `=>dv=sec^2(u)du` `=2/piintv^3du` Apply the power rule, `=2/pi(v^(3+1)/(3+1))` `=2/pi((v^4)/4)` Substitute back `v=tan(u)`  and `u=(pix)/2` `=1/(2pi)tan^4((pix)/2)` Add a constant C to the solution, `=1/(2pi)tan^4((pix)/2)+C`

Great question! This rule of grammar is one that stumps many people, so I am glad you've asked. The difference between apostrophe+S ('s) and  just  the letter S is a matter of the meaning you are trying to convey. The apostrophe+S form is  possessive,  meaning that it describes ownership of something. The S only form is a  pluralization,  meaning there is more than one of something. Let's take a look at an example. I'll use similar sentences to describe the possessive form, the plural form,  and  the possessive plural form! "The cat's meow." In the above statement, I have used the possessive form of apostrophe+S. A great way to figure out whether or not to use the possessive apostrophe+S is to think about whether there is a relationship of ownership going on. In this case, the meow doesn't really "belong" to the cat in the sense that the cat owns an object, but the cat is responsible for the meow. Typically, the word which may be altered by t...

Seamus Heaney's "Digging" refers both to the menial labor performed by the speaker's ancestors, which forms the ostensible subject of the poem, and the labor of writing poetry in which the speaker himself is engaged. The poem expresses the speaker's awe at and distance from the hard work and implicit masculinity of previous generations of men, and simultaneously claims a similar usefulness and importance for his own literary vocation. Structurally, the poem begins and ends by calling our attention to the pen in the hand of the speaker as he writes a poem—presumably the one we're reading. These references bracket the main action of the poem—the physical work of first the speaker's father and grandfather. Heaney's description of their digging is replete with imagery that emphasizes the difficulty of their tasks; the men are "straining" (l.6), "stooping" (l.8), "nicking and slicing" and "heaving" (l.22). Perhaps eve...

Scout wears a dress to Aunt Alexandra's missionary tea party in chapter 24. She mostly attends the party because Jem and Dill go skinny-dipping and it wouldn't be appropriate for her to be with them while they are undressed. So, in the monologue, Scout could grumble about missing out on swimming in the beginning. Then Scout offers to help Calpurnia and takes in a coffee pitcher to the women. This is when Aunt Alexandra invites her to sit down with them. There are two paragraphs where Scout describes the women's clothing and make-up which would be fun for a monologue. For example, Scout wonders, "why ladies put on their hats to go across the street" (229). She also explains that she controls herself by "tightly gripping the arms of the chair, and waited for someone to speak to me" (229). These phrases could be adapted to show how Scout not only notices a lot from her childlike perspective, but also does her best to blend in. Next, you could mention the fa...

An irregular solid can be measured using a technique called   water displacement . When a solid object is placed in water, the amount of water that is displaced by the object is equal to the volume of the object.  For example, we can determine the volume of a small rock as follows: Fill a graduated cylinder with 20 mL of water. We'll call this the  initial volume of the water. Carefully add the rock to the water in the graduated cylinder. Whenever you place an object in a graduated cylinder containing water, the volume level of the water goes up. Let's say that after we added the rock, the volume of the water increased to 27.5 mL. We'll call this the  final volume of the water . The volume of the rock is equal to:         final volume of water - initial volume of water Therefore,          27.5 mL water - 20 mL water = 7.5 mL The rock has a volume of 7.5 mL.

Recall that the  Divergence test follows the condition: If `lim_(n-gtoo)a_n!=0` then sum `a_n` diverges. For the given series `sum_(n=1)^oo ln(1/n)` , we have `a_n = ln(1/n)` . To evaluate it further, we may apply Law of exponent: `1/x^n = x^-n` . `a_n = ln(1/n)` is the same as  `a_n = ln(1/n^1)` Then, `a_n = ln(n^(-1))` .  Apply natural logarithm property: `ln (x^n) = n *ln(x)` . `a_n = (-1) *ln(n)` or `a_n = -ln(n)` Applying the divergence test, we determine the limit of the series as: `lim_(n-gtoo) [ -ln(n)] = -lim_(n-gtoo) ln(n)`                             `= - oo` Conclusion: The limit value (L) being `-oo` implies that the series `sum_(n=1)^oo ln(1/n)` is  divergent.  We can also verify with the graph of `f(n) = ln(1/n)` : As the "`n` " values increase, the function value decreases to negative infinity and does not approach any finite value of L.

The benefit of turning Seven is becoming more independent because you get a front-buttoned jacket. In Jonas’s community, the children are raised collectively until the age of One. This means everyone turns the same age at the same time in December. Jonas’s little sister Lily is about to become an Eight when the book begins. Since Lily is still a Seven, Jonas reminds her of the benefits of turning that particular age. "There are good things each year," Jonas reminded her. "This year you get to start your volunteer hours. And remember last year, when you became a Seven, you were so happy to get your frontbuttoned jacket?" (Ch. 6)  Clothing is used to designate children by age and adults by occupation. Lily’s new jacket had a “row of large buttons that designated her as a Seven,” while younger children wear jackets with buttons on the back so they have to help each other get dressed. This is designed to teach them interdependence. Relying on others is a foundation of t...

In Nadine Gordimer's story "Once upon a Time," the grandmother is surprisingly referred to as "that wise old witch." Nevertheless, the parents believe the grandmother has the entire family's best interests at heart, and they follow her advice when she tells them "not to take on anyone off the street" as a household employee. Later in the story, the grandmother helps the parents increase the height of the wall around their home by giving them bricks for Christmas. She also gives her grandson "a Space Man outfit and a book of fairy tales." The parents no doubt appreciated these gifts and took them as evidence that the grandmother cared for them and their son. The gardener, on the other hand, is referred to as "itinerant," meaning he is not as steady a fixture in the family like the housemaid is. Still, he comes "highly recommended by the neighbors," so he is trustworthy. Because his duty is to care for the grounds, not t...

The scenes where this theme is most obviously explored are those involving the caskets.  These are Act 2, Scenes 1, 7, and 9; and Act 3, Scene 2.   Portia is an heiress.  Her father, before he died, stipulated in his will that his daughter's husband should be chosen by a trial of caskets.  Each hopeful suitor is shown three "caskets" (small chests) and is asked to choose one to open.  If he opens the one that contains the picture of Portia, he can marry her.  One casket is of lead, one of silver, and one of gold, and each has a cryptic riddle that goes with it.   In Act 2, Scene 1, the prince of Morocco arrives to try his luck.  With his first words, he asks Portia not to dislike him because of his dark skin, pointing out that he has blood as red as any white man's.  In Scene 7, the prince chooses the gold casket, only to find it is the wrong one.  Inside it is a poem that contains the famous line, "All that glisters is not gold."  In Scene 9, the prince of ...

Here's the passage from the novel in question; as you can see, the characters never mention a specific psychologist's name: "Excuse me, excuse me; of course it would be rather difficult for Katerina Ivanovna to understand, but do you know that in Paris they have been conducting serious experiments as to the possibility of curing the insane, simply by logical argument? One professor there, a scientific man of standing, lately dead, believed in the possibility of such treatment. His idea was that there's nothing really wrong with the physical organism of the insane, and that insanity is, so to say, a logical mistake, an error of judgment, an incorrect view of things. He gradually showed the madman his error and, would you believe it, they say he was successful? But as he made use of douches too, how far success was due to that treatment remains uncertain.... So it seems at least." Although we can't say for certain, Lebeziatnikov and Raskolnikov may have been dis...

In "The Signal-Man," Dickens creates tension through the descriptions of the setting and the characters. The signal-box, for example, is described as being a "solitary and dismal place" with an "earthy, dead smell" and "barbarous, depressing and forbidding air." This almost claustrophobic setting is combined with the description of the signalman himself: he is so dark and mysterious that the narrator thinks he might be a ghost: The monstrous thought came into my mind…that this was a spirit, not a man. This contributes to the tense atmosphere because it suggests that there is more to the signalman than the narrator has anticipated. It is also significant as Dickens' first allusion to the supernatural.  In addition, Dickens uses foreshadowing to build tension by hinting at the tragic events to come. This begins early in the story, for instance, when the signalman and the narrator first meet: Just then there came a vague vibration in the earth a...

De Beauvior's premise is that sex, for women, is always about becoming "prey" for the man. Sex is always about the objectification of women by men; men are "active" in that they seek to penetrate the woman; women are "passive" in that they are receptacles for male desire. In this way all sex is a kind of rape; women, by virtue of their anatomy, are required to undergo violation. De Beauvoir traces how this objectification is manifest in the psychology of women, with sections dealing with the awakening of desire, loss of virginity, and frigidity. There is a kind of doubleness in feminine sexuality that comes from, on the one hand, the clitoris as the center of sexual pleasure, and, on the other, the vagina as the center of biological reproduction. Perhaps the most memorable section of the chapter, if one can be singled out, is her attempt to distinguish the nature of feminine sexual pleasure from male pleasure. Male pleasure is finite, and has a definit...

Your post presents two distinct ideas regarding William Shakespeare's tragedy  Hamlet . I'll address each individually:  Compare Laertes and Hamlet as sons.  Hamlet and Laertes have a startling amount in common, which is not immediately apparent to the reader given Hamlet's immediate presentation as somewhat insane, which contrasts sharply against Laertes' apparent success and composure. However, each son is desperately loyal to his father, which in turn motivates many of their respective actions. Where the two men differ is in their philosophical reflection; Laertes, upon the news of first his father's and then Ophelia's deaths, is intent on revenge. This is unlike Hamlet, who agonizes over the certainty of his father's killer's identity, the morality of revenge, and the mortality of man.  What is the nature of Claudius' questions?  I'm assuming you're referring to IV.vii, in which Claudius asks Laertes a series of questions. His questions a...

I can explain the explanation, though I am not convinced that it is correct in all its aspects. The explanation is based on the assumption that India will only export goods that it does not need.  That is, it assumes that India will not import anything if there is still unfulfilled domestic demand for that good.  For example, this assumes that India will not export any rice until all domestic buyers have been able to purchase as much as they want.  While I do not agree with this assumption, it is the basis for the explanation. So, we are assuming that India will only export goods that it does not need at home.  Therefore, there is no way that exporting will lead to shortages.  If India satisfies, for example, its domestic demand for rice, then no shortages can occur if it exports the rest of the rice.   India is only exporting things that it does not need at home.  This is why Argument II is invalid.  When India exports goods, it gains foreign currency.  The countries that buy the Indi...