Notes

After reading Langston Hughes’ short story “Thank You, M’am,” the statement, “Family integration is important to raise children soundly,” is validated. It is eleven o’clock at night, in the middle of the city, when Roger, an unkempt, young man resorts to thievery in order to get money for a pair of shoes. The victim of his failed robbery attempt is Mrs. Louella Bates Jones Washington, a proud, astute woman on her way home from work. When she has him in her grip she asks him if there is anyone home to remind him to wash his face. He replies there is not. She tells him that if he were her son, she would at least make him wash his face. After she drags him back to her rooming house, she directs him to wash up, while leaving her purse on the bed where he could reach it and run. The two have a heart to heart talk in which Mrs. Jones reveals some of her past to him, but does not embarrass him by asking questions about his home and family life. In spite of her past transgressions, Mrs. Jones ...

Sodium reacts with water to form sodium hydroxide and hydrogen gas. The well balanced chemical equation for this reaction can be written as: `2Na (s) + 2H_2O -> 2NaOH (aq) + H_2 (g)` Using stochiometry, 2 moles of sodium reacts with 2 moles of water to form 1 mole of hydrogen gas and 2 moles of sodium hydroxide. Here, we have 90 g of sodium and 80 g of water. The molar masses of these two species are 23 g and 18 g. Moles of sodium = 90 g / 23 g/mole = 3.913 moles moles of water = 80 g / 18 g/mole = 4.444 moles Since 2 moles of sodium reacts with 2 moles of water or 1 mole of sodium reacts with 1 mole of water, 3.913 moles of sodium will react with 3.913 moles of water and hence water is in excess. Left over amount of water = 4.444 - 3.913 mole = 0.531 moles  = 0.531 moles x 18 g/mole = 9.56 g of water. Thus, 9.56 g of water will be let over. Since 2 moles of sodium produces 1 mole of hydrogen, 3.913 moles will produce 3.913 x 1/2 moles = 1.96 moles of hydrogen. At STP, 1 mole of a ...

Recall that indefinite integral follows `int f(x) dx = F(x) +C` where: `f(x)` as the integrand function `F(x)` as the antiderivative of `f(x)` `C` as the constant of integration.  For the given  integral problem: `int x^2 sin(x) dx` , we may apply integration by parts :` int u *dv = uv - int v *du.` Let: `u = x^2`  then `du =2x dx`   `dv= sin(x) dx` then `v = -cos(x)` Note: From the table of integrals, we have `int sin(u) du = -cos(u) +C` . Applying the formula for integration by parts, we have: `int x^2 sin(x) dx= x^2*(-cos(x)) - int ( -cos(x))* 2x dx`                               `= -x^2cos(x)- (-2) int x*cos(x) dx`                               `=-x^2cos(x)+2 int x *cos(x) dx` Apply another set of integration by parts on `int x *cos(x) dx` . Let: `u =x` then `du =dx`        `dv =cos(x) dx` then `v =sin(x)` Note: From the table of integrals, we have` int cos(u) du =sin(u) +C` . `int x *cos(x) dx = x*sin(x) -int sin(x) dx`                               `= xsin(x) -(-cos(x))`        ...

One can find apostrophe, metonymy, and possibly synecdoche in this poem by Emily Dickinson. Apostrophe is a dramatic or formal address, often to an inanimate object, such as , "O Life!" However, it can be a kind of exclamatory address to someone absent. So the "Sir" in line one is an apostrophe, as is "Sire" in the first line of the last stanza. Metonymy names a thing by using something associated with it. In this poem, in the last stanza, the speaker is referring to the sun, but she names it "Sunrise." The idea is that a person is able to see simply because the sun produces light. In the same way, the speaker loves her lover simply because he produces those spontaneous feelings in her. Synecdoche is harder to get from this poem. With synecdoche, a thing is named for one of its parts. One might think about the "Eye" being a synecdoche for the whole person, but that doesn't seem to be what Dickinson wants to say here. She seems to wa...

Martin Luther became a heretic according to the Catholic Church when he posted his  Ninety-Five Theses  on the church doors at Wittenberg. It was a common practice to post an academic challenge for others to read on the community bulletin board, i.e., the church doors. At the same time Luther posted his Theses , he sent a copy and a letter to the archbishop who passed the Theses on to the councillors at Aschaffenburg (later known as the University of Mainz). Considering the Ninety-Five   Theses heretical, the councillors sent a copy to the pope, i.e., the Bishop of Rome.   As was customary in academic circles of the 16th century, John Tetzel proposed his own anti-theses to Luther’s “innovations” in opposition to the “traditional teachings of the church.” To defend his Ninety-Five Theses from Tetzel’s anti-theses, Luther wrote the Resolutiones , which he sent to Bishop Scultetus of Brandenburg. Bishop Scultetus recommend that Luther keep silent and abstain from further writing on the...

Nick is related to old money because he is Daisy's cousin. Like Tom, Daisy comes from a wealthy background and might be considered a "Kentucky Blueblood." Importantly, however, Nick's own nuclear family is not old money or new money. His family background is probably better labelled as "upper middle class." In discussing his family, Nick first mentions the moral upbringing he received as a prominent facet of his family life. This moral component of his background is foundational to themes of the work and to the commentary the novel presents regarding ambition, wealth and the American Dream. After establishing his moral inheritance, Nick then goes on to share the fact that his family is well-off but that his father also works for a living (in contrast to Tom and Daisy, who have so much money they do not need to work).  Nick boasts a bit about his roots: "My family have been prominent, well-to-do people in this Middle Western city for three generations....

Given , `y' - y = e^xroot3(x)` ----------(1) this equation is already in linear form of first order ,so this is of the form `y' +Py=Q` ------------(2) then the general solution `y=((int (I.F) (Q) dx)+c)/(I.F)` where I.F is the integration function =` e^(int p dx)` so on comapring the equations (1) and (2) we get, `P =-1 ,  Q= e^xroot3(x)` so the `I.F = e^(int p dx) = e^(int -1 dx)= e^(-x)` now the general solution is `y=((int (I.F) *Q dx )+c)/(I.F)` =>`y= ((int (e^(-x)) (e^xroot3(x)) dx)+c)/(e^(-x))`  `= (int root3(x) dx + c)/e^(-x) ` `= ((x^(4/3))/(4/3) +c)/(e^(-x))` `=((x^(4/3))/(4/3) +c)*e^(x)` is the general solution.

This reference appears in the opening pages of “Three Men in a Boat.” The narrator recalls a time when he went to the British Museum to discover a treatment for hay fever. He searched through a medical book for the answer, and then began to turn pages at random to read up on other ailments. To his horror he found that he had the symptoms of almost every disease or malady that was listed. At first he thought this status would make him a perfect example for medical study, since he suffered from everything. “What an acquisition I should be to a class! Students would have no need to ‘walk the hospitals,’ if they had me. I was a hospital in myself.” Then he began to worry about himself and his real health. Savvy readers should realize that the narrator is prone to exaggeration and tends to react disproportionately to many situations. He is setting the tone for the rest of the action in the book.

According to Colin Turnbull, there is a deep connection between the generations in Pygmy society; he believes that American culture lacks this sense of interconnection and social cohesion. Throughout the book, Turnbull relates both his fascination with and admiration for the rituals that bond successive generations. The molimo, elima , and nkumbi characterize the three main rituals that encapsulate Pygmy life. Boys as young as nine to twelve years old must endure circumcision, whippings, and other tortures for two to three months before they emerge with full adult privileges. Eschewing the image of Pygmies as "one-legged troglodytes," Turnbull  portrays the tribe as pragmatic realists who demonstrate a deep respect for family and community. Similar to the nkumbi , the elima signifies the "transition from girlhood to the full flowering of womanhood." Under the watchful eye of parents, young girls are able to accept the sexual attentions of eligible bachelors within t...

Mitosis is the process by which the nuclear material of a eukaryotic cell divides just prior to cytokinesis or cell division. The first step that occurs after the cell enters the mitotic phase is prophase. During prophase, the nuclear envelope degenerates and the chromatin (DNA) condenses into chromosomes. This helps to protect the DNA in the absence of the nuclear envelope. The centrioles begin to move toward opposite poles of the cell.   The next step of mitosis is metaphase. During metaphase, the chromosomes, consisting of a pair of identical sister chromatids, line up along the metaphase plate (along the center of the cell). Microtubules (mitotic spindle) extend from the centrioles at opposite poles to the centromeres of the sister chromatids and attach. During the next phase, anaphase, the connected microtubules pull the sister chromatids of each chromosome to opposite ends of the cell so that every chromosome present in the parent cell is now represented at each end of the cell. ...

The whole magic behind Stockton's story "The Lady, or the Tiger?" is that the ending doesn't tell the reader which fate the princess's lover receives. The story thrives on the ambiguity left in the wake of a compelling tale. If readers discover if a lady or a tiger emerges from the door indicated by the princess, then nothing would be left for readers to decide after reading it. The narrator leaves readers with the following: "The question of her decision is one not to be lightly considered, and it is not for me to presume to set myself up as the one person able to answer it. And so I leave it with all of you: Which came out of the opened door—the lady, or the tiger?"  The narrator says in the above passage that since the lover's fate should not be taken lightly, the narrator shouldn't be the one to reveal the princess's decision. As a result, the author/ narrator hands over the decision to readers, which empowers them to decide the ending of...

To determine the convergence or divergence of the series `sum_(n=1)^oo (-1)^n/3^n` , we may apply the Ratio Test. In Ratio test , we determine the limit as: `lim_(n-gtoo)|a_(n+1)/a_n| = L`  Then, we follow the conditions: a) `L lt1` then the series converges absolutely b) `Lgt1` then the series diverges c) `L=1` or does not exist  then the test is inconclusive .The series may be divergent, conditionally convergent, or absolutely convergent. For the given series `sum_(n=1)^oo (-1)^n/3^n` , we have `a_n =(-1)^n/3^n` .  Then, `a_(n+1) =(-1)^(n+1)/3^(n+1)` . We set up the limit as: `lim_(n-gtoo) | [(-1)^(n+1)/3^(n+1)]/[(-1)^n/3^n]|`  To simplify the function, we flip the bottom and proceed to multiplication: `| [(-1)^(n+1)/3^(n+1)]/[(-1)^n/3^n]| =| (-1)^(n+1)/3^(n+1) *3^n/(-1)^n|` Apply the Law of Exponent: `x^(n+m) = x^n*x^m` . It becomes: `| ((-1)^n (-1)^1)/(3^n *3^1)*3^n/(-1)^n|` Cancel out common factors `(-1)^n` and `(3^n)` . `| (-1)^1/ 3^1 |` Simplify: `| (-1)^1/ 3^1 | =| (-1)/ 3 |`...

The molecular weight of potassium hydroxide, KOH = 56 g/mol Molarity (M) of a solution is defined as the moles per unit volume of a substance. Thus, if we have 1 L of solution, we have 6.9 moles of potassium hydroxide in a 6.9 M solution.  This is also equal to 386.4 g (= 56 g/mol x 6.9 mol) of potassium hydroxide in 1 L of solution. Since potassium hydroxide makes up only 30% of the solution, the actual mass of the solution is: mass of solution = 386.4 g / (30/100) = 1,288 g The density of a substance is the ratio of mass to its volume. Here we have a solution that has a mass of 1,288 g and a volume of 1 L. Thus the density of such a solution is: density = mass / volume = (1,288 g / 1 L) = 1,288 g/L  or 1.288 kg/L Hope this helps. 

Those lines are the first two lines from stanza four of Richard Lovelace's poem "To Althea, from Prison."  In the poem, Lovelace is using those lines to explain that his imagination, soul, and love are free from any sort of physical prison made by men.   Those two lines do appear in the short novel  Tuck Everlasting , but Winnie's use of the quote is a bit different from Lovelace's poem.  In Chapter 24, Winnie sneaks out of her house in order to help the Tucks rescue Mae from jail.  When Winnie sees the jail and its barred windows, those two lines pop into her head.  Here, too high for Winnie to see into, was a barred window through which, from the room in front, light glowed faintly. Winnie peered up at it, at the blackness of the bars with the dim gold of the light between. Into her head came lines from an old poem: Stone walls do not a prison make, Nor iron bars a cage. Winnie doesn't know why the lines come to her, but the lines do make sense in Mae's ...

The primary narrator of Walk Two Moons is Salamanca Tree Hiddle, or Sal. She tells the story in two parts. One part is of her life in Euclid, Ohio, after she and her father moved there from Bybanks, Kentucky, before her mother left. The other part is of her road trip with her grandparents, to whom she tells the first story in a series of flashbacks, along with incidents from her life in Bybanks before her mother left. Sal is what is called an unreliable narrator, which is one who does not tell all she knows. The events in the two stories have already happened in her past, but she waits until the end to reveal the truth to the reader. She drops hints along the way, which a second reading will make obvious. She is going with her grandparents to Idaho to reach her mother and bring her home by her mother’s birthday. While she says that her mother left her and her father to visit a cousin, she lets the reader assume that she might come back. It is not until the final chapters that Sal reve...

In Act I, Scene 1 of Shakespeare's Romeo and Juliet a fight breaks out in the streets of Verona between the Montagues and Capulets. The families are bitter enemies and the feud is described as an "ancient grudge." As soon as Lord Capulet hears the noise in the street he calls for his "long sword." Lady Capulet, who is by his side, remarks that he would be better off with a "crutch" and that he has no business with a sword. The suggestion, of course, is that Lord Capulet is simply too old to be fighting in the street. Likewise, Lady Montague warns Lord Montague not to fight either and holds him back: "Thou shalt not stir one foot to seek a foe." This reference to the two family patriarchs being too old to engage in street brawls is also revealed in Lord Capulet's remark to Count Paris in Act I, Scene 2: But Montague is bound as well as I, In penalty alike, and ’tis not hard, I think, For men so old as we to keep the peace.

The phrase "the bliss of solitude" appears in the fourth and final stanza of William Wordsworth's poem "I Wandered Lonely as a Cloud" (also sometimes referred to as "The Daffodils"). The first three stanzas of the poem recount Wordsworth's joy in seeing a field of "golden daffodils" along a lake on one of his many walks through England's Lake District. The fourth stanza answers the question which closes the third stanza: "What wealth the show to me had brought." In other words, Wordsworth wonders what redeeming quality the flowers may have for him. He acknowledges in the last stanza that when he is alone "in pensive mood" the daffodils "flash upon that inward eye/ Which is the bliss of solitude." That "inward eye" is most certainly the poet's soul or spiritual vision, and when he is alone the thought of the daffodils makes for a unique and extremely pleasurable feeling. It is in this quiet a...

Russell Banks’ 1991 novel The Sweet Hereafter was inspired by the true story of a school bus crash in Alton, TX that took the lives of 21 children. Banks’ story takes place in a small town that similarly has to deal with the aftermath of a school bus accident that kills numerous local children. The story is told from the points of view of four different characters—Dolores Driscoll, the school bus driver; Billy Ansel, a parent of two children who die in the accident; Mitchell Stephens, a lawyer; and Nichole Burnell, a teen survivor of the crash. In a New York Times review of the novel (link provided below), Banks himself explains why he chose this narration structure: "I wanted to write a novel in which the community was the hero, rather than any single individual. I wanted to explore how a community is both disrupted and unified by a tragedy." Readers see these events unfold from distinct points of view, reminding us that individual experience shapes perception, with each ch...

In an argument about the morality of the death and life sentence, the young lawyer stated that both forms of punishment were equally immoral, but he would choose the life sentence. He reasoned that it was better to live in confinement, rather than not live at all. The banker challenged the lawyer's remarks, and a bet was placed. The banker offered 2 million to the lawyer if he could stay in solitary confinement for five years. The lawyer agreed but also raised the stakes to fifteen years on his part. During his confinement, the lawyer studied different subjects. He improved his knowledge about the inner workings of the world and claimed that he was wiser based on what he had studied. "Your books have given me wisdom. All that the unresting thought of man has created in the ages is compressed into a small compass in my brain. I know that I am wiser than all of you. The banker read a letter by the lawyer stating his new found knowledge and wisdom. In his letter, the lawyer forfe...

The scarlet ibis is symbolic of Doodle himself.  First, the scarlet ibis is not native to the area.  It is native to the tropics.   "It lives in the tropics-South America to Florida. A storm must have brought it here." So what you have is a bird that is completely out of place in its current surroundings.  That is a lot like Doodle.  He is small, fragile, and handicapped.  Brother tries to incorporate Doodle in all kinds of things, but Doodle just can't quite keep up in the world that Brother demands.  The bird too is small and fragile.  It too is injured and broken in a way that prevents it from surviving in the world that it finds itself in.   At that moment the bird began to flutter, but the wings were uncoordinated, and amid much flapping and a spray of flying feathers, it tumbled down, bumping through the limbs of the bleeding tree and landing at our feet with a thud. I also see the scarlet ibis death scene as symbolic foreshadowing of Doodle's death.  There are ...

The attitudes toward African and particularly Asian (Kipling wrote "The White Man's Burden" about American deliberations over invading the Philippines) peoples expressed in this poem are complex. Kipling clearly sees colonial peoples as inferior to whites. He describes them, after all, as "half-devil and half-child." He does not think they can possibly be sophisticated enough to appreciate the benefits of civilization, and those who try to bring it to them will earn "the blame of those ye better." Kipling is also completely convinced that imperialism, because it brings the alleged benefits of Western civilization to "inferior" peoples around the world, is a noble pursuit. These racist attitudes are as typical of Kipling's time as they are repugnant today. But Kipling's condescension aside, he is urging the wealthy, privileged, comfortable classes in the Western world to put aside self interest and serve others. The fact that the peopl...

In this story, Waverly’s mother teaches her the art of “invisible strength.”  What that means is that sometimes you can accomplish more by quietly working toward a goal.  Waverly learns to do this with chess.  She learns not to brag or frets about her losses. An example of this is when Waverly is learning to play from a mentor, one of the men in the park, Lau Po.  When she loses and throws away the pieces, he lets her know that this does not follow chess etiquette.  Part of being a good chess player is learning from your mistakes and not being a sore loser. Waverly recounts some of the rules she learned about playing chess, including these. Never announce "Check" with vanity, lest someone with an unseen sword slit your throat.  Never hurl pieces into the sandbox after you have lost a game, because then you must find them again, by yourself, after apologizing to all around you. In many ways, these are also the rules for life.  Do not brag, especially before you are sure you ha...

One lesson that The Story of My Life imparts is that every child deserves an education suited to him or her. Before Anne Sullivan starts working with Helen Keller, Keller is deemed unable to communicate because people don't know how to reach her. However, with the correct type of education and a teacher who understands her, Keller learns how to communicate with sign language and how to read. Therefore, no child should be deemed uneducable. Another important message is the value of each person and his or her ability to contribute to society. When Anne Sullivan starts working with Keller, she treats her student with the respect she would give to any student who could speak and hear. The only difference in the way she treats Keller is that Sullivan uses sign language instead of speech. As a result, Keller learns to respect herself and to understand that she is capable of great thoughts and achievements. In addition, Keller's story teaches us the value of struggle. She had to stru...

I might argue that Katniss wasn't completely innocent before competing in the Hunger Games.  Katniss comes from District 12, which is poor to begin with; however, Katniss is from the poorest part of that district.  She's been having to hunt for food for herself and her family for years.  Her mother is present, but is often overwhelmed, so Katniss is basically the only care provider for her family.  She's been putting her name into the lottery system multiple times over for many years.  She's definitely not an innocent babe in the woods.   I do believe that Katniss furthers her loss of innocence over the course of the novel.  One very concrete example of that is the fact that Katniss kills other combatants during the competition.  She's never killed a human being before, and during her time in the arena, she kills multiple people.  Another example is Rue's death.  Katniss feels like she is responsible.  Lastly, Katniss is completely conscious of the fact that she...

`int(5x-2)/(x-2)^2dx` Let's use partial fraction decomposition on the integrand, `(5x-2)/(x-2)^2=A/(x-2)+B/(x-2)^2` `5x-2=A(x-2)+B` `5x-2=Ax-2A+B` comparing the coefficients of the like terms, `A=5` `-2A+B=-2` Plug in the value of A in the above equation, `-2(5)+B=-2` `-10+B=-2` `B=-2+10` `B=8` So now `int(5x-2)/(x-2)^2dx=int(5/(x-2)+8/(x-2)^2)dx` Now apply the sum rule, `=int5/(x-2)dx+int8/(x-2)^2dx` Take the constant's out, `=5int1/(x-2)dx+8int1/(x-2)^2dx` Now let's evaluate each of the above two integrals separately, `int1/(x-2)dx` Apply integral substitution `u=x-2` `=>du=dx` `=int1/udu` Use the common integral :`int1/xdx=ln|x|` `=ln|u|` Substitute back `u=x-2` `=ln|x-2|` Now evaluate the second integral, `int1/(x-2)^2dx` Apply integral substitution:`v=x-2` `dv=dx` `=int1/v^2dv` `=intv^(-2)dv` Apply the power rule, `=v^(-2+1)/(-2+1)` `=-v^(-1)` `=-1/v` Substitute back `v=x-2` `=-1/(x-2)` `:.int(5x-2)/(x-2)^2dx=5ln|x-2|+8(-1/(x-2))` Add a constant C to the solution, `...

A scientist could measure the boiling point of a piece of metal the same way he or she would measure the boiling point of any other substance.  You would subject the piece of metal to a measured amount of heat in a controlled fashion.  First, the metal would melt from a solid to a liquid (the melting point).  Then, the liquid metal would start to bubble and produce vapor at the boiling point.  For most chemicals this would not be too difficult a study to perform.  You would only require a heat source like a hotplate and thermometer.  The difficulty in doing this with a metal is that most metals tend to have extremely high melting points.  For example, nickel has a boiling point of almost 3,000 degrees C.  So the difficulty would arise here in obtaining a heat source that could reach that temperature and also obtaining a thermometer that can operate at that temperature.

To find the positive values of p in which the series `sum_(n=3)^oo 1/(nln(n)(ln(ln(n)))^p)` , we may apply the integral test. Integral test is applicable if f is positive, continuous, and decreasing function and `a_n=f(x)` . The infinite series `sum_(n=k)^oo a_n` converges if and only of the improper integral `int _k^oo f(x)dx ` converges to a finite number. If the integral diverges then the series also diverges. For the infinite series `sum_(n=3)^oo 1/(nln(n)(ln(ln(x)))^p)` , we have: `a_n=1/(nln(n)(ln(ln(n)))^p)` Then, `f(x) =1/(xln(x)(ln(ln(x)))^p)` The `f(x)` satisfies the conditions for integral test for the interval `[3,oo)` We set-up the improper integral as: `int_3^oo1/(xln(x)(ln(ln(x)))^p) dx.` Apply u-substitution by letting `u = ln(x)` then `du =1/xdx` . `int 1/(xln(x)(ln(ln(x)))^p) dx=int 1/(ln(x)(ln(ln(x)))^p)* 1/xdx`                       `=int 1/(u(ln(u))^p) du` Apply another set of substitution: let` v =ln(u)` and `dv = 1/u du` . `int 1/(u(ln(u))^p) du=int 1/(ln(u))^p* ...

Hello! Denote the minimum number of weeks after which Carlos will attend all three classes during one week as `N.` Our task is to find that `N.` The next art classes will be after `4` weeks since now, then after `4+4=8` weeks since now and, in general, after `4*A` weeks since now, where `A` is any natural number. For chess club the formula is `2*C,` and for fencing lessons the formula is `3*F.` And all these events will happen simultaneously after `N` weeks, i.e. all these numbers, `4A,` `2C` and `3F,` must be equal to `N:` `4A = 2C = 3F = N.` We see that `4,` `2` and `3` are divisors of `N,` and `N,` in turn, is a multiple of `4,` `2` and `3.` This means `N` is a common multiple of `4,` `2` and `3,` and we are interested in the least common multiple, `N=LCM(4,2,3).` Let's find `N=LCM(4,2,3) = LCM(2^2, 2^1, 3^1).` It must contain all prime factors from `4,` `2` and `3,` they are `2` and `3.` And `2` must be at the power `2` to make a multiple of `4.` The result is  `2^2*3=12.` Th...

Bobbie learns that it is impossible to predict the consequences of one small act of carelessness. In the poem, Bobbie goes mountain-climbing with his friend, David. The two friends climb a mountain in the Ramparts Range, Sundance Peak, Mount Inglismaldie, the Fortress, and the Finger in the Sawback Range. They also climb Mount Gleam, but it is a fictitious mountain. It is while climbing the Finger that David loses his balance and falls fifty feet. The accident occurs when David reaches out to steady Bobbie; in trying to save his friend from certain death, David loses his own foothold. Later, we learn that the accident happened because Bobbie neglected to test his foothold as he climbed the Finger. Thus, he blames himself bitterly for David's suffering. For his part, David refuses to let Bobbie torture himself. He tries to get Bobbie to see that an unintentional mistake does not make someone a villain. David bleeds profusely from the fall; from the poem, we can deduce that David has...

The opening lines of Philbrick's  Freak the Mighty  inform the reader about one of the first things Kevin does for Max: he teaches him how to use his brain.  "I never had a brain until Freak came along and let me borrow his for a while, and that's the truth, the whole truth. The unvanquished truth, is how Freak would say it, and for a long time it was him who did the talking" (1). Kevin teaches Max to think for himself and how to find answers when he has questions. For example, Kevin shows Max how to use a dictionary to improve his vocabulary and speech. Max even receives a personal dictionary from Kevin for Christmas. It has all of the interesting words Kevin likes along with his own definitions. Once Max knows how to use a dictionary, he feels empowered to teach himself about words he doesn't understand. Another thing Kevin teaches Max is to be brave. First, Kevin takes Max on quests just like King Arthur's noble knights did. This is Max's introduction t...

The activities of plants are coordinated by chemical compounds called hormones which are released by stimulated cells. These hormones exist in the form of molecules called signalling molecules. They are responsible for transmitting information to various receptor cells in different parts of the plant. There are various types of signalling molecules. They vary in size, function and shape depending on the role they are expected to play. When a signalling molecule encounters a receptor cell, it binds to the cell membrane of the receptor cell, releasing a chemical signal which is picked up by the receptor cell. The receptor cell converts the signal received to a form which it can easily comprehend and respond to by a process called signal transduction. The signal transduction process may be a simple one-step process or a series of steps which modify the signal by a relay of signaling molecules until it finally triggers a specific response in the cell. The response elicited in the cell ensu...

There are no doubt various answers to this question, but two technologies that allowed major tenets of cell theory to be established are the microscope and x-ray crystallography. The microscope was essential in discovering one aspect of cell theory--that the cell is the basic structural and functional unit of life. The microscope allowed scientists to directly observe that all life was composed of similar units. Later microscopes with higher magnification showed the cells' organelles; there were differences in what types of organelles were present, but similar types of organization became apparent. X-ray crystallography helped establish another part of cell theory--that DNA is used to transmit genetic information. X-ray crystallography was used by Rosalind Franklin to create photographs that were then used by James Watson and Frances Crick to determine the structure of DNA. The double-helix shape (with complementary base pairs, an earlier discovery) provided a mechanism for how gen...

This excerpt comes from Canto XI, which reads, "Eftsoones that dreadful Dragon they espide, /Where stretcht he lay upon the sunny side,/Of a great hill, himselfe like a great hill." Spencer's verse is written in stanzas; the first eight lines of each stanza are in iambic pentameter, which is composed of five "feet" or iambs. Each foot is made up of an unstressed syllable followed by a stressed syllable. "Iambic pentameters" have five of these feet. The last line of each stanza is written in iambic hexameter, having six feet (also known as an Alexandrine). That means that in lines 31-33 of this canto, there is an unstressed syllable followed by a stressed syllable, each composing a foot. There are five of these feet in each line. When marking lines, you should draw a diagonal stress mark (an acute accent) over each stressed syllable and a breve accent (which looks like a "u") over each unstressed syllable. Draw a vertical line between each foo...

Indefinite integrals 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 sin(5theta)sin(4theta) d theta`  has an integrand in the form of a trigonometric function. To evaluate this, we apply the identity: `sin(A)sin(B) =[-cos(A+B) +cos(A-B)]/2` The integral becomes: `intsin(5theta)sin(4theta)d theta= int[-cos(5theta+4theta) + cos(5theta -4theta)]/2 d theta`  Apply the basic properties of integration:` int c*f(x) dx= c int f(x) dx` . `int[-cos(5theta+4theta) + cos(5theta -4theta)]/2 d theta= 1/2int[-cos(5theta+4theta) +cos(5theta -4theta)] d theta`  Apply the basic integration property:`int (u+v) dx = int (u) dx + int (v) dx` . `1/2 *[int-cos(5theta+4theta)d theta+cos(5theta -4theta)d theta]` Then apply u-substitution to be able to apply integration formula for cosine function: `int cos(u) du= sin(u) +C` ....

We are asked to graph the function `y=log_2(x-3) ` : The graph is a translation of the graph of `y=log_2x ` 3 units right. Some points on the graph: (25/8,-3),(13/4,-2),(7/2,-1),(4,0),(5,1),(7,2),(11,3) The domain is x>3; the range is all real numbers. There is a vertical asymptote at x=3, and the x-intercept is x=4. The graph is increasing on its domain, and with calculus it is concave down on its domain. The graph:

George, Harris, J. (the narrator) and a fox terrier named Montmorency spend almost two weeks in a boat following the course of the River Thames in southern England. At various times, and especially at the beginning, it seems as though we’re reading a comedy of errors. The men don’t appear to have much experience in boating. They have trouble with just about everything: packing for the trip, navigating the boat, putting up the canvas tent, cooking meals, etc. Their difficulties make for good storytelling by the narrator. But by the end, we can see that the personalities and talents of each man complement those of his friends. They make a successful informal working team, in spite of all of their individual deficiencies and differences of opinion. The bottom line is that they’re good as friends. This adventure will probably not be the only one they tackle together.

In his article "What's Wrong with Torture?" Sussman writes that while coercion and torture can overlap, they are distinct because coercion operates only on the victim's rational responses and normal cognitive processes. Coercion involves telling the victim that the oppressor will act against his or her rational interests, and therefore the victim can use reasoning to respond to these threats. Torture, on the other hand, involves manipulating the victim by appealing to his or her emotions and vulnerabilities in a situation that involves disorientation. In other words, in the process of torture, a victim does not always know what is rational and cannot use his or her rational facilities to figure out the best course of action. It is possible to coerce another person only through using reason and rationality, while torture involves manipulating the other person's emotions.   Coercion is not as bad as torture because it presents the victim with a rational set of actio...

One important long-term effect of the Boxer Rebellion was that the defeat of the uprising enabled Western powers to maintain a major presence (including a military presence) in China, to the detriment of Chinese sovereignty. Once the Boxers were defeated, the Western powers and Japan extracted reparations payments (which most of them returned) and forced China to accept a limited Western military presence in Beijing, where the uprising really took shape. Beyond this, the rebellion destabilized and discredited the Qing Dynasty, which was humiliated in its aftermath. Following the rebellion, the youthful Qing ruler, Pu Yi, was overthrown in a revolution that established a republic. Several years of civil war were followed by the Japanese invasion of Manchuria and later of China proper. So in many ways, the most important long-term effect of the defeat of the Boxers was many years of domestic unrest and turmoil.

In Amy Tan’s story “Two Kinds,” the daughter, Jing-Mei “June” Woo, changes from a child into a young woman. She reaches adulthood and a deeper understanding of her mother. As a child, June acquiesces to her mother’s belief that in America you can be anything, including a child prodigy. The two watch television shows and read magazines that show how children become famous for their talents. Even when her mother tries to “Americanize” her looks with haircuts and treatments, the daughter is compliant. As she grows older, June begins to understand she is not a prodigy. But not only is she not a prodigy, she does not work hard or apply herself as her mother wants her to. Although her mother works at menial jobs to provide for June, the two have conflicting ideas about the daughter’s life. After June fails to live up to her mother’s expectations in her piano recital, the two quarrel. Neither one minces words. The mother tells her daughter there are only two kinds of daughters: those who foll...

Thesis Statement: Harper Lee explores the theme of prejudice, which is a significant and relevant topic in today's society, throughout her novel To Kill a Mockingbird to comment on America's deep-seeded race and class issues. A good thesis statement should make a judgment or claim about the main idea that can be supported throughout the remainder of the essay. Harper Lee examines prejudice through the eyes of the naive narrator, Scout Finch. The majority of the town of Maycomb, Alabama is prejudiced against black people, and there are many examples of characters criticizing Atticus Finch for defending Tom Robinson throughout the novel. A few instances include Cecil Jacobs and Francis Hancock's comments to Scout in Chapter 9 and Mrs. Dubose's racially motivated insults in Chapter 11. Tom Robinson also becomes a victim of racial injustice because of the prejudiced jury's decision to convict him. In addition to racial prejudice, Lee also examines prejudiced feelings ...

Evaluate ` sum_(n=1)^(infty)(2n+1)/(n^2(n+1)^2) ` Consider the sequence of partial sums: n=1 3/4 n=2 3/4+5/36=8/9 n=3 3/4+5/36+7/144=15/16 n=4 3/4+5/36+7/144+9/400=24/25 The mth partial sum is given by ` 1-1/(m+1)^2 ` Since the limit of this expression as m grows without bound is 1, this will be the sum. Thus the sum is 1.

Elizabeth Proctor is the wife of John Proctor, and both are members of the Massachusetts Bay Colony.  Elizabeth Proctor becomes implicated in the conflict of the play by way of Abigail Williams. Abigail is the apparent leader of a group of young girls who claim to have encountered witches in the colony. Abigail was formerly employed by the Proctors as a maid, and, during that time, she had an affair with John. As the play progresses, Abigail reveals that she still desires John, and that she resents that he refuses to leave his wife to be with her.  Spiteful, Abigail accuses Elizabeth Proctor of being a witch. The court system places the burden on Elizabeth to prove that she is innocent, which she is unable to do. She is offered the choice of being freed, if she will confess to practicing witchcraft, or being killed if she will not. Elizabeth refuses to confess, revealing a principled streak that is similar to that of her husband. She refuses to disclose her husband's affair with Ab...

Dora and Emily both want to be ladies. Dora, having come from a well-to-do family, was born into and brought up in this lifestyle. She is concerned about what a lady should do and should not do. Emily, however, is from a working-class family. Though she does not know exactly what a lady should do and act like, her main goal is to keep her family safe, instead of risking their lives at sea. Her misunderstanding of what a lady is leads her to a life that no lady would countenance: she elopes with Steerforth, who eventually deserts her. She is forced into prostitution, as far from being a lady as she can be. Dora marries David, but fails in that most important “duty” of a woman (as conceived in that time period): having children. Emily rejoins her family and does the best she can, especially after Ham dies.

Montresor is likely telling this story to his confessor at the end of his life. While we don't know this for a fact, several context clues indicate this is an end-of-life confession. First, the story is set in Italy, a Catholic country, so it's very likely Montresor is Roman Catholic and therefore would hope to be absolved of his sins by a priest before death. It's significant that Montresor says in the last line that the events he narrates occurred fifty years before, noting that no mortal has disturbed Fortunato's bones for "half a century." This would indicate he is an old man, likely on his deathbed. Further, in the first line of the story, he addresses the person to whom he is narrating his tale as "you who so well know the nature my soul." He seems to be speaking to just one individual who knows him well: Who would know his "soul" better than his priest?

Robert Frost's poem “Mending Wall” gives the reader the initial impression that the wall in question is a good thing, but it doesn't take long to see that the speaker does not really care for the wall at all. The poem's ambiguity lies in the fact that we cannot really be certain if we need walls at all—do they help us or hurt us? Frost hints at the fact that it depends on the type of wall we are talking about. The title implies that the wall needs work, or “mending.” The reader immediately assumes that if the wall needs to be mended then it must be important. Why would we bother to fix something that we didn't need in the first place? But, in the poem's first line, Frost brings that assumption into question: Something there is that doesn’t love a wall, He reverses the usual word order a bit with “Something there is” (instead of “There is something”) for reasons that probably only he could tell you. But the line immediately changes our feeling about the wall, and we ...

`(y-1)sin(x)dx - dy = 0` To solve, express the equation in the form `N(y)dy = M(x)dx`. So bringing same variables on one side, the equation becomes: `(y-1) sin(x) dx = dy` `sin(x) dx = dy/(y - 1)` Then, take the integral of both sides. `int sin(x) dx = int dy/(y-1)` For the left side, apply the formula `int sin (u) du = -cos(u) + C` . And for the right side, apply the formula `int (du)/u =ln|u| + C` . `-cos(x) +C_1 = ln|y-1|+C_2` From here, isolate the y. `-cos(x) + C_1 - C_2 = ln|y-1|` Since C1 and C2 represent any number, express it as a single constant C. `-cos(x) +C = ln|y-1|` Then, eliminate the logarithm in the equation. `e^(-cos(x)+C) = e^(ln|y-1|)` `e^(-cos(x) + C) = |y-1|` `+-e^(-cos(x) + C) = y-1` To simplify the left side, apply the exponent rule `a^m*a^n=a^(m+n)` . `+-e^(-cos(x))*e^C= y-1` `+-e^C*e^(-cos(x))=y-1` Since `+-e^C` is a constant, it can be replaced with C. `Ce^(-cos(x))=y - 1` `Ce^(-cos(x))+1=y` Therefore, the general solution is  `y=Ce^(-cos(x))+1` .

The best evidence that I can point you toward is the immediacy that the children fall into place and begin playing the rhyming game.   The children decide that the first game that they all should play is hide-and-seek.  Then there is an argument about who should be it.  If you have ever played the game, you are familiar with this argument.  Mira quickly steps in to intervene, and she starts pushing and shoving kids into a circle of sorts.  While she is doing that, she is yelling "Make a circle, make a circle!'' Once the kids are in that circle, nobody explains anything.   There is no explanation about how the rhyming game works.  The rule about how and when to clap in rhythm is never stated.  Mira simply shouts out "Now clap!"  The children all know exactly what to do, and the children all know exactly when they have been eliminated and are safe from being "it."  That familiarity tells readers that the clapping game to choose a person is something that ...

The catalyst to the organized gay rights movement in the United States — what instigated work toward gay rights being a  movement —  was the Stonewall riot in New York City on July 28, 1969. Officers raided the illegal Stonewall Inn, a gay bar, leading to several days of confrontations between the police and gay people. Pro-gay demonstrations culminated in the first gay pride parade. After that, gay people began to realize they could fight back against the legal, social, and psychological stigmas that kept them in the closet.  As of 1969, homosexuality in the United States was classified as a mental illness — a form of deviance — and sodomy was illegal. Because of this, gay people were largely forced into underground lives. After 1969, as the movement took off in the heady period of political activism and social change in the late sixties and early seventies, the Gay Activists Alliance and the Gay Liberation Front groups formed. Awareness of gay issues led the American Psychiatric Asso...

Initially, Proctor is hopeful that Mr. Hale will have as much common sense as he has heard.  In Act One, as he leaves the Parris household, Proctor says, "I've heard you to be a sensible man, Mr. Hale.  I hope you'll leave some of it in Salem."  Proctor has high hopes that Hale will bring his wisdom and rationality to the town which is fraught with suspicion and superstition.  However, Proctor's opinion of Hale changes in Act Two, when Hale comes to the Proctors' home to question John and his wife.  Hale is somewhat suspicious of Proctor because he hasn't been to church regularly, his youngest son is not christened, and he cannot list all the commandments.  After the marshal arrives to arrest Elizabeth and Hale defends the court's proceedings, Proctor calls him a "broken minister" and he orders the minister "Out of [his] sight," calling him a "coward" because he is unwilling to stand up in the face of this corrupt court.  ...

The effects of the "generation gap" in Romeo and Juliet are complex. On the one hand, we clearly witness Juliet rebelling against her father and mother through her romance and marriage to Romeo. She openly defies them in Act III after Tybalt's death when her father tells her of her arranged marriage to Paris, and her father responds with rage and exasperation with his young daughter: Wife, we scarce thought us blest That God had lent us but this only child; But now I see this one is one too much, And that we have a curse in having her. Though Romeo's relationship with his parents is not fully explored in the play, he also goes against his family by marrying Juliet. Of course, there is a powerful sense in which the young people of the play are bound by the traditional hatreds of their elders, and Romeo and Juliet reject these hatreds through their marriage and their deaths, which ironically reconcile the two families. On the other hand, we witness another dimension to...

Jane Eyre both attacks the conventional religious hypocrisy of the Victorian era and depicts Jane as a deeply moral, feeling and upright person who is true to her Christian faith as she understands it.  The novel depicts religious hypocrisy through the figure of Mr. Brocklehurst, surely one the more odious characters in English literature, who lives in warm, well-dressed, well-fed comfort while subjecting the girls at the Lowood School Jane attends to a harsh regime of hunger, cold and mortification of vanity through short hair and plain clothes, a regime meant to improve their souls. Jane experiences intense anger at the deprivations Mr. Brocklehurst forces the girls to endure for their spiritual salvation while apparently not feeling he or his family needs such moral improvement or suffering. Thus, the novel calls into the question conventional religious morality that allows the poor to be treated differently than the rich for "their own good."  Jane loves the deeply relig...

To evaluate the series `sum_(n=2)^oo ln(n),` we may apply the  divergence test : If `lim_(n-gtoo) a_n != 0` then `sum a_n` diverges. From the given series `sum_(n=2)^oo ln(n)` , we have `a_n=ln(n)` . Applying the diveregence test,we determine the convergence and divergence of the series using the limit: `lim_(n-gtoo)ln(n) = oo`  When the limit value  (L) is `oo ` then  it satisfies `lim_(n-gtoo) a_n != 0 .`  Therefore, the  series `sum_(n=2)^oo ln(n)` diverges. We can also verify this with the graph: `f(n) = ln(n)` . As the value of `n` increases, the function value also increases and does not approach any finite value of L. 

A caesura is a pause that usually occurs in the middle, or towards the end, of a poetic line. There are two types of caesura: masculine, which is a harder pause and usually occurs after a long or accented syllable in the line, and feminine, which is a softer pause and usually occurs after a non-stressed and short syllable. There are several examples of caesurae in "The Wanderer." This poem's first caesura occurs in the first few lines: "No man, to whom / I'd clearly speak..." The caesura, a masculine caesura, occurs after the comma before "to whom" and creates a kind of rhythm.  Another example of a caesura in this poem occurs a few lines later: "So I, wandering..." The caesura, masculine again, occurs after the comma. A caesura often is used to create breath and call the reader's attention to some information in the line, and, in this case, the caesura emphasizes the "I," and the fact that this speaker is wandering. 

Though a number of issues contributed to the fall of tsarism in Russia, it is hard to deny Grigori Rasputin certainly played a part in the downfall of the Romanov dynasty and, ultimately, tsarism in Russia. Rasputin found favor with the Romanov family when he seemed to heal the tsar and tsarina's young son of hemophilia. Because he was able to help their son when nobody else could, Tsar Nicholas and Tsarina Alexandria desired to keep Rasputin close. Over time, Rasputin became more than a spiritual healer to the royal family; he also became a confidante and an advisor. This was problematic because Rasputin often offered poor advice that led to increased turmoil in the Russian military and in the lives of Russian citizens.  As the Romanovs continued to follow Rasputin's advice and counsel, their favorability among the people of Russia decreased. Ultimately, the people of Russia would no longer stand for the Romanov dynasty, evident by the Bolshevik Revolution, which ushered in a ...

Recall the  Root test  determines the 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 the Root Test to determine the convergence or divergence of the series `sum_(n=0)^oo 6^n/(n+1)^n` . For the given series `sum_(n=0)^oo 6^n/(n+1)^n` , we have `a_n =6^n/(n+1)^n` Applying the Root test, we set-up the limit as:  `lim_(n-gtoo) |6^n/(n+1)^n|^(1/n)=lim_(n-gtoo) (6^n/(n+1)^n)^(1/n)`  Apply the Law of Exponents: `(x^n/y^n) = (x/y)^n` and `(x^n)^(m)= x^(n*m)` . `lim_(n-gtoo) (6^n/(n+1)^n)^(1/n) =lim_(n-gtoo) ((6/(n+1))^n)^(1/n)`                              `=lim_(n-gtoo) (6/(n+1))^(n*(1/n))`                              `=lim_(n-gtoo) (6/(n+1))^(n/n)`                              `=lim_(...