Summarize the major research findings of "Toward an experimental ecology of human development."

Based on findings of prior research, the author, Bronfenbrenner proposes that methods for natural observation research have been applied in a manner that fails to consider the changing environments that affect human behavior. Observation in one natural setting is not enough to fully understand human behavior. The examples the author offers relate to observation studies of child behavior and development. Bronfenbrenner suggests that researchers cannot fully understand child development within the context of a single setting, with a single set of adults.
The child may behave one way at home with both parents but display different behavior and react differently to each of his/her parents in a setting outside the home, such as at school, at a medical appointment, or in another setting outside the home. The author suggests that age, socioeconomic status, and other demographics may influence how the child responds to the father and to the mother. Bronfenbrenner gives an example of a child from a middle-class family, whose interactions favor the mother in a laboratory setting and the father in a home setting. At the same time, the child from a lower economic class tends to favor the father in the laboratory setting and the mother in the home setting. Therefore, unless the researcher is seeking to answer a single, specific question related to child development and the specific environment, a richer, more robust methodology is needed to make general observations related to child development and parent interactions across all settings. 
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.458.7039&rep=rep1&type=pdf

Single Variable Calculus, Chapter 3, 3.5, Section 3.5, Problem 79

Show that $\displaystyle a(t) = v(t) \frac{dV}{ds}$ of a particle that moves along a straight line with displacement $s(t)$, velocity $v(t)$ and the acceleration $a(t)$. Explain the difference between the meanings of the derivatives $\displaystyle \frac{dv}{dt}$ and $\displaystyle \frac{dv}{ds}$

Recall that $a(t) \displaystyle = \frac{dV}{dt}$ and $v(t) = \displaystyle \frac{ds}{dt}$


$
\begin{equation}
\begin{aligned}

a(t) =& \frac{dV}{dt} = \frac{dV}{ds} \left( \frac{ds}{dt} \right) = \frac{dV}{ds} v
\\
\\
& \text{So,}
\\
\\
a(t) =& v \frac{dV}{ds}
\\
\\


\end{aligned}
\end{equation}
$


$\displaystyle \frac{dV}{dt}$ represents how the velocity changes with respect to time. On the other hand, $\displaystyle \frac{dV}{ds}$ represents how the velocity changes with respect to displacement of a certain particle.

Does the quote "a plague on both your houses" have any significance in the play of Romeo and Juliet?

Mercutio utters this line -- "A plague o' both your houses!" -- after he has been killed by Tybalt.  Tybalt came looking for Romeo in order to challenge him to a fight because he was offended by Romeo's presence at the Capulets' big party the night before.  When Tybalt eventually finds Romeo, Romeo has just come from marrying Juliet -- Tybalt's cousin -- and so Romeo refuses to fight this man who he is now related to, by marriage.  Mercutio, not knowing this, interprets Romeo's refusal to fight as a "dishonorable, vile submission" (3.1.72), and he fights Tybalt on Romeo's behalf.  Romeo comes between them in a well-meaning but ill-advised attempt to stop the fight and promote peace, and Tybalt is able to stab Mercutio under Romeo's arm.  For several reasons, then, Mercutio feels that his death is actually the fault of both Romeo and Tybalt: as he lays dying, he curses both "houses," or families, for their roles in his death.  He curses each family to have some tragedy, and, obviously, both families do experience tragedy when their children -- Romeo and Juliet -- kill themselves rather than live without one another.

int_0^(1/2) arctan(x^2) dx Use a power series to approximate the value of the integral with an error of less than 0.0001.

 From a table of power series, recall that we have:
arctan(x) = sum_(n=0)^oo (-1)^n x^(2n+1)/(2n+1)
To apply this on the given problem, we replace the "x " with "x^2 ".
We get:
arctan(x^2) =sum_(n=0)^oo (-1)^n (x^2)^(2n+1)/(2n+1)
                        =sum_(n=0)^oo (-1)^n x^(2*(2n+1))/(2n+1)
                        =sum_(n=0)^oo (-1)^n x^(4n+2)/(2n+1)
                        = x^2 -x^6/3+x^10/5-x^14/7 +...
The integral becomes:
int_0^(1/2) arctan(x^2)dx = int_0^(1/2) [x^2 -x^6/3+x^10/5- ...]
To determine the indefinite integral, we integrate each term using Power Rule for integration: int x^n dx = x^(n+1)/(n+1) .     
int_0^(1/2) [x^2 -x^6/3+x^10/5-...]
=[x^3/3 -x^7/21+x^11/55-...]_0^(1/2)  
Applying definite integral: F(x)|_a^b = F(b)-F(a) .
F(1/2) or F(0.5)=0.5^3/3 -0.5^7/21+0.5^11/55- ...
                            = 0.0416667 - 0.0003720+0.0000089-...
F(0)=0^3/3 -0^7/21+0^11/55-...
          =0 -0+0 -...     All terms go to zero.
 We stop at the 3rd term since we only need error less than 0.0001 .
int_0^(1/2) arctan(x^2)dx =0.0416667 - 0.0003720+0.0000089
                                = 0.0413036
Thus, int_0^(1/2) arctan(x^2)dx~~0.0413 .

How is the neighborhood described?

The narrator of "Sonny's Blues" describes the neighborhood as "filled with a hidden menace which was its very breath of life." Though the place where he lives is a relatively new housing project, it has become, in his words, "already rundown." The playground is not populated in the daytime with children playing the innocent games of childhood; it is populated at night. Though Baldwin's narrator does not say what goes on there, readers understand that it is far from wholesome.
The narrator observes that the neighborhood where he lives as an adult is not much different from where he and Sonny grew up; it is, he says, as if "I was simply bringing him back into the danger he had almost died trying to escape." The streets of Harlem he describes are filled with subway stations, bars with jukeboxes spilling music into the streets, and neighborhood people gathering outside a barbecue joint to hold an impromptu street revival. The narrator remembers his and Sonny's mother telling their father they should try "to move to a neighborhood that might be safer for the children." He also remembers times when their apartment was filled with friends and neighbors on Sunday afternoons after big dinners when he felt safe and loved, but also aware of the dangers outside that lay waiting.

which process changes sedimentary rock into igneous rock

In the rock cycle, the thing that determines the type of a rock is the way the rock was formed. Igneous rocks are formed by the cooling and solidifying of molten rock (magma or lava), sedimentary rock is formed by deposition of sediments which are either compacted or cemented together, and metamorphic rock is formed when other rocks are subjected to extreme pressure and/or heat that is not enough to actually melt the rock. The heat and/or pressure can deform the rock and also cause different minerals to form, or else change the shape and distribution of existing minerals.
In the determination of whether a rock’s type is igneous, sedimentary, or metamorphic, it doesn’t matter what knd of rock it came from. It only matters how it was made. The rock in the question is igneous rock, so it had to solidify from molten rock. To become molten, the original sedimentary rock had to melt. Once molten, of course, the structure of the previously existing rock would disappear. The process that would transform a sedimentary rock, or any other rock, into an igneous rock, then, is melting or, to be more specific, melting followed by cooling and solidifying.

How is the following quote ironic, and what theme does it show? "We've got to have rules and obey them. After all, we're not savages."

In chapter 2, the boys fail to make a sustainable signal fire, and Ralph mentions that they need to put people in charge of maintaining the fire at all times. Ralph also says that they should have more rules and Jack agrees by saying,

"We've got to have rules and obey them. After all, we're not savages. We're English, and the English are best at everything." (Golding, 33)

Jack's comment is ironic because as the novel progresses, Jack and his band of hunters reveal their savage, primitive nature. Jack and his hunters paint their faces and become bloodthirsty barbarians as they hunt pigs, murder Simon and Piggy, and even attempt to kill Ralph.
After landing on the island, they rapidly descend into savagery and live like uncivilized beings. Jack's comment also emphasizes the theme of civility vs. savagery. As English schoolboys, Jack and the others have been taught that they are inherently civil and superior to other races, ethnicities, and cultures. However, Golding portrays all humans as inherently evil, wicked individuals without the restraints and influence of society to prevent them from acting like savages and indulging in their true desires.

Interpret the poem "Queen-Anne's-Lace."

The key device used by the poet in this poem is personification; he describes the flower Queen Anne's Lace as if it were a lover, combining the literal (the plant is powerful, "taking / the field by force; the grass / does not rise above it") with the figurative ("wherever / his hand has lain there is / a tiny purple blemish").
We may assume that the "he" in the poem represents the sun, driving the flowers to "blossom under his touch." As the sun and the Queen Anne's Lace are characterized as lovers, so the white spread of bloom across the field, the result of their growth together, is described as "desire," spreading in the form of blossoms. Like desire, too, the spread of blossom seems to reach a climax, after which the field is "empty," the flowers scattered as the "wish to whiteness" has gone over and the flowers have receded with the end of spring.

What two jobs does Jack claim for the choirboys?

In chapter one, "The Sound of the Shell," Jack and Ralph compete to be "chief" of the boys. When Ralph gets more votes than Jack does, Ralph graciously gives command of the choir to Jack. Jack says he wants them to be the island's hunters. After that, Jack leads the hunters as they stalk and eventually kill a pig.
In chapter two, "Fire on the Mountain," Ralph tells the other boys that his father is in the navy and has told him that the Queen has maps of the world, including the island on which they're stranded. He is convinced that a ship will come near and suggests that they maintain a signal fire on top of the highest hill. Jack volunteers his choir, the hunters, to be the ones who gather wood. Later, he declares that he will divide the choir into groups that will both maintain a lookout shift and keep the signal fire burning.

In chapter 1, the boys elect Ralph as chief, and he immediately tells Jack that the choir belongs to him. The first job that Jack claims for the choir is to be the group's hunters. Throughout the novel, Jack leads his choir on numerous hunting expeditions, where they brutally kill pigs and hold feasts. Jack and his hunters become bloodthirsty and are obsessed with hunting by the end of the novel. In chapter 2, Ralph holds an assembly and attempts to create a civil, organized society. The second job that Jack claims for his choir involves maintaining the signal fire. Jack volunteers his choir to watch over and feed the signal fire on the top of the mountain. Later on, Jack relieves his hunters from their duty of maintaining the signal fire and leads them on a hunting expedition. Unfortunately, a ship passes by the island, and the hunters are not on top of the mountain to fuel the signal fire, which leads to a heated argument between Ralph and Jack over duties and priorities.

How is the parent-child relationship shown through the novel Frankenstein by Mary Shelley?

A chief way Mary Shelley shows the parent-child relationship in Frankenstein is first through Victor's loving parents, who bestow affection and every kindness on him, feeling he was given to them by God. They therefore believe that they owe him a tender upbringing. As he recalls it:

Much as they were attached to each other, they seemed to draw inexhaustible stores of affection from a very mine of love to bestow them upon me. My mother’s tender caresses and my father’s smile of benevolent pleasure while regarding me are my first recollections. I was their plaything and their idol, and something better—their child, the innocent and helpless creature bestowed on them by heaven, whom to bring up to good, and whose future lot it was in their hands to direct to happiness or misery, according as they fulfilled their duties towards me.

Victor goes on to remember an idyllic childhood provided by his caring and gentle parents:

No human being could have passed a happier childhood than myself. My parents were possessed by the very spirit of kindness and indulgence. We felt that they were not the tyrants to rule our lot according to their caprice, but the agents and creators of all the many delights which we enjoyed.

Victor himself becomes a "parent" in a very different way, playing God and bringing a creature to life through assembling and animating dead body parts. The dysfunctional relationship of Victor to his creation could not be more different than Victor's loving relationship with his own parents. Victor is repulsed by his "child" and rejects it when it comes to life:

Breathless horror and disgust filled my heart. Unable to endure the aspect of the being I had created, I rushed out of the room. . . . A mummy again endued with animation could not be so hideous as that wretch.

When Victor next encounters his creation, he is again filled with horror and wants to kill it, knowing the creature has murdered his loved ones. The creature, however, pleads with Victor to be a loving father, telling Victor that he owes him kindness, for he is the one who gave him life:

Remember that I am thy creature; I ought to be thy Adam, but I am rather the fallen angel, whom thou drivest from joy for no misdeed. Everywhere I see bliss, from which I alone am irrevocably excluded. I was benevolent and good; misery made me a fiend. Make me happy, and I shall again be virtuous.

The creature, feared and hated by everyone, recognizes that loving parenting will bring out his benevolent side and make him good. On the inside, Frankenstein's creation desires to be a caring member of society. It is simply his outward shell that is hideous. He only becomes a murderer because everyone has rejected him: the love he tried to show was met with fear, hatred, and disgust.
Nevertheless, Victor is unable to get past the creature's outer appearance and, now, the havoc the creature has brought to Victor's family through acting out his rage and grief in murder. Victor is never able to transcend his repulsion toward his "child." He is never able, ironically, to replicate the loving and caring behavior he most appreciated from his own parents.
Shelley is critiquing playing God, but she is also suggesting that having played God, Victor is responsible for the outcome of his actions and should have treated his creation as a decent parent would.

What is the theme of the play The Admirable Crichton?

The major theme in the play is social class and how it's determined in and out of English society.
Social class and the various ways it's maintained, as well as its effects on people, is an important factor in the story. When a group of English aristocrats and their servants are marooned on an island, none of the pampered people know how to care for themselves. Though they try to conform to English standards at first, the only person who is able to thrive in the environment is the butler Crichton. He quickly becomes the leader of the group and this is affirmed several times despite power struggles from Lord Loam and the other aristocrats. When they're rescued and return to traditional society, however, everyone reassumes their normal place. Only Lady Mary says that perhaps England itself is wrong for the way it puts people in social classes; Crichton is a product of English society, though, and disagrees with her. He says, "My lady, not even from you can I listen to a word against England."

One of the most abiding themes of the play is the fluidity of social class, and especially how easily it can change under certain environmental conditions. Crichton, a humble butler, becomes the dominant character on the desert island, due to his intelligence and resourcefulness. In the so-called civilized world, Crichton would never get the opportunity to show his true character. But here on a desert island he flourishes among the hapless aristocrats who are supposedly his social superiors.
Social class is presented in the play as being highly artificial, a product of an equally artificial society. It says something about the rigidities of class structure in Edwardian England that someone from a relatively humble background can only really achieve a position of authority on a remote desert island, far away from his native shores. There is a natural aristocracy in this world, it would seem, and Crichton is a part of it, but only—appropriately enough—in the natural world.

College Algebra, Chapter 9, 9.1, Section 9.1, Problem 70

Define the sequence
$\displaystyle G_n = \frac{1}{\sqrt{5}} \left( \frac{(1+\sqrt{5})^n - (1-\sqrt{5})^n}{2^n} \right)$
Find the first 10 terms of this sequence using a calculator. Compare to the Fibonacci Sequence $F_n$

$
\begin{equation}
\begin{aligned}
G_ 1 = \frac{1}{\sqrt{5}} \left( \frac{(1 + \sqrt{5})^1 - (1 - \sqrt{5})^1}{2^1} \right) = 1\\
\\
G_ 2 = \frac{1}{\sqrt{5}} \left( \frac{(1 + \sqrt{5})^2 - (1 - \sqrt{5})^2}{2^2} \right) = 1\\
\\
G_ 3 = \frac{1}{\sqrt{5}} \left( \frac{(1 + \sqrt{5})^3 - (1 - \sqrt{5})^3}{2^3} \right) = 2\\
\\
G_ 4 = \frac{1}{\sqrt{5}} \left( \frac{(1 + \sqrt{5})^4 - (1 - \sqrt{5})^4}{2^4} \right) = 3\\
\\
G_ 5 = \frac{1}{\sqrt{5}} \left( \frac{(1 + \sqrt{5})^5 - (1 - \sqrt{5})^5}{2^5} \right) = 5\\
\\
G_ 6 = \frac{1}{\sqrt{5}} \left( \frac{(1 + \sqrt{5})^6 - (1 - \sqrt{5})^6}{2^6} \right) = 8\\
\\
G_ 7 = \frac{1}{\sqrt{5}} \left( \frac{(1 + \sqrt{5})^7 - (1 - \sqrt{5})^7}{2^7} \right) = 13\\
\\
G_ 8 = \frac{1}{\sqrt{5}} \left( \frac{(1 + \sqrt{5})^8 - (1 - \sqrt{5})^8}{2^8} \right) = 21\\
\\
G_ 9 = \frac{1}{\sqrt{5}} \left( \frac{(1 + \sqrt{5})^9 - (1 - \sqrt{5})^9}{2^9} \right) = 34\\
\\
G_{10} = \frac{1}{\sqrt{5}} \left( \frac{(1 + \sqrt{5})^{10} - (1 - \sqrt{5})^{10}}{2^{10}} \right) = 55\\
\end{aligned}
\end{equation}
$

Using Fibonacci Sequence $F_n = F_{n-1} + F_{n -2}$
Since $F_1 = 1$ and $F_2 = 2$, then

$
\begin{equation}
\begin{aligned}
F_3 &= F_2 + F_1 = 1 + 1 = 2 &&& F_7 &= F_6 + F_5 = 8 + 5 = 13\\
\\
F_4 &= F_3 + F_2 = 2 + 1 = 3 &&& F_8 &= F_7 + F_6 = 13 + 8 = 21\\
\\
F_5 &= F_4 + F_3 = 3 + 2 = 5 &&& F_9 &= F_8 + F_7 = 21 + 13 = 34\\
\\
F_6 &= F_5 + F_4 = 5 + 3 = 8 &&& F_{10} &= F_9 + F_8 = 34 + 21 = 55
\end{aligned}
\end{equation}
$

Calculus of a Single Variable, Chapter 7, 7.4, Section 7.4, Problem 7

Arc length (L) of the function y=f(x) on the interval [a,b] is given by the formula,
L=int_a^bsqrt(1+(dy/dx)^2) dx, if y=f(x) and a <= x <= b,
Now let's differentiate the function,
y=3/2x^(2/3)
dy/dx=3/2(2/3)x^(2/3-1)
dy/dx=1/x^(1/3)
Now let's plug the derivative in the arc length formula,
L=int_1^8sqrt(1+(1/x^(1/3))^2)dx
L=int_1^8sqrt(1+1/x^(2/3))dx
L=int_1^8sqrt((x^(2/3)+1)/x^(2/3))dx
L=int_1^8(1/x^(1/3))sqrt(x^(2/3)+1)dx
Now let's evaluate first the indefinite integral by using integral substitution,
Let t=x^(2/3)+1
dt=2/3x^(2/3-1)dx
dt/dx=2/(3x^(1/3))
dx/x^(1/3)=3/2dt
intsqrt(x^(2/3)+1)(1/x^(1/3))dx=int3/2sqrt(t)dt
=3/2(t^(1/2+1)/(1/2+1))
=3/2(t^(3/2)/(3/2))
=t^(3/2)
=(x^(2/3)+1)^(3/2)
L=[(x^(2/3)+1)^(3/2)]_1^8
L=[(8^(2/3)+1)^(3/2)]-[(1^(2/3)+1)^(3/2)]
L=[5^(3/2)]-[2^(3/2)]
L=11.18033989-2.828427125
L=8.351912763
Arc length (L) of the function over the given interval is ~~8.352

Precalculus, Chapter 9, 9.4, Section 9.4, Problem 72

You need to remember what a quadratic model is, such that:
a_n = f(n) = a*n^2 + b*n + c
The problem provides the following information, such that:
a_0 = 3 => f(0) = a*0^2 + b*0 + c => c = 3
a_2 = 0 => f(2) = a*2^2 + b*2 + c => 4a + 2b + c = 0
a_6 = 36 => f(6) = a*6^2 + b*6 + c => 36a + 6b + c = 36
You need to replace 3 for c in the next two equations, such that:
4a + 2b + 3 = 0 => 4a + 2b = -3
36a + 6b + 3 = 36 => 36a + 6b = 33 => 18a + 2b = 11
Subtract the equation 4a + 2b = -3 from the equation 18a + 2b = 11 :
18a + 2b - 4a - 2b = 11 + 3
14a = 14 => a = 1
Replace 1 for a in equation 4a + 2b = -3 , such that:
4 + 2b = -3 => 2b = -7 => b = -7/2
Hence, the quadratic model for the given sequence is a_n = n^2 - (7/2)*n + 3.

Why does Angela search under the hoods of the cars in chapter 14?

In chapter 14 of The Westing Game, Angela checks under the hood of the cars because she and Sydelle believe there may be more clues under one of them. In chapter 8, Angela and Sydelle receive the following clues: good, hood, from, spacious, grace. Sydelle reads these as one sentence: “Good gracious from hood space.” She says that as soon as the parking lot is cleared, they can search the hoods of the cars. She suggests that maybe they’ll find more clues or a map or the murder weapon. After Sydelle is injured in the restaurant bomb at the end of chapter 13, Angela takes it upon herself to search the parking lot. She disguises herself in her mother’s old beaver coat and hat and Turtle’s red boots and searches each car in the parking lot, but she doesn’t find anything.

In chapter 14 of The Westing Game, the teams are actively working on sets of clues in order to solve the mystery and win the game. Per Sydelle's instructions, Angela searches under the hood of each car in the parking lot of Sunset Towers, with the goal of either finding another clue or in some way getting closer to making sense of their clues. The words Sydelle and Angela have gathered so far are GOOD, HOOD, FROM, SPACIOUS, GRACE, KING, QUEEN, PURPLE, WAVES, ON(NO), GRAINS, and MT. In an attempt to make sense of the seemingly unrelated string of words, Sydelle repeatedly puzzles over and rearranges them, resulting in the phrase "good gracious from hood space," the answer to which she suspects may be found in the parking lot. Since Angela finds nothing of interest when searching the cars, we can conclude that this particular mission was unsuccessful.

Who was Herodotus?

Herodotus was an ancient Greek historian, known as "the father of history" due to his innovations in historiography, or the study of history. Prior to Herodotus, history as a formal academic discipline didn't really exist. Past events tended to be jumbled up with myth, fable, and legend, so much so that it was difficult to establish what had really happened in history.
Herodotus adopted a completely new method for studying history, as can be seen in his monumental account of the Persian Wars. Known simply as The Histories, they set out to provide an exhaustive account of what really happened during this epic conflict. Previously, historical accounts tended to be fragmentary, little more than disjointed bits of travelogue. Herodotus was the first to recognize the importance of combining all the various pieces of information concerning a historical event into a coherent narrative that would enable the reader to gain a broader perspective on things.
However, Herodotus's encyclopedic approach to writing history has been criticized for insufficient academic rigor. There's very little in the way of analysis in Herodotus's work; he presents all the elements of his story as if they were of equal importance. Furthermore, Herodotus did not entirely dispense with myth and fable; they are still present in his narrative, though they are generally much easier to discern than in previous chronicles. For the most part, Herodotus used fictitious elements to serve the needs of the narrative, to make it flow more naturally and more entertaining to read.
Whatever his shortcomings as a historian, Herodotus put the academic study of history on a firm footing. To a large extent, historians ever since have been building upon foundations that he first established.

What is a brief account of the packing incident in Three Men in a Boat by Jerome K. Jerome?

The "packing incident" can be found in chapter 4. It's another great sequence that continues to show that J., Harris, and George are complete, bumbling idiots that don't know it. The incident begins with the men having gathered all of their stuff together that needs to be packed. J. volunteers to do the packing, and the other two men sit back to watch. This bugs J. because what he intended was to volunteer to tell the other guys what needed to be packed when and where.

This was hardly what I intended. What I had meant, of course, was, that I should boss the job, and that Harris and George should potter about under my directions, I pushing them aside every now and then with, “Oh, you—!” “Here, let me do it.” “There you are, simple enough!”—really teaching them, as you might say.

J. eventually gets the bag all packed, and then Harris mentions that the boots didn't get packed. J. then has to unpack some stuff, pack the boots, and repack the stuff. He then can't remember if he packed his toothbrush or not, so he proceeds to unpack everything in order to find it. He finds the toothbrush and repacks everything only to have George ask about the soap being packed. J. has had enough by this point and says that he doesn't care about the soap.
Next, George and Harris make an attempt to pack the food and dishes. It's a hilarious sequence in which dishes are broken, jars of food are smashed, and butter is smeared everywhere.

They upset salt over everything, and as for the butter! I never saw two men do more with one-and-twopence worth of butter in my whole life than they did. After George had got it off his slipper, they tried to put it in the kettle. It wouldn’t go in, and what was in wouldn’t come out. They did scrape it out at last, and put it down on a chair, and Harris sat on it, and it stuck to him, and they went looking for it all over the room.

Which is more important to Sophocles, family or authority? Look at Antigone, Ismene, Creon, and Haimon and at what happens to them and their relationships. Cite specific quotes from the play to support each claim.

Antigone comes from a seriously dysfunctional family. Antigone's father, Oedipus, former King of Thebes, killed his father, Laius, who was King of Thebes before Oedipus. Oedipus didn't know that Laius was his father when he killed him, but the fact remains that Oedipus killed his own father.
Antigone's mother, Jocasta, is also Oedipus's mother. Antigone is therefore her father's sister. Oedipus didn't know that Jocasta was his mother when he married her and had children with her, but the fact remains that Oedipus married his own mother.
When it was discovered in Oedipus Rex that Oedipus had married his own mother, Jocasta, his wife/mother, took her own life. Oedipus then poked out his own eyes when he discovered Jocasta's body and exiled himself from Thebes.
Antigone has a younger sister, Ismene, who is afraid of her own shadow. Antigone also has (had) two brothers, Polyneices and Eteocles, who killed each other in a civil war over the throne of Thebes, which is where the story of Antigone begins.
Creon, Antigone's uncle and brother of Jocasta, is now King of Thebes. Compared to Antigone's side of the family, Creon and his family seems almost normal. According to legend, Creon and his wife, Eurydice, had seven children, although only one son, Haemon, appears in Antigone. Haemon is betrothed to Antigone, which, if Antigone's family history is any indication, does not bode well for Haemon.
Antigone loves her family. She complains about them and about the problems of being Oedipus's daughter (and sister), but she loves them nonetheless and says,

Ismene, sister of my blood and heart,See'st thou how Zeus would in our lives fulfillThe weird of Oedipus, a world of woes!For what of pain, affliction, outrage, shame,Is lacking in our fortunes, thine and mine?

Antigone tells Ismene about Creon's edict that Eteocles is to be given a state funeral and a hero's burial since he fought on the side of Thebes, but Polyneices is to be left unburied in the desert. Anyone who defies Creon's edict will be punished by death.
Antigone puts it to Ismene directly:

So stands it with us; now 'tis thine to showIf thou art worthy of thy blood or base.

Antigone is asking Ismene if, in spite of all the hardship that the family has endured, Ismene is worthy of being considered a member of their family and doing what's right by helping Antigone bury Polyneices.
Ismene avoids answering the question and asks Antigone why she intends to bury Polyneices in spite of Creon's edict. Antigone answers,

My brother, and, though thou deny him, thine.No man shall say that I betrayed a brother.

There it is. This is how Antigone feels about family in general, and her brother in particular.
Ismene keeps pressing the point, hoping that Antigone will change her mind. Antigone replies,

What right has he to keep me from my own?

This discussion is going nowhere. Disgusted with Ismene's cowardice, Antigone leaves her to go bury Polyneices by herself.
Unlike Antigone, Creon believes wholeheartedly in the authority of the state and his own authority as King:

Now that his two sons perished in one day,Brother by brother murderously slain,By right of kinship to the Princes dead,I claim and hold the throne and sovereignty.Yet 'tis no easy matter to discern... if one who reigns supremeSwerve from the highest policy, tongue-tiedBy fear of consequence, that man I hold,And ever held, the basest of the base.And I contemn the man who sets his friendBefore his country. For myself, I callTo witness Zeus, whose eyes are everywhere,If I perceive some mischievous designTo sap the State, I will not hold my tongue;Nor would I reckon as my private friendA public foe, well knowing that the StateIs the good ship that holds our fortunes all:Farewell to friendship, if she suffers wreck.Such is the policy by which I seekTo serve the Commons ...

Creon sets a very high standard for himself, and it remains to be seen whether he can meet that standard.
Creon's son, Haemon, does his best to speak on Antigone's behalf, while at the same time trying not to antagonize Creon. Creon repeatedly falls back on his position in the state, and as the state, to justify his edict and his death sentence against Antigone.

CREON. ... But he who overbears the laws, or thinksTo overrule his rulers, such as oneI never will allow. Whome'er the StateAppoints must be obeyed in everything,But small and great, just and unjust alike. ...
Is not this maid an arrant law-breaker?
HAEMON. The Theban commons with one voice say, No.
CREON. What, shall the mob dictate my policy?
... Am I to rule for others, or myself?
HAEMON. A State for one man is no State at all.
CREON. The State is his who rules it, so 'tis held.

The Chorus calls Antigone to task for defying Creon's edict and putting her own feelings and beliefs above the state:

Religion has her chains, 'tis true,Let rite be paid when rites are due.Yet is it ill to disobeyThe powers who hold by might the sway.Thou hast withstood authority,A self-willed rebel, thou must die.

Teiresias, the blind seer-prophet, appears to tell Creon that the gods are offended by his actions and hold Creon accountable for the unrest caused by his edict and by his decision to condemn Antigone to death:

O King, thy willful temper ails the State,For all our shrines and altars are profanedBy what has filled the maw of dogs and crows,The flesh of Oedipus' unburied son.Therefore the angry gods abominateOur litanies and our burnt offerings...

Teiresias prophesizes dire consequences if Creon goes through with Antigone's execution.

Know then for sure, the coursers of the sunNot many times shall run their race, beforeThou shalt have given the fruit of thine own loinsIn quittance of thy murder, life for life;For that thou hast entombed a living soul,And sent below a denizen of earth,And wronged the nether gods by leaving hereA corpse unlaved, unwept, unsepulchered.Herein thou hast no part, nor e'en the godsIn heaven; and thou usurp'st a power not thine.

The Chorus joins in against Creon.

CHORUS. Son of Menoeceus, list to good advice. ...
Go, free the maiden from her rocky cell;And for the unburied outlaw build a tomb.
CREON. Is that your counsel? You would have me yield?
CHORUS.Yea, king, this instant. Vengeance of the godsIs swift to overtake the impenitent.

Creon hurries to the cave where Antigone has been closed up, but he arrives too late. Antigone has already taken her own life. Haemon is there, too, and he first tries to kill Creon, and failing that, he kills himself. When Eurydice hears about Haemon's death, she kills herself as well.
Creon's blind adherence to the rules of the state—his rules—leads to the death of three members of his family, and benefits the state in no way whatsoever.
Is the family more important to Sophocles than the state? Although it appears that Sophocles has constructed the play to clearly champion the family, he also warns of the damage that can be done to the state and to the family by a family member who fails to respect and conform to the laws of the state.
Are the conflicts that arise in Antigone between the family and the state caused by Antigone putting the family before the state, or by Creon putting the state before the family? Is it Creon's edict that results in the deaths of Antigone, Haemon, and Eurydice, or is it Antigone's defiance of Creon's edict that results in their deaths?

While both family and authority are important to Sophocles, the importance of honoring family seems a bit more important to him when the fates of Antigone and her family are considered. Creon's realization that he caused the tragedy in the story by defying the gods implies that honoring family is the will of the gods—because the gods were displeased when he chose to honor the laws of the land as the King of Thebes.
Antigone chooses to bury her brother, whom her Uncle Creon, the new King of Thebes, ordered to be left unburied and unsanctified as punishment for warring against his brother. She doesn't deny her crime and accepts her death sentence when it is handed down. In the end, she kills herself before the death sentence is rescinded. Antigone values family over authority, saying:

I urge no more; nay, wert thou willing still,I would not welcome such a fellowship.Go thine own way; myself will bury him.How sweet to die in such employ, to rest,--Sister and brother linked in love's embrace--A sinless sinner, banned awhile on earth,But by the dead commended; and with themI shall abide for ever. As for thee,Scorn, if thou wilt, the eternal laws of Heaven.

To Antigone, honoring her family is also honoring the gods.
Ismene refuses to help Antigone bury Polyneices. She says it's not possible to do so, because his corpse is being guarded. When Antigone is caught, Ismene falsely confesses —but Antigone defends her. Nevertheless, Ismene is imprisoned by Creon and later released before Antigone's death. Ismene chooses to obey the law and preaches the same to Antigone, saying:

Shall we not perish wretchedest of all,If in defiance of the law we crossA monarch's will?—weak women, think of that,Not framed by nature to contend with men.Remember this too that the stronger rules;We must obey his orders, these or worse.

Ismene survives the play, but many of the people she loves are dead. 
Haemon, Creon's son and Antigone's fiance, appears to support his father but subtly tries to convince him to spare Antigone, claiming the city is on her side. He tries to appeal to Creon, saying that Creon isn't considering true justice and is immature in thought. Haemon insists: "A State for one man is no State at all. As Monarch of the desert thou wouldst shine," telling his father that his thoughts are flawed. They exchange harsh words, and Haemon swears he'll never speak to Creon again as he leaves. After Antigone is found dead, Haemon attempts to kill his father and then kills himself.
Creon orders Antigone to be put to death for burying Polyneices in defiance of his order. Though he spares Ismene, he has Antigone sealed in a cave. When a blind prophet warns him the gods are displeased with his treatment of Polyneices and Antigone, he sends men to free her—only to find that she's dead. He loses his son and wife to suicide and blames himself for what has happened, saying:

Lead me away. I have been rash and foolish.I have killed my son and my wife. I look for comfort; my comfort lies here dead. Whatever my hands have touched has come to nothing. Fate has brought all my pride to a thought of dust . . .

In the end, Sophocles respects both family and authority but considers honoring family to be the will of the gods, which must be respected.

How do you view the character Lily in The House of Mirth by Edith Wharton?

Edith Wharton's The House of Mirth presents Lily as an extremely shallow character who desperately wants to elevate her social status through a suitable marriage. For this reason, she refuses to wed Seldon, who is her closest friend and confidante. Her inability to control the wealth she does have eventually causes her financial ruin, and her family wants nothing to do with her when rumors begin. This would imply that Lily is indeed selfish and materialistic.
However, smaller plot details shade Lily's character in a different way. Twice she denies courses of action which would solve her financial difficulties because they would contradict her ethical values, first by denying the married Mr. Gus Trenor's attempts at wooing her, and then refusing to blackmail Mrs. Bertha Dorset (the woman spreading rumors about Lily) when she uncovers another affair.
Lily is a romantic at heart, and though she desires money and social status, she also wants real love in her marriage. Failing to find this, she commits suicide at the end of the novel.
Lily is not a flat character with only shallow and materialistic qualities, but rather a well-rounded tragic heroine who cannot achieve her dreams without sacrificing her sense of self, and ends up recognizing the impossibility of her goals and refusing to go on any longer.

What is the irony of the gifts that Jim and Della exchanged?

Irony is when events turn out the opposite of what is planned. In this story, newlyweds Della and Jim plan an amazing Christmas gift for each other. Both also make a big sacrifice to get the gift they think will bring joy to the other person.
Della sells her beautiful, beloved hair, that falls past her knees, to get money for Jim's gift. She uses the money to buy Jim an expensive watch chain for his beloved watch.
Jim sells his cherished watch to buy an expensive comb and brush set for Della's beautiful hair.
The irony is that both gifts are useless to the recipient. Both Jim and Della sold what made the gift precious: Della has little hair left to brush, and Jim has no watch left to attach his watch chain to.
Nevertheless, each one demonstrated love for the other, and this, O'Henry says, is the most important gift of all.

The irony regarding Jim's and Della's Christmas gifts to each other arises from the fact that neither individual can use their significant other's specific gift. Jim ends up selling his expensive watch in order to buy Della a pair of precious combs for her beautiful hair, while Della sells her long hair to purchase Jim a watch fob for his prize timepiece. Ironically, each person has sold their most prized possession in order to pay for an expensive gift that compliments their special personal belonging. Jim is the first to recognize the situational irony when he enters his home and sees that Della has cut all of her hair off. Jim stands with a "strange expression" on his face while Della attempts to explain that she sold her precious hair. After Della opens Jim's gift and discovers that he bought her an expensive set of combs, Della tells Jim that she wishes to see his watch and realizes that he no longer has it. Ironically, each person's gift is useless, but their love for each other is evident, and they appreciate each other's personal sacrifice.

Why does Columbus come to believe that the Native Americans are incredibly generous?

They ... brought us parrots and balls of cotton and spears and many other things, which they exchanged for the glass beads and hawks' bells. They willingly traded everything they owned... --Christopher Columbus

When Christopher Columbus reached the Bahamas in October of 1492, he believed that he had reached islands off the coast of India.  For this reason, he called the people that he met Indians.  The description above is directly from the journal of Columbus.  It is obvious that his impression of them is that they are generous because of the gifts that the Natives immediately brought him. Columbus realized through their generosity that he could enslave and exploit this population.  The population of the Taino was wiped off of the island within a generation of their generous meeting with Columbus.  Columbus forced the Taino to work in mines for the benefit of his new colony and the crown of Spain.     
http://webhome.auburn.edu/~sayejoh/4050/s/Columbus.pdf

https://www.smithsonianmag.com/travel/what-became-of-the-taino-73824867/

How would you define and describe apartheid law? Why did the government introduce this law and how did it affect people on a daily basis?

Apartheid was a system that was in place in South Africa. It kept white people in power and separated the races.
A good example of an apartheid law was the Reservation of Separate Amenities Act of 1953. This law provided for separate facilities in many public places for white people and non-white people, including restaurants, schools, theaters, and bathrooms. There were many amendments to this Act, including one that said these facilities didn’t have to be equal in terms of quality.
The government passed this law to keep the races apart. The government also wanted to keep white people in power.
This law affected people significantly. Non-white people weren’t treated equally to white people. Their facilities were inferior to those white people had. This Act sent a strong message about how white people viewed those who weren’t white. Non-white people had limited opportunities and experiences because of this law.
https://omalley.nelsonmandela.org/omalley/index.php/site/q/03lv01538/04lv01828/05lv01829/06lv01857.htm

In the poem "The Road Not Taken " by Robert Frost, do you think it is on a positive side that he chose "the road less travelled by"?

In Frost's poem, "The Road Not Taken," all we know from the narrator is that his having chosen the less traveled road has "made all the difference" (line 20).  Whether this is a positive or a negative choice as applied to any particular individual is a matter of opinion.  Bear in mind that no matter which the narrator had chosen, it would have "made all the difference" (line 20).
Which is positive and which is negative depends, I would say, on the kind of personality one has.  A person who is risk-averse is likely to be happier in the end following a more traveled road.  A person who is risk-seeking is likely to be happier following the less-traveled road.  This is because the roads are a metaphor for our paths through life.  At many junctures, we decide to do what most people do, to follow a path where most people have gone before, or to follow a path that is a bit different, one that is more likely to bring about atypical results.  To apply this to the lives of most people I know, for example, one graduates from high school, goes to college, gets a job, gets married, and has children.  However, some I know decided not to go to college but to go travel through Europe for ten years or join the Peace Corps.  A few went to New York and became starving artists. My brother spent a few years on the road as a musician and dancer.  For him, the road was a great choice.  The less-traveled road can lead to great adventures and it can also lead to some very hard times. 
Think about what kind of person you are.  To decide whether this is a positive or negative choice means viewing the choice from your own perspective, since all the narrator tells us is that it made a difference, which is meaningless in a way, since if he had been presented with five different paths to follow, the choice of any would have made a difference. 

Precalculus, Chapter 3, 3.3, Section 3.3, Problem 22

log_5(1/125)=x Rewrite log5 1/125 :
1/125=125^-1 This gives:


log_5(125^-1) , bring down the power
-1(log_5(125)) , rewrite 125 in term of power of 5
-1(log_5(5^3)) , again bring down the power
(-1*3)(log_5(5)) , note log_5(5)=1 Answer: x = -3

How does Meggie in The Thorn Birds relate to Scarlett O'Hara in Gone with the Wind?

Both of these characters are women whose rebellious nature make their lives and relationships difficult. They both engage in behaviors that are seen as socially unacceptable and damage their reputations in this way. They both also experience various tragedies in their lives that cause them to develop skills of perseverance.
Both Scarlett and Meggie are extremely attractive women whose beauty is legendary in their communities. Growing up beautiful leads to them understanding the effect their beauty has on men, and they learn to develop their charms in order to manipulate others. But this manipulation is much more conscientious in Scarlett than it is in Meggie.
Scarlett has a more pronounced sense of entitlement than Meggie does and believes she deserves to get what she wants. She was raised within the antebellum South in a wealthy family and so was coddled and praised and taught to be very feminine. Even though the man she loves, Ashley Wilkes, is engaged to another woman, Scarlett insists on continuing to try and seduce him. She even contrives to be alone with him in an inappropriately intimate way after he is married. Scarlett is well aware of the impact of her feminine wiles.
Meggie's inappropriate behavior, on the other hand, is mainly caused by her innocence and lack of experience. Her mother, an old fashioned Irish Catholic, didn't bother to tell Meggie the facts of life, and so when she experiences her first menstrual period, she is afraid and ends up confessing her fear to the parish priest, Father Ralph, who is embarrassed. The two have a close relationship, and he is there as a friend to her as she grows up. When Meggie gets a bit older, Ralph is captivated by her beauty, and Meggie senses that she has a hold on him and tries to seduce him, despite how inappropriate this is.
Meggie does not have the sophistication Scarlett O'Hara has at the same age, because she is much more socially isolated and is raised within the confines of a strict Catholic family. But because of her limited experience, Ralph is the only man she is close to apart from her family members, so he is almost like an experiment for Meggie. She also loves him, but her idea of love is rather juvenile and romantic at first. Meggie's attempt to seduce Father Ralph parallels Scarlett O'Hara's behavior when she tries to seduce an engaged man. But for Father Ralph, having a sexual relationship as a priest is forbidden, so the implications go beyond impropriety to being morally dangerous and sinful.

What views on marriage does Charlotte Bronte present in her novel Jane Eyre?

Charlotte Bronte, through her character Jane Eyre, shows a strong belief in the sanctity of a legal marriage. To Jane the marriage bond is not merely a convenience but a sacred trust. Therefore, when she finds out that Rochester, who is ready to marry her, is already married, she reacts with horror. From Jane's standpoint, it simply is not right to engage in a bigamous marriage, even if Bertha is insane. In Jane's eyes, one marries for better or for worse, and Bertha's condition in no way alleviates Rochester of his responsibilities toward Bertha as her husband.
Jane reveals her strong moral fiber in rejecting Rochester when she finds out he is already married. She loves him deeply, and it would be easy to rationalize his relationship with Bertha as something other than a real marriage. It would also be easy to ignore a first marriage that few people even know exists. Nevertheless, Jane will not do this. She flees Rochester instead of compromising herself with a false bond.

Bronte (and Jane Eyre) believed that marriage should be a match between intellectual and spiritual equals. One of the things that made marriage difficult for Jane was the power (legal and sexual) it gave the husband over the wife. You can see these issues at work in the section towards the end of the book where Jane has to decide if she will marry St John: on the one hand, St John appeals to her sense of duty and self sacrifice, but ultimately she rejects him because of his evident pride, arrogance, and sense of superiority. Rochester, in contrast, has actually been trapped in a bad marriage; Bertha's power over him -- her existence! -- ruins his hope for "true love" with Jane. Rochester clearly does not consider Bertha to be his wife in any real way, but is unable to escape the legal and moral bonds of marriage. In a sense, Rochester has lived the experience Jane avoids with St John -- servitude to an unloving spouse. Jane ultimately marries Rochester because she believes that they are spiritual and intellectual equals -- Rochester, in his crippled state at the end of of the book, requires Jane's care, but Jane, for her part, requires Rochester's understanding. 

What do the bridge, cats, goats, and pigeon symbolize?

The bridge could be said to symbolize a means of escape for the old man from his present life, a chance to start a new life in another town. But it could just as easily symbolize an uncertain future. The solider narrator tells the old man that the road at the end of the bridge leads towards Barcelona. But as the old man doesn't know anyone there, he stays put. He's already been forced to leave his hometown due to the ravages of war, and feels that he's come to the end of his life's journey. The bridge may represent the chance of a new beginning, but not to an old man who's pretty much given up on life. In that sense, this is one bridge too many, an insurmountable hurdle that the old man cannot and will not overcome.
The old man's extensive menagerie—his cats, his goats, his pigeons—could be said to symbolize hope. As long as the old man was able to take care of his animals, he had some hope in life, something to live for. But once he was forced to leave his animals behind in San Carlos, the old man had nothing more to live for, and what little hope he had effectively died inside him.

What was the significance of Reconstruction for the nation's future?

The Civil War was one of the darkest times in American History. Over 625,000 men would die fighting this war from 1861–1865. Much of the Confederate States lay in ruin. The period after the war is known as Reconstruction. It would become a catalyst for dramatic social changes over the next century.  
The assassination of Abraham Lincoln was a dark day for the defeated south. Lincoln had formulated a plan of amnesty for the former rebels and was determined to let the Confederacy "up easy." Unfortunately, John Wilkes Booth ended any hopes for a quick and painless reconciliation with the northern states. 
Radicals in Congress assumed control of Reconstruction and immediately began to change the social climate in the former Confederacy. The 13th, 14th, and 15th amendments to the Constitution gave former slaves freedom, citizenship and the right to vote. These amendments helped to introduce biracial democracy to the south for the first time. 
Restrictive voting measures such as the requirement to own property, were abolished. In many southern states black voters outnumbered whites. As a result, African-Americans were elected to Congress, including two members of the Senate.
One of the biggest social changes to occur during the Reconstruction period involved education. Schools were funded by state governments and kids of all races were now able to achieve an education. One of the lasting legacies of Reconstruction governments across the south is the land-grant colleges which dot the landscape of the former Confederacy.
These social changes were not without their critics. Some whites attempted to re-establish white supremacy through militaristic groups such as the KKK and the establishment of Jim Crow Laws. The end of Reconstruction in 1877 would usher in almost a century of oppression and discrimination of blacks throughout the south. 
Without question Reconstruction introduced social changes that enabled former slaves to better function as citizens. Those changes would take almost a century to be fully realized as the implementation of segregation in response to those changes made progress slow to a crawl.
 

Is The Jungle Book fiction or non-fiction?

The Jungle Book by Rudyard Kipling is a collection of stories that are all entirely fictional. We can be absolutely certain of this given that most of the stories concern anthropomorphic animals that communicate in the English language not only with each other, but with humans as well. The Jungle Book has been an invaluable work of fiction for over a century, particularly for children, and has been adapted into several versions of film and other media. Though The Jungle Book is largely concerned with animals as its primary characters, the stories and morals are less about the natural world and far more concerned with representing human archetypes with the animals themselves. To this end, the book teaches lessons about morality and society in an entertaining and easily digestible way, as it is speculated that Kipling first wrote the stories for his daughter.

All of these stories are fictional. The Jungle Book is a series of fictional stories that feature anthropomorphic animals who have the characteristics of humans and speak. Some stories feature Mowgli, a boy raised by wolves. The animals in the stories include not only the wolf family but also Baloo—a bear—and Bagheera, the black panther. These animals attempt to instruct Mowgli in the Law of the Jungle. Other stories in the book include the tale of Rikki-Tikki-Tavi, a mongoose taken in by a British family. The mongoose battles against venomous cobras to protect the family. Another story in the collection is "Toomai of the Elephants," the story of an elephant driver and his little son, who glimpses the dance of the elephants that no human has ever before seen. 

Why did Homer include types of help from the immortals and Odysseus himself instead of presenting only one way to overcome obstacles?

By including both help from the gods and instances of Odysseus helping himself with his wit and strength, Homer is able to show that Odysseus is a hero favored by the gods and able to allow Odysseus to escape situations that would not have been escapable without divine intervention.
If Homer had allowed Odysseus to overcome all obstacles with help from the gods, Odysseus would have been lucky, but he would not have been a hero. If Homer allowed Odysseus to succeed without help from the gods, Homer would have been guilty of minimizing the role that the gods played in the lives of Homer's audience. Many of the situations that Odysseus found himself in would have been impossible to escape without help from the gods, especially because his immediate situation resulted from angering Poseidon, a major Greek god.
Odysseus offends Poseidon when he blinds Polyphemus, and, as a result, Odysseus is sent on a voyage that keeps him away from home for decades. Because a god—Poseidon—is the cause of Odysseus's long misfortune, he needs divine intervention to overcome the problem. Odysseus cannot stand against a god and succeed. He needs other gods.
Luckily, Athena is willing to intervene for him. Her patronage causes Zeus and Hermes to assist him as well, getting him out of many spots that might have otherwise resulted in his death. For example, Hermes tells Calypso that Zeus wants Odysseus to journey home. If he had not done this, Odysseus might have been stuck with Calypso forever. The assistance of the gods helps Odysseus overcome obstacles that a mortal man would not have been able to.
But Odysseus does not always need the gods to escape trouble. For example, when he and his men escape Polyphemus, it is Odysseus who plans to tie the men to the bellies of sheep, to get the Cyclops drunk, and to give him a false name so that the other Cyclops will not give chase. His cleverness and strength as he navigates the difficult challenges are what make Odysseus himself a hero and a worthy king of Ithaca. In fact, his own resilience and skill also make him someone who is worthy of receiving help from the gods. Homer uses Odysseus's ability to get out of danger and make his way home to Ithaca to show the reader that Odysseus is a hero who deserves help from the gods.

Need a Thesis Statement for an Essay on the Short Story ‘Virgins’ by Danielle Evans I need to write an essay on the short story "Virgins" by Danielle Evans, and I am having difficulty coming up with a thesis for the essay. Using the lens of feminist criticism, the essay needs to address questions such as how does the story represent and/or contradict the experience of women and what does the story reveal about the operations of patriarchy (politically, socially, or psychologically). I am drawing a blank as to what I can use as a suitable thesis statement to build upon for this essay.

I cannot really write a thesis statement for you, but I can suggest some potential lines of argument.
Jasmine and the narrator are trying to negotiate the complicated passage to adulthood: they are busy trying to understand who they are as people, and part of that is coming to terms with their sexuality. One potential thesis could address the issue of identity. In terms of feminism, patriarchy, and the rest, the story shows how men are constantly defining the female characters as sexual objects—it is basically about the choices they have to make given that every man around them is constantly evaluating them as a potential sexual partner. Your thesis could evaluate the difference between how the narrator thinks of herself, and how men perceive her.
Another approach would be to think about the different men in the story, particularly Michael and his brother, paying particular attention to the end of the story. Your thesis could examine how Michael's friendship with the girls and his own attitudes about sexuality are different from his brother's attitude and the other male characters.
Another approach would be to consider the story from the point of view of rape culture. Is any of the sex in the story truly consensual? Part of this thesis would consider the different meanings male and female characters attach to sex. What is sex good for?
There is so much to think about here. Another approach would be to find and think about key moments or phrases in the story (does the story itself have a kind of "thesis statement"?) or to think about the title. One moment that really struck me is when the girls ask the men they are going off with toward the end of the story if they "look like virgins" and, when told no, the narrator says, "I didn't know whether to feel pissed off or pretty." The doubt and ambivalence these girls feel is at the heart of what this story expresses.
Good luck with your paper!

What were the effects of WWII on the United States?

There were several effects of WWII on the United States, and I will summarize them below in terms of social and economic changes.
Economic Changes
The biggest impact of WWII on the United States was economic stimulation.  In order to prepare for war, industry experienced a boom and continued to grow after the war ended.
Social Changes
After the war ended, there was a shift from urban, city life back to rural life—this time, however, in the form of suburbs.  Families, supported by a strong and growing economy, were able to start purchasing homes outside the city and rely on either public transportation or cars to commute to jobs.  Women were also working more, a result of their efforts to work to help support American troops during wartime.  With a transition to suburban life came the growth of mass consumerism, as a better economy and growth in technology and industry led to a desire for new goods.  This was also the period where the "baby boomer" generation was born; in a stable, post-war United States, populations exploded.
It should be noted, however, that African Americans did not enjoy the same prosperity. Racial tensions and divides, segregation, and Jim Crow laws in the South among other things encouraged the Civil Rights Movement.

Why does Homer Barron come to town?

Homer Barron comes to town as the foreman of a construction company from the north which has been contracted to pave the town's sidewalks. Homer is charming and has a tendency to be in the spotlight, and the town quickly takes to him and regards him fondly. However, some of the more old-fashioned members of the community are quick to judge his supposed courting of Emily, considering her to be too high-class for a day laborer like Homer. Homer represents the often uncomfortable upheaval of the values of traditionalists in the south after the war. He comes to town representing modern change, with machinery and industry. This makes his eventual cruel fate of staying with Emily forever (through death) all the more ironic.

Following the death of Emily's father, the community mentions that she was sick for a long time and remained reclusive inside her home. In the third section of the short story, the town gives a contract to a construction company from the North to pave their sidewalks. The community mentions that Homer Barron is the foreman in charge of supervising and overseeing the construction job. Homer Barron is a Yankee who is well-liked throughout the community and begins courting Emily Grierson. Being that Homer Barron is a working-class man from the North, the community disapproves of his relationship with Emily Grierson, who hails from a prestigious Southern family and is considered socially superior. Unfortunately, Homer Barron mysteriously disappears after Emily poisons him with arsenic. Homer Barron also symbolically represents Northern business interests influencing the South following the Civil War.

The sources from the documentary hypothesis P and D curate earlier tradition and innovate new ideas in service of agendas that appear to be systematic. Describe the ideological and legal systems of each, then compare and contrast. Are their ideologies complementary, competing, or something else? Include attention to the depiction of "constitutional law," political authority, social relationships within Israel and with non-Israelites, cultic practice, and concepts of holiness and purity.

The D, or Deuteronomist source, is thought to have written most of Deuteronomy and the books of Joshua through Second Kings in the 7th and 6th centuries BCE. This source's legal system was based on the bond of the Israelites to the Covenant or people's commitment to following the Commandments, and this source interpreted bad events as people's failure to follow the Covenant with God. Moses, who received the commandments, was the ultimate political and religious authority. D's source of holiness and purity relied on people's ability to follow laws and morals, for example those given in Deuteronomy, and to avoid worshipping God in places other than Jerusalem. This source spoke often about worshipping Yahweh alone and destroying other forms of worship. D took a moralistic approach and included many long sermons. The central holy area for this source is Mount Horeb and Sinai. This source advocates destruction of the Canaanites and other non-Israelites. 
The P, or priestly source, is thought to have written in the 6th century BCE, during the period of exile in Babylon. This source, unlike D, stressed the importance of cultic practice and following laws and rituals. This source rejected the idea of a divinely appointed king and gave political power to the priestly class. The legal system was based on the Levites, or the priestly class, and their temple in Jerusalem. Purity in this source came from following rituals. P also emphasizes the idea of the Israelites as God's chosen people and the importance of avoiding intermarriage with non-Israelites. 
In some ways, these sources are incompatible, as D gives ultimate authority to the Covenant and laws, while P gives ultimate authority to the priestly class and rituals. D follows a moralistic approach to religion, while P follows a ritual approach. They both, however, stress Israelites' special bond with God and urge non-assimilation with non-Israelites as well as the importance of the temple in Jerusalem.
http://www.cs.umd.edu/~mvz/bible/doc-hyp.pdf

int sqrt(16-4x^2)dx Find the indefinite integral

 Given ,
int sqrt(16-4x^2)dx
This Integral can be solved by using the Trigonometric substitutions  (Trig substitutions)
For sqrt(a-bx^2) we have to take x= sqrt(a/b) sin(u)
 
so here , For
int sqrt(16-4x^2)dx -----(1)
 x can be given as
x= sqrt(16/4) sin(u)= sqrt(4) sin(u) = 2sin(u)
so, x= 2sin(u) => dx = 2 cos(u) du
Now substituting x in (1) we get,
int sqrt(16-4x^2)dx
=int sqrt(16-4(2sin(u))^2) (2 cos(u) du)
= int sqrt(16-4*4(sin(u))^2) (2 cos(u) du)
= int sqrt(16-16(sin(u))^2) (2 cos(u) du)
= int sqrt(16(1-(sin(u))^2)) (2 cos(u) du)
= int sqrt(16(cos(u))^2) (2 cos(u) du)
= int (4cos(u)) (2 cos(u) du)
= int 8cos^2(u) du
= 8 int cos^2(u) du
= 8 int (1+cos(2u))/2 du
= (8/2) int (1+cos(2u)) du
= 4 int (1+cos(2u)) du
= 4 [int 1 du +int cos(2u) du]
= 4 [u+(1/2)(sin(2u))] +c  
but x= 2sin(u)
=> (x/2)= sin(u)
=> u= sin^(-1) (x/2)
so,
4 [u+(1/2)(sin(2u))] +c
=4 [sin^(-1) (x/2)+1/2sin(2(sin^(-1) (x/2)))] +c  
so,
int sqrt(16-4x^2)dx
=4sin^(-1) (x/2)+2sin(2(sin^(-1) (x/2))) +c

Is Eddie a sympathetic character? How he has changed during the play?

It is difficult to describe Eddie Carbone as a sympathetic character. For one thing, he is an extraordinarily self-centered man who expects the whole world to revolve around him. Everything he does in the play is related to his own needs and his own elevated sense of self-importance. More than anything else, he cannot face up to the reality of everyday life. As a result, he constructs a fantasy world all of his own where he is the center of attention and the dominant figure always in control.
However, he cannot control events, not least because he cannot control his own emotions. He tries to suppress his true feelings for Catherine, but it eventually becomes obvious to those around him how much he desires her. Eddie has painstakingly constructed this nice little world for himself in which he is the undisputed boss, but his repressed emotional life threatens to destroy everything he has.
Despite his many faults, Eddie is nonetheless a fascinating character, riven with complex and often contradictory motives. He develops throughout the play, albeit not in a particularly admirable way. The arrival of Rodolpho and Marco at his apartment represents the moment when he begins to change. He is no longer in control; the center of attention in everybody's life has shifted elsewhere. Catherine, the girl he secretly lusts after, arouses his jealousy when she starts spending more time with Rodolpho. Eddie's insinuation that Rodolpho is gay is a way for him to deal with his own complex sexuality. When he was head of the house, Eddie could play the part of the macho Italian-American patriarch without too much difficulty. However, the presence of Rodolpho changes all that. The one-dimensional facade that Eddie has presented to the world outside all these years is starting to crack and all his inner demons are now coming to the surface.
Eddie begins to start acting irrationally. He knows that his life is spiraling out of control, and he desperately wants to get it back. The fateful decision to contact the Immigration Bureau and snitch on Marco and Rodolpho should be seen in this light. All the things that previously meant so much to Eddie are now to be sacrificed in a last-ditch attempt to save the identity he has built for himself, which keeps his deepest, darkest feelings and drives in check.
The manner of Eddie's death at the hands of Marco provides a redemption of sorts. However, in some ways, it is also deeply regressive, a throwback to his traditional self-image of the macho paterfamilias achieving validation through an act of heroic violence. In his last few moments on earth, Eddie has come full circle. He has finally been freed from the tempestuous impulses that led to his destruction. He has also finally escaped from his self-constructed fantasy world. However, he could never have truly lived outside of that world, and he could only ever have achieved freedom from himself in death. Therein lies his tragedy and also any sympathy we may have for him.

Is Brutus right to join the conspiracy?

It is possible to make an argument for both sides of this debate. Brutus himself wrestles with the fact that he has always been "Caesar's angel," a close friend of Caesar's and one who was dearly loved by him. He does not want to kill his friend. However, he truly believes that Caesar wants to establish himself as a king in Rome, and that, although he has "no personal cause to spurn at him," "the general [cause]" is a compelling reason enough. He attempts to distance himself from his personal attachment to Caesar by describing him as a "serpent's egg," and those who are loyal to the ideals of the Republic must "kill him in the shell" in order to save Rome.
Later, when he is explaining himself to the assembled crowd, Brutus justifies his part in the conspiracy by asking if they would "rather Caesar were living and die all slaves, than that Caesar were dead, to live all free men?" Brutus says that he did love Caesar very much, but "loved Rome more." He loves his country so much that the death of Caesar seemed, to him, the only way to ensure that Rome would not be subjugated under Caesar's abuse of power.
Even Marc Antony, at the end of the play, describes Brutus as "the noblest Roman of them all," stating that, unlike the other conspirators, it was not "envy" of Caesar that drove his actions, but "a general honest thought / And common good to all." So, although Brutus's part in the conspiracy ends in his own death, it can be argued at least that he believed he was right in joining the conspiracy, and that he was acting out of love for his country.

Calculus of a Single Variable, Chapter 3, 3.2, Section 3.2, Problem 42

The mean value theorem is applicable to the given function, since it is a polynomial function. All polynomial functions are continuous and differentiable on R, hence, the given function is continuous and differentiable on interval.
The mean value theorem states:
f(b) - f(a) = f'(c)(b-a)
Replacing 1 for b and 0 for a, yields:
f(2) - f(-1) = f'(c)(2+1)
Evaluating f(2) and f(-1) yields:
f(2) =(2+1)/2 => f(2) =3/2
f(-1) = (-1+1)/(-1) => f(-1) = 0
You need to evaluate f'(c), using quotient rule:
f'(c) = ((c+1)/c)' => f'(c) = ((c+1)'*c - (c+1)*c')/(c^2) => f'(c) = (c - c - 1)/(c^2) => f'(c) = -1/(c^2)
Replacing the found values in equation f(2) - f(-1) = f'(c)(2+1):
3/2-0= -3/(c^2) =>1/2 =-1/(c^2)=>c^2 = -2 !in R
Hence, in this case, there is no valid c value for the mean value theorem to be applied.

How is slave trade responsible for African underdevelopment?

The slave trade contributed heavily to Africa's underdevelopment. Europe used Africa as a source for slaves, in many cases taking the strongest citizens possible. African states went to war with each other in order to obtain slaves to sell to the Europeans. This weakened the states, and even today the poorest states in Africa are the ones that contributed the most slaves to the global slave trade. The slave trade destroyed cultures and made it almost impossible for kingdoms to continue to flourish. When Europeans started to colonize Africa in earnest during the 1800s, they found weakened states that were no match for European military and administrative power. Europe's colonization of the region would not have been possible if not for centuries of the slave trade. Europe then proceeded to take natural resources from the continent without providing any benefit to the native peoples who lived there. While chattel slavery is rare now, its legacy still continues. 

As a first generation Chinese immigrant, what challenges does the mother face?

In “Rules of the Game,” the relationship between the mother and her daughter is fraught with tension (as in much of Amy Tan’s writing). This tension reveals the struggles that the mother faces as a first-generation immigrant.
Although much of the narrative revolves around the daughter’s discovery of competitive chess, the tension in the story derives from the daughter’s relationship with her mother. This is a common theme in Tan’s writing, as the daughter often becomes the avatar of the mother’s American Dream. This conflict comes to a head in “Rules of the Game” when the daughter fights with her mother at the market:

Why do you have to use me to show off? If you want to show off, then why don't you learn to play chess?

The mother sees chess as both a road to success and as a representation of the struggle of adapting to life in the United States:

"This American rules," she concluded at last. "Every time people come out from foreign country, must know rules. You not know, judge say, Too bad, go back. They not telling you why so you can use their way go forward. They say, Don't know why, you find out yourself. But they knowing all the time. Better you take it, find out why yourself." She tossed her head back with a satisfied smile.

Although the mother is not able to master chess—literally or metaphorically—her daughter is. In the closing moments of the story, the metaphor of chess transforms, and the daughter imagines it as a contest between herself and her mother. Her mother wants so badly for success through her daughter, but this desire damages their relationship.

In "The Passionate Shepherd to His Love" what does the speaker urge his love to do?

"The Passionate Shepherd to His Love" by Christopher Marlowe is written in what is called the pastoral style. This was a style of poetry quite common in Marlowe's day, a style that presented an idealized view of rural life, an idyll usually populated by satyrs, dryads, cavorting nymphs, and other lesser deities of Greek and Roman mythology.
In the first line, the speaker invites his lover to

Come live with me and be my love

He goes on to present the object of his affections with a sumptuous visual feast of natural beauty that he hopes will entice her to come and live with him:

And we will all the pleasures prove, 
That Valleys, groves, hills, and fields, 
Woods, or steepy mountain yields.

The speaker is gently trying to persuade his love; he feels that, if he can present a sufficiently appealing picture of their life together, then she will relent. Perhaps the narrator senses a certain ambivalence on her part. Perhaps the speaker's love finds the whole idea too good to be true. Time for the speaker to turn up the charm, and say it with flowers:

And I will make thee beds of Roses 
And a thousand fragrant posies, 
A cap of flowers, and a kirtle 
Embroidered all with leaves of Myrtle

Not only that, but our speaker will even create a brand new wardrobe for his lady love:



A gown made of the finest wool 
Which from our pretty Lambs we pull; 
Fair lined slippers for the cold, 
With buckles of the purest gold; 
 
A belt of straw and Ivy buds, 
With Coral clasps and Amber studs



It all sounds quite heavenly. But the narrator still feels that he needs to seal the deal:


The Shepherds’ Swains shall dance and sing 
For thy delight each May-morning: 
If these delights thy mind may move, 
Then live with me, and be my love.



So there we are. There is an offer of ravishing natural beauty, the most divine new wardrobe imaginable, and the sweet, harmonious tones of shepherds' panpipes as the couple dances delightfully, basking in the warm, radiant glow of Maytime dawn. This is the sublime Arcadian vision set before the speaker's lover.
 
But despite Marlowe's best efforts we are still far from certain as to whether or not his beloved will accept this tempting offer. For one thing, we don't anything about her, or what kind of world she'd like to inhabit. Maybe she is a nymph, and doesn't want to spend time with a mortal swain whose looks will one day fade. This is what Sir Walter Raleigh suggests in his classic rejoinder, "The Nymph's Reply to the Shepherd."
 
Unless we get the lady lover's side of the story, then we will remain uncertain as to what will happen. And it's this uncertainty that makes "The Passionate Shepherd to His Love" much more than just a conventional love poem in the pastoral style.

Precalculus, Chapter 5, 5.4, Section 5.4, Problem 22

(5pi)/12=pi/4+pi/6

sin(u+v)=sin(u)cos(v)+cos(u)sin(v)
sin(pi/4+pi/6)=sin(pi/4)cos(pi/6)+cos(pi/4)sin(pi/6)
sin(pi/4+pi/6)=(sqrt2/2)(sqrt3/2)+(sqrt2/2)(1/2)=sqrt2/4(sqrt3+1)

cos(u+v)=cos(u)cos(v)-sin(u)sin(v)
cos(pi/4+pi/6)=cos(pi/4)cos(pi/6)-sin(pi/4)sin(pi/6)
cos(pi/4+pi/6)=(sqrt2/2)(sqrt3/2)-(sqrt2/2)(1/2)=sqrt2/4(sqrt3-1)

tan(u+v)=(tan(u)+tan(v))/(1-tan(u)tan(v))
tan(pi/4+pi/6)=(tan(pi/4)+tan(pi/6))/(1-tan(pi/4)tan(pi/6))=(1+(sqrt3/3))/(1-(1)(sqrt3/3))=((3+sqrt3)/3)/((3-sqrt3)/3)=(3+sqrt3)/(3-sqrt3)
After rationalizing the denominator the answer is 2+sqrt3.

In Boyne's The Boy in the Striped Pajamas, what does Bruno's view of reading reveal about his character?

In chapter 9 of Boyne's The Boy in the Striped Pajamas, Bruno gets a private teacher named Herr Liszt during his stay in the house at Auschwitz. He quickly discovers that Liszt enjoys teaching history and geography the best. When Bruno tells his teacher that he prefers reading and art over learning about history and geography, Liszt says the following:

"Those things are useless to you . . . A sound understanding of the social sciences is far more important in this day and age" (97).

Bruno asks his teacher why reading is not considered important. Herr Liszt explains that only books that "matter in the world" are useful. Apparently, fictional story books are considered useless. Bruno tells his teacher that he also enjoys performing plays with his grandmother back in Berlin, but this does not impress Liszt. In fact, he tells Bruno that his job is to get the boy's head out of his "storybooks" (98). The fact that Bruno loves reading fiction and performing plays demonstrates his interest in being creative and imaginative. Furthermore, Bruno has not yet been spoiled by any Nazi indoctrination, prejudice, or propaganda.
 
 

What are Hamlet's most notable character traits? Do you see these traits as generally positive or negative?

Hamlet's character has been an enigma to readers and theatergoers for four hundred years. Hostile critics such as Leo Tolstoy—the great Russian novelist disliked Shakespeare's plays overall—and T.S. Eliot noted numerous inconsistencies in Hamlet's behavior which, in their opinion, made the entire tragedy defective as a work of art. In the age of film we have seen wildly different interpretations of Hamlet by actors ranging from Laurence Olivier to Derek Jacobi to Kenneth Branagh (and others). There is no straightforward or definitive answer to the question of whether Hamlet is a "realistic" character, or whether his traits are largely positive or negative. The puzzle about him is real, and there is no obvious solution.
That said, we can still make some observations about Hamlet and argue that both the character and the play are so iconic and enduring that the criticisms of Eliot, and others, are irrelevant. Most readers and audiences respond to Hamlet, in my view, precisely because his character has something irrational about it, something that reveals deep truths about human nature, not in spite of, but because of its inconsistencies and paradoxes.
Hamlet says he loves Ophelia, but he is abusive to her. This could be (and has often been so interpreted) because he is carrying out his elaborate ruse of appearing insane, but there's no proof that his behavior does not simply stem from cruelty. At Ophelia's funeral, Hamlet goes ballistic and attacks Laertes, absurdly claiming that "forty thousand brothers" could not have loved Ophelia as much as he, Hamlet, did.
Though Hamlet's obsession is to avenge his father's death, his attitude toward the Ghost is curious. He pledges vengeance but seems to mock the Ghost, calling him an "old mole." Hamlet's mindset, throughout the entire play, seems to be one of agonized self-reflection, coupled with contempt for the outside world and for the established order. He is abusive to his mother as well as to Ophelia. He evidently feels no remorse over accidentally killing Polonius. This last fact is especially interesting. Traditionally, Polonius has been portrayed as a basically harmless and rather silly old man. In Branagh's film the part is acted in a strikingly different way by Richard Briers. Not only does Polonius seem nasty and cynical, but also, one can't help thinking that he harbors incestuous feelings for Ophelia when he tries to "comfort" her after Hamlet screams at her, "To a nunnery, go!" So perhaps Hamlet's hostility to Polonius is justified, though in most interpretations, this is not the case.
All of the above would suggest that Hamlet is largely a very negative person, with a kind of boiling rage directed both inwardly and outwardly. He is clearly narcissistic and even paranoid. One wonders if he wishes to kill Claudius not just because Claudius has married Gertrude, but because Hamlet has a generalized hatred of all people. At times, Claudius, in spite of having committed murder, arguably has more claim on our sympathy than Hamlet does, not only in the scene where Claudius is praying, but also earlier, when Hamlet is taunting him, saying, "I eat the air, promise cramm'd. You cannot feed capons so." Claudius is befuddled, and honestly responds, "I have nothing with this answer, Hamlet. These words are not mine."
If, then, Hamlet has so many negative qualities, why is it that it's absolutely unthinkable to consider him a villain like Iago, or even an antihero or hero-villain, like Macbeth? I think there are two principal reasons. Hamlet is clearly a man who is suffering. In John Gielgud's recorded performance, the words "To a nunnery, go!" are pronounced with such agony that we can see, or hear, that Hamlet is dwelling in a kind of inferno. Hamlet cannot understand what is happening to him, either because the death of his father has driven him mad, or because his personality is already dysfunctional and pathological. Yet, his chief character trait, in my opinion, is alienation.
Though Hamlet views himself a stranger in the world, the words Shakespeare gives him arouse our sympathies at critical moments in the tragedy. "To be or not to be" is a soliloquy so powerfully expressive of the universal human condition that, arguably, nothing else in literature equals it. No one can listen to these words and not feel that the character who speaks them is a man who represents, and speaks for, all of us.
In summary, Hamlet is a man of largely negative outward traits. But his inner soul is in turmoil, and he is therefore an emblem of humanity. And his loyalty to his father's memory is perhaps a positive trait that cancels out the negative ones. His inconsistency and irrationality make sense, from the standpoint of drama, because these are characteristics, shown by Shakespeare in a larger-than-life form, that all people, everywhere, can understand and can identify with.

Single Variable Calculus, Chapter 7, Review Exercises, Section Review Exercises, Problem 48

Prove that $\displaystyle \frac{d}{dx} \left( \frac{1}{2} \tan^{-1} x + \frac{1}{4} \ln \frac{(x + 1)^2}{x^2 + 1} \right) = \frac{1}{(1 + x)(1 + x^2)}$

Solving for the left-hand side of the equation


$
\begin{equation}
\begin{aligned}

\frac{d}{dx} \left( \frac{1}{2} \tan^{-1} x + \frac{1}{4} \ln \frac{(x + 1)^2}{x^2 + 1} \right) =& \frac{1}{2} \frac{d}{dx} (\tan^{-1} x) + \frac{1}{4} \ln (x + 1)^2 - \frac{1}{4} \ln (x^2 + 1)
\\
\\
=& \frac{1}{2} \frac{d}{dx} (\tan^{-1} x) + \frac{2}{4} \frac{d}{dx} [\ln (x + 1)] - \frac{1}{4} \frac{d}{dx} [\ln (x^2 + 1)]
\\
\\
=& \frac{1}{2} \cdot \frac{1}{ 1 +x^2} + \frac{1}{2} \cdot \frac{1}{x + 1} \frac{d}{dx} (x + 1) - \frac{1}{4} \cdot \frac{1}{x^2 + 1} \frac{d}{dx} (x^2 + 1)
\\
\\
=& \frac{1}{2(1 + x^2)} + \frac{1}{2(x + 1)} - \frac{1}{4(x^2 + 1)} \cdot 2x
\\
\\
=& \frac{1}{2 (1 + x^2)} + \frac{1}{2(x + 1)} - \frac{2x}{4 (x^2 + 1)}
\\
\\
=& \frac{1}{2 (1 + x^2)} + \frac{1}{2(x + 1)} - \frac{x }{2 (x^2 + 1)}
\\
\\
=& \frac{1}{2} \left( \frac{1}{1 + x^2} + \frac{1}{x + 1} - \frac{x}{x^2 + 1} \right)
\\
\\
=& \frac{1}{2} \left( \frac{1 - x}{x^2 + 1} + \frac{1}{x + 1} \right)
\\
\\
=& \frac{1}{2} \left[ \frac{(1 - x)(x + 1) + x^2 + 1}{(x^2 + 1)(x + 1)} \right]
\\
\\
=& \frac{1}{2} \left[ \frac{\cancel{x} + 1 - \cancel{x^2} - \cancel{x} + \cancel{x^2} + 1}{(x^2 + 1) (x + 1)} \right]
\\
\\
=& \frac{1}{\cancel{2}} \left[ \frac{\cancel{2}}{(x^2 + 1) (x + 1)} \right]
\\
\\
=& \frac{1}{(x^2 + 1) (x + 1)}
\\
\\
& \text{or}
\\
\\
=& \frac{1}{(1 + x) (1 + x^2)}




\end{aligned}
\end{equation}
$

Why did Wendy and Peter focus their attention on the African veldt?

The text of Ray Bradbury's 1950 short story entitled "The Veldt" provides many clues as to why Wendy and Peter focus their attention on the African veldt.
Bradbury's story is futuristic, imagining a time when houses do everything for the inhabitants. In this case, the HappyLife Home cooks, cleans, bathes, entertains, and takes care of every aspect of daily living. The children have a nursery that reads their thoughts and brings their imaginations to life, complete with three-dimensional visuals, smells, and sounds. Lydia and George Hadley have catered to their children's whims in every way. When they become concerned about the nursery, they divulge the children's obsession with it to the reader. Consider this exchange between George and Lydia, in which George is asking his wife to lock the nursery:

“And lock the nursery for a few days until I get my nerves settled.”
“You know how difficult Peter is about that. When I punished him a month ago by locking the nursery for even a few hours — the tantrum be threw! And Wendy too. They live for the nursery.”
“It’s got to be locked, that’s all there is to it.”
“All right.”

Later, George is reflecting on his decision to purchase the HappyLife Home system and thinking about how it works. He hints as to why Wendy and Peter would be conjuring an African veldt—they are thinking about revenge and death.


"Remarkable how the nursery caught the telepathic emanations of the children’s minds and created life to fill their every desire. The children thought lions, and there were lions. The children thought zebras, and there were zebras. Sun — sun. Giraffes — giraffes. Death and death. That last. He chewed tastelessly on the meat that the table had cut for him. Death thoughts. They were awfully young, Wendy and Peter, for death thoughts. Or, no, you were never too young, really. Long before you knew what death was you were wishing it on someone else. When you were two years old you were shooting people with cap pistols."

George and Lydia begin reflecting on the things that have gone wrong. George repeats a proverb that says children are like carpets—they must be stepped on occasionally. He reflects that he and his wife have never lifted a finger to correct their children. He admits to his wife that the children have become insufferable, and points to several examples in which they as parents had to say no for safety reasons. Their children's requests have become more and more outrageous. The parents call in a psychologist who explains that the purpose of the room is to analyze children's neuroses and then provide treatment. His recommendation is to immediately close the nursery and bring the children to him every day for treatment.
But Wendy and Peter have become addicted to the nursery, and virtually estranged from their parents. They know that their parents are the only thing that stands between them and the nursery. They have set a trap to dispose of their parents in the nursery, in an African veldt.

For Wendy and Peter, the nursery is the center of their lives in their Happylife home. The home does everything for the family, leaving the family, especially, Mrs. Hadley, at loose ends. The Happylife nursery "parents" the children, indulging their desire to watch films of the African veldt. According to the psychologist, David McClean, who comes to evaluate the children after the parents become concerned about their obsessive interest in the veldt and its harsh "law of the jungle" ethos, including the screams of people being eaten by lions, the psychologist advises that they turn off the view screens in the nursery. The veldt dehumanizes the children and allows them to indulge the natural aggressions children feel toward their parents to an unnatural level.

Single Variable Calculus, Chapter 3, 3.7, Section 3.7, Problem 4

Suppose that a particle moves according to a Law of Motion

$\displaystyle f(t) = \frac{t}{1 + t^2}$, where $t$ is measured in
seconds and $s$ in feet.

a.) Determine the velocity at time $t$.




$
\begin{equation}
\begin{aligned}

\text{velocity } =& s'(t) = \frac{ds}{dt}
\\
\\
& \text{Using Quotient Rule}
\\
\\
v(t) =& \frac{\displaystyle (1 + t^2) \frac{d}{dt} (t) - t \frac{d}{dt} (1 + t^2)}{(1 + t^2)^2}
\\
\\
v(t) =& \frac{(1 + t^2)(1) - t (2t) }{(1 + t^2)^2}
\\
\\
v(t) =& \frac{1 + t^2 - 2t^2}{(1 + t^2)^2}
\\
\\
v(t) =& \frac{-t^2 + 1}{(1 + t^2)^2}

\end{aligned}
\end{equation}
$


b.) What is the velocity after $3 s$?


$
\begin{equation}
\begin{aligned}

\text{The velocity after $3 s$ is } v(3) =& \frac{-(3)^2 + 1}{(1 + (3)^2)^2}
\\
\\
v(3) =& -0.08 ft/s

\end{aligned}
\end{equation}
$


c.) When is the velocity at rest?

The velocity is at rest when $v(t) = 0$


$
\begin{equation}
\begin{aligned}

0 =& \frac{-t^2 + 1}{(1 + t^2)^2}
\\
\\
t^2 =& 1
\\
\\
t =& \pm \sqrt{1}
\\
\\
t =& 1 \text{ and } t = -1
\end{aligned}
\end{equation}
$


The required time is $t = 1$ since the position function is defined only for positive values of $t$.

d.) When is the particle moving in the positive direction?

The particle is moving in the positive direction when $v(t) > 0$


$
\begin{equation}
\begin{aligned}

& \frac{-t^2 + 1}{(1 + t^2)^2} > 0

\end{aligned}
\end{equation}
$


Assume $\displaystyle \frac{-t^2 + 1}{(1 + t^2)^2}$ we have $t = 1$


Dividing the interval $t \geq 0$ into two parts we have,

(i) $0 \leq t \leq 1$

Let's assume $t = 0.5: \displaystyle \frac{-(0.5)^2 + 1}{(1 + (0.5)^2)^2}= 0.48 > 0$

(ii) $t > 1$

Let's assume $\displaystyle t = 3: \frac{-(3)^2 + 1}{(1 + (3)^2)^2} = -0.08 < 0$

Therefore, we can conclude that the particle is speeding up at the
interval $0 \leq t \leq 1$. However, the particle is moving in the positive direction.

e.) Find the total distance traveled during the first $8 s$.

Since we know that the particle starts at and changes direction at
$t = 1$, we take the distance that the particle traveled on the intervals $(0,1)$ and $(1,8)$


$
\begin{equation}
\begin{aligned}

\text{Total distance } =& |f(1) - f(0)| + f(8) - f(1) | ; f(t) = \frac{t}{1 + t^2}
\\
\\
=& |0.5 - 0 | + \left|\frac{8}{65} - \frac{1}{2} \right|
\\
\\
=& 0.5 + \left| - \frac{49}{130} \right|
\\
\\
=& 0.5 + \frac{49}{130}
\\
\\
=& 0.8769 ft

\end{aligned}
\end{equation}
$



f.) Illustrate the motion of the particle.







g.) Find the acceleration at time $t$ and after $3 s$.

Using Quotient Rule and Chain Rule,


$
\begin{equation}
\begin{aligned}

\text{acceleration } =& v'(t) = \frac{dv}{dt}
\\
\\
a(t) =& \frac{\displaystyle (1 + t^2)^2 \cdot \frac{d}{dt} (-t^2 + 1) - (-t^2 + 1) \cdot \frac{d}{dt} (1 + t^2)^2 }{[(1 + t^2)^2]^2 }
\\
\\
a(t) =& \frac{(1 + t^2) \cdot (-2t) - (-t^2 + 1) [2 (1 + t^2) \cdot (2t)] }{[(1 + t^2)^2]^2}
\\
\\
a(t) =& \frac{\cancel{(1 + t^2)} [-2t(1 + t^2) - 4t (-t^2 + 1)] }{(1 + t^2)^{\cancel{4}}}
\\
\\
a(t) =& \frac{-2t - 2t^3 + 4t^3 - 4t}{(1 + t^2)^3}
\\
\\
a(t) =& \frac{2t^3 - 6t}{(1 + t^2)^3}
\\
\\
\text{Acceleration at } t = 3,
\\
\\
a(3) =& \frac{2(3)^3 - 6 (3)}{(1 + (3)^2)^3}
\\
\\
a(3) =& 0.036 ft/s^2
\end{aligned}
\end{equation}
$


h.) Graph the position, velocity and acceleration functions $0 \leq t
\leq 8$.







i.) When is the particle speeding up? When is it slowing down?

Based from the graph, the particle is speeding up when the velocity
and acceleration have the same sign (either positive or negative). Notice in the curve that the acceleration changes direction in between $1 < t < 2$ where $a(t) = 0$ so,


$
\begin{equation}
\begin{aligned}

0 =& \frac{2t^3 - 6t}{(1 + t^2)^3}
\\
\\
2t^3 =& 6t
\\
\\
t^2 =& 3
\\
\\
t =& \pm \sqrt{3}
\end{aligned}
\end{equation}
$


Hence, we can conclude that the particle is speeding up at interval

$1 < t < \sqrt{3}$

On the other hand, the particle is slowing down when the velocity and acceleration have opposite sign that is $0 \leq t \leq 1$ and $\sqrt{3} \leq t \leq 8$.

You are an employee of a US firm that produces personal computers in Thailand and then exports them to the US and other countries for sale. The personal computers were originally produced in Thailand to take advantage of relatively low labor costs and a skilled workforce. Other possible locations considered at that time were Malaysia and Hong Kong. The US government decides to impose punitive 100% ad valorem tariffs on imports of computers from Thailand to punish the country for administrative trade barriers that restrict US exports to Thailand. 1. How do you think your firm should respond? 2. What does this tell you about the use of targeted trade barriers?

In the case that the United States imposes punitive 100 percent ad valorem tariffs, the entire cost of the import is taxed.
There are various reasons why the government would want to impose tariffs, with the main reason in this case being that the government is trying to punish Thailand for their trade barriers against US exports. Since a political agenda is the only reason for the tariff, the firm can conclude that there is no defect in the actual product coming from Thailand.
There are various ways the firm could respond. Since there is no defect in Thailand’s computers, the firm could turn to the World Trade Organization to settle the trade dispute in order to further reap the benefits of Thailand’s efficiency and cheap labor costs.
Another way the firm could respond is to revisit Malaysia and Hong Kong as possible locations for future computer production. This option is risky since there is no guarantee that the computers will be of the same quality as Thailand’s. The labor could also cost more, thus affecting the overall cost of the computers. This affects the consumers in the sense that they could be charged more money, or they might not receive the same quality computer that they were used to.
The use of targeted trade barriers tends to affect the consumers of a certain product and not the producers. The manufacturers can easily migrate to another location for labor; however, it is the consumer that will need to pay for the potential difference in price or quality.
http://fbemoodle.emu.edu.tr/course/view.php?id=1441

Possible Response of U.S. Firm
A U.S. firm responding to a U.S. ad valorem tariff (product value tariff) imposed on a country to where the manufacture of the firm's product is outsourced might be (1) a relocation to a free trade zone (FTZ) or (2) a political appeal through lobbying to have the punitive tariff repealed. Since the newly imposed U.S. tariff--adding a duty at 100 percent of the value of the computer--is a retaliation for a Thai administrative trade barrier that adopts rules for regulating U.S. imports into Thailand, the U.S. computer firm can escape the consequences of the governmental policy issue by moving manufacturing to Malaysia or Hong Kong (alternative early contenders). Such a relocation is not unprecedented as shown by the (economically and environmentally disasterous) removal of electronics companies from Mexico's maquiladoras, after their boom in the late 1990s, to relocate in Asia to take advantage of lower costs.Another option is to focus on lobbying in the political arena for the reduction of punitive trade barriers. One strategy would be lobbying to incentivize Thailand's importation of U.S. goods through an appropriate means. Another strategy would be to aim to focus attention in bilateral talks on reducing subsidiaries, regarding such reduction as an economic priority.
Targeted Trade Barriers
Economists generally agree that targeted trade barriers restrict economic growth, causing global demand to decline and threatening global market stability. An example of this occurred in 2009 when Mexico retaliated against U.S. cancellation of a Mexico-U.S. agreement regarding Mexican truck drivers. Examining targeted trade barriers and potential responses tells us that protectionist trade policies and targeted trade barriers carry negative ramifications for the health of the global market.
https://www.britannica.com/topic/international-trade/State-interference-in-international-trade

Why couldn’t Leslie go to Terabithia that weekend?

In Bridge to Terabithia, Leslie cannot go to Terabithia on the weekends because Mr. Burke is in the process of repairing the old Perkins place and wants Leslie to be around. Mrs. Burke is busy writing a book, so she is unable to help. This leaves Leslie responsible for "hunting and fetching" for her absentminded father. Leslie has a talent for finding the items that he misplaces, and her father enjoys having her for company. Additionally, Leslie loves fixing up the house, appreciates being needed by her father, and enjoys the fact that she is gaining a better understanding of her father. 
This is troublesome for Jess, who finds it difficult to create the same sense of magic in Terabithia when he goes there alone; he believes that the magic is "reluctant" to come to him when Leslie is not there.

Calculus: Early Transcendentals, Chapter 3, 3.5, Section 3.5, Problem 27

Note:- 1) If y = x^n ; then dy/dx = n*x^(n-1) ; where n = real number
2) If y = u*v ; where both u & v are functions of 'x' , then
dy/dx = v*(du/dx) + u*(dv/dx)
3) If y = k ; where 'k' = constant ; then dy/dx = 0
Now, the given function is :-
(x^2) + xy + (y^2) = 0
or, 2x + y + x*(dy/dx) + 2y*(dy/dx) = 0
Thus, putting x = y = 1 ; we get
3 + 3*(dy/dx) = 0
or,
or, dy/dx = -1 = slope of the tangent to the curve at (1,1)
Thus, equation of the tangent line to the given curve at the point (1,1) is :-
y - 1 = (-1)*(x - 1)
or, y -1 = -x + 1
or, x + y = 2 equation of the tangent

Single Variable Calculus, Chapter 3, 3.7, Section 3.7, Problem 30

a.) Using Quotient Rule

$
\begin{equation}
\begin{aligned}
S = \frac{dR}{dx} &= \frac{\left(1+4x^{0.4}\right) \frac{d}{dx}\left( 40 + 24x^{0.4}\right) - [ 40 + 24x^{0.4}]\frac{d}{dx} \left(1+4x^{0.4}\right)}{\left(1+4x^{0.4}\right)^2}\\
\\
\frac{dR}{dx} &= \frac{\left(1+4x^{0.4}\right)\left(9.6x^{-0.6}\right) - [40 + 24x^{0.4}] \left(1.6x^{-0.6}\right) }{\left(1+4x^{0.4}\right)^2}\\
\\
\frac{dR}{dx} &= \frac{9.6x^{-0.6} + 38.4x^{-0.2}-65x^{-0.6}-38.4x^{-0.2}}{\left(1+4x^{0.4}\right)^2}\\
\\
\frac{dR}{dx} &= \frac{-54.4x^{-0.6}}{\left(1+4x^{0.4}\right)^2}
\end{aligned}
\end{equation}
$


Therefore, the sensitivity is $\displaystyle s = \frac{dR}{dx} = \frac{-54.4}{x^{0.6}\left(1+4x^{0.4}\right)^2}$

b.)



The graph shows that a small stimulus $x$ produces a large reaction on the body and indicates an extremely high sensitivity which is something we do not expect.

What is molality?

In chemistry, the concentration of a solution refers to the amount of solute dissolved in a solution. There are various ways to report concentrations depending on the units used. Some of the most common ones are molarity, molality, and percentages. Percent of a solute can be weight by volume (w/v) or weight by weight (w/w), which is simply the ratio of the mass of the solute to the total volume or weight of the solution.
Molarity and molality makes use of the ratio of the moles of solute to either the volume (in liter) of solution or the mass (in kilogram) of solvent, respectively. Molality is most often used in experiments that involve a significant change in temperature as molarity is sensitive to temperature due to expansion/compression that may result to significant changes in volume - and hence, apparent concentration.
In brief, molality is one way to express the concentration of a solution. It is the ratio of the number of moles of solute to the mass in kilograms of solution:
m = (n_(solute))/(mass_(solvent)) .