What does the book Frindle teach small kids?

Frindle can be seen as teaching children how language develops and how it works. Ultimately, words in themselves mean nothing; meaning is derived from how they are used. We can look up a word in the dictionary and find out its definition, but the way we use words on a daily basis gives them their deepest meaning, one that forms the basis of our communication with each other.

Mrs. Granger has a somewhat pedantic understanding...

Frindle can be seen as teaching children how language develops and how it works. Ultimately, words in themselves mean nothing; meaning is derived from how they are used. We can look up a word in the dictionary and find out its definition, but the way we use words on a daily basis gives them their deepest meaning, one that forms the basis of our communication with each other.

Mrs. Granger has a somewhat pedantic understanding of words, deriving from her education and work as a teacher. That object the children use for writing isn't a "frindle;" it's a pen, because that's what it says in the dictionary. The author isn't suggesting that it's wrong to use the word "pen." After all, its own meaning has also derived from its use over time. But the point that's being made in the story is that the word "pen" arose in the exact same way as "frindle." And eventually we find out that Mrs. Granger understood this all along. She deliberately prohibited the use of "frindle" by her pupils because she knew it would become popular. She knew that widespread use of the word would give it its meaning.

One of the things that Swift examined critically in Gulliver's Travels is the government's role in education. Where in the book does it talk about...

When Gulliver is among the Lilliputians, he learns about their system of education. Swift writes, "parents are the last of all others to be trusted with the education of their own children." Parents must deliver their children, both boys and girls, to state-run nurseries when the children are 20 months old. There, the children are trained to occupy roles that are similar to those of their parents. In other words, the sons of the wealthy receive...

When Gulliver is among the Lilliputians, he learns about their system of education. Swift writes, "parents are the last of all others to be trusted with the education of their own children." Parents must deliver their children, both boys and girls, to state-run nurseries when the children are 20 months old. There, the children are trained to occupy roles that are similar to those of their parents. In other words, the sons of the wealthy receive a particular form of education, and sons of the merchants receive another form of education (girls' education is different). Only the children of laborers do not attend school. 

State-run education is still a very important topic today and one that is fiercely debated. Some critics argue that American education perpetuates inequality, as the system of education among the Lilliputians does, because children of wealthier families generally go to schools with better resources and get better educations than do children of less well-to-do families. Therefore, the way in which Swift satirizes education in Gulliver's Travels mirrors the modern debate over the way in which our school system prevents social mobility and keeps the elite in a dominant position. 

In The Iliad, what are four results of Achilles' pride?

There are four major results of Achilles' pride to be found throughout TheIliad, including alienation, wrath, vengeance, and death.

Alienation

The Greek warrior Agamemnon insults Achilles' pride by demanding that he surrender Briseis. Briseis was a maid Achilles had claimed as a prize of war, and Agamemnon's demand challenges Achilles' status as a leader. As a result, he withdraws from the Greek forces and does nothing to help when the Trojans attack. This...

There are four major results of Achilles' pride to be found throughout The Iliad, including alienation, wrath, vengeance, and death.

Alienation

The Greek warrior Agamemnon insults Achilles' pride by demanding that he surrender Briseis. Briseis was a maid Achilles had claimed as a prize of war, and Agamemnon's demand challenges Achilles' status as a leader. As a result, he withdraws from the Greek forces and does nothing to help when the Trojans attack. This alienation segues directly into the next result of Achilles' pride, which is his wrath.

Wrath

Achilles' pride commonly results in wrath, which is a major theme throughout The Iliad. The Muse is even asked to sing of the "wrath of Achilles." Achilles has a strong sense of honor that leads him to wrath as a response to certain events that violate his high standards of honor, particularly the capture of Briseis. To the Greeks, honor was based on the pursuit of excellence, nobility, valor, and accomplishment. The wrath of Achilles is strongly related to each concept, and all stem from his pride as a warrior. Whenever Achilles' pride leads him to feel that his honor has been violated, wrath is the result.

Vengeance

When Achilles' friend Patroclus is killed by Hector, Achilles' pride plays a large role in his quest for vengeance. It is also his pride, both in himself as a warrior and in his friendship with Patroclus, that leads him to kill Hector on the battlefield. Despite Achilles' disdain for the fallen warrior, Hector's father successfully recovers his son's body by appealing to Achilles' pride through begging.

Death

As the son of a mortal man and a goddess, Achilles was given the choice between living with the gods in a peaceful existence and pursuing glory among the humans. He chooses the life of a warrior and, in doing so, dies the death of an honored mortal. This choice exemplifies Achilles' pride better than any other. Rather than live a peaceful and long life without valor, his pride motivates him to lead the dangerous life of a warrior. Achilles is the greatest warrior among the Achaeans, which further bolsters his pride and confidence.

Throughout The Iliad, it is heavily implied that Achilles' fabled heel is a metaphor for his pride. After being dipped in the river Styx, Achilles is invulnerable everywhere except the heel by which his mother held him. Both his pride and his heel serve as his primary weaknesses. In the end, Achilles is killed by an arrow that strikes his vulnerable heel. Hector's brother is the one who shoots the arrow and kills Achilles out of vengeance. Because Achilles' pride was the primary reason he killed Hector, it could be argued that his pride indirectly leads to his own death.

Through these four results of Achilles' pride, we see that this characteristic is both his greatest strength and his most fatal weakness.

How did Bryon feel about the girls he dated in That Was Then, This Is Now? What did this reveal about him?

Throughout the novel, Bryon portrays himself as a ladies man who enjoys flirting and hooking up with various girls. In Chapter 1, Bryon mentions that he's not afraid to lie to girls if he can get away with it. He then admits to telling girls he was in love with them insincerely. As the novel progresses, Bryon begins to fall in love with Cathy. He says the only thing about Cathy that bothers him is...

Throughout the novel, Bryon portrays himself as a ladies man who enjoys flirting and hooking up with various girls. In Chapter 1, Bryon mentions that he's not afraid to lie to girls if he can get away with it. He then admits to telling girls he was in love with them insincerely. As the novel progresses, Bryon begins to fall in love with Cathy. He says the only thing about Cathy that bothers him is that she is not obsessed with him like most girls. After Cathy meets Bryon's ex-girlfriend, he is pleasantly surprised to find out she is not jealous of Angela. He says Cathy was the first girl he dated who wasn't scared of other women. Bryon decides Cathy has more sense than the other girls he's dated. Bryon's confessions about his past relationships and feelings towards females reveal he is a rather shallow individual. Bryon's attitude towards women suggests he also has self-esteem issues because he was attracted to jealous girls who lacked confidence. His nonchalant attitude toward authentic relationships also depicts his immature personality.

What are some quotes from chapter 9 in Percy Jackson and the Olympians: The Lightning Thief?

In chapter nine of Percy Jackson and the Olympians: The Lightning Thief, Percy is moved to cabin three by Chiron, where he is not forced to share his space with anyone. Despite having his own breathing space, this makes Percy very unhappy:

Just when I'd started to feel accepted, to feel I had a home in cabin eleven and I might be a normal kid—or as normal as you can be when you're a...

In chapter nine of Percy Jackson and the Olympians: The Lightning Thief, Percy is moved to cabin three by Chiron, where he is not forced to share his space with anyone. Despite having his own breathing space, this makes Percy very unhappy:

Just when I'd started to feel accepted, to feel I had a home in cabin eleven and I might be a normal kid—or as normal as you can be when you're a half-blood—I'd been separated out as if I had some rare disease.

This chapter marks the continuation of Percy's struggle with his identity as a half-blood and the son of Poseidon, one of the Big Three gods. When Grover comes to fetch Percy to go see Mr. D, Percy thinks:

I figured it was a crime for me just to be alive.

Dionysus seems to reflect that negativity back to Percy, as he cruelly states:

If I had my way . . . I could cause your molecules to erupt in flames We'd seep up the ashes and be done with a lot of trouble. But Chiron seems to feel this would be against my mission at this cursed camp: to keep you little brats safe from harm.

During this chapter, Percy also gets confirmation that conflict is raging between Poseidon and Zeus. Zeus thinks that Poseidon has stolen his master bolt in order to have the Cyclops construct illegal copies of it in order to eventually stage a coup against Zeus and dethrone him. Zeus believes that Percy himself may have been responsible for sneaking into Olympus and stealing the weapon on behalf of his father. The war that may break out as a result is described as follows:

Imagine the world in chaos. Nature at war with itself. Olympians forced to choose sides between Zeus and Poseidon. Destruction. Carnage. Millions dead. Western civilization turned into a battleground so big it will make the Trojan War look like a water-balloon fight. 

`int x^2/sqrt(2x-x^2) dx` Complete the square and find the indefinite integral

Recall that indefinite integral follows `int f(x) dx = F(x) +C`

where:

`f(x)` as the integrand function

`F(x)` as the antiderivative of `f(x)`

`C` as the constant of integration..

To evaluate the given integral problem: `int x^2/sqrt(2x-x^2) dx` , we apply completing the square on the expression: `2x-x^2` .

Completing the square:

Factor out `(-1)`  from `2x-x^2` to get `(-1)(x^2-2x)`

The `x^2-2x` or `x^2-2x+0` resembles` ax^2+bx+c` where:

`a= 1` and `b =-2` that we can plug-into `(-b/(2a))^2` .

`(-b/(2a))^2= (-(-2)/(2*1))^2`

               `= (2/2)^2`

               ` = 1^2`

               ` =1`

To complete the square, we add and subtract `1` inside the ():

`(-1)(x^2-2x) =(-1)(x^2-2x+1 -1)`

Distribute `(-1)` in "`-1` "to move it outside the () .

`(-1)(x^2-2x+1 -1)= (-1)(x^2-2x+1)+ (-1)(-1)`

                                        `= (-1)(x^2-2x+1)+ 1`

Apply factoring for the perfect square trinomial: `x^2-2x+1= (x-1)^2`

`(-1)(x^2-2x+1)+ 1=-(x-1)^2 + 1`

                                         `= 1-(x-1)^2`

Apply  `2x-x^2=1-(x-2)^2`  to the integral, we get: `int x^2/sqrt(1-(x-1)^2) dx`

Apply u-substitution by letting `u =x-1` then `x = u+1` and `du =dx` . The integral becomes:

`int x^2/sqrt(1-(x-1)^2) dx=int (u+1)^2/sqrt(1-u^2) du`

Apply FOIL method on `(u+1)^2` , we get:

`(u+1)^2 = (u+1) *(u+1)`

               `= u*u +u*1 + 1*u +1*1`

              `= u^2 +u+u+1`

              `= u^2+2u +1`

Plug-in `(u+1)^2= u^2+2u +1` on the integral, we get:

`int (u+1)^2/sqrt(1-u^2) dx =int (u^2+2u +1)/sqrt(1-u^2) du`

 Apply the basic integration property: `int (u+v+w) dx = int (u) dx + int (v) dx+int (w) dx` .      

`int (u^2+2u +1)/sqrt(1-u^2) du=int u^2/sqrt(1-u^2) du +int (2u)/sqrt(1-u^2) du+int 1/sqrt(1-u^2) du`

Each integral resembles formula from integration table for rational function with roots. For the first integral, we follow: `int (x^2 dx)/sqrt(a^2-x^2) =-(xsqrt(a^2-x^2))/2 +(a^2arcsin(x/a))/2 +C` .

Then,

`int u^2/sqrt(1-u^2) du =-(usqrt(1-u^2))/2 +(1arcsin(u/1))/2`

                       ` =-(usqrt(1-u^2))/2 +arcsin(u)/2`

For second integral,  we follow:  `int x/sqrt(a^2-x^2)dx= -sqrt(a^2-x^2)+C` .

`int (2u)/sqrt(1-u^2) du =2int u/sqrt(1-u^2) du`

                         `=2 *[-sqrt(1-u^2)]`

                          `=-2sqrt(1-u^2)`

For the third integral, we follow:  `int dx/(a^2-x^2)dx=arcsin(x/a)+C` .

`int 1/sqrt(1-u^2) du = arcsin(u/1) or arcsin(u)`

Combining the results, we get:

`int (u^2+2u +1)/sqrt(1-u^2) du=-(usqrt(1-u^2))/2 +arcsin(u)/2-2sqrt(1-u^2)+arcsin(u) +C`

 Plug-in `u = x-1` , we get the indefinite integral as:

`int x^2/sqrt(2x-x^2) dx`

`=-((x-1)sqrt(1-(x-1)^2))/2 +arcsin(x-1)/2-2sqrt(1-(x-1)^2)+arcsin(x-1) +C`

Recall `1-(x-1)^2 = 2x-x^2` then  the integral becomes:

`int x^2/sqrt(2x-x^2)dx`

`= (( -x+1)sqrt(2x-x^2))/2 +arcsin(x-1)/2-(4sqrt(2x-x^2))/2+(2arcsin(x-1))/2 +C`

`= [arcsin(x-1) + 2arcsin(x-1)]/2 + [( -x+1)sqrt(2x-x^2)-4sqrt(2x-x^2)]/2+C`

`=(3arcsin(x-1))/2 + ((-x-3)sqrt(2x-x^2))/2 +C`

`=(3arcsin(x-1))/2 +((-1)(x+3)sqrt(2x-x^2))/2 +C`

`=(3arcsin(x-1))/2-((x+3)sqrt(2x-x^2))/2 +C`

or  `(3arcsin(x-1))/2-(xsqrt(2x-x^2))/2 -(3sqrt(2x-x^2))/2+C`

What happens in chapters 20 and 21 of The Journey to the West?

In The Journey to the West, Chapter 20 begins with the Tang priest encountering trouble on the Yellow Wind Ridge. Sanzang has been traveling with his followers for half a day when they reach the mountain. A whirlwind forms and Monkey remarks that it smells like a "tiger" or "monster wind." A striped tiger soon attacks the group and Pig confronts the beast. The tiger sheds its skin and transforms into a hurricane, carrying...

In The Journey to the West, Chapter 20 begins with the Tang priest encountering trouble on the Yellow Wind Ridge. Sanzang has been traveling with his followers for half a day when they reach the mountain. A whirlwind forms and Monkey remarks that it smells like a "tiger" or "monster wind." A striped tiger soon attacks the group and Pig confronts the beast. The tiger sheds its skin and transforms into a hurricane, carrying Sanzang off while he is reciting his meditations.

Chapter 21 begins as the wind monster takes a captured Sanzang to the Yellow Wind Cave in the Yellow Ridge. Sanzang is bound and offered up to the monster's leader as a meal. Monkey soon learns where Sanzang is being held and challenges the Yellow Wind Monster to a fight. After dozens of rounds of intense fighting, the Great Sage and the monster find themselves evenly matched. Monkey plucks out a hair, chews it into many smaller pieces, and transforms each piece into a clone of himself. Multiplied by a hundred, Monkey's army becomes a formidable threat to the monster.

The battle takes a turn when the wind monster releases a large yellow hurricane on the group. The hurricane catches Monkey's clones up in the air and makes it impossible for them to fight. Monkey finally recovers but discovers that the Bodhisattva Lingji is the only one who can stop the hurricane wind. Once the Bodhisattva Lingji travels down from the mountain, he is able to overcome the monster. The chapter ends after the group learns the truth of the monster's original form as a brown marten that was turned into a spirit monster.