How can I write a three-sentence summary of Fahrenheit 451?

This is a very difficult book to summarize in only three sentences. These are long winded sentences and massively simplify the events in the text. This is just an example, but I would be very hard pressed to fit much more in without run on sentences with extra conjunctions. You might try something like this:

Guy Montag, a fireman who burns books for a living in a world where reading is illegal, meets Clarisse, a thoughtful girl and a lover of books. She gives him a new lease on life and the desire to change things, resulting in him stealing books. Those books are found and burned, so Montag flees to a community of people who introduce themselves by a book they have memorized.

The play opens (Act I, Sc. 1) with three witches speaking. What might they be talking about and why might they have decided on this specific...

In the opening scene, the three "weird sisters" mention that they are going to meet with Macbeth. They all say, "Fair is foul, and foul is fair" (1.1.10), introducing the paradox of the drama, and one that perplexes Macbeth, leading him to nefarious acts that he will consider "fair" because they further his ambition.

Because the Chain of Being in which the Elizabethans believed constitutes the structure of Shakespeare's plays, the psychological composition of his characters, and the fates that they confront, the supernatural element is essential to Macbeth as it is in other plays. Nevertheless, the preternatural element in this drama is a stronger element than in many of the other plays, perhaps because Macbeth is an impressionable character who is deeply affected by outside influences. Furthermore, in Scene 3 of this opening act, the three witches call themselves the "[T]he weird sisters," with "weird" meaning that they are Destiny-serving; therefore, they are the carriers of Macbeth's fate, and play an essential role in the tragedy.

`x/(16x^4 - 1)` Write the partial fraction decomposition of the rational expression. Check your result algebraically.

`x/(16x^4-1)`

Let's factorize the denominator,

`16x^4-1=(4x^2)^2-1`

`=(4x^2+1)(4x^2-1)`

`=(4x^2+1)(2x+1)(2x-1)` 

Let `x/(16x^4-1)=A/(2x+1)+B/(2x-1)+(Cx+D)/(4x^2+1)`

`x/(16x^4-1)=(A(2x-1)(4x^2+1)+B(2x+1)(4x^2+1)+(Cx+D)(2x+1)(2x-1))/((2x+1)(2x-1)(4x^2+1))`

`x/(16x^4-1)=(A(8x^3+2x-4x^2-1)+B(8x^3+2x+4x^2+1)+(Cx+D)(4x^2-1))/((2x+1)(2x-1)(4x^2+1))`

`x/(16x^4-1)=(A(8x^3-4x^2+2x-1)+B(8x^3+4x^2+2x+1)+4Cx^3-Cx+4Dx^2-D)/((2x+1)(2x-1)(4x^2+1))`

`x/(16x^4-1)=(x^3(8A+8B+4C)+x^2(-4A+4B+4D)+x(2A+2B-C)-A+B-D)/((2x+1)(2x-1)(4x^2+1))`

`:.x=x^3(8A+8B+4C)+x^2(-4A+4B+4D)+x(2A+2B-C)-A+B-D`

equating the coefficients of the like terms,

`8A+8B+4C=0`        ----- equation 1

`-4A+4B+4D=0`     ----- equation 2

`2A+2B-C=1`            ----- equation 3

`-A+B-D=0`             ------ equation 4

Now we have to solve the above four equations to find the solutions of A,B,C and D.

From equation 1,

`4(2A+2B+C)=0`

`2A+2B+C=0`

Subtract equation 3 from the above equation,

`(2A+2B+C)-(2A+2B-C)=0-1`

`2C=-1`

`C=-1/2`

From equation 2,

`4(-A+B+D)=0`

`-A+B+D=0`

Now subtract equation 4 from the above equation,

`(-A+B+D)-(-A+B-D)=0`

`2D=0`

`D=0`

Now plug in the values of C in the equation 3,

`2A+2B-(-1/2)=1`

`2A+2B+1/2=1`

`2A+2B=1-1/2`

`2(A+B)=1/2`

`A+B=1/4`       ----- equation 5

Plug in the value of D in the equation 4,

`-A+B-0=0`

`-A+B=0`      ---- equation 6

Now add the equations 5 and 6,

`2B=1/4`

`B=1/8`

Plug in the value of B in the equation 6,

`-A+1/8-0`

`A=1/8`

`:.x/(16x^4-1)=(1/8)/(2x+1)+(1/8)/(2x-1)+((-1/2)x)/(4x^2+1)`

`x/(16x^4-1)=1/(8(2x+1))+1/(8(2x-1))-x/(2(4x^2+1))`

Why was Nelson Mandela an influential individual?

Nelson Rolihlahla Mandela was not just influential, he was revolutionary.

Knowing the sociopolitical context of South Africa is critical to understand the gravity of Mandela's actions fully. While Mandela was growing up, South Africa was under apartheid, a system of segregation between the white, European ruling class and native people of color. In this system, native people were severely oppressed and subject to restrictions the ruling class was not. Even after apartheid was formally "over," some of these restrictions persisted. One such restriction that Mandela organized a campaign against were "pass laws," which required native people of color to carry a sort of identification card that was to be shown any time they wanted to gain access to a "whites only" space. 

As a young man, Mandela worked with the African National Congress to advocate for people of color. In 1952, he lead the Defiance Campaign, demonstrating with and supporting others in civil disobedience against unjust laws in South Africa. The government deemed this to be an act of communism, and Mandela and several others involved were sentenced to nine months of hard labor as punishment. 

For his persistent efforts in fighting against the institutionalized racial oppression of apartheid and post-apartheid South Africa, Mandela was elected to the African National Congress while in prison. In 1994, Mandela was elected president of South Africa in the country's first truly democratic election — previously, only the white ruling class could vote. All his life, Mandela spoke openly and ardently about the injustices occurring in South Africa. His persistence is remarkable and honorable. Today, Mandela is representative of the struggle people faced under apartheid and the good things that can come through diligently fighting for what is right. 

Mandela's influence is not only felt in South Africa; many in the United States and elsewhere have been inspired to participate in civil disobedience against unjust institutions as a result of Mandela's work.

What is the population of Noblesville, Indiana?

The population of Noblesville, Indiana (according to the United States Census Bureau) was 57,584 in the year 2014. In comparison, the population of the city was 52,135 in 2010, representing a change of 10.5% over the period. The state of Indiana, in comparison, had a population growth of only 1.7%, over the same period. The city has a higher per capita income (at $31,261 in 2013 dollars) as compared to the state (at $24,635). 

Noblesville is a small town, with an estimated area of 31.37 square miles and had a population density of 1656.4 people per square mile (in 2010). In comparison, the state of Indiana is much less densely populated with a population density of 181 people per square mile (in 2010).

Hope this helps. 

Is Charlotte Bronte's Jane Eyre a feminist novel?

Feminism advocates that social, political, and all other rights should be equal between men and women. Bronte's Jane Eyre discusses many of the struggles and prejudices that nineteenth century middle-class women faced. All rights were not equal between men and women at that time, and Jane's greatest desire is to have a family and to feel accepted and loved. This does not necessarily mean that the novel is not feminist, but the main character's goal is not to change the legal and political world in order to gain equal rights for women. However, by the end of the story, she does not settle for anything less than the most equal relationship and living circumstances possible for the time period. And at the time, it must have seemed pure fantasy for a governess to acquire her own money and marry higher than her social class. 

Erica Jong's introduction in the Signet Classic edition provides great insight into how Jane Eyre could be considered a feminist novel by saying the following: 

"And indeed she cannot marry Rochester until he knows he is as dependent on her as she is on him. Their odysseys have equalized them: Jane has become an independent woman and Rochester has been cured of entitlement. Only thus can a woman and man become equals in a patriarchal society" (ix).

Bronte portrays Jane as a traditional woman who wants a husband and family while also maintaining her value as an individual in her own right. Many women today want the same things--to have a family and career. However, even though Jane isn't seeking social or political equality, she does find equality in marriage. This could be a big part of the message that Bronte wanted to convey, which would mean that her desired results would have, in fact, been one of the first feminist novels. 

What quote from the story shows that Young Goodman Brown's name is ironic?

There are a few good quotes which might illuminate the ironic nature of Young Goodman Brown's name. I will present a few below with my comments:

...and after this one night, I'll cling to her skirts and follow her to Heaven...With this excellent resolve for the future, Goodman Brown felt himself justified in making more haste on his present evil purpose.

We have been a race of honest men and good Christians, since the days of the martyrs. And shall I be the first of the name of Brown, that ever took this path and kept--

And when he had lived long, and was borne to his grave, a hoary corpse, followed by Faith, an aged woman, and children and grand-children, a goodly procession, besides neighbors, not a few, they carved no hopeful verse upon his tombstone; for his dying hour was gloom.

From the quotes above, you can see that Young Goodman Brown is an ironic name for our protagonist. He leaves his wife, Faith, behind to fulfill an evil errand. This action is a symbolic representation of Goodman Brown setting aside his own Puritan values to delve into the realm of the mysterious and the world of innate evil.

Dark romantic works of the 19th century often centered on a repudiation of the Transcendentalist doctrine of human infallibility. The world is portrayed with pessimism and gloomy foreboding in these works. In our story, Goodman Brown finds his world turned upside down when he discovers that his own father and grandfather participated in the Puritan persecution of the Quakers as well as the atrocities in King Phillip's War. Goodman Brown is visibly shaken by these so-called revelations of the depravity inherent in his family history. Meanwhile, he himself seeks to participate in the machinations of a macabre ceremony, presided over by the Devil and witches of ill-repute.

To Goodman Brown, it seems as if everyone he has ever respected is at the demonic congregation of souls. The end result of his 'experience' renders him a pitiful facsimile of the once confident and trustful young husband that he was. In the end, his dying hour speaks of despair and hopelessness, by all representations, an ironic and unfortunate development, in spite of the positive connotations in his given name.