What would you expect to happen if one electronics device stopped working in a series circuit?

If one electronic device goes out within a series circuit, then all the other electronic devices that are a part of that series circuit would also go out.

A series circuit is a closed circuit that allows for only one path through which a current can flow. An old fashioned string of Christmas lights is an excellent example of a series circuit. When one light goes out, the circuit is "opened" and the flow of electricity stops at the location of the burned-out light bulb. Another type of circuit is a parallel circuit.

Parallel circuits are closed circuits that have two or more paths through which a current can flow. If one item of the circuit goes out, then that part of the parallel circuit will no longer work. However, the current can still travel through the other paths of the parallel circuit. This allows other electronic devices to continue working even when one goes out. Therefore, most household wiring is composed of parallel circuits.

Identify two names given to the narrator by her husband.

The husband in “The Yellow Wallpaper” called his wife, the narrator “a blessed little goose” and a “little girl.”  These “terms of endearment” showed how the narrator was treated like a child by her husband.  Sent to an asylum to recuperate, the narrator was suffering from what many think was postpartum depression since she just had a child.  Any mental illness would have been taboo to talk about at that time, and the husband is just placating her strange condition.  As the narrator slipped more and more into depression and started imagining strange images in the wallpaper, the husband just wanted to calm her and began to call her childish names.  This behavior by the husband was indicative of how women were often thought to be at the time the story was written, the Victorian era.  Women were not taken seriously and often thought of as weak and sickly.  Women would have “the vapors” or fainting spells (probably due to the tight corsets they wore) and were often thought of as the frailer sex.  The husband affirmed a sexist behavior by calling his wife names as if she were a child that could be soothed and made better.

`int (x e^(2x))/(1 + 2x)^2 dx` Evaluate the integral

This is integration by parts

rewrite it as:

`int [x e^(2x)] {dx /[(2x + 1)^2]} `

let:
`[x e^(2x)] = u → {e^(2x) + x [2e^(2x)]} dx = du →`
`{e^(2x) + 2x e^(2x)} dx = du → `

factoring out `e^(2x)`

`[e^(2x)](1 + 2x) dx = du `

`dx /[(2x + 1)^2] = dv → `

dividing and multiplying by 2
`(1/2) {2dx /[(2x + 1)^2]} = dv → `
`(1/2) {d(2x + 1) /[(2x + 1)^2]} = dv → `
`(1/2) [(2x + 1)^(-2)] d(2x + 1) = dv → `
`(1/2) [(2x + 1)^(-2+1)]/(-2+1) = v → `
`(1/2) [(2x + 1)^(-1)]/(-1) = v → `

`-1 /[2(2x + 1)] = v `

thus, integrating by parts, you get:

`int u dv = u v - int v du → `

`int [x e^(2x)] {dx /[(2x + 1)^2]} = `

`[x e^(2x)]{-1 /[2(2x + 1)]} - ∫ {-1 /[2(2x + 1)]} [e^(2x)](1 + 2x) dx = `

`(-1/2){[x e^(2x)] /(2x + 1)} + ∫ {[e^(2x)](1 + 2x) /[2(2x + 1)]} dx = `

canceling `(2x + 1)` ,

`(-1/2){[x e^(2x)] /(2x + 1)} + (1/2) ∫ e^(2x) dx = `

`(-1/2){[x e^(2x)] /(2x + 1)} + (1/2) [(1/2)e^(2x)] + C = `

factoring out `[(1/2)e^(2x)]` ,

`[(1/2)e^(2x)] {- [x/(2x + 1)] + (1/2)} + C = `

`[(1/2)e^(2x)] {(- 2x + 2x + 1) /[2(2x + 1)]} + C = `

`[(1/2)e^(2x)] {1 /[2(2x + 1)]} + C `

Thus

`int [x e^(2x)] / [(2x + 1)^2] dx = (1/4) {[e^(2x)] /(2x + 1)} + C`

How does Tybalt's violent nature lead to his death in Romeo and Juliet?

In the play Romeo and Juliet, we meet Tybalt in Act 1, scene 1, just as Benvolio tries to make peace among the fighting servants of both noble houses. Tybalt arrives and taunts Benvolio for trying to break up the fight, while challenging him on the spot,

     Tybalt

What, art thou drawn among these heartless hinds?
Turn thee, Benvolio, look upon thy death.

     Benvolio

I do but keep the peace: put up thy sword,
Or manage it to part these men with me.

     Tybalt

What, drawn, and talk of peace! I hate the word,
As I hate hell, all Montagues, and thee:
Have at thee, coward!

Tybalt's fighting words, his hatred for the Montagues and his bullying character are evident in this exchange. Rather than help to stop the brawl, he forces poor, peace-loving Benvolio, a Montague, to fight him instead.

We see more evidence of Tybalt's angry, violent nature in Act 1, scene 5, at the Capulet Ball, when he hears the voice of a Montague among the guests and immediately asks for his sword

This, by his voice, should be a Montague.
Fetch me my rapier, boy. What dares the slave
Come hither, cover'd with an antic face,
To fleer and scorn at our solemnity?
Now, by the stock and honour of my kin,
To strike him dead, I hold it not a sin.

He believes the voice belongs to Romeo Montague and takes it upon himself to kill him but is stopped by his uncle, Lord Capulet, who won't have any fighting at his party that night.

The next time we meet Tybalt is in Act 3, scene 1. Still festering with rage over the party incident, he calls Romeo a villain and challenges him to a fight. Mercutio, Romeo's best friend, insults Tybalt and makes him so angry that they soon partake in a sword fight, in which Mercutio is slain. Seeing his friend die by the hand of Tybalt, Romeo, who up until now has always been a lover rather than a fighter, picks up a sword and fights with Tybalt. Romeo's fresh adrenaline and Tybalt's exhausted body influence the outcome of their fight and soon Tybalt lies dead.

The hostile, impulsive and violent nature of Tybalt contributed to his death. He was very hot-tempered, confrontational, would not be placated and regarded the sword as the answer to every quarrel.

In The Crucible, how do the townspeople move the plot of the tragedy in Salem?

The townspeople bear a lot of responsibility for jumpstarting the accusations and heightening the tension at the beginning of the play.  There are rumors circulating that Betty Parris flew over Ingersoll's barn, and the Putnams -- a very powerful local and vocal family -- are absolutely convinced that witches are to blame for the deaths of their babies and the sicknesses of Betty and Ruth, their daughter, and they have clearly spread their story to anyone who will listen.  The Putnams and others like them, townsfolk who are so willing to believe in witchcraft as the root of their problems rather than look to themselves for the cause, live in fear and become instigators of the hysteria that catches and spreads so quickly. 

Further, when the court is in session in Act Three, the villagers, according to the stage direction which indicates that they are shouting and screaming, add to the feeling that the trials are a circus; they egg on the accusers as well as the judges.  This is how hysteria works -- it affects groups who begin to adopt a sort of mob mentality where they act only on emotion.  If the villagers were not so eager to believe, then they might have demanded better evidence; however, as a result of their intense desire to find a scapegoat for their anxieties and troubles, they are easily led and powerful enough to move the story along.

What year was the story A Christmas Carol set in?

The story was published in 1843, and takes place in the early 1800’s (1800-1850).

Dickens is careful not to give a specific year that the story is set during the story.  This adds to its timelessness.  The closest he gets is the comment that the Ghost of Christmas Present makes when Scrooge asks about his family.

“Have never walked forth with the younger members of my family; meaning (for I am very young) my elder brothers born in these later years?” pursued the Phantom.

“I don’t think I have,” said Scrooge. “I am afraid I have not. Have you had many brothers, Spirit?”

“More than eighteen hundred,” said the Ghost. (Stave 3)

This means that the story takes place at least after 1800, of course.  It likely that the "present" is set approximately around the year it was written.  The ghost is telling Scrooge that he lives for only one day (which is why he says he is young), and when he says that he has more than eighteen hundred brothers and sisters he means that each of them represents Christmas Day.  Scrooge’s response is really more of a quip, but he is, as always, thinking about money.

Of course, while 1843 might be Scrooge’s present, the story itself shifts into his past and his future.  Thus, it takes place anywhere from the beginning of the nineteenth century to the mid to late-1850’s.  It does not take place in just one year, because Scrooge and his ghosts travel through time in a way.  However, they still end up back in Scrooge’s present.

Dickens intended for his story to be read for years and years.  He wanted to make it a timeless classic.  In that sense, he succeeded admirably.  People have still read and enjoyed this book for years, and continue to do so today.

Was the trade-off worth it in The Giver?

The tradeoff is not worth it because the community executes its people without consequence.

Every community has to decide between security and freedom.  The more freedom you give your citizens, the less security you will have.  Jonas’s community clearly opted for the least amount of freedom in order to make everyone happier.  The tradeoff was not worth it, because there is no sense of humanity in their community.

The community is a surveillance state.  This means that all citizens are watched twenty-four hours a day no matter where they are.  There are cameras everywhere and an overseer called the Speaker communicates with them regarding anything they need, but also makes them aware of any wrong move.

In addition to the cameras, there are always people watching.  Town elders watch the children for most of their lives, and if they are not watching then ordinary people are watching them all the time.

The community was extraordinarily safe, each citizen watchful and protective of all children. (Ch. 6)

Jonas just accepts the surveillance as part of life until he begins his training as Receiver of Memory.  He is completely shocked that the Receiver has the ability to turn the speaker and cameras off.  Jonas has never seen a speaker with an off button.  No one else in the community ever gets any privacy.

The advantage to this is that with Sameness no one ever feels uncomfortable.  People are watched over and protected, and everyone has a job and a house and enough food.  There are no unwanted pregnancies, because the population is controlled and all of the babies are created by the community.  There are no broken families because family units are carefully constructed.  Two adults are paired and then given two children, a boy and a girl.

The disadvantage to these perfect families and the strict rules is that when someone does not comply, the community is extremely ruthless in dealing with it.  Babies who do not meet strict guidelines are released, and citizens who break the rules are released.  When they decide that the old people have lived long enough, they are released as a matter of course.

There were only two occasions of release which were not punishment. Release of the elderly, which was a time of celebration for a life well and fully lived; and release of a newchild, which always brought a sense of what-could-we- have-done. (Ch. 1)

We would love to think that killing babies is rare in the community, but it clearly isn’t.  It happens twice during the book.  The twin is actually killed and Gabriel would have been if Jonas had not rescued him and escaped.  Clearly killing babies is a normal occurrence.  Jonas’s father is not pleased with it, but never seeks to question it.

The other tradeoff the community makes is with the Stirrings pills.  In an effort to keep complete control of the community’s citizens, the community has created some kind of hormone blocker.  It ensures that the citizens never have strong feelings. The problem is that they never really get to experience the full spectrum of human emotion.  They live in a state of eternal numbness.

For Jonas, the first time he experience feelings is in the memories.

Jonas nodded. "I liked the feeling of love," he confessed. … "I wish we still had that," he whispered.  "Of course," he added quickly, "I do understand that it wouldn't work very well. And that it's much better to be organized the way we are now. I can see that it was a dangerous way to live." (Ch. 16)

It is true that feelings and emotions can be dangerous.  They make people uncomfortable.  They also lead people to make decisions.  Decisions are carefully controlled in the community.  No one really has a choice about anything.  Every choice is made for them.

Jonas starts to realize that the fact that no one in his community has ever had an independent thought or a real feeling is what is dangerous.  The danger is not in letting people live their own lives, it is in letting the government control them.  This is how innocent people end up dead.  When Jonas starts to understand what is really happening in the community, he cannot allow it to continue.  He escapes in an act of rebellion that ensures that the memories will be returned to the people and the complete control their community has over them will come to an end.