How does Anne Frank describe her hair?

Anne calls her hair a “mass of curls.” 

Many teenagers are unhappy with their appearance. Anne is no exception.  She tries to make her hair something to be proud of, but she often feels she comes up short.

Anne describes her procedure for getting ready, which includes curling her hair and bleaching her face.  It is normal teenage stuff. 

I brush my teeth, curl my hair, manicure my nails and dab peroxide on my upper lip to bleach the black hairs -- all this in less than half an hour. (Wednesday, August 4,1943) 

Even though they are in hiding, Anne likes to look out for her appearance.  The families have limited bathroom time, and of course they never go out, but Anne still wants to look nice. 

She is obsessed with movie stars, and tries to make her hair look like theirs.  Anne’s family and the Van Daans do not approve. 

Whenever I come sailing in with a new hairstyle, I can read the disapproval on their faces, and I can be sure someone will ask which movie star I'm trying to imitate. My reply, that it's my own invention, is greeted with skepticism. … By that time I'm so sick and tired of their remarks that I race to the bathroom and restore my hair to its normal mass of curls. (Friday, January 28, 1944) 

Soon, Anne is getting herself ready and trying to make herself look nice for Peter.  She goes from finding him annoying to becoming his friend, and then finally something more.  Now Anne has a reason to primp.  It is a small bit of normalcy in a very abnormal situation.

Why did Gatsby switch cars?

From what I can see, your answer lies in Chapter Seven. In this chapter, Daisy suggests that everyone should go into town.

Meanwhile, the atmosphere in Tom and Daisy's house is charged with a percolating tension that threatens to erupt into outward conflict. At lunch, Daisy is brazenly affectionate with Gatsby; she doesn't bother to hide the fact that she's infatuated with her lover.

For his part, Tom senses that Daisy is past all pretense when it comes to Gatsby, and he's definitely angry about being so obviously cuckolded. It's Tom who suggests that he and Gatsby switch cars. Meanwhile, Gatsby isn't too keen on the idea; he's just a tad uncomfortable with the idea of driving his lover's husband's car. Gatsby finds himself in a difficult position; if he objects, Tom is the kind of man who has no qualms about making an embarrassing scene. If Gatsby consents, he's playing into Tom's hands and publicly consenting to being emasculated in front of Daisy.

Since it's a no-win situation for Gatsby, he decides to cut his losses and to let sleeping dogs lie. He reluctantly consents to let Tom drive his car, while Tom drives his. For his part, Tom feels a need to exert himself in order to salvage what masculine pride he has left. After bullying his way through the exchange, Tom, calling his rival's car a "circus wagon," attempts to get Daisy to ride with him in Gatsby's car. However, Daisy evades her husband's grasp and decides to ride with Gatsby in Tom's car.

Daisy leaves Tom aghast and furious at her blatant disrespect. It's obvious that Tom meant to embarrass Gatsby, but the tables have now been turned on him. So, in truth, Gatsby only consented to switch cars with Tom because the latter pressured him into doing so.

`y=ln(sinx) , [pi/4 , (3pi)/4]` Find the arc length of the graph of the function over the indicated interval.

The arc length of a function of x, f(x), over an interval is determined by the formula below:

`L=int_a^bsqrt(1+((dy)/(dx))^2)dx`

So using the function given, let us first find `(dy)/(dx):`

`d/(dx)(ln(sin(x)))=(1/(sin(x)))*(cos(x))=(cos(x))/(sin(x))=cot(x)`

We can now substitute this into our formula above:

`L=int_a^bsqrt(1+((dy)/(dx))^2)dx=int_(pi/4)^((3pi)/4)sqrt(1+(cot(x))^2)dx`

Which can then be simplified to:

`L=int_(pi/4)^((3pi)/4)sqrt(1+cot^2(x))dx=int_(pi/4)^((3pi)/4)sqrt(csc^2(x))dx=int_(pi/4)^((3pi)/4)csc(x)dx`

Then you find the definite integral as you normally would.  (Using the method shown on the link below, you can find the integral of csc(x).)

`L=int_(pi/4)^((3pi)/4)csc(x)dx=-ln|csc(x)+cot(x)|_(pi/4)^((3pi)/4)`

`L=-ln|csc((3pi)/4)+cot((3pi)/4)|-(-ln|csc(pi/4)+cot(pi/4)|)`

`L=-ln|sqrt(2)+(-1)|-(-ln(sqrt(2)+1|)=-ln|sqrt(2)-1|+ln|sqrt(2)+1|`

Here, we will switch the two natural logarithm terms and use the quotient property to combine them into a single log:

`L=ln|sqrt(2)+1|-ln|sqrt(2)-1|=ln|(sqrt(2)+1)/(sqrt(2)-1)|`

If you rationalize the denominator (by multiplying by the conjugate and simplifying) and use the power property of logs, you are left with:

`L=ln|(sqrt(2)+1)^2/1|=ln|(sqrt(2)+1)^2|=2ln|sqrt(2)+1|`

So the exact value of the arc length of the graph of the function over the given interval is `2ln|sqrt(2)+1|`

which is approximately equal to 1.76.

If you had unlimited money and time, how would you stage Act 1 Scene 2 of A Midsummer Night's Dream? What would it look like?

Act 1 Scene 2 of A Midsummer Night's Dream is set in the house of Peter Quince, one of the six "mechanicals". He is the author and director of the play-within-a-play. His name suggests that he might be a carpenter or descended from a family of carpenters. 

The first decision you need to make in staging this is period. You can set the play in its putative time period, ancient Athens, Shakespeare's period, another period of your choice, or a generic setting of a dream world outside of real time.

Part of the entertainment in the scenes with the mechanicals is broad physical comedy. Personally, I would create a simple space with limited rugged, movable props and furniture to allow the actors space for broad physical comedy. I wood furnish the set with rough-hewn wood furniture, including a rectangular table with a few pewter candlesticks, several pages of the "manuscript" of the play, quill pens and an inkstand. The table would be surrounded by a few wood benches and a couple of stools, and off to one side of the room might be a chest or some shelves. At least one of the stools would have a break away leg, so that it would collapse when an actor sat on it. 

How do you get rid of radioactive waste?

Radioactive waste disposal involves finding a safe place to store it until it’s no longer radioactive. Different types of waste give different levels of radiation. Radioactive waste disposal is divided into three general categories: low level, intermediate level, and high-level waste. Low-level waste typically has short-lived radioactivity. It does not require cooling nor shielding to handle. An example of this would be a lab coat that has been contaminated by radioactive material. It is disposed of through shallow land burial.

Intermediate-level waste requires shielding to handle but not cooling. An example of this would be metal fuel cladding at a nuclear power plant. This type of waste is stored at a nuclear waste repository. Please note that the United States does not define this category, but other countries do. High-level waste requires both shielding and cooling to handle.  Used nuclear fuel is an example of this. High-level waste is stored in a deep geological repository.

There are other waste categories, but this should be enough to get you started. See the links below for further research.

What is ionization energy?

Ionization energy can be thought of as the energy needed to make an ion from an atom. In more technical terms, it is the amount of energy required to remove an electron from a neutral atom. Since more than 1 electron can be removed from an atom of a large number of elements, we denote the ionization energy as the first ionization energy, second ionization energy, etc. 

There is a noticeable trend in the ionization energies of elements as we move across a period or down a group, in the periodic table of elements. As we move across a period, the ionization energy increases, since the nuclear pull on the outermost electrons increases. The ionization energy decreases as we go down a group, due to shielding by inner electrons and increase in distance between the nucleus and the outermost electrons.

What role does hope play in our lives?

Hope is the idea that something in the future might happen. Hope carries an element of optimism that the future event, whether in this life or the next, will be beneficial. Human life is challenging; we face and fear mortality and are constantly dealing with loss. Hope is one thing that keeps us going in the face of our troubles and struggles. 

Hope also contributes to our sense of purpose in life. If life is only struggle, people have a hard time being motivated to do the things they need to do. Hope leads us to work harder at work in hope of a raise or promotion, to love more deeply because we hope we will be loved back, to work for eternal things that will influence what happens beyond our death. That may be based on religious beliefs about the afterlife or the desire to leave an earthly legacy. Hope can be a tiny, sweet feeling that keeps us going even when we are facing the storms of life.