Give some examples of mixtures, compounds, and solutions.

Materials can be classified as either elements, compounds or mixtures. An element is the purest form of a substance and cannot be further sub-divided into different or non-identical materials. A compound is made up of two or more elements combined together in a certain fixed ratio. It can be sub-divided into its constituents chemically. A mixture is composed of two or more compounds and can be sub-divided into its constituents by physical methods.

Some examples of elements include iron, aluminum, sodium, gold, silver, uranium, etc. Some examples of compounds include water (H2O), carbon dioxide (CO2), glucose (C6H12O6), methane (CH4), etc. Some examples of mixtures include trail-mix, mixed salad, etc. 

A solution is formed by mixing a solute into a solvent. For example, mixing sugar (solute) in water (solvent) forms sugar water solution. Similarly, saline water solution can be prepared by mixing salt with water. 

Hope this helps. 

`y = 1/2 (1/2ln((x+1)/(x-1)) + arctanx)` Find the derivative of the function

The derivative of y in terms of x is denoted by  `(dy)/(dx)` or `y’` .

 For the given problem: `y = 1/2(1/2ln((x+1)/(x-1)) +arctan(x))` , we may apply the basic differentiation property: `d/(dx) c*f(x) = c d/(dx) f(x)` .

`d/(dx)y =d/(dx) 1/2[1/2ln((x+1)/(x-1)) +arctan(x)]`

`y'=1/2d/(dx) [1/2ln((x+1)/(x-1)) +arctan(x)]`

Apply the basic differentiation property: `d/(dx) (u+v) = d/(dx) (u) + d/(dx) (v)`

`y'=1/2[d/(dx) (1/2ln((x+1)/(x-1))) +d/(dx)(arctan(x))]`

For the derivative of `d/(dx)(1/2ln((x+1)/(x-1)))` , we may apply again the basic derivative property:`d/(dx) c*f(x) = c d/(dx) f(x)` .

`d/(dx) (1/2ln((x+1)/(x-1)))=1/2d/(dx) (ln((x+1)/(x-1)))`

For the derivative part, follow the basic derivative formula for natural logarithm function: `d/(dx) ln(u)= (du)/u` .

 Let `u =(x+1)/(x-1)` then `du = -2/(x-1)^2` .

 Note For the derivative of `u=(x+1)/(x-1)` ,we apply the Quotient Rule: `d/(dx)(f/g) = (f'*g-f*g')/g^2` .

Let:

`f= (x+1)` then `f'=1`

`g=(x-1)` then `g'=1`

Then,

`d/(dx)((x+1)/(x-1))= (1*(x-1)-(x+1)*(1))/(x-1)^2`

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

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

                ` =(-2)/(x-1)^2`

Applying: `d/(dx) ln(u)= (du)/u` on:

`1/2d/(dx)(ln((x+1)/(x-1)))= (1/2) *(((-2)/(x-1)^2))/(((x+1)/(x-1)))`

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

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

Cancel common factors 2 and `(x-1)` from top and bottom:

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

Recall `(x-1)*(x+1) = x^2-x+x-1 = x^2-1` then the derivative becomes:

`1/2d/(dx)(ln((x+1)/(x-1)))=-1/(x^2-1)`

For the derivative of `d/(dx)(arctan(x))` , we apply basic derivative formula for inverse tangent:

`d/(dx)(arctan(x))=1/(x^2+1)`

Combining the results, we get:

`y'=1/2[d/(dx) (1/2ln((x+1)/(x-1))) +d/(dx)(arctan(x))]`

`y'=(1/2) [-1/(x^2-1) +1/(x^2+1)]`

`y' =(1/2) [-1/(x^2-1) *(x^2+1)/(x^2+1) +1/(x^2+1)*(x^2-1)/(x^2-1)]`

`y' =(1/2) [(-(x^2+1) +(x^2-1))/((x^2-1) (x^2+1))]`

`y' =(1/2) [(-x^2-1+x^2-1)/((x^2-1) (x^2+1))]`

`y' =(1/2) [(-2)/((x^2-1) (x^2+1))]`

`y' =(-1)/((x^2-1) (x^2+1))`

or

`y'= (-1)/(x^4-1)`

What were the long-lasting consequences of Reservation of Separate Amenities Act?

The Reservation of Separate Amenities Act created legal segregation in South Africa. This law allowed for segregation in public facilities including restaurants, schools, transportation, and theaters. This law stated that segregation could occur even if the facilities were not equal in quality.

The long-term impact of this law and others that made up the apartheid system was that the races were kept apart, and the white minority remained in control of the government. It also created a great deal of tension between white South Africans and non-white South Africans.

Eventually, there was a great deal of international pressure placed on the South African government to end the system of apartheid. Several countries imposed sanctions on South Africa. Travel, trade, and international sporting competitions were reduced or banned.

This pressure eventually worked as the Reservation of Separate Amenities Act ended in 1990, and apartheid ended in 1994.

Are we in a post-television era now?

As James Poniewozik wrote for TIME magazine in 2014, the ways people engage with video media are changing rapidly. Since television sets became popular household appliances throughout the Western world in the 1950's, the pattern of engaging with television programming has remained fairly consistent-- until the last few years. For the past half a century, people watched television by turning on their set when their desired program was scheduled to air. This changed a little bit with the introduction of the VCR and services like Tivo, which allow people to record a program and watch it later. On-demand video services also allowed people to watch their programs on their own time, but these three things weren't really enough to inspire people to ditch their cable service altogether.

Throughout the past several years, companies like Netflix have dramatically altered the way we engage with television and film. Subscription services allow viewers access to a wider variety of programming than is currently broadcast, with the benefit of being able to watch these media whenever is convenient for us. I can think of two major changes in our behavior with regards to television viewing. In the past our watching a television program was dependent upon a broadcast schedule, but subscription services now allow us to watch on our own schedule. Additionally, the broadcast-dependent behavior of watching television typically meant that people would only watch one episode of a program in a thirty minute or one hour sitting. Subscription services may have many more episodes available, allowing for something called "binge watching."

Of course, many people use their subscription services to stream programs and films through their television set. Such services may also be used on computers, tablet devices, and even smart phones. I feel that rather than saying we are in a "post-television" era, it might be better to say we are in a "post-broadcast" era. Watching television is no longer dependent upon the broadcast schedule, but many people are still reliant upon a television set to watch video media.

What are three instances when music influenced or affected Brent in Whirligig by Paul Fleischman?

Two appear in the fifth chapter, “Twinkle, Twinkle Little Star.” Here Brent is staying at the hostel in San Diego, when he hears and sees a man playing a concertina. (A concertina is an accordion, also called a squeezebox, which is often depicted as an instrument of Italians and a sound of Italy.) It makes a “cheery, reedy sound.” Brent envies “the man his power to entertain himself and others.” By the end of the chapter, Brent has bought himself a harmonica. He teaches himself some basic songs. Then he uses the harmonica to christen the new whirligig with music. From this point on, he plays the harmonica at various parts of his journey. He had not been particularly musical beforehand.

In the final chapter, “Everybody Swing!” Brent is in Weeksboro, Maine. He comes upon a place where people are square dancing. The music is “brisk, bouncy, and infectious.” He sees that the dancers form in essence “a human whirligig, set in motion by music instead of wind.” Someone grabs his hand and invites him to join along, and amazingly enough, he does. The Brent we met at the beginning of the book would never have done this, let alone with a bunch of strangers. But he quite enjoys himself here, in the final pages. This is one example of his transformation during this challenging time.

How does Angus Tuck feel about living forever?

Angus Tuck does not enjoy the prospect of living forever.  He wishes that he could live and die like all other living creatures.  

The reader (and Winnie Foster) learns in chapter twelve that Angus Tuck does not enjoy immortality. In that chapter, Angus invites Winnie out on the pond with him.  He uses the time to explain why it is important for Winnie to keep the spring a secret.  He also confesses to Winnie that he deeply wishes for the chance to go back to a life in which he can die.  He explains to Winnie that part of living is dying.  To Angus, without the ability to die, a person can't really claim that he or she is really living.  That person is simply existing . . . like rocks on a road.  

"If I knowed how to climb back on the wheel, I'd do it in a minute. You can't have living without dying. So you can't call it living, what we got. We just are, we just be, like rocks beside the road."

What is the result when silver nitrate reacts with sodium chloride?

Silver nitrate which is AgNO3 and sodium chloride which is NaCl are both soluble in water. When aqueous solutions of the two are mixed a double replacement reaction takes place. It's also called a precipitation reaction, because an insoluble precipitate forms:

`AgNO_3_(aq) + NaCl_((aq))-> AgCl_((s)) + NaNO_3_(aq)`

Written as an ionic equation:

`Ag^+_(aq) + NO_3^+_(aq) + Na^+_(aq) +Cl^-_(aq) -> AgCl_((s)) + Na^+_(aq) + NO_3^-_(aq)`

Solid AgCl (silver chloride) forms because it's not soluble in water.

Precipitation reactions are often represented by net ionic equations, which leave out the aqueous (dissolved) ions that appear on both sides of the equation. The net ionic equation for this reaction is:

`Ag^+_(aq) + Cl^-_(aq)> AgCl_((s))`

The ions that are not included in the net ionic equation are called spectator ions because they are present but don't participate in the reaction.

To determine the outcome of a double replacement reaction, write formulas for products by switching the ions in the reactants. The negative ion of each reactant will be in a compound with the positive ion of the other. Now use a table of solubility rules to determine if either product is insoluble. If so, it will precipitate. If both products are soluble there will be no precipitate. Ions that are aqueous on both sides of the reaction are spectator ions and they cancel out.