Notes

Volume, in the context of matter, is the amount of space that is occupied by an object (matter). In some cases, the boundary of this space is evident. For instance, for a solid, the shape of the object dictates the space it occupies. It is a different case for fluids - or matter that flows - like gases and liquids.  For fluids, the shape of the particular gas or the liquid is the same shape as the container. If you pour water from a water bottle to a bowl, the shape of the water changes from that of the water bottle to that of the bowl. The same is true for a gas. A gas inside a star-shaped balloon is star-shaped, and it is round in a round balloon. Liquids and gases take up the shape of the container because of the nature of the interactions in the atoms or molecules that make up the object. For solids the atoms/molecules are very tightly packed. This is not the case for liquids and gases where the molecules have more freedom. A main difference between molecules in liquids and gases i...

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According to Dog Whistle Politics: How Coded Racial Appeals Have Reinvented Racism and Wrecked the Middle Class, George H.W. Bush originally rejected the idea of using race in his 1988 presidential campaign.  However his campaign manager, Lee Atwater, convinced him race could be the key to his victory. Willie Horton was the perfect criminal to help Bush’s poll numbers.  Horton escaped while on furlough, raped a woman and stabbed and bound her fiancee.  Michael Dukakis, the Democratic presidential candidate, vetoed a bill that would make murderers ineligible for furloughs.  Bush used this opportunity to blame Dukakis for this horrible crime.  Atwater began using the Horton case in political ads.  He never blatantly mentioned race, but knew how the public would react to a black male raping a white female in the presence of her fiancee.  Bush, who was once lagging in the polls quickly gained more supporters.   In the month following the ads, Bush gained 12 percent of the Dukakis supporter...

The doctor has no interest in treating Coyotito until Kino finds the pearl, and Coyotito was getting better before seeing the doctor. Coyotito is stung by a scorpion, which is of course very dangerous for a baby.  His parents act quickly.  Kino kills the scorpion (smashing it to dust in anger), and Juana tends to the wound using home remedy methods. But Juana had the baby in her arms now. She found the puncture with redness starting from it already. She put her lips down over the puncture and sucked hard and spat and sucked again while Coyotito screamed. (Ch. 1) Sucking the poison out of the wound is a common technique.  It must be administered very soon after the bite or sting, so that the poison does not get a chance to enter the bloodstream.  In this case, it must have worked.  Coyotito does not die. Juana wants to take him to a doctor anyway. It is unusual for anyone from the village to go to a doctor.  The doctor is a colonist, and is only interested in money. A wonderful thing, a...

Indefinite integrals are written in the form of `int f(x) dx = F(x) +C`  where: `f(x)` as the integrand           `F(x)` as the anti-derivative function             `C`  as the arbitrary constant known as constant of integration For the given problem: `int cos(6x)cos(2x) dx` has a integrand in a form of trigonometric function. To evaluate this, we apply the identity: `cos(A)cos(B) =[cos(A+B) +cos(A-B)]/2` The integral becomes: `int cos(6x)cos(2x) dx = int[cos(6x+2x) +cos(6x-2x)]/2dx`  Apply the basic properties of integration: `int c*f(x) dx= c int f(x) dx` . `int[cos(6x+2x) +cos(6x-2x)]/2dx = 1/2int[cos(6x+2x) +cos(6x-2x)]dx`  Apply the basic integration property: `int (u+v) dx = int (u) dx + int (v) dx` . `1/2 *[intcos(6x+2x) dx+int cos(6x-2x)dx]` Then apply u-substitution to be able to apply integration formula for cosine function: `int cos(u) du= sin(u) +C` . For the integral: int cos(6x+2x) dx, we let `u = 6x+2x =8x` then `du= 8 dx` or `(du)/8 =dx` . `intcos(6x+2x) dx=intcos(8x) d...

Given to solve, `lim_(x->-2) (x^2-3x+10)/(x+2)` as `x->-2` then the `(x^2-3x+10)/(x+2) =0/0` form so upon applying the L 'Hopital rule we get the solution as follows, as for the general equation it is as follows `lim_(x->a) f(x)/g(x) is = 0/0` or `(+-oo)/(+-oo)` then by using the L'Hopital Rule we get  the solution with the  below form. `lim_(x->a) (f'(x))/(g'(x))` so , now evaluating `lim_(x->-2) (x^2-3x+10)/(x+2)` =`lim_(x->-2) ((x^2-3x+10)')/((x+2)')` =`lim_(x->-2) (2x-3)/(1)` now plugging the value of `x= -2` then we get = `(2(-2)-3)` = `-7`

Aspirin or acetylsalicylic acid is made by reacting salicylic acid with a base. There are various ways to synthesize aspirin (but the method of calculating the percent yield is the same for any chemical reaction). One way is to react salicylic acid with acetic anhydride, a base, in the presence of pyridine as a catalayst. In brief, pyridine hydrogen bonds with the phenolic hydrogen, thus activating it for acetylation.  The chemical equation for this is as follows: `2C_7H_6O_3 + C_4H_6O_3 -> 2C_9H_8O_4 + H_2O ` , where the chemical species are salicylic acid, acetic anhydride, aspirin, and water, respectively. Note that pyridine is not in the balanced chemical equation since it only acts as a catalyst and is not consumed in the chemical reaction. Percent yield is a parameter used to determine efficiency of chemical reactions. It is very important in industrial and pharmaceutical chemical industries - in calculating cost-benefit of a reaction and synthesis of a drug, for instance, or...