Single Variable Calculus, Chapter 3, 3.7, Section 3.7, Problem 12

a.) Recall that the volume of the cube is $\text{Vol } = x^3$ where $x$ is the sides of the cube.

$
\begin{equation}
\begin{aligned}
\frac{dV}{dx} &= \frac{d}{dx} (x^3)\\
\\
\frac{dV}{dx} &= 3x^2

\end{aligned}
\end{equation}
$


when $x = 3$mm


$
\begin{equation}
\begin{aligned}
\frac{dV}{dx} &= 3(3)^2\\
\\
\frac{dV}{dx} &= 27 \frac{mm^3}{mm}

\end{aligned}
\end{equation}
$

$\displaystyle \frac{dV}{dx} = 27$ means that the volume is increasing at a rate of $\displaystyle 27 \frac{mm^3}{mm}$ when the length of the cube is 3$mm$.

b.) Recall that the surface area of the cube is equal to $A = 6s^2$ and the rate of change of the volume of the cube is...

$
\begin{equation}
\begin{aligned}
V'(s) &= 3s^2 && \text{;where } s^2 = \frac{A}{6}\\
\\
V'(s) &= 3 \left( \frac{A}{6}\right)\\
\\
V'(s) &= \frac{A}{2}
\end{aligned}
\end{equation}
$

Calculus of a Single Variable, Chapter 5, 5.2, Section 5.2, Problem 36

int(2-tan(theta/4))d theta=
Use additivity of integral: int(f(x)pm g(x))dx=int f(x)dx pm int g(x)dx. int2d theta-int tan(theta/4)d theta=
Since the first integral is easy int 2d theta=2theta+C we will concentrate on the second integral. To solve it we will make substitution: u=theta/4, du=(d theta)/4=>d theta=4du
int tan(theta/4)d theta=4int tan u du=-4ln|cos u|+C
Return the substitution.
-4ln|cos(theta/4)|+C
Now we subtract the two integrals to obtain the final result.
2theta-(-4ln|cos(theta/4)|)+C=2theta+4ln|cos(theta/4)|+C

Suppose birdwatchers observed an increase in the falcon population in recent years. Suggest a reason for this increase.

Although there could be a number of factors for the same, the most significant one is the ban on DDT. 
DDT was a very commonly used insecticide in the agricultural fields around the world. However, its widespread use was associated with a decline in the population of birds, such as the bald eagle and peregrine falcon. This chemical was later banned in the United States in 1972 and in several other countries in the following decades. The elimination of DDT from the ecosystem resulted in an increase in the population of birds, such as the falcon and the bald eagle. 
Some other reasons, that may have attributed to a recent increase in the population of falcons, could be the captive breeding of falcons, which reduces the mortality rate of young birds, increase in their prey population, protection of birds through enactment and implementation of laws, etc. 
Hope this helps.

In the novel Lord of the Flies, what are some quotes that help the reader understand the characters Samneric?

Samneric is the rather dismissive name given to Sam and Eric, the usually childish, irresponsible, unthinking twins. Sam and Eric are, figuratively, inseparable, and usually act with one mind. In this sense, they might be considered symbolic of the unthinking herd mentality that Golding is highlighting in the novel.
In chapter 6, Samneric describe their supposed encounter with the beast to the rest of the boys. The boys listen “with terror to the description the twins breathe at them . . . (and) soon the darkness (is) full of claws, full of the unknown and menace.” What Samneric actually saw, in the light from the fire, was the figure of the dead parachutist. Nonetheless, their story plays upon and exacerbates the existing fear of the beast, and thus Samneric are significant here in a dramatic sense. They are also significant in this moment because their story is rooted in false perceptions. This points to one of the main ideas in the story, namely the idea that the boys’ fears, represented in this instance by the “darkness,” are really only extensions or reflections of their own darkness, whether that be their ignorance or their primal instincts.
A little later in chapter 6, when Samneric are developing their story, they take turns with the conch. Golding writes that “one conch did for both twins, for their substantial unity was recognized.” Throughout the novel, Golding presents the twins as if they are one person. Indeed, in chapter 1, the other boys are initially incredulous at the “cheery duplication” in the twins’ physical features. Golding also says that the twins “breathed together . . . (and) grinned together.” The fact that Samneric are presented as indistinguishable, and inextricable, foreshadows the emergence of the collective, tribal identities that subsume so many of the boys later in the story. The twins are a small-scale warning against the inability to think independently. The island as a whole becomes a large-scale example of the same warning.
In chapter 11, Samneric are tortured by Jack and Roger and forced to accept Jack’s authority. Initially the other boys are reluctant to attack Samneric, but once they accept Samneric’s “otherness,” they join in the attacks much more freely. Golding writes, "Now the painted group felt the otherness of Samneric, felt the power in their own hands. They felled the twins clumsily and excitedly." Samneric are thus significant in this instance because they help to convey the link between prejudice and violence. When we consider people as “other,” whether that be because of their race, ethnicity, nationality of for a host of other possible reasons, we also tacitly endorse violence against those people. When we consider people as “other,” they seem to become separate and less than, and in some instances even inhuman. This is demonstrated neatly in this example with Samneric, and has been demonstrated on innumerable occasions throughout history.

Samneric are twins who are virtually inseparable throughout the novel. In Chapter 1, Ralph uses the conch shell to call the missing boys together on the island. The last two boys to arrive at the platform are the twins, Sam and Eric. Golding writes,

"They were twins, and the eye was shocked and incredulous at such cheery duplication. They breathed together, they grinned together, they were chunky and vital" (23).

Golding's initial portrayal of Sam and Eric remains unchanged throughout the novel as the twins are essentially considered one person.
In Chapter 6, the twins are supposed to be taking turns watching and feeding the fire, but they end up falling asleep because they do everything together. Golding writes,

"In theory one should have been asleep and one on watch. But they could never manage to do things sensibly if that meant acting independently, and since staying awake all night was impossible, they had both gone to sleep" (96).

Samneric are not considered intelligent, responsible, or independent. They do not follow through with taking turns and end up falling asleep during their duty.
After they return from the mountain, Ralph holds and assembly to discuss what Samneric saw on top of the mountain. While the twins are addressing the group, Golding writes,

"By custom now one conch did for both twins, for their substantial unity was recognized" (100).

Again, Samneric are considered one person and do not need to take turns using the conch shell to address the group.

What is Alabama?

Alabama is a U.S. state located in the Southeastern region of the country.  The state is primarily inland, though a small portion of it lies along the coast of the Gulf of Mexico to the south.  Alabama shares its borders with four other U.S. states.  To the south, Alabama shares a border with Florida.  To the east it borders Georgia, and to the west Mississippi.  To the north, Alabama shares a border with Tennessee.  
The state of Alabama was established in 1819.  It was the 22nd U.S. state.  The capital city of Alabama is Montgomery.  During the Civil War, Alabama was part of the Confederate States of America.  Alabama was a slave state until the end of the Civil War.
Agriculture has historically been the primary industry in the state, and it continues to be important today.  Today, manufacturing and mining are other important industries.

y=6/(x-1) Graph the function. State the domain and range.

y=6/(x - 1)
First, determine the vertical asymptote of the rational function. Take note that vertical asymptote refers to the values of x that make the function undefined. Since it is undefined when the denominator is zero, to find the VA, set the denominator equal to zero.
x - 1 = 0
x=1
Graph this vertical asymptote on the grid. Its graph should be a dashed line. (See attachment.)
Next, determine the horizontal or slant asymptote. To do so, compare degree of the numerator and denominator.
y=6/(x-1)
degree of numerator = 0
degree of the denominator = 1
Since the degree of the numerator is less than the degree of the denominator, the asymptote is horizontal, not slant.  And its horizontal asymptote is:
y=0
Graph this horizontal asymptote on the grid. Its graph should be a dashed line.(See attachment.)
Next, find the intercepts.
y-intercept:
y=6/(0-1)=-6
So the y-intercept is (0,-6)
x-intercept:
0=1/(x-6)
(x-6)*0 = 1/(x-6)*(x-6)
0=1
So, the function has no x-intercept.
Also, determine the other points of the function. To do so, assign any values to x, except 1. And solve for the y values.
x=-10 , y=6/(-10-1)=-6/11
x=-5 , y=6/(-5-1)=-1

x=-1 , y=6/(-1-1)=-3
x=2 , y=6/(2-1)=6
x=3 , y=6/(3-1)=3
x=5 , y=6/(5-1)=3/2
x=10 , y=6/(10-1)=2/3
Then, plot the points (-10,-6/11) ,   (-5,-1) ,   (-3,-3/2) ,   (-1,-3) ,   (0,-6) ,   (2,6) ,   (3,3) ,   (5,3/2) ,   and   (10,2/3) . 
And connect them.
Therefore, the graph of the function is:

Base on the graph, the domain of the function is (-oo,1) uu (1,oo) .  And its range is (-oo, 0) uu (0,oo).

What does Gatsby mean when he says that Daisy's voice is full of money? Does he mean it negatively?

The protagonist of of The Great Gatsby is Jay Gatsby, a wealthy man who is quite taken with Daisy, a debutante originally from a very wealthy family in Kentucky. We also learn that Jay is a former love of Daisy’s.
Describing Daisy’s voice as full of money does a couple of things. First, Jay views Daisy, like money, as an object he is obsessed with possessing. He has spent his life amassing a wealth he thinks would win her over. Secondly, Daisy is a lady of leisure who has never worked a day in her life or known any real hardship, such as hunger or homelessness. She is petty, privileged, spoiled, and gossipy.
I don’t think he necessarily means it negatively. One could argue that he knows she is shallow and materialistic, as is he. Here, he seems to be making an observation. If anything, it could speak to his attraction to her more. Gatsby is obsessed with two things: acquiring the kind of status and wealth that might win Daisy back, and Daisy herself.