A construction company has adjoined a $1000 \mathrm{ft}^2$ rectangular enclosure to its office building. Three sides of the enclosure are fenced in. The side of the building adjacent to the enclosure is $100 \mathrm{ft}$ long and a portion of this side is used as the fourth side of the enclosure. Let $x$ and $y$ be the dimensions of the enclosure, where $x$ is measured parallel to the building, and let $L$ be the length of fencing required for those dimensions.

Find a formula for $L$ in terms of $x$ and $y$.

A rectangular enclosure at the zoo is 35 feet long by 18 feet wide. The zoo wants to double the area of the enclosure by adding the same distance x to the length and width. Write and solve an equation to find the value of x. What are the dimensions of the enclosure.

As shown in the accompanying figure, a camera is mounted at a point $3000 \mathrm{ft}$ from the base of a rocket launching pad. The rocket rises vertically when launched, and the camera's elevation angle is continually adjusted to follow the bottom of the rocket.

Find the domain of the function in the previous part.

A farmer has 64 yards of fencing and wants to create a rectangular enclosure for his animals. What is the enclosure with the greatest area?

As shown in the accompanying figure, a camera is mounted at a point $3000 \mathrm{ft}$ from the base of a rocket launching pad. The rocket rises vertically when launched, and the camera's elevation angle is continually adjusted to follow the bottom of the rocket. Find the domain of the function in part (a).

Express the length $L$ of a chord of a circle with radius $10 \mathrm{~cm}$ as a function of the central angle $\theta$ (see the accompanying figure).

As shown in the accompanying figure, a pendulum of constant length $L$ makes an angle $\theta$ with its vertical position. Express the height $h$ as a function of the angle $\theta$.

Use the equation $y=1+\sqrt{x}$ to answer the following questions.

(a) For what values of x is y = 4?

(b) For what values of x is y = 0?

(c) For what values of x is y ≥ 6?

(d) Does y have a minimum value? A maximum value? If so, find them.

Use the equation $y=1+\sqrt{x}$ to answer the following questions.

Does $y$ have a minimum value? A maximum value? If so, find them.

Use the following equation which is given as $y=1+\sqrt{x}$ to answer the following question. Does $y$ have a minimum value? A maximum value? If so, find them.

Use the equation $y=x^2-6 x+8$ to answer the following questions.

For what values of $x$ is $y=-10$?

Sketch the graph of the function g(x) = x + |x|.

Let f(x) = 3x + 1 and

$$g ( t ) = t ^ { 2 } - 2 t + 1$$

. Find the value. f(r + 8)

Find the planar density and packing fraction for FCC nickel in the $(100)$, $(110)$, and $(111)$ planes. Which, if any, of these planes are close packed?