Fill in the Blanks in the following sentence.

If $y=\frac{k x}{v^2}$, where k is a constant, then y varies _____ as _____, and varies ______ as _____.

A credit card promotion offers a discount on all purchases made with the card. The discount is directly proportional to the size of the purchase. If you save $1.35 on a$20 purchase, how much will you save on a $173 purchase?

Recall that the weight of an object is inversely proportional to the square of its distance from the center of Earth. If you weigh 115 pounds on the surface of Earth, how much would you weigh in space 50,000 miles from Earth's surface? (The radius of Earth is about 4,000 miles.)

One of Murphy's Laws says that the time t spent debating a budget item is inversely proportional to the number d of dollars involved. According to this law, if a committee spends 45 minutes debating a $5,000 item, how much time will they spend debating a$10,000,000 item?

Complete the following sentence with directly, Inversely, or neither directly nor inversely.

Your height above the ground while on a Ferris wheel varies _____ as the number of minutes you have been riding it.

Complete the following sentence with directly, Inversely, or neither directly nor inversely.

The wall area that can be painted with a gallon of paint varies _____ as the thickness of the applied paint.

Complete the following sentence with directly, Inversely, or neither directly nor inversely.

The volume of a circular cylinder of a given height varies _____ as the square of the radius of its base.

For this problem consider the formula for the surface area of a sphere S.A .= $4 \pi r^2$

Show that the Fundamental Theorem of Variation is true for the points $(2,16 \pi)$ and $(4,64 \pi)$.

Suppose pay varies directly as time worked and Paul makes $400 for working 25 hours.

a. What is the constant of variation?

b. How much will Paul make for working 32 hours?

Fill in the Blanks, in the following problem.

A slope of $-\frac{2}{5}$ means that for every change of 5 units to the right there is a change of _______ units _______. It also means that for every change of 1 horizontal unit there is a vertical change of _______ unit.

Fill in the Blanks in the following sentence.

In the equation w = kyz, where k is a constant _____ varies _____ as _____.

If T varies directly as the third power of s and the second power of w, and if T = 10 when s = 2 and w = 1, find T when s = 8 and w = $\frac{1}{2}$.

For this question, consider the function f with equation $f(x)=\frac{15}{x}$.

State the domain and range of f.

Find the constant of variation if you are pedaling 21 mph and have 11 teeth on the back gear.