The force required to prevent a car from skidding on a flat curve varies directly as the weight of the car and the square of its speed, and inversely as the radius of the curve. It requires 290 lb of force to prevent a 2,200 lb car traveling at 35 mph from skidding on a curve of radius 520 ft. How much force is required to keep a 2,800 lb car traveling at 50 mph from skidding on a curve of radius 415 ft ?

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.

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?

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

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

State the domain and range of f.

Fill in the Blanks in the following sentence.

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

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.

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 $(4,64 \pi)$.

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 = $\frac{1}{2}$.

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

The number of people that can sit comfortably around a circular table varies _____ with the radius of the table.

Translate Einstein's famous equation for the relationship between energy and mass, $E=m c^2$, into variation language. ( E = energy, m = mass, c = the speed of light, which is a constant.)

Translate the following sentence into a variation equation.

The electromagnetic force F between two bodies with a given charge is inversely proportional to the square of the distance d between them.