Use graphing technology to graph the equation given below.

$$z=-\frac{4.85}{m}$$

Two protons will repel each other with a force F that depends on the distance d between them. Some values of F are given in the table given below. Note that d is measured in $10^{-10}$ meters, and F is measured in $10^{-10}$ newtons.

a. Graph the given data.

b. Find a general variation equation to represent the situation.

c. Find the value of the constant of variation and use it to rewrite the variation equation.

d. Use your variation equation from Part c to answer the question.

With what force will two protons repel each other if they are $1 \times 10^{-10}{~m}$ apart?

$$\begin{array}{c|ccccc} d & 1.5 & 3 & 4.5 & 6 & 7.5 \\ \hline F & 103 & 26 & 11 & 6 & 4 \end{array}$$

For the variation equation given below, how does the y-value change when an x-value is doubled? Give two specific ordered pairs (x, y) that support your conclusion.

$$y=\frac{5}{x^2}$$

In the graph of $d=\frac{1}{5} t$, the slope of the line is $\frac{1}{5}$. Write a sentence to describe this slope in the context of lightning and thunderstorms, using the appropriate units.

Fill in the Blank space in the following problem.

If y = kx$^n$, and x is divided by c, then y is _______.

Sonia calculated the volume of a cylindrical can of cat food with a radius of 1.5 inches and a height of 1.2 inches to be about 9.2 cubic inches.

a. Use the equation $V=k r^2h$ to calculate the constant of variation k that she used.

b. Did Sonia use the correct formula? How do you know?

The lengths of the femur and tibia within a species of mammal are typically directly proportional. If the femur of one household cat is 116.0 mm long and its tibia is 122.8 mm long, how long is the tibia of a cat whose femur is 111.5mm long?

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

a. Evaluate f(-10) and f(15).

b. Graph f in the window $-12 \leq x \leq 12$ and $-12 \leq y \leq 12$ and sketch the graph.

For the following problem, Suppose k< 0.

State the domain and range of the function $f: x \rightarrow k x^2$.

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 _____.

Officer Friendly measured the length L of car skid marks when the brakes were applied at different starting speeds S. He obtained the following data.

$$\begin{array}{l|ccccc} S(\mathrm{kph}) & 40 & 60 & 80 & 100 & 120 \\ \hline L(\mathrm{~m}) & 9 & 20 & 36 & 56 & 81 \end{array}$$

a. Graph the given data.

b. Find a general variation equation to represent the situation.

c. Find the value of the constant of variation and use it to rewrite the variation equation.

d. Use your variation equation from Part c to answer the question.

How far would a car skid if the brakes were applied at 150 kph ?

An object is tied to a string and then twirled in a circular motion. The tension in the string varies directly as the square of the speed of the object and inversely as the length of the string. When the length of the string is 2 ft and the speed is 3 ft/sec, the tension on the string is 130 lb. If the string is shortened to 1.5 ft and the speed is increased to 3.4 ft/sec, find the tension on the string.

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 ?

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?