Question

When you stand on snow, the average pressure P (in pounds per square inch) that you exert on the snow varies inversely with the total area A (in square inches) of the soles of your footwear. Suppose the pressure is 0.43 pound per square inch when you wear the snowshoes shown. Write an equation that gives P as a function of A. Then find the pressure if you wear the boots shown. (A=400in^2)

Find the pressure if you wear the boots shown below. (A=60in^2)

Answer 1

The equation that gives the pressure as a function of the area is P = 172/A. If the boots have an area of 60 square inches, the pressure exerted is 2.87 pounds per square inch.

When standing on snow, the average pressure exerted varies inversely with the total area of the soles of the footwear.

Let P be the pressure and A be the area.

This relationship can be expressed as:

P = k/A

Where k is a constant.

We are given that the pressure is 0.43 pounds per square inch when wearing the snowshoes.

Let's substitute this into the equation:

0.43 = k/400

Solving for k:

k = 0.43 * 400 = 172

Now we can rewrite the equation as:

P = 172/A

For the boots with an area of 60 square inches:

P = 172/60 = 2.87 pounds per square inch.

Answer 2

0.43*0.43

Explanation: