Chapter 7.1, Problem 26E

To determine

To Find: The equation that gives $P$ as a function of $A$ . Then find the pressure when you wear the boots shown.

Answer to Problem 26E

  $P=\frac{154.8}{A}$

Explanation of Solution

Given: When you stand on the snow the average pressure $P$ that you exerts on the snow varies inversely with the total area $A$ of the soles of the footwear. Suppose the pressure is $0.43$ pound per square inch when you wear the snow shoes shown.

  

We know that Equation for inverse variation: $xy=a,y=\frac{a}{x}$

Then

The equation that gives $P$ as a function of $A$ is

  $P=\frac{a}{A}$

Now we have to find the pressure when you wear the boots

Put $A=360,P=0.43$

  $\begin{array}{l}P=\frac{a}{A}\\ 0.43=\frac{a}{360}\\ a=154.8\end{array}$

Substitute $a=154.8$ in inverse variation equation

Thus

  $P=\frac{154.8}{A}$