Question

The pressure p(in lbs/in^2) that a 160 pound persons shoe exerts on the ground when walking varies inversely with the area A(in in^2) of the sole of the shoe when the shoes have a sole area of 40 in^2 The pressure is 4 lbs/in^2 find equation that relates these variables
A=

Answer 1

Answer:

$A = \dfrac{40}{P}$

Step-by-step explanation:

Pressure $p(in lbs/in^2)$  varies inversely with the area $A(in in^2)$ of the sole of the shoe.

This is written as:

$P \propto \frac{1}{A}\\ Introducing the constant of variation \\P = \dfrac{k}{A}$

When:

$When: A= 40 in^2, P =4 lbs/in^2\\ Substituting into the equation\\P = \dfrac{k}{A}\\4 = \dfrac{k}{40}\\ Cross multiply\\k=4*40\\k=160\\Therefore, the equation that connect these variables is given as:\\P = \dfrac{40}{A}\\ In terms of P\\AP=40\\\\A = \dfrac{40}{P}$