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

`A = (40)/(P)`

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 (1)/(A)\\ $Introducing the constant of variation$\\P = (k)/(A)`

When:

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