Question

11. The total number of months m that it takes to produce p tennis rackets

Answer 1

Your question is missing formula for m which is given as;

formula for   $m= \frac{p^3}{90}$

Answer:

a.the inverse of the function is $p=\sqrt[3]{90m}$.

b.p=12 (thousands)

Step-by-step explanation:

Given Data:

Formula for  $m= \frac{p^3}{90}$  , where m is the total number of months it takes to produce p tennis rackets (in thousands).

Required:

a. Find the inverse of the function.

b. How many tennis rackets will be produced in 20 months? Round your answer to the nearest  whole tennis racket.

Solution:

a.Inverse of the function:

$m= \frac{p^3}{90}\\\\multiply\ both\ sides\ by\ 90\ we\ get\\p^3=m*90\\\\p^3=90m\\\\taking\ cube\ root\ we\ get\\\\p=\sqrt[3]{90m}$

the inverse of the function is $p=\sqrt[3]{90m}$........Eq1

b. How many tennis rackets will be produced in 20 months?

put m=20 in Eq1, we get

$p=\sqrt[3]{90*20}\\\\p=\sqrt[3]{1800}\\\\p=12.16$

If we round the answer to nearest whole tennis racket we get p=12 (thousands)

thus, in 20 moths 12 (thousands) tennis rackets will be produced