Mathematics: 11. The total number of months m that it takes to produce p tennis rackets (in thousands) is given by the formula m = 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.

the 2nd and last options Step-by-step explanation:...

11. The total number of months m that it takes to

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21.01.2022

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

formula for $m= \frac{p^3}{90}$

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

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