Question

Hello, please help me solve this problem:



The weight w (in pounds) that can be supported by a shelf made from half-inch Douglas fir plywood can be modeled by w=(82.9/d)3 where d is the distance (in inches) between the supports for the shelf. Find the inverse of the function. Then find the distance between the supports of a shelf that can hold set of encyclopedia weighing 66 pounds.

Answer 1

The inverse of the function is given by:

$w = \frac{82.9}{\sqrt[3]{d}}$

• Considering a weight of 66 pounds, the distance is of 1.98 inches.

How to find the inverse function?

• To find the inverse function, considering x and y as inputs, we exchange x and y in the original function, then isolate y.

In this problem, the function is:

$w(d) = \left(\frac{82.9}{d}\right)^3$

The output is w, input d, hence we exchange them, and isolate w.

$d = \left(\frac{82.9}{w}\right)^3$

$dw^3 = 82.9^3$

$w^3 = \frac{82.9^3}{d}$

$w = \sqrt[3]{\frac{82.9^3}{d}}$

$w = \frac{82.9}{\sqrt[3]{d}}$

Considering a weight of 66 pounds, $w = 66$, hence the distance is:

$dw^3 = 82.9^3$

$d = \frac{82.9^3}{66^3}$

$d = 1.98$

Considering a weight of 66 pounds, the distance is of 1.98 inches.

You can learn more about inverse functions at https://brainly.com/question/26131242