How do you solve this problem?

Question

The length L (in millimeters) of an antelopes bone can be modeled by the equation: L=24.1d^(2/3)

where d is the diameter (in millimeters) of the nail. What is the diameter of an antelopes bone that is 179.57 millimeters long?

Answer 1

We are given the equation L=24.1d^2/3 and are asked to find the value of "d" when L = 179.57. Here, we substitute this value for L into the equation:

179.57 = 24.1d^2/3

Divide both sides by 24.1:

7.451037344 = d^2/3

To solve for "d", we must isolate "d". Given that "d" is raised to the 2/3 power, we must raise both sides of the equation by the reciprocal power to ensure that "d" is by itself, which in this case would be 3/2:

(7.451037344)^3/2 = [d^2/3]^3/2

20.3387899 = d

Therefore, the diameter of the bone is approximately 20.34 millimeters.