Question

The function m(r)=21r³ models the mass in grams of a spherical titanium ball as a function of the ball's radius in centimeters. Write the inverse model to represent the radius r in centimeters of a spherical titanium ball as a function of the ball's mass m in grams.

Answer 1

The inverse model to represent the radius r as a function of the ball's mass m is r = ∛(m/21).

Step-by-step explanation:

The function m(r) = 21r³ represents the mass of a spherical titanium ball as a function of its radius. To write the inverse model to represent the radius r as a function of the ball's mass m, we can solve the equation for r.

To do this, we need to isolate r. So, divide both sides of the equation by 21 and then take the cube root of both sides:

r = ∛(m/21)

Therefore, the inverse model to represent the radius r as a function of the ball's mass m is r = ∛(m/21).