Question

I need 33. B) find the exact time when the radius reaches 10 inches

100 points! Plz help

Answer 1

Step-by-step explanation:

You have found a function r(V(t)). We can see that this function is a one variable function. The variable is time.

So in this specific function we can call r(v(t)), r(t).

So:

$r(t) = \sqrt[3]{ \frac{3 \times (10 + 20t)}{4\pi} }$

If α is the moment that the radius is 10 inches and since the function above gives radius in inches we have to solve the equation:

$r( \alpha ) = 10$

Which is the same as:

$\sqrt[3]{ \frac{3 \times (10 + 20 \alpha )}{4\pi} } = 10 \\ \frac{3 \times (10 + 20 \alpha )}{4\pi} = 1000 \\ (10 + 20 \alpha ) = \frac{4000\pi}{3} \\ 20 \alpha = \frac{(4000\pi - 30)}{3} \\ \alpha = \frac{(4000\pi - 30)}{60}$