Question

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

100 points! Plz help

Answer 1

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]{ (3 * (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]{ (3 * (10 + 20 \alpha ))/(4\pi) } = 10 \\ (3 * (10 + 20 \alpha ))/(4\pi) = 1000 \\ (10 + 20 \alpha ) = (4000\pi)/(3) \\ 20 \alpha = ((4000\pi - 30))/(3) \\ \alpha = ((4000\pi - 30))/(60)`