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NeX [460]
3 years ago
9

I need 33. B) find the exact time when the radius reaches 10 inches 100 points! Plz help

Mathematics
1 answer:
stealth61 [152]3 years ago
3 0

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}

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