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Fourth of nine questions.

I'm using screen shots to ensure you see what I see.

All answers are integers in the range 0 to 9.

Where required, assume g=9.81

They haven't done a good job of making this word problem even remotely interesting.

The equation is given:

x' = -4(x-8)^(1/3)

You have initial value x(0)=72. You want to find t1 such that x(t1)=35.

This differential equation is trivial because it is separable:

(x-8)^(-1/3) dx = -4 dt

(3/2) (x-8)^(2/3) = -4t + C

Plugging in t=0, x=72, we get C = 24, so:

(3/2) (x-8)^(2/3) = -4t + 24

Then plug in x=35:

(3/2) (35-8)^(2/3) = -4t + 24

and get t = 21/8 = 2.625.

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