## anonymous 5 years ago The volume of water remaining in a hot tub when it is being drained satisfies the differential equation dV/dt = −2 ( V)^(1/2) , where V is the number of cubic feet of water that remain t minutes after the drain is opened. Find V if the tub initially contained 121 cubic feet of water.

1. anonymous

First separate variables and solve the differential equation for V

2. anonymous

$dV/V ^{1/2} = -2dt$

3. anonymous

so $\int\limits_{?}^{?}dV/V ^{1/2} = \int\limits_{?}^{?} -2dt$

4. anonymous

where both of those are indefinite integrals

5. anonymous

alright great! I've got it from there! Thank you very much.

6. anonymous

No problem, let me know if you get stuck anywhere else with this one

7. anonymous

$V = t ^{2}-22t+121$ was the final answer i found

8. anonymous

yes i did too except i left it as (-t+11)^2

9. anonymous

perfect :)

10. anonymous

thanks again!