anonymous
  • anonymous
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.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
First separate variables and solve the differential equation for V
anonymous
  • anonymous
\[dV/V ^{1/2} = -2dt\]
anonymous
  • anonymous
so \[\int\limits_{?}^{?}dV/V ^{1/2} = \int\limits_{?}^{?} -2dt\]

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anonymous
  • anonymous
where both of those are indefinite integrals
anonymous
  • anonymous
alright great! I've got it from there! Thank you very much.
anonymous
  • anonymous
No problem, let me know if you get stuck anywhere else with this one
anonymous
  • anonymous
\[V = t ^{2}-22t+121\] was the final answer i found
anonymous
  • anonymous
yes i did too except i left it as (-t+11)^2
anonymous
  • anonymous
perfect :)
anonymous
  • anonymous
thanks again!

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