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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.

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  1. anonymous
    • 5 years ago
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    First separate variables and solve the differential equation for V

  2. anonymous
    • 5 years ago
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    \[dV/V ^{1/2} = -2dt\]

  3. anonymous
    • 5 years ago
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    so \[\int\limits_{?}^{?}dV/V ^{1/2} = \int\limits_{?}^{?} -2dt\]

  4. anonymous
    • 5 years ago
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    where both of those are indefinite integrals

  5. anonymous
    • 5 years ago
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    alright great! I've got it from there! Thank you very much.

  6. anonymous
    • 5 years ago
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    No problem, let me know if you get stuck anywhere else with this one

  7. anonymous
    • 5 years ago
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    \[V = t ^{2}-22t+121\] was the final answer i found

  8. anonymous
    • 5 years ago
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    yes i did too except i left it as (-t+11)^2

  9. anonymous
    • 5 years ago
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    perfect :)

  10. anonymous
    • 5 years ago
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    thanks again!

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