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Math Help - Calculus

  1. #1
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    Calculus

    I need some help on this problem. A snowball is melting at the rate of 6.00\; \frac{cm^3}{min} If it remains spherical, how fast is the radius decreasing when the radius is 2.00\; cm ?
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Vitamin View Post
    I need some help on this problem. A snowball is melting at the rate of 6.00\; \frac{cm^3}{min} If it remains spherical, how fast is the radius decreasing when the radius is 2.00\; cm ?
    the volume of a sphere is given by:

    V = \frac 43 \pi r^3

    differentiate implicitly with respect to t (time)

    \Rightarrow \frac {dV}{dt} = 4 \pi r^2 \frac {dr}{dt}

    you are given dV/dt (note that this is negative) and r, you want dr/dt, so solve for it
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  3. #3
    MHF Contributor Mathstud28's Avatar
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    ok

    Quote Originally Posted by Vitamin View Post
    I need some help on this problem. A snowball is melting at the rate of 6.00\; \frac{cm^3}{min} If it remains spherical, how fast is the radius decreasing when the radius is 2.00\; cm ?
    you are given that \frac{dV}{dt}=-6...now by using V_{sphere}=\frac{4}{3}\pi{r^3}...we have our equation...differntiating we get \frac{dV}{dt}=4\pi{r^2}\cdot{dr}{dt}...we know the values of \frac{dV}{dt} and r so plug and solve
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  4. #4
    MHF Contributor Mathstud28's Avatar
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    Ahhh

    Quote Originally Posted by Jhevon View Post
    the volume of a sphere is given by:

    V = \frac 43 \pi r^3

    differentiate implicitly with respect to t (time)

    \Rightarrow \frac {dV}{dt} = 4 \pi r^2 \frac {dr}{dt}

    you are given dV/dt (note that this is negative) and r, you want dr/dt, so solve for it
    Not this enter your answer e^{.0321651651654} seconds before me thing again haha
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  5. #5
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Mathstud28 View Post
    Not this enter your answer e^{.0321651651654} seconds before me thing again haha
    that's right1 i can read your mind and tell which problem you are planning to answer next. so i just hurry up and answer it before you. Muhuhahahahahahahaha
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  6. #6
    MHF Contributor Mathstud28's Avatar
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    Well....

    Quote Originally Posted by Jhevon View Post
    that's right1 i can read your mind and tell which problem you are planning to answer next. so i just hurry up and answer it before you. Muhuhahahahahahahaha
    Haha its sad because I believe you
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