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Math Help - Ice Cube

  1. #1
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    Exclamation Ice Cube

    I have two problems that are just bugging me and can't figure out how to get the answers. So I am begging you guys to help me out with them.

    A) A cube is melting a uniform rate of 3 in^2/hr. Fin the rate at which each side of the cube is decreasing when each side is 7in. Answer should be in in/min.

    B) A cube of ice is melting at a rate of 2in^3/hr, find the rate at which the surface area is decreasing when the sides are 5inches. Answer should be in in^2/min.

    Thanks for the help if you can.
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  2. #2
    Eater of Worlds
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    A) A cube is melting a uniform rate of 3 in^2/hr. Fin the rate at which each side of the cube is decreasing when each side is 7in. Answer should be in in/min.
    The volume of the cube is V=x^{3}

    We are given \frac{dV}{dt} = -3, \;\ x=7

    We need dx/dt.

    Differentiate implicitly:

    \frac{dV}{dt}=3x^{2}\cdot\frac{dx}{dt}

    Plug in the knowns and solve for dx/dt.
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