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Math Help - Rates of change

  1. #1
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    Rates of change

    A trough is 12 feet long and 3 feet across the top (see figure). Its ends are isosceles triangles with altitudes of 3 feet.
    (a) If water is being pumped into the trough at 2 cubic feet per minute, how fast is the water level rising when h is 1.3 foot deep?

    _________ ft/min
    (b) If the water is rising at a rate of inch per minute when h = 2.1, determine the rate at which water is being pumped into the trough.
    _________ ft^3/min
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  2. #2
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    Quote Originally Posted by tradar View Post
    A trough is 12 feet long and 3 feet across the top (see figure). Its ends are isosceles triangles with altitudes of 3 feet.
    (a) If water is being pumped into the trough at 2 cubic feet per minute, how fast is the water level rising when h is 1.3 foot deep?

    _________ ft/min
    (b) If the water is rising at a rate of inch per minute when h = 2.1, determine the rate at which water is being pumped into the trough.
    _________ ft^3/min

    Have a look here: http://www.mathhelpforum.com/math-he...-calculus.html
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  3. #3
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    That helped for the first part...THANKS!

    how do I relate that to the second part?
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  4. #4
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    Quote Originally Posted by tradar View Post
    That helped for the first part...THANKS!

    how do I relate that to the second part?
    I assume that you found out:

    \dfrac{dV}{dt} = 12h\cdot \dfrac{dh}{dt}

    With question a) you plug in the values for \dfrac{dV}{dt} and h and calculate \dfrac{dh}{dt}

    while with b) you plug in the values for \dfrac{dh}{dt} and h and calculate \dfrac{dV}{dt}
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