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Math Help - Related rates, again

  1. #1
    Junior Member
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    Nov 2007
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    Related rates, again

    I need help with this question on my assignment:

    a water trough is 10m long and a cross-section has the shape of an isosceles triangle that is 1m across at the top and is 50cm high. The trough is being filled with water at a rate of 0.4m^3/min. How fast will the water level rise when the water is 40cm deep?

    Please and thank you.
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  2. #2
    Member
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    Mar 2008
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    The volume of water in the tank at a water level h is V = \frac{1}{2}(10)bh. Where b = 2h is the width of the water at the surface.

    So \frac{dV}{dt} = \frac{d(10h^2)}{dt} = 20h\frac{dh}{dt} =  .4.

    Therefore \frac{dh}{dt} = \frac{.4}{20h} and at h=.4 this is exactly \frac{dh}{dt}=\frac{1m}{20sec}
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