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    The ends of a long water trough 8ft. long are equilateral triangles whose sides are 2 feet long.?
    If water is being pumped into the trough at a rate of 5 cubic feet/minute, find the rate at which the water level is rising when the depth is 8 inches.
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    So let V= volume of water in trough, D= depth of water, t = time (in minutes)
    We have:
    dV/dt = 5 (given)
    V = constant x D^2 (you can work out the constant by finding the area of an equilateral triangle prism with the given dimensions and a height of D)
    We want to find dD/dt at D=2/3 (since 8 inches = 2/3 feet)


    So find dV/dD, invert to find dD/dV.
    Chain rule gives dD/dt = dD/dV x dV/dt
    then substitute D = 2/3 to find rate of change at a depth of 8 inches...
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Updated: November 7, 2015
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