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Math Help - Calculus.....

  1. #1
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    Calculus.....

    A cable is to be run from a power plant on one side of a
    river to a factory on the other side. It costs $4 per
    meter to run the cable over land, while it costs $5 per
    meter to run the cable under water. Suppose the river
    is 300 meters wide and the factory is 1000 meters
    downstream from the power plant.
    What is the most economical route to lay the cable?
    How much will it cost?
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  2. #2
    Behold, the power of SARDINES!
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    Quote Originally Posted by spencersin View Post
    A cable is to be run from a power plant on one side of a
    river to a factory on the other side. It costs $4 per
    meter to run the cable over land, while it costs $5 per
    meter to run the cable under water. Suppose the river
    is 300 meters wide and the factory is 1000 meters
    downstream from the power plant.
    What is the most economical route to lay the cable?
    How much will it cost?
    Always draw a diagram (sorry I used ft instead of meters )

    Calculus.....-capture.jpg

    From the diagram we can find the cost function by multiplying the distance by cost per meter

    c(x)=4(1000-x)+5\sqrt{(300)^2+x^2}

    Now we take the derivative to get

    \frac{dc}{dx}=-4+\frac{5x}{\sqrt{(300)^2+x^2}}

    Now we set this equal to zero and solve for x.
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  3. #3
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    thanks for your help...^^
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