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Math Help - Hyperbolas Word Problem

  1. #1
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    Hyperbolas Word Problem

    Natural draft cooling towers are shaped like hyperbolas for more efficient cooling of power plants. The hyperbola in the tower at the right can be modeled with the equation x^2/16-y^2=225=1 with the units in meters. Find the width of the tower at the top and at its narrowest point in the middle.
    The picture shows a tower that is 150 m tall and the sides of the tower form a hyperbola opening to the left and right.

    I know we can make the center (0,0) and the vertices would be (4,0) and (-4,0). I am confused though because the covertices would be (0,-15) and (0,15). This would give a height of 30m, but the diagram shows a height of 150 m.

    It is on p. 653, #32 here:

    http://www.glencoe.com/sites/common_...H10_895267.pdf
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  2. #2
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    Re: Hyperbolas Word Problem

    With "x^2" and "y^2", we have the hyperbola centered at the origin. This makes 150 m modeled as 75 m above the x-axis and 75 m below. It would behoove us, then, to give some thought to y = 75 and see what comes out. Why are you trying to restrict it to the vertices?
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  3. #3
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    Re: Hyperbolas Word Problem

    Got it, thanks! Just plugged 75 for y, solved for x, and doubled it to get the answer.
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