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Math Help - question on semi elliptical arch bridge

  1. #1
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    question on semi elliptical arch bridge

    the arch bridge takes the shape of a circular arc. the portion of the arch bridge above the water has a span of 30m and a rise of 10m. a boat passes through the arch bridge. if the cross section of the boat is modeled by a rectangle with vertical sides, find correct to 2 decimal places the width of the boat which has the largest cross sectional area above water level. justify your answer.
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  2. #2
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    You state semi-elliptical in the heading, but circular in the problem. It is

    an ellipse with semi-major axis length 15 and semi-minor axis length 10.

    The equation of said ellipse is \frac{x^{2}}{15^{2}}+\frac{y^{2}}{10^{2}}=1

    The area of the rectangle, designating the boat, has area A=2xy

    Solve the ellipse equation for y and sub into the area formula.

    Differentiate w.r.t. x, set to 0 and solve for x. y will follow.
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  3. #3
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    thanks (:
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