Question #270951

A semi-elliptical archway over a one-way road has a height of 9 ft and width of 36 ft. Your van has a width of 12 ft and height of 8 ft. Will your van be able to clear the opening of the archway?

1
Expert's answer
2021-11-25T13:59:05-0500

Suppose that the eqaution of of our semi-ellipse is


x2182+y292=1,y0\dfrac{x^2}{18^2}+\dfrac{y^2}{9^2}=1, y\geq 0

If x=6x=6


62182+y292=1\dfrac{6^2}{18^2}+\dfrac{y^2}{9^2}=1

y2=819,y0y^2=81-9, y\geq0

y=62y=6\sqrt{2}

Since 62>8,6\sqrt{2}>8, then van will be able to clear the opening of the archway.


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