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.
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
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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