An arch has the shape of a semi-ellipse. The arch has a height of 8 feet and a span of 20 feet. Find an equation for the ellipse and use it to find the height, in feet, of the arch at a distance of 5 feet from the center. (Round your answer to the nearest hundredth if necessary.)

At a distance of 5 feet from the center, the height is 6.93 ft

Step-by-step explanation:

Assume that the center of the ellipse is at the origin. The general equation for an ellipse is:

Where "a" is half of the span of the ellipse, and "b" is the height of the arch (half of the amplitude of the ellipse). Thus, the equation is:

For x = 5 feet, the height of the arch is:

At a distance of 5 feet from the center, the height is 6.93 ft

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