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

x > 1.3

step by step:

8.5−0.9x> 9.8−1.9x

step 1: simplify both sides of the inequality.

−0.9x+8.5> −1.9x+9.8

step 2: add 1.9x to both sides.

−0.9x+8.5+1.9x> −1.9x+9.8+1.9x

1x+8.5> 9.8

step 3: subtract 8.5 from both sides.

1x+8.5−8.5> 9.8−8.5

1x> 1.3

step 4: divide both sides by 1.

1x/1 > 1.3/1

7.3

step-by-step explanation: