Will a truck that is 12 feet wide carrying a load that reaches 12 feet above the ground clear the semielliptical arch on the one-way road that passes under the bridge shown in the figure on the right?
It clear the arch because the height of the archway of the bridge 6 feet from the center is approximately feet. (Round to two decimal places as needed.)

Step 1 ：The problem is asking whether a truck of a certain height and width can pass under a semielliptical arch. The height of the truck is given as 12 feet, and the width is also given as 12 feet. The height of the arch at a distance of 6 feet from the center is not given, but we are asked to calculate it.

Step 2 ：The semielliptical arch can be represented by the equation of an ellipse in the form \((x/a)^2 + (y/b)^2 = 1\), where a is the semi-major axis (half the width of the arch at its widest point), b is the semi-minor axis (half the height of the arch at its highest point), x is the horizontal distance from the center of the arch, and y is the height above the ground.

Step 3 ：We are given that the truck is 12 feet wide, so we can assume that the truck will be 6 feet from the center of the arch. We need to find the height of the arch at this point.

Step 4 ：We can rearrange the equation of the ellipse to solve for y: \(y = b\sqrt{1 - (x/a)^2}\).

Step 5 ：We don't know the values of a and b, but we can assume that they are such that the arch is just high enough for the truck to pass under. So we can set y equal to the height of the truck, 12 feet, and solve for b.

Step 6 ：Given that x = 6, y = 12, and a = 12, we can solve for b to find that b = 13.85640646055102.

Step 7 ：The height of the arch at a distance of 6 feet from the center is approximately 13.86 feet. Since the height of the truck is 12 feet, the truck will be able to clear the arch.

Step 8 ：Final Answer: The truck will clear the arch. The height of the arch at a distance of 6 feet from the center is approximately \(\boxed{13.86}\) feet.