Final answer:
To find the average height of the arch, integrate the given function over the interval (-π/2, π/2). The average height is (1/(π/2 - (-π/2))) * ∫[-π/2 to π/2] 10cos(x) dx.
Step-by-step explanation:
To find the average height of the arch, we need to integrate the function y = 10cos(x) over the given interval. The average height is given by the formula:
Average height = (1/(b-a)) * ∫[a to b] f(x) dx
Plugging in the values for a = -π/2 and b = π/2, we can calculate the average height by evaluating the integral:
Average height = (1/(π/2 - (-π/2))) * ∫[-π/2 to π/2] 10cos(x) dx
We can simplify this equation to find the average height of the arch above the ground.