Question

he gateway arch in st. louis is 630ft high and has a 630-ft base. its shape can be modeled by the parabola y = 630 ? 1 − ? x 315 ?2? find the average height of the arch above the ground.

Answer 1

The average height of the Gateway Arch above the ground is 420 ft.

Step-by-step explanation:

The height of the arch above the ground can be found by evaluating the equation y = 630 - (1/315)x^2. The average height of the arch is equal to the average value of y over the entire range of x values. Since the base of the arch is 630 ft and the arch is symmetric, the range of x values is from -315 ft to 315 ft. To find the average height, we integrate the equation from -315 to 315 and divide the result by the length of the interval, which is 630 ft. Using integral calculus, the average height of the arch above the ground is calculated to be 420 ft.