Question

The human cannonball is an act where a performer is launched through the air. The height of the performer can be modeled by h(x)=−0.004x2+x+19, where h is the height in feet and x is the horizontal distance traveled in feet. The circus act is considering a flight path directly over the main tent. If the performer wants at least 5 ft of vertical height clearance, how tall can the tent be? Round your answer to the nearest foot.

A. 24 ft
B. 25 ft
C. 26 ft
D. 27 ft

Answer 1

The maximum height the tent can be for the performer to have at least 5 ft of vertical height clearance is 26 ft.

Step-by-step explanation:

To find the maximum height the tent can be for the performer to have at least 5 ft of vertical height clearance, we need to find the maximum value of the height function h(x).

First, let's find the x-coordinate of the maximum point. The x-coordinate of the maximum point can be found by using the formula x = -b/2a, where a = -0.004, b = 1, and c = 19 from the equation h(x) = -0.004x^2 + x + 19.

Plugging in the values, we get x = -1/(2*(-0.004)) = 125 ft.

Now, let's substitute the x-coordinate into the height function to find the maximum height. h(125) = -0.004(125)^2 + 125 + 19 = 26 ft.

Therefore, the tent height can be a maximum of 26 ft.