Question

The height in feet of the curved roof of an aircraft hangar can be modeled by y=-0.02x^2+1.6x, where x is the horizontal distance in feet from one wall at ground level. What is the greatest height of the hangar?

Answer 1

The maximum height is the highest level of height an object can reach. . The greatest height of the hangar is 32feet

How to calculate the maximum height of a function?

The maximum height is the highest level of height an object can reach. Given the height in feet of the curved roof of an aircraft hangar can be modeled by y=-0.02x^2+1.6x

The velocity of the aircraft is zero at the maximum height. Therefore:

dy/dx = -0.04x + 1.6  = 0

Determine the value of x

0.04x = 1.6
x = 1.6/0.04
x = 40

Substitute x = 40 into the function to get the greatest height

y=-0.02x^2+1.6x

y=-0.02(40)^2+1.6(40)

y = -32 + 64

y = 32ft

Hence the greatest height of the hangar is 32feet

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