“A football is punted into the air. It’s height in feet is found by using the equation h(T) = -5t squared +27.5t+2.5, where T represents the time in seconds and h(T) represents the height of the football in feet. How high does the football get. Round to the nearest thousandth”

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MrRoyal MrRoyal · Answer 1 · 2022-03-18T10:47:52+01:00

How high the football gets is a function of the maximum height of the ball

The football goes 40.313 ft high

The equation that models the height of the ball is given as:

[tex]h(t) = -5t^2 +27.5t+2.5[/tex]

Differentiate the function

[tex]h'(t) = -10t +27.5[/tex]

Set to 0

[tex]-10t +27.5 = 0[/tex]

Collect like terms

[tex]10t =27.5[/tex]

Divide by 10

[tex]t =2.75[/tex]

Substitute 2.75 for t in [tex]h(t) = -5t^2 +27.5t+2.5[/tex] to calculate how high the ball get

[tex]h_{max} = -5 * 2.75^2 +27.5 * 2.75+2.5[/tex]

[tex]h_{max} = 40.3125[/tex]

Approximate

[tex]h_{max} = 40.313[/tex]

Hence, the football goes 40.313 ft high