A baseball is hit so that its height in feet after t seconds is s(t)=-5t^2+36t+5 How high is the baseball after 1 second? Find the maximum height of the baseball

Answers are below

Step-by-step explanation:

The baseball is 36 ft in the air after 1 second. The maximum height of the baseball of 69.8 ft.

To find these answers, I used the graph below.

36 feet,

max height = 69.8 feet

Step-by-step explanation:

s(t)= -5t²+36t+5

at 1 second, t = 1 (substitute this into the equation)

s(1) = -5(1)²+36(1)+5

= -5 + 36 + 5

= 36 feet

recall that for a quadratic equation in the form y = ax²+bx + c, the maximum / minimum is given by x=-b/(2a)

in our case, b = 36 and a = -5

Note: since the coefficient of x² is a negative number, we can confirm that the curve will have a maximum value (note that if negative, then it will have a minimum)

hence maximum will occur at t = -b/(2a)

= - (36) / (2)(-5)

= -36 / -10

= 3.6 s  (substitute this into the equation)

s(3.6)= -5(3.6)²+36(3.6)+5

= 69.8 feet

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step-by-step explanation:

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