During a baseball game a player hits a ball while a bird is flying across the field. Let t be the time in seconds since the ball is hit and h be the height in feet. The height of the baseball over time is modeled by the equation h=-16t^2+65t and the height of a bird over time is modeled by the equation h=8t+20.

What do the intersection points of the equations represent?

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Answer:

The best and most correct answer among the choices provided by your question is the third choice or letter C. (The time when the height of the ball and the bird are the same)

Step-by-step explanation:

 Since both of these equations measure height versus time, the intersection points represent the time when the height of the ball and the bird are the same.

The intersection points of the equations is (1.44, 31.52).

Given that the height of the baseball over time is given by:

h = -16t² + 65t

The height of the bird over time os given by:

h = 8t + 20

The point of intersection of the equations is gotten using:

8t + 20 = -16t² + 65

16t² + 8t - 45 = 0

t = -1.94 or t = 1.44

Since the time cannot be negative, hence t = 1.44 seconds.

h(1.44) = 8(1.44) + 20 = 31.52 feet

Hence, the intersection points of the equations is (1.44, 31.52).

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