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The function H(t) = −16t2 + 32t + 50 shows the height H(t), in feet, of a baseball after t seconds. A second baseball moves in the air along a path represented by g(t) = 30 + 30.4t, where g(t) is the height, in feet, of the object from the ground at time t seconds.

Part A: Create a table using integers 0 through 3 for the 2 functions. Between what 2 seconds is the solution to H(t) = g(t) located? How do you know? (6 points)

Part B: Explain what the solution from Part A means in the context of the problem. (4 points)

If you could help at all it would be greatly appreciated, have a nice day

Respuesta :

Answer:

A) between seconds 1 and 2

B) one ball reaches a maximum and falls, the other one always rises

Step-by-step explanation:

H(t) = -16t² + 32t + 50

g(t) = 30 + 30.4t

A) To complete the table replace the values of t in the function, for example: H(2) =-16(2)² + 32(2) + 50 = 50

t    H(t)    g(t)

0   50     30

1    66     60.4

2   50     90.8

3   2       121.2

The solution to H(t) = g(t) is located between seconds 1 and 2, because before t = 1, H(t) > g(t), and after t = 2 g(t) > H(t)

B) The ball that follows function H(t) increase its height, reaches a maximum and, then, decreases its height. The ball that follows function g(t) increases its height all the time. In the beginning, the ball that follows function H(t) increases its height faster than the other ball, but after it reaches its maximum height, its height starts to decrease, giving the opportunity to the other ball to reach it.

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