The function h(t) = −16t2 + 64t + 12 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) = 10 + 10.4t, where g(t) is the height, in feet, of the object from the ground at time t seconds.
create a table using integers 1 through 4 for the 2 functions. between what 2 seconds is the solution to h(t) = g(t) located? how do you know?
explain what the solution from part a means in the context of the problem.

We are given the two functions:

H(t) = −16 t^2 + 64 t + 12

g(t) = 10 + 10.4 t

Now let us calculate for values of H(t) and g(t) by plugging in the values of t = 1 to 4 in each function as shown in the table below:

t                              H(t)                        g(t)

1                              60                           20.4

2                              76                           30.8

3                              60                           41.2

4                              12                           51.6

Looking at the table, we can say that the time when H(t)=g(t) must be between t=3 and t= 4 seconds.

At t=3 seconds H(t) is above g(t), and at t = 4 seconds H(t) is below g(t). Therefore the two functions must be at the same height in between.

Part B. The solution in Part A gives us the exact time where the two objects have the same height. Further, we can see from the table that H(t) is decreasing meaning the projectile is going down while g(t) is increasing so the other projectile is going up.

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step-by-step explanation: