Question

Two baseball players at your school throw a baseball into the air. The height of the first player's throw f in feet with respect to time t in seconds can be modeled by the equation f(t) = -16t^2 + 25t + 4, and the height of the second player's throw g in feet with respect to time t can be modeled by the equation g(t) = -16t^2 + 10t + 4.5. Write an equation f(t) that models the average height between the two throws.

Answer 1

The average height between two baseball throws modeled by f(t) = -16t^2 + 25t + 4 and g(t) = -16t^2 + 10t + 4.5 is calculated by taking the sum of the two functions and dividing by 2, resulting in h(t) = -16t^2 + 17.5t + 4.25.

Step-by-step explanation:

To find the equation that models the average height between two baseball throws, we simply take the average of the two height functions, f(t) and g(t). The height of the first player's throw is modeled by f(t) = -16t^2 + 25t + 4, and the height of the second player's throw is modeled by g(t) = -16t^2 + 10t + 4.5. The average height function, h(t), can be found by adding f(t) and g(t) together, and dividing by 2.

h(t) = (f(t) + g(t)) / 2

Substituting the given functions into this formula, we get:

h(t) = (-16t^2 + 25t + 4 + (-16t^2 + 10t + 4.5)) / 2

Simplifying, we find:

h(t) = (-32t^2 + 35t + 8.5) / 2

h(t) = -16t^2 + 17.5t + 4.25

This equation represents the average height of the baseball between the two throws as a function of time.