The function h(t) = -16t² + 72t will equal zero when the ball hits the ground:
-16t² + 72t = 0. Solving for the time, t, we factor -16t² + 72t : 16t (-t + 4.5) = 0.
This results in t = 0 and t = 4.5 sec. The ball hits the ground after 4.5 sec.
Problem 12.
Starting with A:(-5,3): Reflecting A over the y-axis results in B: (5,3). Translating B 3 units to the right results in C: (8,3). Finally, translating C down by 4 units results in D: (8,-1) (answer).
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The equation of this line is given by:
y = -1/2x + 1.
<h3>What is a linear function?</h3>
A linear function is modeled by:
y = mx + b
In which:
- m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
- b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.
Given two points, the slope is given by <u>change in y divided by change in x</u>. In this problem, we have points (0,1) and (2,0), hence:
m = (1 - 0)/(0 - 2) = -1/2.
Point (0,1) also means that the y-intercept is of b = 1, hence the equation of this line is given by:
y = -1/2x + 1.
More can be learned about linear functions at brainly.com/question/24808124
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