Answer:
The correct option is;
Domain: [1.8, 12.76]
Range: [0, 590.90]
Step-by-step explanation:
The given function is h(t) = -4.92·t² + 17.69·t + 575
The maximum height reached is found from equating the derivative of the function to 0 as follows;
d(h(t))/dt = d(4.92·t² + 17.69·t + 575)/dt = -2×4.92·t + 17.69
d(h(t))/dt = 0 gives;
-2×4.92·t + 17.69 = 0
-9.84·t + 17.69 = 0
-9.84·t = -17.69
t = -17.69/-9.84 = 1.79 ≈ 1.8
h(1.8) = -(4.92×1.8²) + 17.69×1.8 + 575 = 590.9
Also we have from equating the function to zero
h(t) = -4.92·t² + 17.69·t + 575 = 0
(t - 12.75)(t + 9.2) = 0
Therefore, when t = 12.76 h(t) = 0,
Therefore, we have; the domain which is the set of values of the independent variables is [1.8, 12.76]
The range = [0, 590.90].
