Question

The function h(t) --4.922 +17.69+575 is used to model the height of an object being tossed from a tall building, where h(t) is

Answer 1

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].