Respuesta :
Correct question is;
The function h(t) = -4.92t ² + 17.69t + 575 is used to model an object being tossed from a tall building, where h(t) is the height in meters and t is the time in seconds. Rounded to the nearest hundredth, what are the domain and range?
Answer:
The domain and range are:
Domain: [0, 12.76]
Range: [0, 590.9]
Step-by-step explanation:
For the domain;
Let's find the root of the given function h(t) = -4.92t ² + 17.69t + 575.
We will do it by Equating h(t) to zero and using quadratic formula;
So;
-4.92t ² + 17.69t + 575 = 0
t = [-17.69 ± √(17.69² - 4(-4.92 × 575))]/(2 × -4.92)
Solving with a calculator, the roots are
t = -9.16 or t = 12.76
We ignore the negative root and make use of the positive root.
Thus, the domain is:
[0, 12.76]
For the range:
Let's find the derivative of the given function:
Thus;
h'(t) = -9.84t + 17.69
Again like we did for the domain, we will equate to zero to find t
Thus;
-9.84t + 17.69 = 0
t = 17.69/9.84
t ≈ 1.8
Thus, this is the time at which the object being tossed reaches the maximum height of the function.. Thus max height at t = 1.8 is;
h(1.8) = (-4.92 × 1.8²) + (17.69 × 1.8) + 575
h(1.8) = -15.9408 + 31.842 + 575
h (1.80) ≈ 590.9
So the range is; [0, 590.9]
