The function h(t) = -4.922 +17.694+ 575 is used to model the height of an object being tossed from a tall building, where h(t) is the height in meters and t is the time in seconds. What are the domain and range? Round to the nearest hundredth.

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?

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]

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step-by-step explanation:

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