The function h(t)=-16t^(2)+144 represents the height, h(t), in feet, of an object fron the ground at t seconds after it is dropped. A realistic domain (for time) for this function is: -3

Question

The function h(t)=-16t^(2)+144 represents the height,  h(t), in feet, of an object fron the ground at  t seconds after it is dropped. A realistic domain (for time) for this function is:  -3 <= t <= 3  0 <= t <= 3  quad0 <= ℏ <= 144 all real numbers

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Function Domain: The function h(t) = -16t^2 + 144 represents the height of an object from the ground after it is dropped. The domain of this function is the set of all possible values of t for which the function is defined. Since t represents time, it cannot be negative because we cannot measure time before the object is dropped.Find Ground Impact Time: We need to consider the realistic scenario of the object being dropped and eventually hitting the ground. The height h(t) will be zero when the object hits the ground. To find when this happens, we set h(t) to zero and solve for t. 0 = -16t^2 + 144Solve for t: Divide both sides of the equation by -16 to simplify. 0 = t^2 - 9Discard Negative Solution: Take the square root of both sides to solve for t. t = √9 or t = -√9 t = 3 or t = -3Realistic Domain: Since time cannot be negative in this context, we discard the negative solution. The object hits the ground at t = 3 seconds. Therefore, the realistic domain for the function, considering the context of the problem, is from the time the object is dropped (t = 0) until the time it hits the ground (t = 3).

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