Question

You are tossing an apple. After t seconds, the height of the apple in feet is given by h = -16t2 + 38.4t + 0.96. What is the domain of this function in this situation?
A) t ≥ 0
B) all real numbers
C) 0 ≤ t ≤ 2.4
D) 1.2 ≤ t ≤ 24

Answer 1

Using function concepts, it is found that the domain is 0 ≤ t ≤ 2.4, given by option C.

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The height of the apple after t seconds is given by:

$h(t) = -16t^2 + 38.4t + 0.96$

• The domain of a function is the set that contains all possible input values.
• The possible input values for this situation are the values of t between 0 and the instant in which the apple hits the ground, which is t for which $h(t) = 0$.

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$h(t) = -16t^2 + 38.4t + 0.96$

Which is a quadratic equation with $a = -16, b = 38.4, c = 0.96$

To find the solutions:

$\Delta = b^2 - 4ac = (38.4)^2 - 4(-16)(0.96) = 1536$

$t_1 = \frac{-b + \sqrt{\Delta}}{2a} = \frac{-38.4 + \sqrt{1536}}{2(-16)} = -0.0247$

$t_2 = \frac{-b + \sqrt{\Delta}}{2a} = \frac{-38.4 - \sqrt{1536}}{2(-16)} = 2.4$

The apple is in the air for 0 ≤ t ≤ 2.4, which means that the domain is given by option C.

A similar problem is given at brainly.com/question/23932338