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:
[tex]h(t) = -16t^2 + 38.4t + 0.96[/tex]
- 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 [tex]h(t) = 0[/tex].
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[tex]h(t) = -16t^2 + 38.4t + 0.96[/tex]
Which is a quadratic equation with [tex]a = -16, b = 38.4, c = 0.96[/tex]
To find the solutions:
[tex]\Delta = b^2 - 4ac = (38.4)^2 - 4(-16)(0.96) = 1536[/tex]
[tex]t_1 = \frac{-b + \sqrt{\Delta}}{2a} = \frac{-38.4 + \sqrt{1536}}{2(-16)} = -0.0247[/tex]
[tex]t_2 = \frac{-b + \sqrt{\Delta}}{2a} = \frac{-38.4 - \sqrt{1536}}{2(-16)} = 2.4[/tex]
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 https://brainly.com/question/23932338
