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Artyom0805 [142]
2 years ago
12

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 dom

ain of this function in this situation?
A) t ≥ 0
B) all real numbers
C) 0 ≤ t ≤ 2.4
D) 1.2 ≤ t ≤ 24
Mathematics
1 answer:
Nesterboy [21]2 years ago
7 0

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

----------------------

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 <u>set that contains all possible input values.</u>
  • 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.

----------------------

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

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