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zepelin [54]
2 years ago
6

The height in feet, h, of a model rocket t seconds after launch is given by the equation h(t) = 3+70t - 16t^2. The average rate

of change in h(t) between t = 1 second and t = 3 second is 6. What does the average rate of change tell you about the rocket?​
Mathematics
1 answer:
andriy [413]2 years ago
8 0

Answer:

The average rate of change

\frac{dh}{d t} = 70 (1) - 16(2t)

At   t = 1

\frac{dh}{d t} = 70 (1) - 16(2t) = 38

at t=3



Step-by-step explanation:

<u><em>Step(I)</em></u>:-

The given function  h(t) = 3+70t - 16t²

                          \frac{dh}{d t} = 70 (1) - 16(2t)

The       \frac{dh}{d t} = 70 (1) - 16(2t) =0

           70 - 32 t = 0

     ⇒   70 = 32 t

   ⇒     t = \frac{70}{32} = \frac{35}{16}

<em>Step(ii</em>):-

The average rate of change in h(t) between t = 1 second and t = 3 second

\frac{dh}{d t} = 70 (1) - 16(2t)

At   t = 1

\frac{dh}{d t} = 70 (1) - 16(2t) = 38

At t = 3



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