Question

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Answer 1

Solving the quadratic equation we conclude that:

• The maximum height is 45ft.
• The rocket is 18 seconds in the air.

How to get the maximum height of the rocket?

The height of the rocket is defined by the quadratic equation:

$d = 90t - 5t^2$

The maximum height is what we get in the vertex of the quadratic equation, such that for this quadratic equation, the vertex is at:

$t = -90/(2*-5) = 9$

So the maximum height is what we get when we evaluate in t = 9:

$d = 90*9 - 5*9^2 = 45$

The maximum height is 45ft.

How to get the time in the air?

Now we need to solve the equation for the largest value of t:

$d = 90*t - 5t^2 = 0$

Rewriting it, we get:

$0 = 90*t - 5*t^2\\\\0 = t*(90 - t*5)$

The maximum solution is what we get when:

0 = 90 - t*5

t = 90/5 = 18

The rocket is 18 seconds in the air.

If you want to learn more about quadratic equations:

https://brainly.com/question/1214333

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