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4. A toy rocket is fired into the air from the top of a barn. It's height (h) above the ground in
yards after t seconds is given by the function: h(t) =- 5t^2+ 10t+ 20.
a) What was the maximum height of the rocket?
b) How long was the rocket in the air before it reached its highest height?

Respuesta :

Answer:

A) 25

Step-by-step explanation:

You use x= -b/2a in order to get your maximum so x= -10/ 2(-5) and you get x=1. You plug 1 into the function as h(1)=-5(1)^2 + 10(1)+ 20 which gets you 25

A function assigns the values. The time it will take for the rocket in the air before it reached its highest height is 1 second.

What is a Function?

A function assigns the value of each element of one set to the other specific element of another set.

A.) The maximum height of the rocket can be found by differentiating the function to get the maximum value of the height funciton.

dh/dt = -5(2t) + 10

Substitute the differentiated value with 0,

0 = -10t + 10

-10t = -10

t = 1

Therefore, the maximum height will be attained when the time is 1 second.

Now, substitute the value of t as 1 second to get the maximum height,

h(t) =- 5t²+ 10t+ 20

h(1) =- 5(1)² + 10(1)+ 20

h(1) = -5 + 10 +20

h = 25 yards

Hence, the maximum height of the rocket is 25 yards.

B.) The time it will take for the rocket in the air before it reached its highest height is 1 second.

Learn more about Function:

https://brainly.com/question/5245372

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