Answer:
x=5.09 seconds (times at max)
Step-by-step explanation:
The time at which the height of the rocket is maximum is 5.09 seconds and the maximum height is 563.14 feet.
It is a polynomial that is equal to zero. Polynomial of variable power 2, 1, and 0 terms are there. Any equation having one term in which the power of the variable is a maximum of 2 then it is called a quadratic equation.
A rocket is launched from a tower.
The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation.
The quadratic equation is given below.
[tex]\rm y=-16x^2+163x+148[/tex]
Differentiate the equation with respect to x, then we have
[tex]\rm y' = \dfrac{dy}{dx}=\dfrac{d}{dx}(-16x^2+163x+148)\\\\y' =-32x + 163[/tex]
For y' = 0, then we have
32x = 163
x = 5.09
Then the maximum value of the rocket will be
[tex]\rm y=-16(5.09)^2+163(5.09)+148\\\\y = - 414.53 + 829.67 + 148\\\\y = 563.14\ ft[/tex]
More about the quadratic equation link is given below.
https://brainly.com/question/2263981
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