Mathematics: 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. Use equation, find the maximum height reached by the rocket, to the nearest 10th of a foot . Y=-16x^2+261x+130

(-2,2)Step-by-step explanation:...

A rocket is launched from a tower. The height

grosst217

18.03.2022

Maximum height of the rocket = 1194.39 feet.

Step-by-step explanation:

The equation that shows the height of the rocket, y in feet, is related to the time after launch, x in seconds is as follows :

y=-16x^2+261x+130 ...(1)

We need to find the maximum height reached by rocket. For maximum height,

$\dfrac{dy}{dx}=0\\\\\dfrac{d(-16x^2+261x+130)}{dx}=0\\\\-32x+261=0\\\\x=\dfrac{261}{32}\\\\x=8.15\ s$

Put x = 8.15 s in equation (1).

$y=-16(8.15)^2+261(8.15)+130\\\\y=1194.39\ \text{feet}$

So, the maximum height of the rocket is 1194.39 feet.

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