Answer
The highest height attained by the rocket = 1194.4 feet
Step-by-step explanation
The height of the rocket, y, in feet as a function of the time, x in seconds as
y = -16x² + 261x + 130
We are then asked to find the maximum height reached by the rocket
To do this, we would use the differentiation analysis to obtain the maximum of this function.
At maximum point for any function,
The first derivative = (dy/dx) = 0
The second derivative = (d²y/dx²) < 0
y = -16x² + 261x + 130
First derivative
(dy/dx) = -32x + 261 = 0
32x = 261
Divide both sides by 32
(32x/32) = (261/32)
x = 8.15625 s
We can then substitute this value of x (time) into the equation to get the maximum height (y)
y = -16x² + 261x + 130
At x = 8.15625 s,
y = -16 (8.15625)² + 261 (8.15625) + 130
= -1064.39 + 2128.78 + 130
= 1194.39
= 1194.4 feet to the nearest tenth.
Hope this Helps!!!