Afireworks rocket is launched from a hill above a lake. the rocket will fall into the lake after exploding at its maximum height. the rocket's height above the surface of the lake is given by g(x)= -16x^2+64+80. what is the maximum height of the rocket?

a) 150 feet c) 120 feet

b) 80 feet d) 144 feet

D

Step-by-step explanation:

At the maximum height, the value of the vertical velocity Vy equals zero. From the value of the equation, we can get the vertical velocity by its first differential.

Differentiating this, we get -32x + 64

We then equate this value to zero. This yield 32x = 64 and x = 2

We now plug the value of x back into the original expression for height.

-16(2)^2 + 64(2) + 80 = -64 + 128 + 80 = 144 feet

let f (x ) is a function and c be a positive real number,   the graph of the function g (x ) = f (cx ) is represented as follows.

when, c > 1,   the function compresses it in the x - direction.

when, 0 < c < 1, the function stretches it.

the function is g ( x ) = (9x )2.

the heighest power of x in g ( x ) = (9x )2 is 2, so the parent function is square function.

the equation of parent function is f ( x ) = x 2 .

the function is g ( x ) = (9x )2 and the parent function is f ( x ) = x 2 .

so, the functions f and g have the following relationship.

g ( x ) = f ( 9x ).

compare the function g ( x ) = f ( 9x ) with g (x ) = f (cx ).

c = 9 ( > 1 ).

so, the function g (x ) = (9x )2 compresses it in the x - direction.

step-by-step explanation: