Please help with this question. A rocket leaves a launcher at a height of 6 feet off the ground with an initial velocity of 128 feet per second. The equation describing the rocket's height after t seconds is h(t)=-16t^2+128t+6. Find the maximum height reached by the rocket and how many seconds it takes for the rocket to reach that height

Given:

The equation describing the rocket's height after t seconds is

To find:

The maximum height and time when it is maximum.

Solution:

We have,

Leading coefficient is -16, which is negative. So, it is a downward parabola.

Vertex of a downward parabola is the point of maxima.

If a quadratic function is , then

In the given function, a=-16, b=128 and c=6.

Putting x=4 in the given function, we get

So, vertex of the function is (4,262).

Therefore, maximum reached by the rocket is 262 feet it 4 seconds.

step-by-step explanation:

i found the koficent of the linear function and i foun c acordind to the strict formula y=kx+c and then i took 2 as an x and replacet it on the formula i found and then foun the y

irst, find the z score of a score of 80. this is given by the formula z = (x-u)/o, where x is the score, u is the mean, and o is the standard deviation. this gives

z = (80-78)/12 = 1/6 = .1667

now, find what percentile a z score of 1/6 correlates to in the normal distribution.

a z score of 1/6 = .1667 is equivalent to the 56.36th percentile of the distribution. so the probability a score is over this is 1-.5636 = .4364

the mean of a sample mean is equal to the original mean. however, the standard deviation of a sample mean is equal to the original standard deviation divided by the square root of n (sample size). so the new standard deviation is 12/sqrt(16) = 3.

the new z score is 80-78/3 = 2/3 = .667. this is equivalent to the 74.86th percentile. so the probability that the mean will be greater than this score is 1-.7486 = .2514.