Answer:
0.51 and 11.24 seconds.
Explanation:
The height h of a rocket with an initial upward velocity of 188 feet per second after t seconds is modeled by the function:

And we want to find all values of t for which the rocket's height is 92.
So, we can set h(t) = 92 and solve for t:

We can divide everything by four:

Rearrange the equation:

We can use the quadratic formula:

In this case, a = 4, b = -47, and c = 23. Substitute:

Evaluate:

Hence, our two solutions are:

So, the rocket reaches a height of 92 feet after 0.51 seconds and again after 11.24 seconds.