Step-by-step explanation:
The height, h in feet, of a rocket is given by, where t is time in seconds.
...(1)
We need to find the maximum height of the rocket and find the time the rocket was in the air. For maximum height, put ![\dfrac{dh}{dt}=0](https://tex.z-dn.net/?f=%5Cdfrac%7Bdh%7D%7Bdt%7D%3D0)
![\dfrac{d(-16t^2+64t+190)}{dt}=0\\\\-32t+64=0\\\\t=\dfrac{64}{32}\\\\t=2\ s](https://tex.z-dn.net/?f=%5Cdfrac%7Bd%28-16t%5E2%2B64t%2B190%29%7D%7Bdt%7D%3D0%5C%5C%5C%5C-32t%2B64%3D0%5C%5C%5C%5Ct%3D%5Cdfrac%7B64%7D%7B32%7D%5C%5C%5C%5Ct%3D2%5C%20s)
So, it will reach its maximum height in 2 seconds.
Now put t = 2 in equation (1) as follows :
![h(2)=-16(2)^2+64(2)+190\\\\=254\ \text{feet}](https://tex.z-dn.net/?f=h%282%29%3D-16%282%29%5E2%2B64%282%29%2B190%5C%5C%5C%5C%3D254%5C%20%5Ctext%7Bfeet%7D)
So, the maximum height of the rocket and find the time the rocket was in the air is 254 feet and 2 seconds respectively.