Answer:
The rate of change of the divers elevation is approximately 24.71 feet/minute
Step-by-step explanation:
The given information are;
The depth to which the scuba diver dove =
The rate at which he dove = -21.3 feet/minute
The time which he spent at that elevation = 10.5 minutes
The elevation the diver then ascended to = ![-8\frac{9}{10} \ feet](https://tex.z-dn.net/?f=-8%5Cfrac%7B9%7D%7B10%7D%20%5C%20feet)
The total time for the dive = ![17\frac{1}{8} \ minutes](https://tex.z-dn.net/?f=17%5Cfrac%7B1%7D%7B8%7D%20%5C%20minutes)
Therefore, the time,
, with which the scuba diver descended to
is given as follows;
![t_d = \dfrac{Distance}{Speed} = \dfrac{-79\frac{9}{10} }{-21.3} \approx 3.75 \ minutes](https://tex.z-dn.net/?f=t_d%20%3D%20%5Cdfrac%7BDistance%7D%7BSpeed%7D%20%3D%20%5Cdfrac%7B-79%5Cfrac%7B9%7D%7B10%7D%20%7D%7B-21.3%7D%20%5Capprox%203.75%20%5C%20%20minutes)
The time,
, it took the scuba diver to elevate to
is given as follows;
=
- (3.75 + 10.5) minutes ≈ 2.8738 minutes
The rate of change of the divers elevation = (Final elevation - Initial elevation)/(Time taken)
∴ The rate of change of the divers elevation = (
- (
))/(2.87 minutes) = 71/2.8738 ≈ 24.71 feet/minute to the nearest hundredth
The rate of change of the divers elevation ≈ 24.71 feet/minute.