A dolphin jumped above the surface of the water. It reached an altitude of 3.5 meters above the surface of the water and then dove 10 meters below the surface of the water. It went from its highest point above the water to its lowest depth in 12.5 seconds. Interpret the quotient to describe the average rate of change in the dolphin's position. Give your answer to the nearest hundredth. (1 point)
a The quotient that describes the rate of change in the dolphin's position is
-0.52 meters/second.
b The quotient that describes the rate of change in the dolphin's position is
- 1.08 meters/second.
c The quotient that describes the rate of change in the dolphin's position is 1.08 meters/second
d The quotient that describes the rate of change in the dolphin's position is 0.52 meters/second.
To find the average rate of change in the dolphin's position, we need to divide the change in position by the time it took.
The change in position is the difference between the highest point above the water (3.5 meters) and the lowest depth below the water (-10 meters), which is 3.5 meters - (-10 meters) = 13.5 meters.
The time it took is 12.5 seconds.
Therefore, the average rate of change in the dolphin's position is 13.5 meters / 12.5 seconds = 1.08 meters/second.
So, the answer is:
c) The quotient that describes the rate of change in the dolphin's position is 1.08 meters/second.
To find the average rate of change in the dolphin's position, we need to divide the change in position by the time it took.
The change in position is the sum of the altitude above the water and the depth below the water:
Change in position = altitude + depth = 3.5 meters + (-10 meters) = -6.5 meters
The time it took for the dolphin to go from its highest point to its lowest depth is given as 12.5 seconds.
Now we can calculate the average rate of change in the dolphin's position:
Average rate of change = change in position / time = (-6.5 meters) / (12.5 seconds)
Calculating this quotient gives us approximately -0.52 meters/second.
Therefore, the correct answer is:
a) The quotient that describes the rate of change in the dolphin's position is -0.52 meters/second.
To find the average rate of change in the dolphin's position, you need to determine the change in position (altitude) divided by the change in time.
The change in position is the difference between the highest point above the water (3.5 meters) and the lowest depth below the water (-10 meters), which gives us a total change in position of 3.5 + (-10) = -6.5 meters.
The change in time is given as 12.5 seconds.
Now we can calculate the average rate of change using the formula:
Average Rate of Change = Change in Position / Change in Time
Average Rate of Change = (-6.5 meters) / (12.5 seconds)
Dividing these values, we find that the average rate of change in the dolphin's position is approximately -0.52 meters/second.
Therefore, the correct answer is:
a) The quotient that describes the rate of change in the dolphin's position is -0.52 meters/second.