A dolphin jumped above the surface of water. It reached an altitude of 3.5 meters above the surface of the water and then dove 10 meters below the surface of 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 dolphins position?
The quotient to describe the average rate of change in the dolphin's position is the change in position divided by the change in time. In this case, the change in position is the sum of the altitude above the water (3.5 meters) and the depth below the water (-10 meters), which is -6.5 meters. The change in time is 12.5 seconds.
Therefore, the average rate of change in the dolphin's position is approximately -0.52 meters per second. This means that, on average, the dolphin was descending at a rate of 0.52 meters per second during the 12.5 seconds it took to go from the highest point above the water to the lowest depth below the water.
To interpret the quotient and describe the average rate of change in the dolphin's position, we need to find the average rate of change or average velocity.
Average velocity is calculated by dividing the change in position (in this case, the distance traveled) by the change in time.
In this scenario:
- The dolphin reached an altitude of 3.5 meters above the surface of the water.
- Then, it dove 10 meters below the surface of the water.
- The total change in position is the sum of these two distances, which is 3.5 + 10 = 13.5 meters.
- The change in time is given as 12.5 seconds.
Therefore, the average rate of change in the dolphin's position is:
Average velocity = Total change in position / Change in time
= 13.5 meters / 12.5 seconds
= 1.08 meters per second.
Interpreting this quotient, we can say that the dolphin's position changed on average by 1.08 meters per second during the 12.5 seconds.
To interpret the quotient, we need to calculate the average rate of change in the dolphin's position. In this case, the average rate of change can be determined by dividing the change in position by the time it took to make that change.
The change in position can be found by subtracting the dolphin's highest point above the water (3.5 meters) from its lowest depth below the water (10 meters):
Change in position = Lowest depth - Highest point above water
= 10 meters - 3.5 meters
= 6.5 meters
The time it took for the dolphin to make this change in position was given as 12.5 seconds.
Therefore, the average rate of change in the dolphin's position can be calculated by dividing the change in position by the time taken:
Average rate of change = Change in position / Time
= 6.5 meters / 12.5 seconds
= 0.52 meters per second
So, the quotient of 0.52 meters per second describes the average rate of change in the dolphin's position. It indicates that, on average, the dolphin was changing its position by approximately 0.52 meters per second during the given time period.