A dolphin jump above the surface of the water. They reach an altitude of 3.5 m above the surface of the water and then throw 10 m below the surface of the water. It went from its highest point above the water to the lowest depth and 12.5 seconds. Interpret the quotient to describe the average rate of change and the dolphins position. Give your answer to the nearest hundred p
The average rate of change can be interpreted as the average speed or velocity of the dolphin as it jumps and dives in the water.
To calculate the average rate of change, we can use the formula:
Average rate of change = Total change in position / Total time taken
The total change in position is the sum of the distance above the surface and below the surface: 3.5 m + 10 m = 13.5 m.
The total time taken is given as 12.5 seconds.
Average rate of change = 13.5 m / 12.5 s
Using a calculator to divide 13.5 by 12.5, we get approximately 1.08.
Therefore, the average rate of change, or the average speed or velocity of the dolphin, is approximately 1.08 meters per second.
Since the dolphin started above the surface of the water, reached a peak height of 3.5 m, and then dove below the surface to a depth of 10 m, we can interpret the positive average rate of change as the dolphin moving upward and downward in the water.
To find the average rate of change, we can use the formula:
Average Rate of Change = Change in Position / Change in Time
In this case, the dolphin goes from its highest point above the water (3.5 meters) to the lowest depth (-10 meters) in 12.5 seconds.
Change in Position = -10 meters - 3.5 meters = -13.5 meters (negative because it goes below the surface)
Change in Time = 12.5 seconds
Average Rate of Change = -13.5 meters / 12.5 seconds
To find the average rate of change to the nearest hundredth, we simply divide:
Average Rate of Change ≈ -1.08 meters/second
Therefore, the average rate of change for the dolphin's position is approximately -1.08 meters per second. This implies that the dolphin is descending underwater at an average rate of 1.08 meters per second.
To find the average rate of change, we need to determine the change in position (distance) of the dolphin and divide it by the time it took for the change to occur.
In this case, the dolphin went from a height of 3.5 meters above the water to a depth of 10 meters below the water. This means the change in position is 3.5 meters + 10 meters = 13.5 meters.
The time it took for this change to occur is given as 12.5 seconds.
Now, we can calculate the average rate of change by dividing the change in position by the time taken:
Average rate of change = Change in position / Time taken
= 13.5 meters / 12.5 seconds
= 1.08 meters per second
Therefore, the average rate of change is approximately 1.08 meters per second.
Now, let's interpret this average rate of change. Since it is positive (+1.08), it means that, on average, the dolphin is moving upwards at a speed of 1.08 meters per second.