A dolphin jumped above the surface of the water. It reached an altitude at 3.5 m above the surface of the water and then go 10 m below the surface of the water it went from its highest point above the water to its lowest dad and 12.5 seconds, interpret the quote Net to describe the average rate of change and the dolphins position give your answer to the nearest hundred.
To interpret the quote, we need to find the average rate of change and the dolphin's position.
The average rate of change is calculated by dividing the change in position by the change in time. In this case, the change in position is from 3.5 m above the surface to 10 m below the surface, which is a total change of 3.5 m + 10 m = 13.5 m. The change in time is given as 12.5 seconds. Therefore, the average rate of change is 13.5 m / 12.5 s = 1.08 m/s.
To find the dolphin's position, we add the highest point above the water (3.5 m) to the change in position (13.5 m). So the dolphin's position is 3.5 m + 13.5 m = 17 m below the surface of the water.
Therefore, to summarize:
- The average rate of change is approximately 1.08 m/s.
- The dolphin's position is approximately 17 m below the surface of the water.
To interpret the average rate of change and the dolphin's position, we need to calculate the average rate of change in terms of position per second.
The dolphin reached an altitude of 3.5 m above the surface of the water and then went 10 m below the surface of the water. This means the total change in altitude is 3.5 m above and 10 m below.
To calculate the average rate of change, we divide the total change in position (3.5 m + 10 m = 13.5 m) by the time taken (12.5 seconds):
Average rate of change = Total change in position / Time taken
Average rate of change = 13.5 m / 12.5 s
Average rate of change ≈ 1.08 m/s
So, the average rate of change of the dolphin's position is approximately 1.08 m/s.
As for the dolphin's position, since it went both above and below the surface of the water, we need to find the net position. The net position is the difference between the maximum altitude reached and the depth below the surface:
Net position = Maximum altitude - Depth below surface
Net position = 3.5 m - (-10 m)
Net position = 3.5 m + 10 m
Net position = 13.5 m
Therefore, the dolphin's net position is approximately 13.5 m.
To find the average rate of change and the dolphin's position, we can divide the change in position by the change in time.
First, let's understand the given information:
- The dolphin jumped above the surface of the water and reached an altitude of 3.5 m above the water.
- Then, it went 10 m below the surface of the water, which means it was 6.5 m deep.
- The time it took for the dolphin to go from its highest point above the water to its lowest point below the water was 12.5 seconds.
Now, let's find the average rate of change:
To find the average rate of change, we need to calculate the change in position and divide it by the change in time.
Change in position = (highest point above water) - (lowest point below water)
Change in position = 3.5 m - (-6.5 m)
Change in position = 3.5 m + 6.5 m
Change in position = 10 m
Average rate of change = Change in position / Change in time
Average rate of change = 10 m / 12.5 s
Average rate of change = 0.8 m/s
Now, let's find the dolphin's position:
To find the dolphin's position, we need to add the highest point above the water to the lowest point below the water and divide it by 2.
Dolphin's position = (highest point above water + lowest point below water) / 2
Dolphin's position = (3.5 m + -6.5 m) / 2
Dolphin's position = -3 m / 2
Dolphin's position = -1.5 m
Therefore, the average rate of change is 0.8 m/s, and the dolphin's position is approximately -1.5 m (to the nearest hundred).