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.
To find the average rate of change in the dolphin's position, we need to determine the total change in position (in this case, in meters) and divide it by the total time taken.
The total change in position is the sum of the maximum altitude above the water and the maximum depth below the water: 3.5 meters + 10 meters = 13.5 meters.
The total time taken is given as 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 (rounded to the nearest hundredth).
Here
1. The quotient that describes the rate of change in the squirrel’s height above the ground is −10.48 feet/second.
2. The quotient that describes the rate of change in the dolphin’s position is −1.08
meters/second.
3. The quotient that describes the average rate of change for the diver’s depth is −0.99
meters/second.
4. −$333.33
5. −4 ounces
To find the average rate of change in the dolphin's position, we will divide the change in position by the time taken.
The change in position is the distance traveled from the highest point above the water to the lowest depth below the water, which 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 taken is given as 12.5 seconds.
Now we can calculate the average rate of change:
Average rate of change = change in position / time taken = -6.5 meters / 12.5 seconds
Calculating this quotient, we get:
Average rate of change ≈ -0.52 meters per second
Therefore, the average rate of change in the dolphin's position is approximately -0.52 meters per second.
To find the average rate of change in the dolphin's position, we need to divide the total change in position by the total time taken.
First, let's calculate the total change in position. The dolphin started 3.5 meters above the water surface and then dove 10 meters below the surface. So the total change in position is 3.5 + 10 = 13.5 meters.
Next, let's calculate the total time taken. The dolphin went from its highest point above the water to its lowest depth in 12.5 seconds.
Now, we can calculate the average rate of change by dividing the total change in position by the total time taken:
Average Rate of Change = Total Change in Position / Total Time Taken
Average Rate of Change = 13.5 / 12.5
Dividing these two values gives us the average rate of change. Evaluating this calculation, we find:
Average Rate of Change = 1.08
Therefore, the average rate of change in the dolphin's position is approximately 1.08 meters per second.