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)
To find the average rate of change in the dolphin's position, we need to divide the total change in position by the time it took for the change to occur. The total change in position is the sum of how high it jumped above the surface and how deep it dove below the surface, which is 3.5 + 10 = 13.5 meters. The time it took for the change to occur is 12.5 seconds. So, the average rate of change in the dolphin's position is 13.5/12.5 = 1.08 meters per second, rounded to the nearest hundredth.
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)
Responses
The quotient that describes the rate of change in the dolphin’s position is 1.08 meters/second.
The quotient that describes the rate of change in the dolphin’s position is 1.08 meters/second.
The quotient that describes the rate of change in the dolphin’s position is −1.08 meters/second.
The quotient that describes the rate of change in the dolphin’s position is negative 1.08 meters/second.
The quotient that describes the rate of change in the dolphin’s position is 0.52 meters/second.
The quotient that describes the rate of change in the dolphin’s position is 0.52 meters/second.
The quotient that describes the rate of change in the dolphin’s position is −0.52 meters/second.
The quotient that describes the rate of change in the dolphin’s position is negative 0.52 meters/second.
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To find the average rate of change in the dolphin's position, we need to calculate the vertical distance traveled divided by the time taken.
From its highest point above the water (3.5 meters), the dolphin dove 10 meters below the surface. Therefore, the total vertical distance traveled is 3.5 + 10 = 13.5 meters.
The time taken to go from the highest point to the lowest depth is 12.5 seconds.
To find the average rate of change, we divide the total vertical distance traveled (13.5 meters) by the time taken (12.5 seconds):
Rate of change = Total distance / Time = 13.5 meters / 12.5 seconds.
Evaluating this expression, we find that the average rate of change in the dolphin's position is approximately 1.08 meters per second. Therefore, the average rate of change in the dolphin’s position is 1.08 meters per second (rounded to the nearest hundredth).
To interpret the quotient that describes the average rate of change in the dolphin's position, we need to calculate the average rate of change. The average rate of change can be determined by dividing the change in position by the change in time.
In this case, the change in position is the distance between the dolphin's highest point above the water (3.5 meters) and its lowest depth below the water (-10 meters). The change in time is given as 12.5 seconds.
To calculate the average rate of change, we can use the formula:
Average Rate of Change = (Change in Position) / (Change in Time)
Substituting the values, we have:
Average Rate of Change = (3.5 meters - (-10 meters)) / 12.5 seconds
= (3.5 meters + 10 meters) / 12.5 seconds
= 13.5 meters / 12.5 seconds
Now we can divide these two values to calculate the average rate of change:
Average Rate of Change = 13.5 meters / 12.5 seconds
≈ 1.08 meters/second
Therefore, the average rate of change in the dolphin's position is approximately 1.08 meters per second.