2. 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 0.52 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 -0.52 meters/second.
To find the average rate of change in the dolphin's position, we need to divide the change in position by the change in time. The change in position is the difference between the altitude above the water and the depth below the water, which is 3.5 meters + 10 meters = 13.5 meters. The change in time is given as 12.5 seconds.
So, the average rate of change in the dolphin's position is 13.5 meters / 12.5 seconds = 1.08 meters/second.
Therefore, the correct answer is:
The quotient that describes the rate of change in the dolphin’s position is 1.08 meters/second.
explain
In this situation, the average rate of change in the dolphin's position is calculated by dividing the change in position by the change in time. The change in position is 13.5 meters, which is the difference 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 12.5 seconds, as given in the problem.
Dividing the change in position (13.5 meters) by the change in time (12.5 seconds) gives the quotient 1.08 meters/second. This means that, on average, the dolphin is changing its position by 1.08 meters per second.
r u sure
I apologize for any confusion. Let me double-check the calculation.
Change in position = highest point above water - lowest depth below water = 3.5 meters - (-10 meters) = 3.5 + 10 = 13.5 meters
Change in time = 12.5 seconds
Average rate of change in position = (change in position) / (change in time) = 13.5 meters / 12.5 seconds ≈ 1.08 meters/second
Therefore, my previous response is correct.
The quotient that describes the rate of change in the dolphin’s position is 1.08 meters/second.
Applications of Dividing Rational Numbers Quick Check
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Question
A scuba diver was at a depth of 15 meters below the surface when she saw something interesting about 10 meters lower. She made the descent in 10.1 seconds. Interpret the quotient to describe the rate of change in the diver’s depth. Give your answer to the nearest hundredth.(1 point)
Responses
The quotient that describes the average rate of change for the diver’s depth is −0.49 meters/second.
The quotient that describes the average rate of change for the diver’s depth is negative 0.49 meters/second.
The quotient that describes the average rate of change for the diver’s depth is 0.99 meters/second.
The quotient that describes the average rate of change for the diver’s depth is 0.99 meters/second.
The quotient that describes the average rate of change for the diver’s depth is −0.99 meters/second.
The quotient that describes the average rate of change for the diver’s depth is negative 0.99 meters/second.
The quotient that describes the average rate of change for the diver’s depth is −3.47 meters/second.
To find the average rate of change in the dolphin's position, we need to divide the change in position by the time taken.
The change in position is the difference between the highest point above the water (3.5 meters) and the lowest depth below the water (-10 meters), which is 3.5 - (-10) = 13.5 meters.
The time taken is given as 12.5 seconds.
Now, we can use the formula for average rate of change:
Average Rate of Change = Change in Position / Time Taken
Plugging in the values, we get:
Average Rate of Change = 13.5 meters / 12.5 seconds
Calculating this gives us the quotient 1.08 meters/second. Therefore, the correct answer is:
The quotient that describes the rate of change in the dolphin’s position is 1.08 meters/second.