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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The correct answer is:
The quotient that describes the rate of change in the dolphin’s position is 0.28 meters/second.
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 negative 0.99 meters/second.
The quotient that describes the average rate of change for the diver’s depth is −3.47 meters/second.
The quotient that describes the average rate of change for the diver’s depth is negative 3.47 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.
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The correct answer is:
The quotient that describes the average rate of change for the diver’s depth is -0.99 meters/second.
To find the average rate of change in the dolphin's position, we need to divide the total change in position by the time taken.
The total change in position is 3.5 meters (from the highest point above water) plus 10 meters (from the lowest depth below the surface), which equals 13.5 meters.
The time taken is 12.5 seconds.
Dividing the total change in position (13.5 meters) by the time taken (12.5 seconds), we get 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.
To find the average rate of change in the dolphin's position, we need to calculate the change in position (distance) divided by the change in time.
First, let's find the change in position. The dolphin reached an altitude of 3.5 meters above the water and then dove 10 meters below the surface. So, the change in position is 3.5 meters + 10 meters = 13.5 meters.
Next, let's find the change in time. The dolphin went from its highest point above the water to its lowest depth in 12.5 seconds. So, the change in time is 12.5 seconds.
Now, we can calculate the average rate of change by dividing the change in position by the change in time:
Average rate of change = Change in position / Change in time
Average rate of change = 13.5 meters / 12.5 seconds
Calculating this value gives us 1.08 meters/second.
Therefore, the quotient that describes the average rate of change in the dolphin's position is 1.08 meters/second (to the nearest hundredth).