Applications of Dividing Rational Numbers Quick Check
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Question
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 −0.52 meters/second.
The quotient that describes the rate of change in the dolphin’s position is negative 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 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 1.08 meters/second.
The quotient that describes the rate of change in the dolphin’s position is 1.08 meters/second.
The correct response is:
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 calculate the change in position (altitude) divided by the time it took.
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) = 3.5 + 10 = 13.5 meters.
The time it took is given as 12.5 seconds.
Now, we can use the formula: average rate of change = change in position / time.
Plugging in the values, we get:
average rate of change = 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.
To find the average rate of change in the dolphin's position, we need to divide the change in position by the time interval.
In this case, the dolphin went from a height of 3.5 meters above the water to 10 meters below the water, resulting in a change in position of 3.5 + 10 = 13.5 meters. The time interval is given as 12.5 seconds.
To find the average rate of change, we divide the change in position by the time interval: 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."