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. [lease explain how you got the answer
To find the rate of change in the diver's depth, we need to calculate the quotient of the change in depth and the time taken for the descent.
The change in depth is the difference between the initial depth and the final depth, which is 10 meters lower. Therefore, the change in depth is 15 meters - 10 meters = 5 meters.
The time taken for the descent is given as 10.1 seconds.
Now, we can calculate the rate of change by dividing the change in depth by the time taken for the descent:
Rate of change = Change in depth / Time taken for descent
Rate of change = 5 meters / 10.1 seconds = 0.495 s/m.
Rounded to the nearest hundredth, the rate of change in the diver's depth is 0.50 s/m.
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.
I apologize, but the correct answer is not among the options you provided.
The correct answer was calculated as 0.495 s/m, rounded to the nearest hundredth, which is approximately 0.50 s/m. This means that the rate of change in the diver's depth is 0.50 meters per second, not negative.
To find the rate of change in the diver's depth, we need to divide the change in depth by the time it took.
The change in depth is the difference between the initial depth and the final depth. In this case, the initial depth is 15 meters below the surface, and the final depth is 10 meters lower than the initial depth. Therefore, the change in depth is 15 + 10 = 25 meters.
The time it took for the diver to descend is given as 10.1 seconds.
Now we can calculate the rate of change in the diver's depth by dividing the change in depth by the time:
Rate of change = Change in depth / Time
Rate of change = 25 meters / 10.1 seconds
Calculating this on a calculator, we get:
Rate of change ≈ 2.48 meters per second
Therefore, the rate of change in the diver's depth is approximately 2.48 meters per second.
To interpret the quotient describing the rate of change in the diver's depth, we need to find the average rate of change. This can be calculated by dividing the change in depth by the change in time.
First, let's calculate the change in depth. The diver descended 10 meters lower, so the change in depth is -10 meters (negative because it indicates a descent).
Next, we'll calculate the change in time. The diver took 10.1 seconds to reach the new depth.
Now, we can calculate the average rate of change by dividing the change in depth (-10 meters) by the change in time (10.1 seconds):
Average rate of change = (-10 meters) / (10.1 seconds)
Evaluating this division, we get:
Average rate of change ≈ -0.99 meters/second
The negative sign indicates a descent, and the value of -0.99 meters/second represents the approximate rate at which the diver's depth decreased.