Ask a New Question
Menu

Question%0D%0AA 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)%0D%0AResponses%0D%0A%0D%0AThe quotient that describes the average rate of change for the diver’s depth is −3.47 meters/second.%0D%0AThe quotient that describes the average rate of change for the diver’s depth is negative 3.47 meters/second.%0D%0A%0D%0AThe quotient that describes the average rate of change for the diver’s depth is −0.49 meters/second.%0D%0AThe quotient that describes the average rate of change for the diver’s depth is negative 0.49 meters/second.%0D%0A%0D%0AThe quotient that describes the average rate of change for the diver’s depth is 0.99 meters/second.%0D%0AThe quotient that describes the average rate of change for the diver’s depth is 0.99 meters/second.%0D%0A%0D%0AThe quotient that describes the average rate of change for the diver’s depth is −0.99 meters/second.%0D%0AThe quotient that describes the average rate of change for the diver’s depth is negative 0.99 meters/second.

1 answer

To find the average rate of change in the diver's depth, we need to calculate the change in depth and divide it by the time taken to make that change.

  1. Initial Depth: The diver was at a depth of 15 meters below the surface.

  2. Final Depth: The diver descends 10 meters lower, so the final depth is:

    \[ 15 \text{ meters} + 10 \text{ meters} = 25 \text{ meters (below the surface)} \]

  3. Change in Depth: The change in depth as the diver descends from 15 meters to 25 meters is:

    \[ 25 \text{ meters} - 15 \text{ meters} = 10 \text{ meters} \]

  4. Time Taken: The time taken for this descent is 10.1 seconds.

  5. Average Rate of Change: The average rate of change of depth can be calculated using the formula:

    \[ \text{Average Rate of Change} = \frac{\text{Change in Depth}}{\text{Time}} = \frac{10 \text{ meters}}{10.1 \text{ seconds}} \]

    Performing the division:

    \[ \frac{10}{10.1} \approx 0.9901 \]

    Rounding to the nearest hundredth, we have:

    \[ \approx 0.99 \text{ meters/second} \]

Since the diver is descending, this value should be expressed as negative:

Therefore, the average rate of change for the diver’s depth is −0.99 meters/second.

The correct response is:

The quotient that describes the average rate of change for the diver’s depth is negative 0.99 meters/second.