Question

a scuba diver has was at a depth of 15 m below the surface when she saw something interesting about 10 m lower. She gave the distance in 10.1 seconds determine the quotient to describe the rate of change in the divers depth give your answer to the nearest hundredth.

Answer 1

To find the rate of change in the diver's depth, we first need to determine the total change in depth she experienced and then divide that by the time it took for that change.

1. **Initial Depth**: The diver was at 15 m below the surface.
2. **Depth Below Surface of Interesting Object**: 10 m lower means she would be at:
\[
15 \, \text{m} + 10 \, \text{m} = 25 \, \text{m} \, \text{below the surface}
\]

3. **Change in Depth**:
\[
\text{Change in depth} = 25 \, \text{m} - 15 \, \text{m} = 10 \, \text{m}
\]

4. **Time Taken**: 10.1 seconds.

5. **Rate of Change in Depth**: The rate of change (quotient) can be calculated using the formula:
\[
\text{Rate of Change} = \frac{\text{Change in Depth}}{\text{Time}} = \frac{10 \, \text{m}}{10.1 \, \text{s}} \approx 0.9901 \, \text{m/s}
\]

Finally, rounding to the nearest hundredth, we get:
\[
\text{Rate of Change} \approx 0.99 \, \text{m/s}
\]

Thus, the quotient to describe the rate of change in the diver's depth is approximately **0.99 m/s**.