Question
A submarine starts at sea level and its depth changes by -15 meters per minute for 2 hours. Which statements describe the submarine’s descent? Select all that apply. 1.The submarine had descended 600 meters after 1 hour. 2. Halfway into its descent, the submarine had descended 900 meters. 3. After 0.5 hour, the submarine had descended 450 meters. 4. The submarine descends to a depth of 1,800 meters. 5. After 2 hours, the depth of the submarine is double what it was after 1 hour. 6. After 2 hours, the depth of the submarine is triple what it was after 0.5 hour.
Answers
GPT-4o mini
To analyze the statements, let's calculate the descent of the submarine step by step.
1. The depth change rate is -15 meters per minute.
2. In 1 hour (60 minutes), the submarine descends:
\[
60 \text{ minutes} \times -15 \text{ meters/minute} = -900 \text{ meters}
\]
After 1 hour, the submarine is at a depth of 900 meters.
3. In 2 hours (120 minutes), the descent calculation is:
\[
120 \text{ minutes} \times -15 \text{ meters/minute} = -1800 \text{ meters}
\]
After 2 hours, the submarine is at a depth of 1800 meters.
4. After 0.5 hours (30 minutes):
\[
30 \text{ minutes} \times -15 \text{ meters/minute} = -450 \text{ meters}
\]
Now, let's evaluate the statements:
1. **The submarine had descended 600 meters after 1 hour.**
- **False.** The submarine descended 900 meters.
2. **Halfway into its descent, the submarine had descended 900 meters.**
- **False.** Halfway into its total descent (900 meters) would be after 30 minutes (450 meters descended).
3. **After 0.5 hour, the submarine had descended 450 meters.**
- **True.** As calculated, after 0.5 hour the descent is indeed 450 meters.
4. **The submarine descends to a depth of 1,800 meters.**
- **True.** After 2 hours, the submarine is at a depth of 1800 meters.
5. **After 2 hours, the depth of the submarine is double what it was after 1 hour.**
- **True.** After 1 hour it was at a depth of 900 meters. After 2 hours, it's at 1800 meters, which is double 900.
6. **After 2 hours, the depth of the submarine is triple what it was after 0.5 hour.**
- **False.** After 0.5 hour it was at 450 meters, and triple that would be 1350 meters. The depth after 2 hours is 1800 meters, which is not triple of 450.
Based on these evaluations, the true statements are: **3, 4, and 5.**
1. The depth change rate is -15 meters per minute.
2. In 1 hour (60 minutes), the submarine descends:
\[
60 \text{ minutes} \times -15 \text{ meters/minute} = -900 \text{ meters}
\]
After 1 hour, the submarine is at a depth of 900 meters.
3. In 2 hours (120 minutes), the descent calculation is:
\[
120 \text{ minutes} \times -15 \text{ meters/minute} = -1800 \text{ meters}
\]
After 2 hours, the submarine is at a depth of 1800 meters.
4. After 0.5 hours (30 minutes):
\[
30 \text{ minutes} \times -15 \text{ meters/minute} = -450 \text{ meters}
\]
Now, let's evaluate the statements:
1. **The submarine had descended 600 meters after 1 hour.**
- **False.** The submarine descended 900 meters.
2. **Halfway into its descent, the submarine had descended 900 meters.**
- **False.** Halfway into its total descent (900 meters) would be after 30 minutes (450 meters descended).
3. **After 0.5 hour, the submarine had descended 450 meters.**
- **True.** As calculated, after 0.5 hour the descent is indeed 450 meters.
4. **The submarine descends to a depth of 1,800 meters.**
- **True.** After 2 hours, the submarine is at a depth of 1800 meters.
5. **After 2 hours, the depth of the submarine is double what it was after 1 hour.**
- **True.** After 1 hour it was at a depth of 900 meters. After 2 hours, it's at 1800 meters, which is double 900.
6. **After 2 hours, the depth of the submarine is triple what it was after 0.5 hour.**
- **False.** After 0.5 hour it was at 450 meters, and triple that would be 1350 meters. The depth after 2 hours is 1800 meters, which is not triple of 450.
Based on these evaluations, the true statements are: **3, 4, and 5.**