Let's solve this step-by-step to find the submarine's position after it ascends to avoid the cliff.
1. Initial Depth:
- The submarine starts at the surface of the ocean. When it submerges, it dives to a depth of -972 feet.
2. Depth Ascended:
- To avoid hitting an undersea cliff, the submarine ascends 329 feet.
3. Calculate the New Depth:
- To find the new depth, we need to add the depth the submarine ascended to its initial depth.
- Since the initial depth is -972 feet and it ascends 329 feet, we perform the following addition:
[tex]\[
\text{New Depth} = -972 + 329
\][/tex]
4. Result:
- Performing the addition, we get:
[tex]\[
-972 + 329 = -643
\][/tex]
Therefore, the integer that represents the submarine's position in feet after it ascends to avoid the cliff is [tex]\(-643\)[/tex] feet. The correct answer is:
[tex]\[ -643 \][/tex]
