Final answer:
The diver's final location is 12 feet below sea level.
Step-by-step explanation:
The given information states that the deep sea diver is initially at a depth of 28 feet below sea level, represented by the integer -28. He then swims down an additional 5 feet to explore a reef, which would result in a new depth of -33 feet. Finally, he swims up 15 feet to watch a school of fish, which would bring his depth to -18 feet. To find the final location of the diver, we need to add these two depths: -33 feet + (-18 feet) = -51 feet. However, we must keep in mind that a negative depth indicates being below sea level. Therefore, we must take the absolute value of the sum, which is 51 feet. However, the question asks for the location in terms of feet below sea level, so we must add a negative sign to the answer. Hence, the final location of the diver is 51 feet below sea level, represented by the integer -51.
Explanation part:
The first step is to add the initial depth of the diver, -28 feet, with the additional 5 feet that he swims down to explore the reef. This can be represented as -28 feet + (-5 feet) = -33 feet. This sum indicates that the diver's depth has decreased by 33 feet, bringing him to a new depth of -33 feet.
In the second step, we need to add the depth of the reef exploration, -33 feet, with the 15 feet that the diver swims up to watch the school of fish. This can be represented as -33 feet + 15 feet = -18 feet. This sum indicates that the diver's depth has increased by 18 feet, bringing him to a new depth of -18 feet.
To find the final location of the diver, we need to add these two depths together: -33 feet + (-18 feet) = -51 feet. However, since the question asks for the location of the diver in terms of feet below sea level, we must take the absolute value of the sum, which is 51 feet. This indicates that the diver is 51 feet away from sea level.
However, the question also specifies that the location should be represented by an integer, and a negative depth indicates being below sea level. Therefore, we must add a negative sign to the answer, giving us a final location of -51 feet. This represents that the diver is 51 feet below sea level, as required by the question. Hence, the final answer is -51 feet, or 51 feet below sea level.