Let's carefully examine the problem and identify the error in the work shown.
The problem states that a small submarine starts at a depth of [tex]\(-1,260\)[/tex] feet and descends [tex]\(5\)[/tex] feet per minute for [tex]\(12\)[/tex] minutes. The objective is to find the new position of the submarine in relation to sea level.
### Step-by-step procedure:
1. Initial Position:
The submarine starts at [tex]\(-1,260\)[/tex] feet. This is already below sea level.
2. Descent Rate:
The submarine is descending at a rate of [tex]\(5\)[/tex] feet per minute. Since it's descending, this rate is represented as [tex]\(-5\)[/tex] feet per minute.
3. Duration of Descent:
The submarine continues to descend for [tex]\(12\)[/tex] minutes.
4. Calculate the Total Descent:
To find the total distance the submarine descends, multiply the descent rate by the duration:
[tex]\[
(-5) \text{ feet/min} \times 12 \text{ minutes} = -60 \text{ feet}
\][/tex]
The total descent is [tex]\(-60\)[/tex] feet.
5. Find the New Position:
Add the total descent to the initial position of the submarine:
[tex]\[
-1,260 \text{ feet} + (-60) \text{ feet} = -1,320 \text{ feet}
\][/tex]
The new position of the submarine is [tex]\(-1,320\)[/tex] feet in relation to sea level.
### Identify the Error in the Shown Work:
Now, let's analyze the incorrect work step-by-step:
[tex]\[
\begin{aligned}
-1,260 + (-5)(12) & \text{ yields } -1,260 + (-60) \\
\end{aligned}
\][/tex]
Up to this point, the calculations are correct: [tex]\((-5) \times 12 = -60\)[/tex].
The next step is where the error occurs:
[tex]\[
1,260 + 60 = -1,200
\][/tex]
Here is the crucial mistake:
- The intermediate term [tex]\("-", or negative) should have been preserved. Instead, it seems like they added \(60\)[/tex] to [tex]\(1,260\)[/tex] and ignored the sign of [tex]\(-60\)[/tex].
### Correct Calculation:
Instead, it should be:
[tex]\[
-1,260 + (-60) = -1,320
\][/tex]
### Summary:
The correct new position of the submarine after descending is [tex]\(-1,320\)[/tex] feet in relation to sea level.
