To determine the diver’s initial position in relation to the surface of the water before they swam up, we need to understand a few points:
1. The diver swims a total of 5.875 feet upward to reach the surface.
2. The surface of the water is considered to be at 0 feet.
Therefore, we need to find the depth, or initial position, of the diver when they started swimming up. The depth is the negative value of the distance swum upwards because depth below the surface is measured negatively.
Let's analyze the given options:
1. -5.9 feet: While close to the correct distance, this depth is slightly more than what we need.
2. [tex]$-5 \frac{3}{4}$[/tex] feet: This can be converted to a decimal value as follows:
[tex]\[
-5 \frac{3}{4} = -5.75 \text{ feet}
\][/tex]
Again, this is close, but not quite the right depth.
3. -58 feet: This is far too deep compared to 5.875 feet.
4. [tex]$-5 \frac{7}{8}$[/tex] feet: This can be converted to a decimal value as follows:
[tex]\[
-5 \frac{7}{8} = -5.875 \text{ feet}
\][/tex]
Among the given choices, only [tex]$-5 \frac{7}{8}$[/tex] feet, which is equivalent to -5.875 feet, represents the diver’s initial position correctly.
Hence, the correct representation of the diver's position in relation to the surface before swimming to the top is:
[tex]$-5 \frac{7}{8}$[/tex] feet.
