Question

c. is the captain above or below water? what integer represents his elevation?
d. is the fishing net above or below the water? what integer represents its elevation?
e. does absolute value represent a location or a distance? how do you show this on a number line?
f. what absolute value expression represents the length of rope above the water?
g. what absolute value expression represents the length of rope below the water?
h. write an inequality to compare the elevations of the captain and the fishing net.
i. write an inequality to compare the length of the rope out of the water and the length of the rope in the water.
j. the captain lowers the rope further into the water. describe what happens to the elevation of the fishing net and to the length of the rope under the water.

Explanation:

To solve these problems, we'll analyze each part based on the context of elevations (positive for above water, negative for below water) and absolute value (representing distance). Let's assume the captain's elevation is \( +23 \) (above water) and the fishing net's elevation is \( -38 \) (below water) from the handwritten notes.

Part c: Captain's Elevation

Step1: Determine position (above/below)

Above water is positive, so the captain is above water.

Step2: Identify the integer

The elevation is \( +23 \) (or \( 23 \)).

Step1: Determine position (above/below)

Below water is negative, so the fishing net is below water.

Step2: Identify the integer

The elevation is \( -38 \).

Absolute value (\( |x| \)) represents the distance from \( 0 \) on a number line (not a location, which is represented by the integer itself). For example, \( |23| = 23 \) (distance from \( 0 \) to \( 23 \)) and \( |-38| = 38 \) (distance from \( 0 \) to \( -38 \)).

Answer:

The captain is above water. The integer representing his elevation is \( 23 \).

Part d: Fishing Net's Elevation