Question

write two inequality statements to compare the following:

1. the relationship between the pacific ocean and the atlantic ocean.
2. the relationship between the indian and the arctic ocean.
3. the relationship between the atlantic ocean and the indian ocean.
4. the relationship between the pacific ocean and the arctic ocean.
5. the captain of a fishing vessel is standing on the deck at 23 feet above sea level. he holds up a rope that is tied to his fishing net that is below him underwater at a depth of 38 feet.

a. draw a diagram to show the location of the captain, the rope, and the fishing net.
b. label your diagram with the following: $-38$, $0$, $23$, $|-38|$, and $|23|$.
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page 8 of 12

Explanation:

Part 2a: Diagram Explanation

To draw the diagram:

1. Define the Vertical Axis: Let the horizontal line represent sea level (position \( 0 \)). Above sea level is positive, below is negative.
2. Captain's Position: Mark a point \( 23 \) units above sea level (label this as the captain’s location).
3. Fishing Net's Position: Mark a point \( 38 \) units below sea level (label this as the fishing net’s location).
4. Rope: Draw a line connecting the captain’s point to the fishing net’s point to represent the rope.

Part 2b: Labeling the Diagram

• Sea Level: Label the horizontal line as \( 0 \).
• Captain’s Height: The captain is at \( 23 \) feet above sea level, so label his position as \( 23 \). The absolute value \( |23| = 23 \) (since absolute value of a positive number is itself), so we can also label this position with \( |23| \).
• Fishing Net’s Depth: The fishing net is \( 38 \) feet below sea level, so its position is \( -38 \). The absolute value \( |-38| = 38 \) (absolute value of a negative number is its positive counterpart), so we can label the net’s position (or the length from sea level to the net) with \( |-38| \).

Final Answer (for Labeling)

• Sea level: \( 0 \)
• Captain’s position: \( 23 \) (or \( |23| \))
• Fishing net’s position: \( -38 \) (and the length from sea level to net: \( |-38| = 38 \))

(Note: The diagram itself is a visual representation, but the labeling follows the above key: \( 0 \) (sea level), \( 23 \) (captain), \( -38 \) (net), \( |23| = 23 \) (captain’s height from sea level), \( |-38| = 38 \) (net’s depth from sea level).)

Answer:

Part 2a: Diagram Explanation

To draw the diagram:

1. Define the Vertical Axis: Let the horizontal line represent sea level (position \( 0 \)). Above sea level is positive, below is negative.
2. Captain's Position: Mark a point \( 23 \) units above sea level (label this as the captain’s location).
3. Fishing Net's Position: Mark a point \( 38 \) units below sea level (label this as the fishing net’s location).
4. Rope: Draw a line connecting the captain’s point to the fishing net’s point to represent the rope.

Part 2b: Labeling the Diagram

• Sea Level: Label the horizontal line as \( 0 \).
• Captain’s Height: The captain is at \( 23 \) feet above sea level, so label his position as \( 23 \). The absolute value \( |23| = 23 \) (since absolute value of a positive number is itself), so we can also label this position with \( |23| \).
• Fishing Net’s Depth: The fishing net is \( 38 \) feet below sea level, so its position is \( -38 \). The absolute value \( |-38| = 38 \) (absolute value of a negative number is its positive counterpart), so we can label the net’s position (or the length from sea level to the net) with \( |-38| \).

Final Answer (for Labeling)

• Sea level: \( 0 \)
• Captain’s position: \( 23 \) (or \( |23| \))
• Fishing net’s position: \( -38 \) (and the length from sea level to net: \( |-38| = 38 \))

(Note: The diagram itself is a visual representation, but the labeling follows the above key: \( 0 \) (sea level), \( 23 \) (captain), \( -38 \) (net), \( |23| = 23 \) (captain’s height from sea level), \( |-38| = 38 \) (net’s depth from sea level).)