Question

a diver begins at 150 feet below sea level, descends at a steady rate of 5 feet per minute for 3.5 minutes, and then ascends 122.2 feet. what is the diver’s current depth? explain how to write a numerical expression to find the answer.

Explanation:

Step1: Determine initial depth

The diver starts at 150 feet below sea level, so we represent this as -150 (or just 150 if we consider depth as positive below sea level; here we'll use positive for depth below, so initial depth \( d_0 = 150 \) feet.

Step2: Calculate descent distance

The diver descends at 5 feet per minute for 3.5 minutes. Distance descended \( d_{\text{descend}} = 5 \times 3.5 \) feet.

Step3: Calculate depth after descent

Depth after descending: \( d_1 = 150 + 5 \times 3.5 \) (since descending increases depth below sea level).

Step4: Calculate depth after ascending

Then the diver ascends 122.2 feet, so we subtract this from the depth after descent (ascending decreases depth below sea level). The numerical expression is \( 150 + 5 \times 3.5 - 122.2 \).

Now compute the value:
First, \( 5 \times 3.5 = 17.5 \)
Then, \( 150 + 17.5 = 167.5 \)
Then, \( 167.5 - 122.2 = 45.3 \)

Answer:

The numerical expression is \( 150 + 5 \times 3.5 - 122.2 \), and the diver’s current depth is 45.3 feet below sea level.