Question

module 11 (linear equations) assignment
score: 17/20 answered: 17/20
question 18
when you dive below the surface of the water, the pressure increases. you can feel this in your ears when you dive to the bottom of a deep swimming pool or spring. the function that describes this relationship is $p = 14.5 + \frac{29}{66}d$, where $d$ is the depth in feet below the surface of the water and $p$ is the pressure in pounds per square inch (psi).
what is the pressure at the surface of the water? (hint: what is the depth at the surface?) select the correct units from the second box.
input box select an answer
what is the pressure at a depth of 66.0 feet?
input box select an answer
what is the pressure at a depth of 264.0 feet?
input box select an answer
which of the following is the graph of the function $p$?
graph 1 graph 2

Explanation:

Part 1: Pressure at the surface

Step 1: Determine depth at surface

At the surface, depth \( d = 0 \) feet (since depth below surface is 0).

Step 2: Substitute \( d = 0 \) into the formula

The pressure function is \( P = 14.5 + \frac{29}{66}d \). Substitute \( d = 0 \):
\( P = 14.5 + \frac{29}{66}(0) \)
\( P = 14.5 \) pounds per square inch (PSI).

Part 2: Pressure at 66.0 feet

Step 1: Identify \( d = 66.0 \)

Depth \( d = 66.0 \) feet.

Step 2: Substitute into the formula

\( P = 14.5 + \frac{29}{66}(66.0) \)
Simplify \( \frac{29}{66}(66.0) = 29 \), so \( P = 14.5 + 29 = 43.5 \) PSI.

Part 3: Pressure at 264.0 feet

Step 1: Identify \( d = 264.0 \)

Depth \( d = 264.0 \) feet.

Step 2: Substitute into the formula

\( P = 14.5 + \frac{29}{66}(264.0) \)
Simplify \( \frac{29}{66}(264.0) = 29 \times 4 = 116 \) (since \( 264 \div 66 = 4 \)), so \( P = 14.5 + 116 = 130.5 \) PSI.

Answer:

s:

• Pressure at surface: \( \boldsymbol{14.5} \) PSI
• Pressure at 66.0 feet: \( \boldsymbol{43.5} \) PSI
• Pressure at 264.0 feet: \( \boldsymbol{130.5} \) PSI

(Note: For the graph, the function \( P = 14.5 + \frac{29}{66}d \) is linear with a positive slope. The graph should be a straight line starting at \( (0, 14.5) \) and increasing. The first graph (with the red line) likely matches this, as it shows a linear increase starting from a positive y-intercept.)