Question

Use the following information. If a scuba diver starts at sea level, the pressure on the diver at a depth of \(d\) feet is given by the formula \(P=64 d+2112,\) where \(P\) represents the total pressure in pounds per square foot. Suppose the current pressure on a diver is 4032 pounds per square foot. Solve the formula for \(d\)

Short answer

After performing the above calculations, one should find \(d = 30\) feet. Thus, for a pressure of 4032 pounds per square foot, the scuba diver is 30 feet below sea level.

Step-by-step solution

Understand and Write Down the Given Formula

First, write down the given formula \(P = 64d + 2112\), which gives the pressure \(P\) as a function of the depth \(d\).

Substituting the Given Pressure

The current pressure on the diver is given as 4032 pounds per square foot. Substitute this value for \(P\) in the equation, resulting in the formula \(4032 = 64d + 2112\).

Solve for \(d\)

To solve for \(d\), first isolate \(64d\) on one side of the equation. Subtract 2112 from both sides of the equation, yielding \(4032 - 2112 = 64d\). Finally, divide both sides by 64 to find \(d\), i.e., \(d = (4032 - 2112) / 64\).