In certain deep parts of oceans, the pressure of sea water, [tex]P[/tex], in pounds per square foot, at a depth of [tex]d[/tex] feet below the surface, is given by the following equation:

[tex]P = 14 + \frac{4d}{9}[/tex]

If a scientific team uses special equipment to measure the pressure underwater and finds it to be 218 pounds per square foot, at what depth is the team making their measurements?

Answer: The team is measuring at [tex]\square[/tex] feet below the surface.

To find the depth at which the pressure is 218 pounds per square foot, we need to solve the given equation for [tex]\( d \)[/tex]:

[tex]\[ P = 14 + \frac{4d}{9} \][/tex]

We are given the pressure [tex]\( P \)[/tex] as 218 pounds per square foot. So, we substitute [tex]\( P = 218 \)[/tex] into the equation:

[tex]\[ 218 = 14 + \frac{4d}{9} \][/tex]

Next, we need to isolate [tex]\( d \)[/tex]. Start by subtracting 14 from both sides of the equation:

[tex]\[ 218 - 14 = \frac{4d}{9} \][/tex]

This simplifies to:

[tex]\[ 204 = \frac{4d}{9} \][/tex]

To eliminate the fraction, multiply both sides of the equation by 9:

[tex]\[ 204 \times 9 = 4d \][/tex]

[tex]\[ 1836 = 4d \][/tex]

Now, divide both sides by 4 to solve for [tex]\( d \)[/tex]:

[tex]\[ d = \frac{1836}{4} \][/tex]

[tex]\[ d = 459 \][/tex]

Therefore, the team is measuring the pressure at a depth of 459 feet below the surface.