High School

In certain deep parts of the ocean, the pressure of seawater, [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{7d}{8} [/tex]

If a scientific team uses special equipment to measure the pressure underwater and finds it to be 147 pounds per square foot, at what depth is the team making their measurements?

Answer :

To determine the depth [tex]\( d \)[/tex] at which the pressure [tex]\( P \)[/tex] is 147 pounds per square foot, we start with the given equation:

[tex]\[ P = 14 + \frac{7d}{8} \][/tex]

Given that [tex]\( P = 147 \)[/tex] pounds per square foot, we can substitute this value into the equation:

[tex]\[ 147 = 14 + \frac{7d}{8} \][/tex]

First, let's isolate the term containing [tex]\( d \)[/tex] by subtracting 14 from both sides of the equation:

[tex]\[ 147 - 14 = \frac{7d}{8} \][/tex]

This simplifies to:

[tex]\[ 133 = \frac{7d}{8} \][/tex]

Next, to solve for [tex]\( d \)[/tex], we need to eliminate the fraction. Multiply both sides of the equation by 8:

[tex]\[ 133 \times 8 = 7d \][/tex]

This yields:

[tex]\[ 1064 = 7d \][/tex]

Now, divide both sides by 7 to isolate [tex]\( d \)[/tex]:

[tex]\[ d = \frac{1064}{7} \][/tex]

Therefore:

[tex]\[ d = 152 \][/tex]

Thus, the depth at which the team is making their measurements is:

[tex]\[ d = 1216 \][/tex] feet.

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