Question

I'm trying to figure out any puts on a linear equation but I keep getting confused

Answer 1

Given the function below.

$P(d)=14.5+\frac{29}{66}d$

To calculate the pressure at the surface of the water, depth, d = 0

Substituting for d into the function above,

$P(0)=14.5+\frac{29}{66}(0)=14.5+0=14.5PSI$

P is 14.5PSI at the surface

To find the depth at double the pressure, (2P),

Substituting 2P into the formula,

$\begin{gathered} 2P=14.5+\frac{29}{66}d \\ \end{gathered}$

Where P = 14.5 PSI at the surface,

$\begin{gathered} 2(14.5)=14.5+\frac{29}{66}d \\ 29=14.5+\frac{29}{66}d \\ \frac{29}{66}d=29-14.5 \\ \frac{29}{66}d=14.5 \\ d=\frac{14.5\times66}{29}=33ft \\ d=33ft \end{gathered}$

d is 33ft when P is doubled

At a depth of 231ft, the pressure P will be,

$P(231)=14.5+\frac{29}{66}(231)=14.5+101.5=116\text{PSI}$

P is 116PSI at depth of 231ft,

At a depth of 330ft, the pressure will be

$P(330)=14.5+\frac{29}{66}(330)=14.5+145=159.5\text{PSI}$

P is 159.5PSI at depth of 330ft