Answer :
Sure! Let's work through each part of the question step by step.
1. What is the pressure at the surface of the water?
At the surface of the water, the depth [tex]\(d\)[/tex] is 0. We use the linear model [tex]\(P = 14.5 + \frac{29}{66}d\)[/tex].
Substituting [tex]\(d = 0\)[/tex], we get:
[tex]\[
P = 14.5 + \frac{29}{66} \times 0 = 14.5
\][/tex]
So, the pressure at the surface of the water is 14.5 PSI.
2. At what depth is the pressure exactly double the pressure at the surface of the water?
We know the pressure at the surface is 14.5 PSI. Doubling this pressure gives us [tex]\(2 \times 14.5 = 29\)[/tex] PSI.
We're looking for depth [tex]\(d\)[/tex] such that:
[tex]\[
14.5 + \frac{29}{66}d = 29
\][/tex]
Solving for [tex]\(d\)[/tex]:
[tex]\[
\frac{29}{66}d = 29 - 14.5 = 14.5
\][/tex]
[tex]\[
d = \frac{14.5 \times 66}{29} = 33
\][/tex]
So, the pressure is exactly double at a depth of 33 feet.
3. What is the pressure at a depth of 99 feet?
Using the same linear model, substitute [tex]\(d = 99\)[/tex]:
[tex]\[
P = 14.5 + \frac{29}{66} \times 99 = 58
\][/tex]
Therefore, at a depth of 99 feet, the pressure is 58 PSI.
4. What is the pressure at a depth of 264 feet?
Again, we use the model and substitute [tex]\(d = 264\)[/tex]:
[tex]\[
P = 14.5 + \frac{29}{66} \times 264 = 130.5
\][/tex]
Hence, at a depth of 264 feet, the pressure is 130.5 PSI.
These steps outline how to find each solution using the linear equation provided.
1. What is the pressure at the surface of the water?
At the surface of the water, the depth [tex]\(d\)[/tex] is 0. We use the linear model [tex]\(P = 14.5 + \frac{29}{66}d\)[/tex].
Substituting [tex]\(d = 0\)[/tex], we get:
[tex]\[
P = 14.5 + \frac{29}{66} \times 0 = 14.5
\][/tex]
So, the pressure at the surface of the water is 14.5 PSI.
2. At what depth is the pressure exactly double the pressure at the surface of the water?
We know the pressure at the surface is 14.5 PSI. Doubling this pressure gives us [tex]\(2 \times 14.5 = 29\)[/tex] PSI.
We're looking for depth [tex]\(d\)[/tex] such that:
[tex]\[
14.5 + \frac{29}{66}d = 29
\][/tex]
Solving for [tex]\(d\)[/tex]:
[tex]\[
\frac{29}{66}d = 29 - 14.5 = 14.5
\][/tex]
[tex]\[
d = \frac{14.5 \times 66}{29} = 33
\][/tex]
So, the pressure is exactly double at a depth of 33 feet.
3. What is the pressure at a depth of 99 feet?
Using the same linear model, substitute [tex]\(d = 99\)[/tex]:
[tex]\[
P = 14.5 + \frac{29}{66} \times 99 = 58
\][/tex]
Therefore, at a depth of 99 feet, the pressure is 58 PSI.
4. What is the pressure at a depth of 264 feet?
Again, we use the model and substitute [tex]\(d = 264\)[/tex]:
[tex]\[
P = 14.5 + \frac{29}{66} \times 264 = 130.5
\][/tex]
Hence, at a depth of 264 feet, the pressure is 130.5 PSI.
These steps outline how to find each solution using the linear equation provided.
