35.1k views
0 votes
At the surface of the ocean, the water pressure is the same as the air pressure above the water, about 15 lblin^2, below the surface the water pressure increases by about 4.54 lblin^2 for every 10ft of descent. F(x) which expresses the water pressure in pounds per square inch as a function of the depth in inches below the ocean surfaces. F(x) = _________ At what depth is the pressure 80 lblin^2? Include the units in the answer: __________

User Monifa
by
7.9k points

1 Answer

3 votes

The pressure above the water is 15 lb/in^2 and for every 10 ft, the pressure rises 4.54 lb/in^2

The equation would be:


f(x)=4.54(lb)/(IN^2)\cdot10ft\cdot x+15(lb)/(IN^2)

If x = 0, the pressure in the surface is 15 lb/in^2, for each 10 ft of x, the pressure rises 4.54 lb/in^2

Now to solve when the pressure is 80 lb/in^2, we subtitute in the equation:


80(lb)/(IN^2)=4.54(lb)/(IN^2)\cdot10ft\cdot x+15(lb)/(IN^2)

And solve for x:


\begin{gathered} (80-15)(lb)/(IN^2)=4.54\frac{lb}{\text{IN}^2}\cdot10ft\cdot x \\ (65(lb)/(IN^2))/(45(lb)/(IN^2)\cdot10ft)=x \\ (1.4317)/(ft)=x \\ \end{gathered}

Then the answer to question 2 is 1.43ft

This is basically a linear equation. The slope is the 4.54lb/in^2 for each 10ft. Then we need to adjust the 10ft of x, to reprensents each step of 10 ft for x. And we need to add the 15lb/in^2 for the surface pressure. With all this, we can construct the function of the pressure dependant of the deepness x.

User Kerem Demirer
by
8.0k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories