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Express the water pressure as a function of the depth below the ocean surface.

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At the surface of the ocean, the water pressure is the same as the air pressure above the water, 15 lb/in2. Below the surface, the water pressure increases by 4.34 lb/in2 for every 10 ft of descent.

(a) Express the water pressure as a function of the depth below the ocean surface.
(b) At what depth is the pressure 100 lb/in2 ?

asked Jan 8, 2015 in CALCULUS by anonymous

1 Answer

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Step 1:

The water pressure at the surface of the ocean is image,

Let image is the water pressure and is the depth of the water level.

The pressure and depth are linearly related.

image

Where is the slope.

At surface of the ocean, the depth is zero and Pressure is image.

image

The water pressure is image.

Step 2:

(a)

The water pressure increases by for every .

Slope image.

Substitute  value in image.

image

The water pressure as a function of depth is image.

Step 3:

(b)

Water pressure image.

Substitute image in the Pressure function image.

The depth of water is .

Solution :

(a) The water pressure as a function of depth is image.

 (b) The depth of water at pressure image is .

answered Jan 13, 2015 by james Pupil

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