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At the beach in San Francisco (0 meters) the pressure of the atmosphere is 101.325 kPa
(kilopascals) and in Denver, 1609.344 meters above sea level, the pressure of the atmosphere
is about 83.437 kPa. Using this data, find a linear equation for pressure P in terms of
altitude h. (Hint: write the pressure and altitude in each location as a point (h, P). Then
use point-slope form to find the equation of the line.)

Sagot :

MrRoyalidn

Answer:

[tex]P = -\frac{17978}{1609344}(h)+101.325[/tex]

Explanation:

Given

[tex]h = height[/tex]

[tex]P = Pressure[/tex]

[tex](h_1,P_1) = (0,101.325)[/tex]

[tex](h_2,P_2) = (1609.344 ,83.437 )[/tex]

Required

Determine the linear equation for P in terms of h

First, we calculate the slope/rate (m);

The following formula is used:

[tex]m = \frac{P_2 - P_1}{h_2 - h_1}[/tex]

Substitute values for P's and h's

[tex]m = \frac{83.347 - 101.325}{1609.344- 0}[/tex]

[tex]m = \frac{-17.978}{1609.344}[/tex]

[tex]m = -\frac{17.978}{1609.344}[/tex]

Multiply by 1000/1000

[tex]m = -\frac{17.978 * 1000}{1609.344*1000}[/tex]

[tex]m = -\frac{17978}{1609344}[/tex]

The equation is then calculated using:

[tex]P - P_1 = m(h - h_1)[/tex]

Substitute values for m, h1 and P1

[tex]P - P_1 = m(h - h_1)[/tex]

[tex]P - 101.325 = -\frac{17978}{1609344}(h - 0)[/tex]

[tex]P - 101.325 = -\frac{17978}{1609344}(h)[/tex]

Make P the subject

[tex]P = -\frac{17978}{1609344}(h)+101.325[/tex]

The above is the required linear equation

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