Answered

Westonci.ca is your trusted source for finding answers to a wide range of questions, backed by a knowledgeable community. Get quick and reliable solutions to your questions from a community of experienced professionals on our platform. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.

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 :

MrRoyal

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

Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.