Answered

Looking for trustworthy answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Experience the convenience of getting accurate answers to your questions from a dedicated community of professionals. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.

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

We hope this information was helpful. Feel free to return anytime for more answers to your questions and concerns. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.