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Atmospheric density at altitude $h$ meters is approximately $1.225 e^{-0.000101 h}$ $\mathrm{kg} / \mathrm{m}^{3}$ for $0 \leq a \leq 5000$ meters. Compute the mass of air in a vertical one-square meter column between 0 and 5000 meters.

Calculus 2 / BC

Chapter 11

Applications of the Fundamental Theorem

Section 1

Volume

Applications of Integration

Harvey Mudd College

Baylor University

Idaho State University

Boston College

Lectures

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Solve each problem.Air…

So if the density off here doesn't decrease, it will be a similar situation like ah that off water. So we can use the polling question So pressure equal do years mass density times, gravity times the height. So from here we can actually calculate the height, which is pressure by airman's density. Let's just write density times gravity. So now, using the given numbers, we have ah, 100,000 Newton per meter squared as pressure. Um, density. From the question, we see that it's one point toe kilogram per meter cubed and gravity is roughly 10 Newton or Katie. So that gives us 8300 meters. So, as expected, if the density didn't get smaller with altitude diet most fair would not need to be as high. Yet, um, to explain the observe pressure and the bottle. All right, Thanks for watching

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