Solve Air Pressure Problem: Find y(x) Given y'(x)

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Discussion Overview

The discussion revolves around a problem related to the efficiency of turbofan engines and the relationship between air pressure and altitude. Participants are asked to find the air pressure function y(x) given that the rate of change y'(x) is proportional to the pressure, with specific conditions at different altitudes.

Discussion Character

  • Homework-related, Mathematical reasoning

Main Points Raised

  • One participant states that the efficiency of turbofan engines depends on air pressure, which is maximum at approximately 10973 m above mean sea level.
  • Another participant reiterates the problem statement and emphasizes that the rate of change of pressure with respect to altitude is given by the equation dp/dz = kp, where k is a constant.
  • There is a condition mentioned that at 5486 m, the pressure is half its value at mean sea level.
  • A participant suggests that showing work might elicit comments on the correctness of the approach taken.
  • A later post indicates that the thread is closed due to a lack of effort shown by the original poster, suggesting a need for adherence to forum rules.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the solution to the problem, and the discussion remains unresolved due to the closure of the thread.

Contextual Notes

The problem lacks detailed assumptions regarding the constant k and the specific form of the function y(x). There is also an absence of mathematical steps or attempts to solve the differential equation presented.

zetshield21
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Problem:
the efficiency of turbofan engines of commercial airplanes depend on air pressure and usually is maximum near about 10973 m, above mean sea level. Find the air pressure y(x) at this height given the rate of change y'(x) is proportional to the pressure, and at 5486 m the pressure has decrease to half its value y0 at mean sea level.

note: please solve my problem please!
 
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Only you can solve this problem. If you show some work, you might get some comments about whether it is correct.
 
zetshield21 said:
Problem:
the efficiency of turbofan engines of commercial airplanes depend on air pressure and usually is maximum near about 10973 m, above mean sea level. Find the air pressure y(x) at this height given the rate of change y'(x) is proportional to the pressure, and at 5486 m the pressure has decrease to half its value y0 at mean sea level.

note: please solve my problem please!

The words in bold imply that

dp/dz = kp, where k is a constant, p is the pressure, and z is the altitude
 
This thread is closed. zetshield21 -- check your PMs. You may only repost if you follow the Homework Help Template and rules.

And guys, when you see somebody post like this with zero effort shown, please click the Report button on the OP's post to have a Mentor deal with it. Thanks.
 

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