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Find the average temperature in the box D= {(x,y,z): 0 sxsIn 3, 0

Find the average temperature in the box D= {(x,y,z): 0 sxsIn 3, 0

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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### Problem Statement Find the average temperature in the box \( D = \{(x, y, z): 0 \leq x \leq \ln 3, \, 0 \leq y \leq \ln 9, \, 0 \leq z \leq \ln 27\} \) with a temperature distribution of \( T(x, y, z) = 15 \, e^{-x-y-z} \). ### Solution **The average temperature is** \(\underline{\phantom{a}}\). *(Type an exact answer.)* --- In this exercise, you are asked to find the average temperature within a defined 3D space, where the temperature distribution is provided as an exponential function. The box \( D \) is defined by logarithmic bounds in each spatial dimension.
Transcribed Image Text:### Problem Statement Find the average temperature in the box \( D = \{(x, y, z): 0 \leq x \leq \ln 3, \, 0 \leq y \leq \ln 9, \, 0 \leq z \leq \ln 27\} \) with a temperature distribution of \( T(x, y, z) = 15 \, e^{-x-y-z} \). ### Solution **The average temperature is** \(\underline{\phantom{a}}\). *(Type an exact answer.)* --- In this exercise, you are asked to find the average temperature within a defined 3D space, where the temperature distribution is provided as an exponential function. The box \( D \) is defined by logarithmic bounds in each spatial dimension.
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