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restaurant is being built on the side of a mountain, the plans are shown below. (a) The vertical curved wall of the restaurant is to be built of glass. What will be the surface area of this wall? h) To be large enough to be profitable the consulting engineer informs the developer that the

restaurant is being built on the side of a mountain, the plans are shown below. (a) The vertical curved wall of the restaurant is to be built of glass. What will be the surface area of this wall? h) To be large enough to be profitable the consulting engineer informs the developer that the

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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4. A restaurant is being built on the side of a mountain, the plans are shown below. (a) The vertical curved wall of the restaurant is to be built of glass. What will be the surface area of this wall? (b) To be large enough to be profitable, the consulting engineer informs the developer that the volume of the interior must exceed TR¹/2. For what R does the proposed structure satisfy this requirement? (c) During a typical summer day, the environs of the restaurant are subject to a tempertaure field given by T(x, y, z) = 3x² + (y− R)² + 16z². A heat flux density V = -kVT (k is a constant depending on the grade of the insulation to be used) through all sides of the restaurant (including the top and the contact with the hill) produces a heat flux. What is the total heat flux? (Your answer will depend on R and k.) x² + y² +z =4R² 2R side view R restaurant y x² + y²-4R² 2R top view x² + (y-R)² = R² R y
Transcribed Image Text:4. A restaurant is being built on the side of a mountain, the plans are shown below. (a) The vertical curved wall of the restaurant is to be built of glass. What will be the surface area of this wall? (b) To be large enough to be profitable, the consulting engineer informs the developer that the volume of the interior must exceed TR¹/2. For what R does the proposed structure satisfy this requirement? (c) During a typical summer day, the environs of the restaurant are subject to a tempertaure field given by T(x, y, z) = 3x² + (y− R)² + 16z². A heat flux density V = -kVT (k is a constant depending on the grade of the insulation to be used) through all sides of the restaurant (including the top and the contact with the hill) produces a heat flux. What is the total heat flux? (Your answer will depend on R and k.) x² + y² +z =4R² 2R side view R restaurant y x² + y²-4R² 2R top view x² + (y-R)² = R² R y
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