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currently at (1, 1, 1). (a) In what direction should he proceed in order to decrease the temperature most rapidly? (b) If the ship travels at eº meters per second, how fast (in degrees per second) will the temperature decrease if he proceeds in that direction? degrees/sec (c) Unfortunately, the metal of the hull will crack if cooled at a rate greater than √17e³ degrees per second. Describe the set of possible directions in which he may proceed to bring the temperature down at no more than that rate. + bj + ck a² + b² + c²= 1,0 < S 5 √17e³}

currently at (1, 1, 1). (a) In what direction should he proceed in order to decrease the temperature most rapidly? (b) If the ship travels at eº meters per second, how fast (in degrees per second) will the temperature decrease if he proceeds in that direction? degrees/sec (c) Unfortunately, the metal of the hull will crack if cooled at a rate greater than √17e³ degrees per second. Describe the set of possible directions in which he may proceed to bring the temperature down at no more than that rate. + bj + ck a² + b² + c²= 1,0 < S 5 √17e³}

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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= Captain Ralph is in trouble near the sunny side of Mercury. The temperature of the ship's hull when he is at location (x, y, z) will be given by T(x, y, z) = currently at (1, 1, 1). (a) In what direction should he proceed in order to decrease the temperature most rapidly? (b) If the ship travels at eº meters per second, how fast (in degrees per second) will the temperature decrease if he proceeds in that direction? degrees/sec ₂-x² - 2y²-3z² 1 where x, y, and z are measured in meters. He is (c) Unfortunately, the metal of the hull will crack if cooled at a rate greater than 17e³ degrees per second. Describe the set of possible directions in which he may proceed to bring the temperature down at no more than that rate. {ai + ai + bj + ck a² + b² + c² = 1, 0 < $ √17e³}
Transcribed Image Text:= Captain Ralph is in trouble near the sunny side of Mercury. The temperature of the ship's hull when he is at location (x, y, z) will be given by T(x, y, z) = currently at (1, 1, 1). (a) In what direction should he proceed in order to decrease the temperature most rapidly? (b) If the ship travels at eº meters per second, how fast (in degrees per second) will the temperature decrease if he proceeds in that direction? degrees/sec ₂-x² - 2y²-3z² 1 where x, y, and z are measured in meters. He is (c) Unfortunately, the metal of the hull will crack if cooled at a rate greater than 17e³ degrees per second. Describe the set of possible directions in which he may proceed to bring the temperature down at no more than that rate. {ai + ai + bj + ck a² + b² + c² = 1, 0 < $ √17e³}
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