MATH 251H Final Exam Version B Solutions

# The pressure p density and temperature t of a certain

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Unformatted text preview: t  e2  1 2  2t  1 t 1  e2 5. The pressure, P, density, , and temperature, T, of a certain ideal gas are related by P  3T. At the point 1, 2, 3 , the density and its gradient are   4 and    0. 2, 0. 4, 0. 1 , while the temperature and its gradient are T  300 and  T  2, 1, 3 . Hence the pressure is P  3  4  300  3600 and its gradient is  P  a. 1802. 4, 2704. 8, 2701. 2 b. 600. 8, 901. 900. 4 c. 68, 132, 42 d. 204, 372, 126 e. 1. 2, 1. 2, 0. 9 P x P  P y P  P z P    x   y   z Correct Choice P T P T P T T  3T   3 x x T  3T   3 y y T  3T   3 z z T  3  300  0. 2  3  4  2  204 x T  3  300  0. 4  3  4  1  372 y T  3  300  0. 1  3  4  3  126 z 6. Find the equation of the plane tangent to the graph of x 2 yz 2 2y 2 z 3  10 at the point 3, 2, 1 . The z-intercept is a. b. c. d. e. 6 25 5 25 6 60 5 3 Correct Choice  F  2xyz 2 , x 2 z 2 4yz 3 , 2x 2 yz 6y 2 z 2 F x, y, z  x 2 yz 2 2y 2 z 3  N   F 3, 2, 1  2 3 2 , 3 2 4 2 , 2 3 2 2 6 2 2  12, 1, 12   NX  NP 12x  y  12z  12 3  2  12 1  50 z-intercept  50  25 12 6 2 7. Han Deut is flying the Millennium Eagle through a dangerous zenithon field whose density is   xyz. If his current position is x, y, z  1, 1, 2 , in what unit vector direction should he travel to decrease the...
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## This note was uploaded on 02/06/2014 for the course MATH 251H taught by Professor Philipb.yasskin during the Spring '11 term at Texas A&M.

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