hmwk7 - intersect along a diameter at an angle of / 6 ....

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Math 215 Homework Set 7: §§ 16.6 – 16.8 Fall 2007 Most of the following problems are modified versions of the recommended homework problems from your text book Multivariable Calculus by James Stewart. 16.6a. Find the region E for which the triple integral ± ± ± E (6 - 3 x 2 - 2 y 2 - 2 z 2 ) dV is a maximum. 16.6b. Find the center of mass of the tetrahedron bounded by the planes x = 0 , y = 0 , z = 0 , x +3 y +2 z = 6 ; ρ ( x, y, z ) = z . 16.6c. Sketch the region of integration for the integral ± 3 0 ± 9 9 - x 2 ± 9 - y 0 f ( x, y, z ) dz dy dx. Rewrite this integral as an equivalent iterated integral in three of the five possible other orders. 16.6d. Find the center of mass of the cube given by - a x a , - a y a and 0 z 2 a ; ρ ( x, y, z ) = x 2 + y 2 + z 2 . 16.6e. Do Problems 33 and 34 of § 16.6 in Stewart’s Multivariable Calculus . 16.8a. Find the volume of one of the smaller wedges cut from a sphere of radius 27 by two planes that
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Unformatted text preview: intersect along a diameter at an angle of / 6 . 16.8b. Find the volume and center of mass of the solid that lies above the cone z = 4 x 2 + y 2 and below the sphere x 2 + y 2 + z 2 = 16 . Assume that the density of the solid is constant. 16.8c. Find the volume of the solid that lies above the cone = / 6 and below the sphere = 9 cos( ) . 16.8d. Evaluate B (3 x 2 + 3 y 2 + 3 z 2 ) dV where B is the ball of radius 13 centered at the origin. 16.8e. Find the center of mass of a solid hemisphere of radius 5 if the density at any point in the hemisphere is proportional to the points distance from the base of the hemisphere. 16.8f. Do Problems 2728 of 16.7 39 and 40 of 16.8 in Stewarts Multivariable Calculus ....
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