2. [-/1 Points] DETAILS SCALCET9 16.8.006. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Use Stokes' theorem to evaluate curl ( F ) . ds . F(x, y, z) = e *yi+ e*j + x2zk, S is the half of the ellipsoid 3x2 + y2 + 3z2 = 3 that lies to the right of the xz-plane, oriented in the direction of the positive y-axis S x 3x2 + y2 + 32 2 = 3 Need Help? Read It10. [0.5/1 Points] DETAILS PREVIOUS ANSWERS SCALCET9 16.3.034. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Let F = Vf, where f(x, y) = sin(x - 7y). Find curves C, and C, that are not closed and satisfy the equation. (a) F . dr = 0 C: r(t) = (7t,t ) Osts1 (b) F . dr = 1 Jcz C,: r(t) = + 7t,t) X , Osts1 Need Help? Read It5. [-11 Points] DETAILS SCALCETQ 16.7.019. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Evaluate the surface integral. ff X2 d5, Sis the boundary of the region enclosed by the cylinder 3/2 + 22 = 4 and the planes x = and X + y = 9 5 Need Help? 5. [-/1 Points] DETAILS SCALCET9 16.8.013. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Use Stokes' theorem to evaluate F . dr where C is oriented counterclockwise as viewed from above. Jc F(x, y, z) = 7x yi + 3x j+ 4e tan (z) k, C is the curve with parametric equations x = cos(t), y = sin(t), z = sin(t), 0 S t s 2n Z A (-1, 0, 0) (1, 0, 0) x Need Help? Read It7. [0/1 Points] DETAILS PREVIOUS ANSWERS SCALCETQ 16.8.021. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER A particle moves along line segments from the origin to the points (1, 0, 0), (1r 4, 1), (0, 4, 1), and back to the origin under the Influence of the force field F(x, y, z) = zzl + Sxyj + 31/2 it. Find the work done. F - dr = 31 } l_lx Need Help? 3. [-/1 Points] DETAILS SCALCET9 16.9.009. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Use the divergence theorem to calculate the surface integral F . ds; that is, calculate the flux of F across S. F(x, y z) = xevi + (z - e)) j - xyk, S is the ellipsoid x2 + 32 + 522 = 9 Need Help? Read It 4. [-/1 Points] DETAILS SCALCET9 16.9.013. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Use the divergence theorem to calculate the surface integral / / F . ds; that is, calculate the flux of F across S. F(x, y z) = x zi + xz j + y In(x + 1)k, S is the surface of the solid bounded by the planes x + 2z = 8, y = 6, X = 0 y = 0, and z = 0 x + 2z = 8 = 6 Need Help? Read It3. [-/1 Points] DETAILS SCALCET9 16.9.009. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Use the divergence theorem to calculate the surface integral F . dS; that is, calculate the flux of F across S. F(x, y z) = xe i + (z - e ) j - xyk, S is the ellipsoid x2+ 3y2 + 5z2 = 9 Need Help? Read It7. [02\" Points] DETAILS PREVIOUS ANSWERS SCALCET915.4.031. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Suppose X and Y are randOm variables with the given joint density function. {lie(0'5" + 0-2?) ifx _>. o, y 2 o 0 otherwise x, Y) = { (a) Is fa joint density function? 0 Yes O No g) (b) Find P(Y a 2). (Round your answer to four decimal places.) [1 Find P(X s 5, Y 5 5). (Round yOur answer to four decimal places.) [:1 (c) Find the expected value of X. Find the expected value of Y. L] 4. [0/1 Points] DETAILS PREVIOUS ANSWERS SCALCET9 15.4.015. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER The boundary of a lamina consists of the semicircles y = v 1 - x2 and y = v 9 _ x2 together with the portions of the x-axis that join them. Find the center of mass of the lamina if the density at any point is proportional to its distance from the origin. ( x, y ) = X Need Help? Read It Watch It1. [OH Points] _ETA|LS _REV|0US ANSWERS SCALCET9 16.7.003. _Y NOTES -SK YOUR TEACHER _RACTICE ANOTHER Let H be the hemisphere x2 + y2 + z2 = 29, z > D, and suppose fis a continuous function with f(4, 3, 2) = 7, f(4, 3, 2) = 8, f( 4,3,2) = 11, and f( 4, 73, 2) = 12 By dividing H into four patches, estimate the value below. (Round your answer to the nearest whole number.) // f(x, y, 2) d5 H 1710 Need Help? _ '_ 1. [OH Points] DETAILS PREVIOUS ANSWERS SCALCET9 16.9.005. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Use the divergence theorem to calculate the surface integral // F - as; that is, calculate the flux of F across 5. s F(x, y, z) = xyezl + xy223j yezk, S is the surface of the box bounded by the coordinate planes and the planes x=7,y=2,andz=1 49 x Need Help? __' 9. [-11 Points] DETAILS SCALCETQ 15.4.034. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Xavier and Yolanda both have classes that end at noon and they agree to meet every day after class. They arrive at the coffee shop independently. Xavier's arrival time is X and Yolanda's arrival time is Y, where X and Yare measured in minutes after noon. The individual density functions are given. 1 'X 'f 2 D 'f 0 S E 10 f1(X)={e ' X r20) = so\" ' V 0 'fx