solve the answers handwritten but please type all the final answers together in the different section after solving. Thanks.

1. [-/1 Points] DETAILS SCALCET9 16.7.003. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Let H be the hemisphere x2 + y2 + z2 = 29, z 2 0, and suppose fis a continuous function with f(4, 3, 2) = 6, f(4, -3, 2) = 8, f(-4, 3, 2) = 11, and f(-4, -3, 2) = 12. By dividing # into four patches, estimate the value below. (Round your answer to the nearest whole number.) (( x, y, 2) ds Need Help? Read It Watch It 2. [-/1 Points] DETAILS SCALCET9 16.7.007. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Evaluate the surface integral. y ds, S is the helicoid with vector equation r(u, v) = (u cos(v), u sin(v), v), Ous 8, 0 Even Need Help? Read It Watch It 3. [-/1 Points] DETAILS SCALCET9 16.7.010. MY NOTES ASK YOUR TEACHER Evaluate the surface integral. *z ds, S is the part of the plane 2x + 2y + 2 = 4 that lies in the first octant Need Help? Read It4. [-/1 Points] DETAILS SCALCET9 16.7.016. Evaluate the surface integral. yz ds, S is the part of the sphere x2 + yz + z? = 1 that lies above the cone z = \\ x2 + 2 Need Help? Read It 5. [-/1 Points] DETAILS SCALCET9 16.7.019. Evaluate the surface integral. xz dS, S is the boundary of the region enclosed by the cylinder yz + z" = 9 and the planes x = 0 and x + y = 7 * 2 = 9- 13 Xty =7 Need Help? Read It Watch It6. [-/1 Points] DETAILS SCALCET9 16.7.023.MI. MY NOTES Evaluate the surface integral F . dS for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z) = xyi + yzj + zxk, S is the part of the paraboloid z = 8 - x2 - yz that lies above the square 0 S x 1, 0 s y $ 1, and has upward orientation Need Help? Read It Watch It Master It 7. [-/1 Points] DETAILS SCALCET9 16.7.024. MY NOTES Evaluate the surface integral F . d's for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z) = -xi - yj + 2"k, S is the part of the cone z = v x2 + y2 between the planes z = 1 and z = 2 with downward orientation z = 2 Need Help? Read It8. [-/1 Points] DETAILS SCALCET9 16.7.040. Find the mass of a thin funnel in the shape of a cone z = v x2 + y2, 1 s z = 5, if its density function is p(x, y, z) = 7 - z. Need Help? Read It 9. [-/1 Points] DETAILS SCALCET9 16.7.042. Let S be the part of the sphere x2 + y + 22 = 25 that lies above the plane z = 3. Let S have constant density k. (a) Find the center of mass. (* , y, Z) =( (b) Find the moment of inertia about the z-axis. Need Help? Read It 10. [-/1 Points] DETAILS SCALCET9 16.7.045. Use Gauss's law to find the charge contained in the solid hemisphere x2 + y2 + 22 s a2, 2 2 0, if the electric field is E(x, y, z) = xi + yj + 3zk. Need Help? Read It Watch It