I need to solve 7 8 9 and 10th question

7. (15 pts) The coordinate transformation r = vv/u, y = vuu can be used to compute th y =4/x. integral f JR 2edA, where R is the region bounded by y = , y = 23, / = 1/r, (a) Transform the region R to a region G in wu-space. Sketch both regions. (b) Compute the Jacobian J(u, ") of the coordinate transformation. (c) Compute the value of the integral 8. (30 pts) In addition to each calculation, be sure to answer the descriptive question. (a) Compute the double integral in dady order of the function f(r,") = a over the region bounded by the triangle with vertices (0.0). (6,0) and (6, 3). What physical quantity is being calculated? (b) Compute the line integral f(r, y) = > over the piecewise smooth curve obtained from the boundary of the triangle in part (a) traversed in the counterclockwise direction. What physical quantity is being calculated? (c) Compute the counter clockwise circulation of the vector field F = ri around the boundary of the triangle in part (a). Why does your result make physical sense? 9. (10 pts) Calculate the circulation of the vector field F Sir (' 4 20)it (22 - y)k along the curve of intersection of the sphere ? with the conc z = VI ty traversed in the counterclockwise direction around the axis when viewed from above. 10. (15 pts) Consider the cone 2 - Ity for 0 (a) Use cylindrical coordinates to parameterize the cone in the form r(r, 0) = f(r.0)it q(r, 0)j + h(r, 0)k. Be sure to indicate the bounds for each variable. (b) Compute the surface arca differential do - Ur. x ral drag (e) Compute the surface area of the conc