6. This problem relates to conversion between different coordinates systems a. Convert the point (x, y, z) = (In/5,2) to cylindrical coordinates.(3 points) b. Convert the point (x, y, z) = ( 2,2\\/,4) to spherical coordinates. (3 points) c. Find an equation in spherical coordinates for the curve x2 + y2 = 16. (3 points) 7. Let the position vector of a particle be r = . a) Calculate the distance traveled by the particle fromt = 0 to t = 2.5 to 3 decimal places of accuracy. (3 points) b) Calculate the speed of the particle at t = 2.5 to 3 decimal places of accuracy. (3 points) 8. 22 A surface has an equation given by sin (x) + cos(2y) = 1 . Find the 7: equation of the tangent plane to this surface at the point [2 ,g, at) (5 points). Use the Lagrange Multiplier Method to nd the maximum and minimum values of x, y) = 5x By subject to the constraint x2 + y2 = 136. No credit will be given if the Lagrange Multiplier method is not used. (8 points) \f