Let E be the portion of the plane 5x + 3y + z = 60 that lies between the surfaces y = 12x and y = 3x2. Find the area of E.

Find the surface area of the part of the plane 3x + 2y+ 4z = 24 that lies in the first octant Surface Area =

Find the area of the surface. The part of the paraboloid z = 1 – x2 - y? that lies above the plane z = -4

Use the Jacobian of a coordinate transformation to find the area of the parallelogram bounded by the lines y = 3x, y = 3x+2, y = 1−x, y = 4−x.

Use the cross product to find the area of the portion of the plane defined by z = x + y which lies above the square [0, 1] x [0, 1] in the xy-plane. Draw a picture.

Determine the intersection point of the line​x=7−ty=2+tz=4−3t​ and the plane π:x+2y+3z−15=0

Find the area of the surface. The part of the plane 3x + 2y + z = 6 that lies inside the cylinder x2 + y2 = 4

Find the area of the surface. The part of the plane x + 2y + 3z = 1 that lies inside the cylinder x2 + y2 = 9

Solve the problem. Describe all solutions of Ax = b, where 2-5 31 A = -2 6-5 70 and b = 310 Describe the general solution in parametric vector form. -3 G -8-17-0