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.

ceeee 1. Find the surface area of the plane 1 E = 96x1 Y₁2) : X 20, y>0, 270, 2x+y+z=16²

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

c. Find the distance from Po = (3,9, 6) to the plane 3.x + 4y – 5 = 0.

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.

Evaluate F-ds, where 5. F(x, y, z) = (3y, –2x, –), %3D and S is the surface that is composed of the part of the surface z = 2x? + 3y2 + 1 lying inside x² + y² = 1. 4 3 8

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