Evaluate F(x,y,z) = (x3 +y³)i + (y³ + z³)j + (z³ + x³)k, and and S is the sphere with center the origin and radius 2. Upload Choose a File

Find the equation of the sphere with its center at (-2, 4, 13) and tangent to 3x + 4y - 12z = 10. (Express numbers in exact form. Use symbolic notation and fractions where needed. Give your answer in the form (x-xo)² + (y-yo)² + (z −zo)² = r².)

What is the center of x² + y? – 30x + 221 = 0? Show all work for full credit.

The equation of a surface, with respect to an orthonormal coordinate system for three-dimensional space, is a3 – 13 – 4x1x2 – 4x1x3 = 1. Identify the type of surface, and find the least distance from a point on the surface to the origin.