vector analysis

Find a unit vector perpendicular (normal) to the surface S given by... see attached!

vector analysis

Suppose that a mountain has the shape of an elliptic paraboloid ... see attached! in the second part X is the cross product of the vectors.

constructing model incidence axioms

Creating models for incidence axioms ________________________________________ Construct a model in which axioms I-1, I-2, I-4, and I-5 are valid but I-3 is not. Axioms: I-1 Each 2 distinct points determine a line I-2 Three non-collinear points determine a plane I-3 If 2 points lie in a plane, then any line determined by those 2 points lies in that plane. I-4 If 2 points meet their intersection is a line I-5 Space consists of at least 4 noncoplanar points, and contains 3 noncollinear points. Each plane contains at least three noncollinear points and each line contains at least two distinct points.

Need help with Geometery

A large cube is 2 feet on each edge. How many cubes - one inch on each edge- will it take to fill the large cube? How do I go about to solve this problem. If the base of a triangle is increased by 20% and the altitude to that base is decreased by 40% then by what percent is the area changed? Is that an increase or a decrease. Decrease by 30%. Is this correct.

A cube has a sphere inscribed inside of it

How do I find the ratio of the volume of the inside sphere to the volume of the outside sphere? A cube has a sphere inscribed inside of it. It has another sphere circumscribed on the outside ot if (it being the cube) What is the ratio of the volume of the inside sphere to the volume of the outside sphere?