Understanding Wave diagrams?

Hi, I am having a bit of trouble understanding a so called "wave diagram". I am reading the book "The Power of Limits" by Gyorgy Doczi, which is about the relationship of shape, music, nature etc to the goldern section. A lot of the book has diagrams relating to an object showing how the forms relate to the goldern section. O ...continues

vector functions of one variable

see attached

vector functions of one variable

see attached.

vector functions of one variable

see attahced

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 ...continues

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 decrea ...continues

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?

Rectangle

How do I go about finding the area of triangle ACE in the following: In rectangle ABDF the following is given: AB=24 BC=7 AF=16 E is the midpoint of FD