Understanding Wave Diagrams : Golden Ratio

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 golden section. On ...continues

Vector Functions : Parametric Representations of Curves (5 problems)

Please see the attached file for the fully formatted problems. 1. What kinds of curves are given by the following parametric representations? • • • 2. Find a parametric representation of each of the following curves: • •

Newton's Law : Application of Parametric Representation

Please see the attached file for the fully formatted problems. Newton’s law states that the total force F (F a vector), acting on a body of mass m, is equal to the product of its mass times the acceleration a (a vector), viz: F=ma, where F and a are vectors. A body of mass m=2kg moves in space following a path wit ...continues

Vector Functions : Parametric Representation of Acceleration and Velocity

Please see the attached file for the fully formatted problems. Show that, if the acceleration of an object is always perpendicular to the velocity, then the speed of the object is constant. (hint, the speed is given by ). Show that, at a local maximum or minimum is perpendicular to .

Find a unit vector perpendicular to a surface.

Please see the attached file for the fully formatted problems. Find a unit vector perpendicular (normal) to the surface S given by z = (x^3)(y^2) + y + 4.

Gradients : Elliptic Paraboloid and Vector Fields

Please see the attached file for the fully formatted problems. Suppose that a mountain has the shape of an elliptic paraboloid , where a and c are constants, x and y are the east-west and north–south map coordinates and z is the altitude above the sea level (x,y,z are measured all in metres). At the point (1,1), in what direc ...continues

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

Geometery : Volume of Cubes and Area of Triangle

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? 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?

Sphere inside of a Cube : Ratio of Volumes

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