Collineation

What are the fixed points of a translation T? A fixed point is a point that is not moved by a given collineation, i.e. P = TP

Plucker coordinate

1. Let d = (1, 2, -2), m = (-8, 5, 1) (a) Check that d and m are orthogonal. I already check that it is orthogonal. DO NOT ANSWER THIS PART. (b) Find a vector v such that d x v = m. In other words, find an affine point on the line with Plucker coordinates (1, 2, -2, -8, 5, 1). 2. Describe a general way to solve 1 a) above. In other words, given two orthogonal vectors, d and m, solve d x v = m.

Estimating errors in measuring volume of small balls in large container

Consider an experimental procedure to measure the average volume of M&M Peanut candies. One hundred piece of the candy are poured into a graduated cylinder with a 30 diameter. The cylinder is then filled with 1 mm diameter beads and shaken so that the beads and candies pack as tightly as possible. Finally, the candies are removed and the change in volume noted. Compute the change in estimated volume if 0.1 mm dia beads were used in place of the 1 mm dia beads. Can you define a relationship that estimates the change in estimated volume of the candies based on the diameter of the beads used in the measurement?

High School Geometry and Algebra review questions

(See attached file for full problem description)

Refer to circle A at right, which has radius 12.

Refer to circle A at right, which has radius 12. 1. Find the circumference Full problem in attached file.