Solutions
... The Broken Stick Problem: Pick two random points on the interval [0, 1], and break up this interval at these two points to get three pieces. (a) What is the probability that these pieces form a triangle? (b) (Hard!) What is the probability that these pieces form an acute triangle? ...
... The Broken Stick Problem: Pick two random points on the interval [0, 1], and break up this interval at these two points to get three pieces. (a) What is the probability that these pieces form a triangle? (b) (Hard!) What is the probability that these pieces form an acute triangle? ...
the skoliad corner - Canadian Mathematical Society
... 80 . Then ABCD is not a parallelogram. Let E on BC be such that \CDE = 40 . Then triangles BAD and CDE are congruent, so that AB = CD. It is easy to see that the other three conditions do guarantee parallelograms. 14. How many of the expressions x3 + y4; x4 + y3; x3 + y3; and x4 , y4; are positive ...
... 80 . Then ABCD is not a parallelogram. Let E on BC be such that \CDE = 40 . Then triangles BAD and CDE are congruent, so that AB = CD. It is easy to see that the other three conditions do guarantee parallelograms. 14. How many of the expressions x3 + y4; x4 + y3; x3 + y3; and x4 , y4; are positive ...
Geometry Section: 7.3 Angle Angle Similarity Algebra Problem of the
... Algebra Problem of the Day: More Factoring ...
... Algebra Problem of the Day: More Factoring ...
Weber problem
In geometry, the Weber problem, named after Alfred Weber, is one of the most famous problems in location theory. It requires finding a point in the plane that minimizes the sum of the transportation costs from this point to n destination points, where different destination points are associated with different costs per unit distance.The Weber problem generalizes the geometric median, which assumes transportation costs per unit distance are the same for all destination points, and the problem of computing the Fermat point, the geometric median of three points. For this reason it is sometimes called the Fermat–Weber problem, although the same name has also been used for the unweighted geometric median problem. The Weber problem is in turn generalized by the attraction–repulsion problem, which allows some of the costs to be negative, so that greater distance from some points is better.