Lassiter Varsity Test 2005
... 28. In the Quadrant I of the xy-plane, a line with slope –1 defines a triangle bound by x, y-axis and the line with area of 405000. This line undergoes a translation of all points (x, y) ( x, y) . What is the area of the new region bound by the translated line, the x-axis, and the y-axis? (Express ...
... 28. In the Quadrant I of the xy-plane, a line with slope –1 defines a triangle bound by x, y-axis and the line with area of 405000. This line undergoes a translation of all points (x, y) ( x, y) . What is the area of the new region bound by the translated line, the x-axis, and the y-axis? (Express ...
Leap Frog Solutions 2013
... Problem 6. Consider the circle of radius 3 whose center is the point (6, 8). Find the x-coordinate of the point on this circle that is closest to the origin (0, 0). Solution. Let P be the point 3 units from (6, 8) on the segment with endpoints (0, 0) and (6, 8). Because this segment is perpendicular ...
... Problem 6. Consider the circle of radius 3 whose center is the point (6, 8). Find the x-coordinate of the point on this circle that is closest to the origin (0, 0). Solution. Let P be the point 3 units from (6, 8) on the segment with endpoints (0, 0) and (6, 8). Because this segment is perpendicular ...
MATHEMATICS WITHOUT BORDERS 2015
... Let А, В, С and D denote the points so that D is not on the same line as А, В and С. There are 6 pairs of lines that connect each pair of points: AD and AC, AD and BD, AD and CD, AC and BD, AC and DC, BD and DC. When two straight lines intersect at a point, they form either 2 acute and 2 obtuse angl ...
... Let А, В, С and D denote the points so that D is not on the same line as А, В and С. There are 6 pairs of lines that connect each pair of points: AD and AC, AD and BD, AD and CD, AC and BD, AC and DC, BD and DC. When two straight lines intersect at a point, they form either 2 acute and 2 obtuse angl ...
Senior Exam 2007 - Wilkes University
... 6) Assume a water tank is in the shape of a right circular cone with the the vertex at the bottom. The height of the tank is 20 feet and the radius of the tank is 12 feet. The tank contains 15π cubic feet of water. What is the height of the water in the tank? ...
... 6) Assume a water tank is in the shape of a right circular cone with the the vertex at the bottom. The height of the tank is 20 feet and the radius of the tank is 12 feet. The tank contains 15π cubic feet of water. What is the height of the water in the tank? ...
Problems and Solutions
... the possible states can be divided into two disjoint sets, one with odd number of of the lamps lit and the other with even number of the lamps lit. We get a bipartite graph where the vertices are the states and two states are connected with an edge if it is possible to get from one state to another ...
... the possible states can be divided into two disjoint sets, one with odd number of of the lamps lit and the other with even number of the lamps lit. We get a bipartite graph where the vertices are the states and two states are connected with an edge if it is possible to get from one state to another ...
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.