Graphing
... They are measured in degrees north and south of the equator. The lines that run northsouth are lines of longitude. They are measured in degrees east and west of the prime meridian. ...
... They are measured in degrees north and south of the equator. The lines that run northsouth are lines of longitude. They are measured in degrees east and west of the prime meridian. ...
Graphing using a Cartesian Plane
... identifies the position with regard to the x-axis while the second number identifies the position on the y-axis Graph - A visual representation of data that displays the relationship among variables, usually cast along x and y axes. Origin – the point (0,0) - where the X axis and Y axis cross. ...
... identifies the position with regard to the x-axis while the second number identifies the position on the y-axis Graph - A visual representation of data that displays the relationship among variables, usually cast along x and y axes. Origin – the point (0,0) - where the X axis and Y axis cross. ...
Ordered Pairs and Linear Equations
... Solutions of linear equations: all of the points whose coordinates (x, y) make the equation a true statement. A line contains an infinite number of points. Therefore, there are an infinite number of ordered pairs that “work” in the equation of a line. If the directions say … ...
... Solutions of linear equations: all of the points whose coordinates (x, y) make the equation a true statement. A line contains an infinite number of points. Therefore, there are an infinite number of ordered pairs that “work” in the equation of a line. If the directions say … ...
Document
... plane. These numbers are the COORDINATES of the point. The first coordinate is the x-COORDINATE and the second is the ...
... plane. These numbers are the COORDINATES of the point. The first coordinate is the x-COORDINATE and the second is the ...
Lecture 1. Three-Dimensional Coordinate System. June 18
... On the plane, we can represent any point by a pair of two Cartesian coordinates (x, y), which are defined by two perpendicular axes: the x-axis and the y-axis. In the space, we have three Cartesian coordinates (x, y, z) and three mutually perpendicular axes: x, y and z-axis. The direction of the z-a ...
... On the plane, we can represent any point by a pair of two Cartesian coordinates (x, y), which are defined by two perpendicular axes: the x-axis and the y-axis. In the space, we have three Cartesian coordinates (x, y, z) and three mutually perpendicular axes: x, y and z-axis. The direction of the z-a ...
Group number 3
... • Circle – the locus of points in the plane (all points), to which the distance from a given point called the center of the circle does not exceed the specified non-negative number, called the radius of the circle. • The segment connecting two points on the boundary of the circle and having its cent ...
... • Circle – the locus of points in the plane (all points), to which the distance from a given point called the center of the circle does not exceed the specified non-negative number, called the radius of the circle. • The segment connecting two points on the boundary of the circle and having its cent ...
Lecture 9: Coordinates on the plane, distance formula, equations
... Suppose Θ(x, y) is any equation in which x and y are the only variables. For example Θ(x, y) might be x2 − y 2 = 16. We say that a specific pair of numbers (a, b) is a solution of Θ(x, y) if Θ(a, b) is true. For example, x2 − y 2 = 16 has (5, 3) as a solution, because 52 − 32 = 16. The set of all so ...
... Suppose Θ(x, y) is any equation in which x and y are the only variables. For example Θ(x, y) might be x2 − y 2 = 16. We say that a specific pair of numbers (a, b) is a solution of Θ(x, y) if Θ(a, b) is true. For example, x2 − y 2 = 16 has (5, 3) as a solution, because 52 − 32 = 16. The set of all so ...
Linear Algebra, Differential Equations and
... Higher order linear differential equation: Homogeneous linear equations of order n with constant coefficients, auxiliary/characteristic equations. Solution of higher order differential equation according to the roots of auxiliary equation. Non-homogeneous linear equations. Working rules for finding ...
... Higher order linear differential equation: Homogeneous linear equations of order n with constant coefficients, auxiliary/characteristic equations. Solution of higher order differential equation according to the roots of auxiliary equation. Non-homogeneous linear equations. Working rules for finding ...
18.085 Computational Science and Engineering I MIT OpenCourseWare Fall 2008
... c) (i) Find the solution to Laplace’s equation inside the unit circle r 2 x 2 y 2 1 if the boundary condition on the circle is u u 0 2 12 cos 2 cos 22. (OK to use polar coordinates.) (ii) Find the numerical value of the solution u at at the center and at the point x 12 , y 0. ...
... c) (i) Find the solution to Laplace’s equation inside the unit circle r 2 x 2 y 2 1 if the boundary condition on the circle is u u 0 2 12 cos 2 cos 22. (OK to use polar coordinates.) (ii) Find the numerical value of the solution u at at the center and at the point x 12 , y 0. ...
Homogeneous coordinates
In mathematics, homogeneous coordinates or projective coordinates, introduced by August Ferdinand Möbius in his 1827 work Der barycentrische Calcül, are a system of coordinates used in projective geometry, as Cartesian coordinates are used in Euclidean geometry. They have the advantage that the coordinates of points, including points at infinity, can be represented using finite coordinates. Formulas involving homogeneous coordinates are often simpler and more symmetric than their Cartesian counterparts. Homogeneous coordinates have a range of applications, including computer graphics and 3D computer vision, where they allow affine transformations and, in general, projective transformations to be easily represented by a matrix.If the homogeneous coordinates of a point are multiplied by a non-zero scalar then the resulting coordinates represent the same point. Since homogeneous coordinates are also given to points at infinity, the number of coordinates required to allow this extension is one more than the dimension of the projective space being considered. For example, two homogeneous coordinates are required to specify a point on the projective line and three homogeneous coordinates are required to specify a point in the projective plane.