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The phrase "linear equation" takes its origin in this correspondence between lines and equations: a linear equation in two variables is an equation whose solutions form a line. If b ≠ 0, the line is the graph of the function of x that has been defined in the preceding section. If b = 0, the line is a vertical line (that is a line parallel to ...
The equation can be determined in this case as follows: [56] Relabel if necessary so that P 1 is to the left of P 2 and let H be the horizontal and v be the vertical distance from P 1 to P 2. Translate the axes so that the vertex of the catenary lies on the y-axis and its height a is adjusted so the catenary satisfies the standard equation of ...
Linear function (calculus) In calculus and related areas of mathematics, a linear function from the real numbers to the real numbers is a function whose graph (in Cartesian coordinates) is a non-vertical line in the plane. [1] The characteristic property of linear functions is that when the input variable is changed, the change in the output is ...
The distance (or perpendicular distance) from a point to a line is the shortest distance from a fixed point to any point on a fixed infinite line in Euclidean geometry. It is the length of the line segment which joins the point to the line and is perpendicular to the line. The formula for calculating it can be derived and expressed in several ways.
Newmark's influence chart. Newmark's Influence Chart is an illustration used to determine the vertical pressure at any point below a uniformly loaded flexible area of soil of any shape. This method, like others, was derived by integration of Boussinesq's equation for a point load. [1]
Wave equation. The wave equation is a second-order linear partial differential equation for the description of waves or standing wave fields such as mechanical waves (e.g. water waves, sound waves and seismic waves) or electromagnetic waves (including light waves). It arises in fields like acoustics, electromagnetism, and fluid dynamics.
Buffon's needle was the earliest problem in geometric probability to be solved; [ 2] it can be solved using integral geometry. The solution for the sought probability p, in the case where the needle length l is not greater than the width t of the strips, is. This can be used to design a Monte Carlo method for approximating the number π ...
Cubic equation. Graph of a cubic function with 3 real roots (where the curve crosses the horizontal axis at y = 0 ). The case shown has two critical points. Here the function is and therefore the three real roots are 2, -1 and -4. In algebra, a cubic equation in one variable is an equation of the form in which a is not zero.