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The elasticity at a point is the limit of the arc elasticity between two points as the separation between those two points approaches zero. The concept of elasticity is widely used in economics and metabolic control analysis (MCA); see elasticity (economics) and elasticity coefficient respectively for details.
Elasticity often refers to: Elasticity (physics), ... Mathematics. Elasticity of a function, a mathematical definition of point elasticity; Arc elasticity;
Elasticity is the measure of the sensitivity of one variable to another. [10] A highly elastic variable will respond more dramatically to changes in the variable it is dependent on. The x-elasticity of y measures the fractional response of y to a fraction change in x, which can be written as
Compatibility conditions are particular cases of integrability conditions and were first derived for linear elasticity by Barré de Saint-Venant in 1864 and proved rigorously by Beltrami in 1886. [1] In the continuum description of a solid body we imagine the body to be composed of a set of infinitesimal volumes or material points.
When the price elasticity of demand is unit (or unitary) elastic (E d = −1), the percentage change in quantity demanded is equal to that in price, so a change in price will not affect total revenue. When the price elasticity of demand is relatively elastic (−∞ < E d < −1), the percentage change in quantity demanded is greater than that ...
Expressed in terms of components with respect to a rectangular Cartesian coordinate system, the governing equations of linear elasticity are: [1]. Equation of motion: , + = where the (), subscript is a shorthand for () / and indicates /, = is the Cauchy stress tensor, is the body force density, is the mass density, and is the displacement.
The y arc elasticity of x is defined as: , = % % where the percentage change in going from point 1 to point 2 is usually calculated relative to the midpoint: % = (+) /; % = (+) /. The use of the midpoint arc elasticity formula (with the midpoint used for the base of the change, rather than the initial point (x 1, y 1) which is used in almost all other contexts for calculating percentages) was ...
In physics, Hooke's law is an empirical law which states that the force (F) needed to extend or compress a spring by some distance (x) scales linearly with respect to that distance—that is, F s = kx, where k is a constant factor characteristic of the spring (i.e., its stiffness), and x is small compared to the total possible deformation of the spring.