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In mathematics, a parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped. It fits several superficially different mathematical descriptions, which can all be proved to define exactly the same curves. One description of a parabola involves a point (the focus) and a line (the directrix). The focus does not lie on the ...
Download as PDF; Printable version; ... This is a gallery of curves used in mathematics, by Wikipedia page. See also list of curves ... Parabola. Hyperbola. Degree 3
Download as PDF; Printable version ... This is a list of Wikipedia articles about curves used in different fields: mathematics (including geometry ... Cubic parabola ...
Quadratic function: Second degree polynomial, graph is a parabola. Cubic function: Third degree polynomial. Quartic function: Fourth degree polynomial. Quintic function: Fifth degree polynomial. Rational functions: A ratio of two polynomials. nth root. Square root: Yields a number whose square is the given one.
The Cauchy distribution, an example of a distribution which does not have an expected value or a variance. In physics it is usually called a Lorentzian profile, and is associated with many processes, including resonance energy distribution, impact and natural spectral line broadening and quadratic stark line broadening.
The basic example of a parabolic PDE is the one-dimensional heat equation u t = α u x x , {\displaystyle u_{t}=\alpha \,u_{xx},} where u ( x , t ) {\displaystyle u(x,t)} is the temperature at position x {\displaystyle x} along a thin rod at time t {\displaystyle t} and α {\displaystyle \alpha } is a positive constant called the thermal ...
While a parabolic arch may resemble a catenary arch, a parabola is a quadratic function while a catenary is the hyperbolic cosine, cosh(x), a sum of two exponential functions. One parabola is f(x) = x 2 + 3x − 1, and hyperbolic cosine is cosh(x) = e x + e −x / 2 . The curves are unrelated.
The following are special examples of a homomorphism on a binary operation: Additive function: preserves the addition operation: f (x + y) = f (x) + f (y). Multiplicative function: preserves the multiplication operation: f (xy) = f (x)f (y). Relative to negation: Even function: is symmetric with respect to the Y-axis.
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