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The function also illustrates the reflective nature of the root and logarithm functions as the equation below only holds true when = (): x y = log y x {\displaystyle {\sqrt[{y}]{x}}=\log _{y}x} Like square roots , the square super-root of x may not have a single solution.
In mathematics, exponentiation, denoted b n, is an operation involving two numbers: the base, b, and the exponent or power, n. [1] When n is a positive integer, exponentiation corresponds to repeated multiplication of the base: that is, b n is the product of multiplying n bases: [1] = ⏟.
The moment generating function of a real random variable is the expected value of , as a function of the real parameter . For a normal distribution with density f {\displaystyle f} , mean μ {\displaystyle \mu } and variance σ 2 {\textstyle \sigma ^{2}} , the moment generating function exists and is equal to
In contrast, the physical radius of the body is proportional to the cube root of its volume. Therefore, as the body accumulates matter at a given fixed density (in this example, 997 kg/m 3 , the density of water), its Schwarzschild radius will increase more quickly than its physical radius.
How much gas is present could be specified by giving the mass instead of the chemical amount of gas. Therefore, an alternative form of the ideal gas law may be useful. The chemical amount, n (in moles), is equal to total mass of the gas (m) (in kilograms) divided by the molar mass, M (in kilograms per mole): =.
The phenomenological Colebrook–White equation (or Colebrook equation) expresses the Darcy friction factor f as a function of Reynolds number Re and pipe relative roughness ε / D h, fitting the data of experimental studies of turbulent flow in smooth and rough pipes.
this expression can be used to decompose higher powers as a linear function of lower powers, which in turn can be decomposed all the way down to a linear combination of and 1. The resulting recurrence relationships yield Fibonacci numbers as the linear coefficients : φ n = F n φ + F n − 1 . {\displaystyle \varphi ^{n}=F_{n}\varphi +F_{n-1}.}
[6] [7] It also explains how the phenomena of electricity and magnetism are related. [1] [2] A defining feature of special relativity is the replacement of the Galilean transformations of Newtonian mechanics with the Lorentz transformations. Time and space cannot be defined separately from each other (as was previously thought to be the case).