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This formula follows from the multiplicative formula above by multiplying numerator and denominator by (n − k)!; as a consequence it involves many factors common to numerator and denominator. It is less practical for explicit computation (in the case that k is small and n is large) unless common factors are first cancelled (in particular ...
In the k-calculus methodology, distances are measured using radar.An observer sends a radar pulse towards a target and receives an echo from it. The radar pulse (which travels at , the speed of light) travels a total distance, there and back, that is twice the distance to the target, and takes time , where and are times recorded by the observer's clock at transmission and reception of the ...
K factor (crude oil refining), a system for classifying crude oil; K-factor (fire protection), formula used to calculate the discharge rate from a fire system nozzle; K-factor (metalurgy), formulae used to calculate the bending capacity of sheet metal; K factor (traffic engineering), the proportion of annual average daily traffic occurring in ...
The K Factor also helps calculate the peak-to-daily ratio of traffic. K30 helps maintain a healthy volume to capacity ratio. [3] K50 and K100 will sometimes be seen. K50 and K100 will not use the 30th highest hourly traffic volumes but the 50th or 100th highest hourly traffic volume when calculating the K factor.
Applying Legendre's formula to the product formula for binomial coefficients produces Kummer's theorem, a similar result on the exponent of each prime in the factorization of a binomial coefficient. [55] Grouping the prime factors of the factorial into prime powers in different ways produces the multiplicative partitions of factorials. [56]
The K-factor is the bending capacity of sheet metal, and by extension the forumulae used to calculate this. [1] [2] [3] Mathematically it is an engineering aspect of geometry. [4] Such is its intricacy in precision sheet metal bending [5] (with press brakes in particular) that its proper application in engineering has been termed an art. [4] [5]
The resulting calculus, known as exterior calculus, allows for a natural, metric-independent generalization of Stokes' theorem, Gauss's theorem, and Green's theorem from vector calculus. If a differential k-form is thought of as measuring the flux through an infinitesimal k-parallelotope at each point of the manifold, then its exterior ...
In mathematics, the K-function, typically denoted K(z), is a generalization of the hyperfactorial to complex numbers, similar to the generalization of the factorial to the gamma function. Definition [ edit ]