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Nth degree, or nth degree, are two words expressing a number to a certain level. In the first word, 'Nth' or 'nth', is a word expressing a number, in two parts, 'n' and 'th', but where that number is not known, (hence the use of 'n') and a correlatory factoring, 'th', (exponential amplification, usually from four onwards (fourth, fifth)), is used to multiply the 'n' (number), to arrive at a ...
In mathematics, the degree of a polynomial is the highest of the degrees of the polynomial's monomials (individual terms) with non-zero coefficients. The degree of a term is the sum of the exponents of the variables that appear in it, and thus is a non-negative integer.
The integer n is called the index or degree, and the number x of which the root is taken is the radicand. A root of degree 2 is called a square root and a root of degree 3, a cube root. Roots of higher degree are referred by using ordinal numbers, as in fourth root, twentieth root, etc. The computation of an n th root is a root extraction.
In statistics, polynomial regression is a form of regression analysis in which the relationship between the independent variable x and the dependent variable y is modeled as an nth degree polynomial in x. Polynomial regression fits a nonlinear relationship between the value of x and the corresponding conditional mean of y, denoted E(y |x).
"The Nth Degree" is the 93rd episode of the American science fiction television series Star Trek: The Next Generation, and the 19th episode of the fourth season. Set in the 24th century, the series follows the adventures of the Starfleet crew of the Federation starship Enterprise-D. Rob Legato directed and oversaw visual effects for the episode.
In fact, the n th roots of unity being the roots of the polynomial X n – 1, their sum is the coefficient of degree n – 1, which is either 1 or 0 according whether n = 1 or n > 1. Alternatively, for n = 1 there is nothing to prove, and for n > 1 there exists a root z ≠ 1 – since the set S of all the n th roots of unity is a group , z S ...
That cos nx is an n th-degree polynomial in cos x can be seen by observing that cos nx is the real part of one side of de Moivre's formula: + = ( + ). The real part of the other side is a polynomial in cos x and sin x , in which all powers of sin x are even and thus replaceable through the identity cos 2 x + sin 2 x = 1 .
In mathematics, a homogeneous function is a function of several variables such that the following holds: If each of the function's arguments is multiplied by the same scalar, then the function's value is multiplied by some power of this scalar; the power is called the degree of homogeneity, or simply the degree.