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The last digit of a fourth power in decimal can only be 0 (in fact 0000), 1, 5 (in fact 0625), or 6.. Every positive integer can be expressed as the sum of at most 19 fourth powers; every integer larger than 13792 can be expressed as the sum of at most 16 fourth powers (see Waring's problem).
Graphs of y = b x for various bases b: base 10, base e, base 2, base 1 / 2 . Each curve passes through the point (0, 1) because any nonzero number raised to the power of 0 is 1. At x = 1, the value of y equals the base because any number raised to the power of 1 is the number itself.
The following list illustrates various frequencies, measured in hertz, according to decade in the order of their magnitudes, with the negative decades illustrated by events and positive decades by acoustic or electromagnetic uses. Factor. ( Hz ) Multiple. Value. Item. 10 −18. 1 attohertz (aHz) ~2.2978 aHz.
In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial.According to the theorem, it is possible to expand the polynomial (x + y) n into a sum involving terms of the form ax b y c, where the exponents b and c are nonnegative integers with b + c = n, and the coefficient a of each term is a specific positive integer depending ...
Sixth power. In arithmetic and algebra the sixth power of a number n is the result of multiplying six instances of n together. So: n6 = n × n × n × n × n × n. Sixth powers can be formed by multiplying a number by its fifth power, multiplying the square of a number by its fourth power, by cubing a square, or by squaring a cube.
Kleiber's plot comparing body size to metabolic rate for a variety of species. [1] Kleiber's law, named after Max Kleiber for his biology work in the early 1930s, is the observation that, for the vast majority of animals, an animal's metabolic rate scales to the 3⁄4 power of the animal's mass. [2] More recently, Kleiber's law has also been ...
The Basel problem is a problem in mathematical analysis with relevance to number theory, concerning an infinite sum of inverse squares. It was first posed by Pietro Mengoli in 1650 and solved by Leonhard Euler in 1734, [1] and read on 5 December 1735 in The Saint Petersburg Academy of Sciences. [2] Since the problem had withstood the attacks of ...
In mathematics, Euler's identity[ note 1] (also known as Euler's equation) is the equality where. is pi, the ratio of the circumference of a circle to its diameter. Euler's identity is named after the Swiss mathematician Leonhard Euler. It is a special case of Euler's formula when evaluated for .