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For example, 3 5 = 3 · 3 · 3 · 3 · 3 = 243. The base 3 appears 5 times in the multiplication, because the exponent is 5. Here, 243 is the 5th power of 3, or 3 raised to the 5th power. The word "raised" is usually omitted, and sometimes "power" as well, so 3 5 can be simply read "3 to the 5th", or "3 to
If N is chosen to be a power of ten, each term in the right sum becomes a finite decimal fraction. The formula is a special case of the Euler–Boole summation formula for alternating series, providing yet another example of a convergence acceleration technique that can be applied to the Leibniz series.
Starting at 0, add 1 for each cell whose distance to the origin (0,0) is less than or equal to r. When finished, divide the sum, representing the area of a circle of radius r, by r2 to find the approximation of π. For example, if r is 5, then the cells considered are: (−5,5) (−4,5)
Fifth power (algebra) In arithmetic and algebra, the fifth power or sursolid[1] of a number n is the result of multiplying five instances of n together: n5 = n × n × n × n × n. Fifth powers are also formed by multiplying a number by its fourth power, or the square of a number by its cube. The sequence of fifth powers of integers is:
Mathematics of three-phase electric power. One voltage cycle of a three-phase system, labeled 0 to 360° (2π radians) along the time axis. The plotted line represents the variation of instantaneous voltage (or current) with respect to time. This cycle repeats with a frequency that depends on the power system.
Exponential functions with bases 2 and 1/2. The exponential function is a mathematical function denoted by () = or (where the argument x is written as an exponent).Unless otherwise specified, the term generally refers to the positive-valued function of a real variable, although it can be extended to the complex numbers or generalized to other mathematical objects like matrices or Lie algebras.
In mathematics, the logarithm to base b is the inverse function of exponentiation with base b. That means that the logarithm of a number x to the base b is the exponent to which b must be raised to produce x. For example, since 1000 = 103, the logarithm base of 1000 is 3, or log10 (1000) = 3.
Power (statistics) In frequentist statistics, power is a measure of the ability of an experimental design and hypothesis testing setup to detect a particular effect if it is truly present. In typical use, it is a function of the test used (including the desired level of statistical significance ), the assumed distribution of the test (for ...