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For example, 3 × 5 is an integer factorization of 15, and (x – 2)(x + 2) is a polynomial factorization of x 2 – 4. Factorization is not usually considered meaningful within number systems possessing division , such as the real or complex numbers , since any x {\displaystyle x} can be trivially written as ( x y ) × ( 1 / y ) {\displaystyle ...
Microsoft Math in Bing app – Math helper as a feature within the Bing mobile app on iOS and Android platforms, released in August 2018 [12] Microsoft Math Solver – Mobile app for iOS (first released in November 2019-No longer available in August 2024.) [13] and Android (first released in December 2019), [14] as well as a Microsoft Edge ...
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
Simplification is the process of replacing a mathematical expression by an equivalent one that is simpler (usually shorter), according to a well-founded ordering. Examples include:
In the case of two nested square roots, the following theorem completely solves the problem of denesting. [2]If a and c are rational numbers and c is not the square of a rational number, there are two rational numbers x and y such that + = if and only if is the square of a rational number d.
x 1 = x; x 2 = x 2 for i = k - 2 to 0 do if n i = 0 then x 2 = x 1 * x 2; x 1 = x 1 2 else x 1 = x 1 * x 2; x 2 = x 2 2 return x 1 The algorithm performs a fixed sequence of operations ( up to log n ): a multiplication and squaring takes place for each bit in the exponent, regardless of the bit's specific value.
The almost 19-year streak of successful JCSAT launches was ended when a Proton-M/Briz-M failed to orbit JCSAT-11 on September 5, 2007. A damaged pyro firing cable on the interstage truss prevented the second stage from controlling its direction, and the rocket and its payload crashed into the Kazakhstan steppes. [ 6 ]
In 2020, Amur is planned to be a 4.1 m (13 ft)-diameter two-stage-to-orbit, medium-lift [8] vehicle of 55 m (180 ft) height, with a gross liftoff mass of 360 t (790,000 lb). [ 14 ] [ 13 ] It is aimed to deliver a payload to low Earth orbit of 10.5 t (23,000 lb), [ 8 ] but could loft 12.5 t (28,000 lb) if the first stage is expended and not ...