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It may be useful to be aware that the difference between two successive square numbers is the sum of their respective square roots. Hence, if one knows that 12 × 12 = 144 and wish to know 13 × 13, calculate 144 + 12 + 13 = 169. This is because (x + 1) 2 − x 2 = x 2 + 2x + 1 − x 2 = x + (x + 1) x 2 = (x − 1) 2 + (2x − 1)
On 12 April 2018, the police said that Rakesh Kumar, who leaked the class 12 economics paper, had leaked class 10 mathematics paper also. [40] Consequently, the Central Board of Secondary Education has put in place a system of "encrypted" question papers, which are supposed to be printed by the schools half an hour before the exam starts. [41]
In abstract algebra, given a magma with binary operation ∗ (which could nominally be termed multiplication), left division of b by a (written a \ b) is typically defined as the solution x to the equation a ∗ x = b, if this exists and is unique. Similarly, right division of b by a (written b / a) is the solution y to the equation y ∗ a = b ...
In mathematics, the harmonic mean is a kind of average, one of the Pythagorean means. It is the most appropriate average for ratios and rates such as speeds, [ 1 ] [ 2 ] and is normally only used for positive arguments.
Equivalence class: given an equivalence relation, [] often denotes the equivalence class of the element x. 3. Integral part : if x is a real number , [ x ] {\displaystyle [x]} often denotes the integral part or truncation of x , that is, the integer obtained by removing all digits after the decimal mark .
In mathematics, a series is, roughly speaking, an addition of infinitely many terms, one after the other. [1] The study of series is a major part of calculus and its generalization, mathematical analysis. Series are used in most areas of mathematics, even for studying finite structures in combinatorics through generating functions.
As can be seen, M appears on both sides of the equation, and for practical purposes a root-finding algorithm must be used for a numerical solution (the equation is a septic equation in M 2 and, though some of these may be solved explicitly, the Abel–Ruffini theorem guarantees that there exists no general form for the roots of these ...
Uncle Sam pointing his finger at the viewer in order to recruit soldiers for the American Army during World War I, 1917-1918 Sheet music cover for patriotic song, 1917. The Selective Service Act of 1917 or Selective Draft Act (Pub. L. 65–12, 40 Stat. 76, enacted May 18, 1917) authorized the United States federal government to raise a national army for service in World War I through conscription.