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In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial.According to the theorem, the power (+) expands into a polynomial with terms of the form , where the exponents and are nonnegative integers satisfying + = and the coefficient of each term is a specific positive integer ...
is the number of collisions made (in ideal conditions, perfectly elastic with no friction) by an object of mass m initially at rest between a fixed wall and another object of mass b 2N m, when struck by the other object. [1] (This gives the digits of π in base b up to N digits past the radix point.)
The +M effect, also known as the positive mesomeric effect, occurs when the substituent is an electron donating group. The group must have one of two things: a lone pair of electrons, or a negative charge. In the +M effect, the pi electrons are transferred from the group towards the conjugate system, increasing the density of the system.
In terms of labelled combinatorial objects, the connection coefficients represent the number of ways to assign m + n − k labels to a pair of labelled combinatorial objects—of weight m and n respectively—that have had their first k labels identified, or glued together to get a new labelled combinatorial object of weight m + n − k. (That ...
The binomial approximation for the square root, + + /, can be applied for the following expression, + where and are real but .. The mathematical form for the binomial approximation can be recovered by factoring out the large term and recalling that a square root is the same as a power of one half.
A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a symbol (e.g., an alphabet letter), or by mathematicians' names to facilitate using it across multiple mathematical problems. [1]
Math enthusiasts around the world, from college kids to rocket scientists, celebrate Pi Day on Thursday, which is March 14 or 3/14 — the first three digits of an infinite number with many ...
Cyclooctadiene iridium methoxide dimer is an organoiridium compound with the formula Ir 2 (OCH 3) 2 (C 8 H 12) 2, where C 8 H 12 is the diene 1,5-cyclooctadiene. It is a yellow solid that is soluble in organic solvents. The complex is used as a precursor to other iridium complexes, some of which are used in homogeneous catalysis. [1]