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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.
In mathematics, the logarithm of a number is the exponent by which another fixed value, the base, must be raised to produce that number.For example, the logarithm of 1000 to base 10 is 3, because 1000 is 10 to the 3 rd power: 1000 = 10 3 = 10 × 10 × 10.
For example, the square root of a number is the same as raising the number to the power of and the cube root of a number is the same as raising the number to the power of . Examples are 4 = 4 1 2 = 2 {\displaystyle {\sqrt {4}}=4^{\frac {1}{2}}=2} and 27 3 = 27 1 3 = 3 {\displaystyle {\sqrt[{3}]{27}}=27^{\frac {1}{3}}=3} .
The observable universe contains as many as an estimated 2 trillion galaxies [95] [96] [97] and, overall, as many as an estimated 10 24 stars [98] [99] – more stars (and earth-like planets) than all the grains of beach sand on planet Earth; [100] [101] [102] but less than the total number of atoms estimated in the universe as 10 82; [103] and ...
The earlier term for the discipline was "political economy", but since the late 19th century, it has commonly been called "economics". [22] The term is ultimately derived from Ancient Greek οἰκονομία (oikonomia) which is a term for the "way (nomos) to run a household (oikos)", or in other words the know-how of an οἰκονομικός (oikonomikos), or "household or homestead manager".
Up until the 1970s, Virginia was a racially divided one-party state dominated by the Byrd Organization. [346] They sought to stymie the political power of Northern Virginia, perpetuate segregation, and successfully restricted voter registration such that between 1905 and 1948 voter turnout was regularly below ten percent.
Germany, [e] officially the Federal Republic of Germany, [f] is a country in Central Europe.It lies between the Baltic and North Sea to the north and the Alps to the south. Its sixteen constituent states have a total population of over 82 million in an area of 357,596 km 2 (138,069 sq mi), making it the most populous member state of the European Union.