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In two dimensions, 2x 1 + 2x 2 is the perimeter of a rectangle with sides of length x 1 and x 2. Similarly, 4 √ x 1 x 2 is the perimeter of a square with the same area, x 1 x 2, as that rectangle. Thus for n = 2 the AM–GM inequality states that a rectangle of a given area has the smallest perimeter if that rectangle is also a square.
[1] It is named after the Russian mathematician Andrey Markov , although it appeared earlier in the work of Pafnuty Chebyshev (Markov's teacher), and many sources, especially in analysis , refer to it as Chebyshev's inequality (sometimes, calling it the first Chebyshev inequality, while referring to Chebyshev's inequality as the second ...
The first of these quadratic inequalities requires r to range in the region beyond the value of the positive root of the quadratic equation r 2 + r − 1 = 0, i.e. r > φ − 1 where φ is the golden ratio. The second quadratic inequality requires r to range between 0 and the positive root of the quadratic equation r 2 − r − 1 = 0, i.e. 0 ...
Semaglutide — the active substance in Ozempic and Wegovy — may help reduce alcohol cravings in people with alcohol use disorder, a new study suggests.
A satirical petition ostensibly aiming to crowdfund a trillion dollars to allow Denmark to buy California has received more than 200,000 signatures.
Jensen's inequality generalizes the statement that a secant line of a convex function lies above its graph. Visualizing convexity and Jensen's inequality. In mathematics, Jensen's inequality, named after the Danish mathematician Johan Jensen, relates the value of a convex function of an integral to the integral of the convex function.
1 discussion was held.) 2 - - - 3 (The following transpired in open 4 court outside the presence of the jury:) 5 - - - 6 COURT CRIER: Come to order, please. 7 This court is reconvened. 8 THE COURT: All right. Before we 9 proceed -- you may be seated everybody. 10 Before we proceed to Ms. Sullivan's 11 opening, regarding the issue of safe and
From January 2008 to December 2012, if you bought shares in companies when Marshall O. Larsen joined the board, and sold them when he left, you would have a 43.1 percent return on your investment, compared to a -2.8 percent return from the S&P 500.