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The location of L 3 is the solution to the following equation, gravitation providing the centripetal force: + = (+ +) + with parameters M 1, M 2, and R defined as for the L 1 and L 2 cases, and r being defined such that the distance of L 3 from the centre of the larger object is R − r.
2.5° by 2.5° Westerhout 5: 2.3° by 1.25° Sh2-54: 2.3° Carina Nebula: 2° by 2° Note: brightest nebula in the night sky, 1.0 apparent magnitude (V) North America Nebula: 2° by 100 ′ Earth in the Moon's sky: 2° - 1°48 ′ [12] Appearing about three to four times larger than the Moon in Earth's sky The Sun in the sky of Mercury: 1.15 ...
Flowchart of using successive subtractions to find the greatest common divisor of number r and s. In mathematics and computer science, an algorithm (/ ˈ æ l ɡ ə r ɪ ð əm / ⓘ) is a finite sequence of mathematically rigorous instructions, typically used to solve a class of specific problems or to perform a computation. [1]
The quadratic formula, which concisely expresses the solutions of all quadratic equations The Rubik's Cube group is a concrete application of group theory. [26] Algebra is the art of manipulating equations and formulas. Diophantus (3rd century) and al-Khwarizmi (9th century) were the two main precursors of algebra.
A method analogous to piece-wise linear approximation but using only arithmetic instead of algebraic equations, uses the multiplication tables in reverse: the square root of a number between 1 and 100 is between 1 and 10, so if we know 25 is a perfect square (5 × 5), and 36 is a perfect square (6 × 6), then the square root of a number greater than or equal to 25 but less than 36, begins with ...
26.2 dyn/cm at 0° 23.7 dyn/cm at 20 °C ... Vapor pressure of acetone based on formula, = + from ...
As another example, to find the area of the region bounded by the graph of the function f(x) = between x = 0 and x = 1, one can divide the interval into five pieces (0, 1/5, 2/5, ..., 1), then construct rectangles using the right end height of each piece (thus √ 0, √ 1/5, √ 2/5, ..., √ 1) and sum their areas to get the approximation
Conversely, if is a normal deviate with parameters and , then this distribution can be re-scaled and shifted via the formula = / to convert it to the standard normal distribution.