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1. y 2 /y 1 > 1: depth increases over the jump so that y 2 > y 1 2. Fr 2 < 1: downstream flow must be subcritical 3. Fr 1 > 1: upstream flow must be supercritical. Table 2 shows the calculated values used to develop Figure 8. The values associated with a y 1 = 1.5 ft are not valid for use since they
Zero divided by a negative or positive number is either zero or is expressed as a fraction with zero as numerator and the finite quantity as denominator. Zero divided by zero is zero. In 830, Mahāvīra unsuccessfully tried to correct the mistake Brahmagupta made in his book Ganita Sara Samgraha: "A number remains unchanged when divided by zero ...
For example, 7 divided by 2 is 3 with a remainder of 1. These difficulties are avoided by rational number arithmetic, which allows for the exact representation of fractions. [75] A simple method to calculate exponentiation is by repeated multiplication.
1 + 2 = 3, 3 + 3 = 6, 6 + 4 = 10, 10 + 5 = 15. This difficulty results from subtly different uses of the sign in education. In early, arithmetic-focused grades, the equal sign may be operational ; like the equal button on an electronic calculator, it demands the result of a calculation.
Human computers were used to compile 18th and 19th century Western European mathematical tables, for example those for trigonometry and logarithms.Although these tables were most often known by the names of the principal mathematician involved in the project, such tables were often in fact the work of an army of unknown and unsung computers.
The quantity 206 265 ″ is approximately equal to the number of arcseconds in a circle (1 296 000 ″), divided by 2π, or, the number of arcseconds in 1 radian. The exact formula is = (″) and the above approximation follows when tan X is replaced by X.
The partial sums of the series 1 + 2 + 3 + 4 + 5 + 6 + ⋯ are 1, 3, 6, 10, 15, etc.The nth partial sum is given by a simple formula: = = (+). This equation was known ...
With this grouping, Huffman coding averages 1.3 bits for every three symbols, or 0.433 bits per symbol, compared with one bit per symbol in the original encoding, i.e., % compression. Allowing arbitrarily large sequences gets arbitrarily close to entropy – just like arithmetic coding – but requires huge codes to do so, so is not as ...