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If the initial point is at the North or South pole, then the first equation is indeterminate. If the initial azimuth is due East or West, then the second equation is indeterminate. If the standard 2-argument arctangent atan2 function is used, then these values are usually handled correctly. [clarification needed]
This has been followed by subsequent spreadsheets, such as Microsoft Excel, and complemented by specialized VLOOKUP and HLOOKUP functions to simplify lookup in a vertical or horizontal table. In Microsoft Excel the XLOOKUP function has been rolled out starting 28 August 2019.
The curve of fastest descent is not a straight or polygonal line (blue) but a cycloid (red).. In physics and mathematics, a brachistochrone curve (from Ancient Greek βράχιστος χρόνος (brákhistos khrónos) 'shortest time'), [1] or curve of fastest descent, is the one lying on the plane between a point A and a lower point B, where B is not directly below A, on which a bead slides ...
Inverting this formula gives the indirect utility function (utility as a function of price and income): (,) = (),where is the amount of income available to the individual and is equivalent to the expenditure ((,)) in the previous equation.
A consumer's indirect utility (,) can be computed from their utility function (), defined over vectors of quantities of consumable goods, by first computing the most preferred affordable bundle, represented by the vector (,) by solving the utility maximization problem, and second, computing the utility ((,)) the consumer derives from that ...
Such transfers may be direct, in that the target address is written in the code itself, or indirect, in that the target address itself is a variable in memory or a CPU register. In a typical function call, the program performs a direct call, but returns to the caller function using the stack – an indirect backward-edge transfer.
The Weir formula is a formula used in indirect calorimetry, relating metabolic rate to oxygen consumption and carbon dioxide production. According to original source, it says: [ 1 ] Metabolic rate (kcal per day) = 1.440 (3.9 VO 2 + 1.1 VCO 2 )
In mathematics, the Euler–Maclaurin formula is a formula for the difference between an integral and a closely related sum. It can be used to approximate integrals by finite sums, or conversely to evaluate finite sums and infinite series using integrals and the machinery of calculus .
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