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The total cost curve, if non-linear, can represent increasing and diminishing marginal returns.. The short-run total cost (SRTC) and long-run total cost (LRTC) curves are increasing in the quantity of output produced because producing more output requires more labor usage in both the short and long runs, and because in the long run producing more output involves using more of the physical ...
The Plateau–Rayleigh instability is named for Joseph Plateau and Lord Rayleigh.In 1873, Plateau found experimentally that a vertically falling stream of water will break up into drops if its length is greater than about 3.13 to 3.18 times its diameter, which he noted is close to π.
Under STP, a reaction between three cubic meters of hydrogen gas and one cubic meter of nitrogen gas will produce about two cubic meters of ammonia.. The law of combining volumes states that when gases chemically react together, they do so in amounts by volume which bear small whole-number ratios (the volumes calculated at the same temperature and pressure).
For a fixed mass of an ideal gas kept at a fixed temperature, pressure and volume are inversely proportional. [2] Boyle's law is a gas law, stating that the pressure and volume of a gas have an inverse relationship. If volume increases, then pressure decreases and vice versa, when the temperature is held constant.
For a given mass of an ideal gas, the volume and amount (moles) of the gas are directly proportional if the temperature and pressure are constant. The law is named after Amedeo Avogadro who, in 1812, [ 2 ] [ 3 ] hypothesized that two given samples of an ideal gas, of the same volume and at the same temperature and pressure, contain the same ...
Another argument for the impossibility of circular realizations, by Helge Tverberg, uses inversive geometry to transform any three circles so that one of them becomes a line, making it easier to argue that the other two circles do not link with it to form the Borromean rings. [27] However, the Borromean rings can be realized using ellipses. [2]
There is a distinction between two types of economies of scale: internal and external. An industry that exhibits an internal economy of scale is one where the costs of production fall when the number of firms in the industry drops, but the remaining firms increase their production to match previous levels.
Graphs of surface area, A against volume, V of the Platonic solids and a sphere, showing that the surface area decreases for rounder shapes, and the surface-area-to-volume ratio decreases with increasing volume. Their intercepts with the dashed lines show that when the volume increases 8 (2³) times, the surface area increases 4 (2²) times.