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The variable y is directly proportional to the variable x with proportionality constant ~0.6. The variable y is inversely proportional to the variable x with proportionality constant 1. In mathematics, two sequences of numbers, often experimental data, are proportional or directly proportional if their corresponding elements have a constant ratio.
Ohm's law states that the electric current through a conductor between two points is directly proportional to the voltage across the two points. Introducing the constant of proportionality, the resistance, [1] one arrives at the three mathematical equations used to describe this relationship: [2]
For example, given the following equation for the force of gravity (according to Newton): F = G m 1 m 2 r 2 {\displaystyle F=G{\frac {m_{1}m_{2}}{r^{2}}}} the force of gravity between two masses is directly proportional to the product of the two masses and inversely proportional to the square of the distance between the two masses.
In statistics, a power law is a functional relationship between two quantities, where a relative change in one quantity results in a relative change in the other quantity proportional to the change raised to a constant exponent: one quantity varies as a power of another. The change is independent of the initial size of those quantities.
Relationships between Boyle's, Charles's, Gay-Lussac's, Avogadro's, combined and ideal gas laws, with the Boltzmann constant k = R / N A = n R / N (in each law, properties circled are variable and properties not circled are held constant) The mathematical equation for Boyle's law is: =
Hooke's law: the force is proportional to the extension Bourdon tubes are based on Hooke's law. The force created by gas pressure inside the coiled metal tube above unwinds it by an amount proportional to the pressure. The balance wheel at the core of many mechanical clocks and watches depends on Hooke's law. Since the torque generated by the ...
The law was named after scientist Jacques Charles, who formulated the original law in his unpublished work from the 1780s.. In two of a series of four essays presented between 2 and 30 October 1801, [2] John Dalton demonstrated by experiment that all the gases and vapours that he studied expanded by the same amount between two fixed points of temperature.
In 1922, Alexander Friedmann derived his Friedmann equations from Einstein field equations, showing that the universe might expand at a rate calculable by the equations. [24] The parameter used by Friedmann is known today as the scale factor and can be considered as a scale invariant form of the proportionality constant of Hubble's law.