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Two functions and () are proportional if their ratio () is a constant function. If several pairs of variables share the same direct proportionality constant, the equation expressing the equality of these ratios is called a proportion , e.g., a / b = x / y = ⋯ = k (for details see Ratio ).
The force of attraction or repulsion between two electrically charged particles, in addition to being directly proportional to the product of the electric charges, is inversely proportional to the square of the distance between them; this is known as Coulomb's law. The deviation of the exponent from 2 is less than one part in 10 15. [8]
If the output of a function is inversely proportional to its input, or inversely proportional to the difference from a given value , the function will exhibit hyperbolic growth, with a singularity at . In the real world hyperbolic growth is created by certain non-linear positive feedback mechanisms. [2]
Zipf's law (/ z ɪ f /; German pronunciation:) is an empirical law stating that when a list of measured values is sorted in decreasing order, the value of the n-th entry is often approximately inversely proportional to n. The best known instance of Zipf's law applies to the frequency table of words in a text or corpus of natural language:
The force is proportional to the product of the two masses and inversely proportional to the square of the distance between them: [11] Diagram of two masses attracting one another = where F is the force between the masses; G is the Newtonian constant of gravitation (6.674 × 10 −11 m 3 ⋅kg −1 ⋅s −2);
For normally distributed random variables inverse-variance weighted averages can also be derived as the maximum likelihood estimate for the true value. Furthermore, from a Bayesian perspective the posterior distribution for the true value given normally distributed observations and a flat prior is a normal distribution with the inverse-variance weighted average as a mean and variance ().
The equation states that flow rate is proportional to the radius to the fourth power, meaning that a small increase in the internal diameter of the cannula yields a significant increase in flow rate of IV fluids. The radius of IV cannulas is typically measured in "gauge", which is inversely proportional to the radius.
Jurin's law, or capillary rise, is the simplest analysis of capillary action—the induced motion of liquids in small channels [1] —and states that the maximum height of a liquid in a capillary tube is inversely proportional to the tube's diameter.