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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.
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 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]
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);
Zipf's law, described as an "empirical statistical law" of linguistics, [7] is another example. According to the "law", given some dataset of text, the frequency of a word is inversely proportional to its frequency rank.
Graham's law states that the rate of diffusion or of effusion of a gas is inversely proportional to the square root of its molecular weight. Thus, if the molecular weight of one gas is four times that of another, it would diffuse through a porous plug or escape through a small pinhole in a vessel at half the rate of the other (heavier gases ...
For example, given the following equation for the force of gravity (according to Newton): = 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 this graph, the attractive force decreases in proportion to the square of the distance (Y = 1/X 2), while the slope (Y ′ = −2/X 3) is inversely proportional to the cube of the distance. The tidal force corresponds to the difference in Y between two points on the graph, with one point on the near side of the body, and the other point on ...