Sentence examples for in proportion to the square from inspiring English sources

The number of different keys increases in proportion to the square of the number of users.

If a building repair requires additional money, residents pay in proportion to the square footage of their apartment.

In chromatography, peak width increases in proportion to the square root of the distance that the peak has migrated.

When t is very small at the start of the process, all the particles are clustered near the origin of r, but, as t increases, the radius of the cluster increases in proportion to the square root of the time, while the density at the centre drops as the three-halves power to keep the total number constant.

Hence, star images appear brighter in proportion to the area of the telescope objective (assuming that the exit pupil is larger than the eye pupil), and the visibility of a star against the sky background is thus improved in proportion to the square of the diameter of the telescope objective lens.

Increasing the mass or decreasing the radius increases the centrifugal force in direct or inverse proportion, respectively, but increasing the speed of rotation increases it in proportion to the square of the speed; that is, an increase in speed of 10 times, say from 10 to 100 revolutions per minute, increases the centrifugal force by a factor of 100.

To date, researchers have mainly used the hypothesis of reduced energy costs to account for improved isolated high-speed actions [33] through a reduction in aerodynamic resistance in approximate proportion to the square of the velocity (e.g., when cycling, running, or throwing objects) [1, 5, 32].

In addition, they are in direct proportion to the square root of the indenters' half-width, which is in good agreement with R-T dislocation model solution.

In addition, it is in direct proportion to the square root of the indenter half-width, which is in accordance with R-T dislocation model solution.

The maximum breathing capacity and the maximum voluntary ventilation of a diver breathing compressed air diminish rapidly with depth, approximately in proportion to the reciprocal of the square root of the increasing gas density.

This law states that two bodies attract each other in proportion to their masses and in inverse proportion to the square of the distance between them (Palmer 1965, 265 271).