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21 results for “proportion”

Formulae (20)

Ratio

a : b = \frac{a}{b}

Compares two quantities by division.

Arithmetic & BasicsBasic

Proportion (Cross Multiply)

\frac{a}{b} = \frac{c}{d} \Rightarrow ad = bc

Two equal ratios; solve using cross multiplication.

AlgebraBasic

Direct Variation

y = kx

y changes directly in proportion to x.

AlgebraIntermediate

Inverse Variation

y = \frac{k}{x}

y changes inversely with x.

Data Science & MLIntermediate

Coefficient of Determination (R²)

R^2 = 1 - \frac{\sum(y_i-\hat{y}_i)^2}{\sum(y_i-\bar{y})^2}

Proportion of variance in the target explained by the model.

PhysicsBasic

Hooke Law

F = -kx

Restoring force of a spring proportional to displacement.

Physics Laws & TheoremsBasic

Hooke's Law

F = -kx

The restoring force of a spring is proportional to its extension.

Physics Laws & TheoremsIntermediate

Kepler's Third Law

T^2 \propto a^3

The square of the orbital period is proportional to the cube of the semi-major axis.

Physics Laws & TheoremsBasic

Boyle's Law

P_1 V_1 = P_2 V_2

At constant temperature, pressure and volume of a gas are inversely proportional.

Physics Laws & TheoremsBasic

Charles's Law

\frac{V_1}{T_1} = \frac{V_2}{T_2}

At constant pressure, volume of a gas is proportional to absolute temperature.

Physics Laws & TheoremsBasic

Gay-Lussac's Law

\frac{P_1}{T_1} = \frac{P_2}{T_2}

At constant volume, pressure of a gas is proportional to absolute temperature.

Physics Laws & TheoremsAdvanced

Gauss's Law

\oint \vec{E} \cdot d\vec{A} = \frac{Q}{\varepsilon_0}

Electric flux through a closed surface is proportional to the enclosed charge.

Physics Laws & TheoremsAdvanced

Planck–Einstein Relation

E = hf

The energy of a photon is proportional to its frequency.

Physics Laws & TheoremsBasic

Hooke Law

F = -kx

Elastic restoring force is proportional to displacement.

Thermodynamics & HeatBasic

Charles's Law

\frac{V_1}{T_1} = \frac{V_2}{T_2}

Volume is proportional to temperature at constant P.

Thermodynamics & HeatIntermediate

Gay-Lussac's Law

\frac{P_1}{T_1} = \frac{P_2}{T_2}

Pressure is proportional to temperature at constant V.

ChemistryIntermediate

Charles's Law

\frac{V_1}{T_1} = \frac{V_2}{T_2}

Volume is proportional to temperature at constant pressure.

ChemistryBasic

Charles Law

\frac{V_1}{T_1} = \frac{V_2}{T_2}

At constant pressure, volume is proportional to temperature.

ChemistryBasic

Gay-Lussac Law

\frac{P_1}{T_1} = \frac{P_2}{T_2}

At constant volume, pressure is proportional to temperature.

Biology & Life SciencesIntermediate

GC Content

\%GC = \frac{G + C}{A + T + G + C} \times 100

Proportion of G and C bases in DNA.

Math Tricks (1)

Anurupyena (Proportion Multiplication)

When numbers are near a convenient working base that is a multiple of a power of 10, use a proportional base to simplify the multiplication.

View trick