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27 results for “portion”

Formulae (26)

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.

Nutrition & FoodAdvanced

Glycemic Load

GL = \frac{GI \times C}{100}

Impact of a food portion on blood sugar, combining quality (GI) and quantity.

Nutrition & FoodIntermediate

Yield Percentage

Y = \frac{m_{EP}}{m_{AP}} \times 100

Edible portion left after trimming, relative to the amount purchased.

Actuarial & InsuranceAdvanced

Risk Premium (Variance Load)

P = E[X] + \theta\,\text{Var}(X)

Premium that adds a load proportional to risk variance.

Robotics & ControlAdvanced

PID Controller

u(t) = K_p e + K_i \!\int e\,dt + K_d \frac{de}{dt}

Control output from proportional, integral and derivative of the error.

Robotics & ControlIntermediate

DC Motor Torque

\tau = k_t I

Torque of a DC motor is proportional to current.

Culinary & Baking MathBasic

Portion Cost

C_p = \frac{C_{total}}{n}

Cost of a single serving from a batch.

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