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44 results for “change”

Formulae (44)

Percentage Change

\% \text{change} = \frac{\text{new} - \text{old}}{\text{old}} \times 100

Increase or decrease of a value as a percentage.

AlgebraIntermediate

Change of Base Formula

\log_b(x) = \frac{\log_k(x)}{\log_k(b)}

Converts a logarithm from one base to another.

AlgebraBasic

Direct Variation

y = kx

y changes directly in proportion to x.

AlgebraIntermediate

Inverse Variation

y = \frac{k}{x}

y changes inversely with x.

AlgebraAdvanced

Change of Base

\log_b x = \frac{\log_k x}{\log_k b}

Convert a logarithm to a different base.

CalculusAdvanced

Partial Derivative

\frac{\partial f}{\partial x}

Rate of change with respect to one variable, holding others fixed.

Linear AlgebraBasic

Identity Matrix

AI = IA = A

The identity matrix leaves any matrix unchanged under multiplication.

Linear AlgebraBasic

Identity Matrix Property

AI = IA = A

Multiplying by the identity leaves a matrix unchanged.

PhysicsIntermediate

Impulse

J = F\Delta t = \Delta p

Change in momentum from a force over time.

PhysicsBasic

Heat Energy

Q = mc\Delta T

Heat needed to change temperature of a substance.

PhysicsBasic

Acceleration

a = \frac{\Delta v}{t}

Rate of change of velocity.

PhysicsIntermediate

Impulse

J = F\Delta t = \Delta p

Change in momentum from a force over time.

Physics Laws & TheoremsBasic

Newton's Second Law

F = ma = \frac{dp}{dt}

Net force equals mass times acceleration (rate of change of momentum).

Physics Laws & TheoremsIntermediate

First Law of Thermodynamics

\Delta U = Q - W

Energy conservation: change in internal energy equals heat added minus work done.

Physics Laws & TheoremsAdvanced

Lenz's Law

\varepsilon \propto -\frac{d\Phi_B}{dt}

Induced current opposes the change in flux that produced it.

Physics Laws & TheoremsIntermediate

First Law of Thermodynamics

\Delta U = Q - W

Change in internal energy equals heat added minus work done.

Physics Laws & TheoremsIntermediate

Lenz Law

\text{induced current opposes change}

Induced currents oppose the change producing them.

Thermodynamics & HeatBasic

Heat Energy

Q = mc\Delta T

Heat needed to change a substance’s temperature.

Thermodynamics & HeatIntermediate

Latent Heat

Q = mL

Heat for a phase change at constant temperature.

Thermodynamics & HeatAdvanced

Entropy Change

\Delta S = \frac{Q}{T}

Reversible entropy change at temperature T.

Thermodynamics & HeatIntermediate

Linear Thermal Expansion

\Delta L = \alpha L_0 \Delta T

Length change of a solid when heated.

Modern & Quantum PhysicsAdvanced

Compton Shift

\Delta\lambda = \frac{h}{m_e c}(1 - \cos\theta)

Wavelength change of scattered photons.

ChemistryIntermediate

Enthalpy Change

\Delta H = H_{products} - H_{reactants}

Heat absorbed or released at constant pressure.

ChemistryAdvanced

Hess Law

\Delta H = \sum \Delta H_{steps}

Total enthalpy change is the sum of step changes.

Biology & Life SciencesBasic

Surface Area to Volume

SA:V = \frac{\text{surface area}}{\text{volume}}

Ratio governing cellular exchange efficiency.

Biology & Life SciencesIntermediate

Surface-to-Volume Ratio

SA:V = \frac{\text{surface area}}{\text{volume}}

Ratio governing cell exchange efficiency.

Nutrition & FoodIntermediate

Weight Change from Energy Balance

\Delta m = \frac{E_{deficit}}{7700}

Approximate body-fat change (kg) from a cumulative calorie deficit or surplus.

EngineeringIntermediate

Linear Thermal Expansion

\Delta L = \alpha L_0 \Delta T

Change in length due to temperature change.

Materials & CivilIntermediate

Linear Thermal Expansion

\Delta L = \alpha L_0 \Delta T

Change in length due to temperature change.

Business & CommerceAdvanced

Month-over-Month Growth

g = \left(\dfrac{V_1}{V_0}\right) - 1

The percentage change in a metric from one period to the next.

EconomicsBasic

GDP Growth Rate

g = \dfrac{GDP_1 - GDP_0}{GDP_0}\times 100\%

The percentage change in real output between two periods.

EconomicsIntermediate

Price Elasticity of Demand

E_d = \dfrac{\%\Delta Q_d}{\%\Delta P}

How responsive quantity demanded is to a change in price.

EconomicsIntermediate

Price Elasticity of Supply

E_s = \dfrac{\%\Delta Q_s}{\%\Delta P}

How responsive quantity supplied is to a change in price.

EconomicsIntermediate

Spending Multiplier

k = \dfrac{1}{1 - MPC}

How much total output rises from an initial change in spending.

EconomicsIntermediate

Price Elasticity of Demand

E_d = \frac{\%\Delta Q}{\%\Delta P}

Responsiveness of demand to price changes.

EconomicsBasic

Inflation Rate

\pi = \frac{CPI_1 - CPI_0}{CPI_0}\times 100

Percentage change in the price index.

Currency & ForexBasic

Currency Conversion

Foreign = Domestic \times Rate

Convert an amount from one currency to another using the quoted exchange rate.

Currency & ForexBasic

Inverse Exchange Rate

Rate_{B/A} = \dfrac{1}{Rate_{A/B}}

Flip a quoted rate to express it from the other currency’s point of view.

Currency & ForexBasic

Currency % Change

\%\Delta = \dfrac{Rate_1 - Rate_0}{Rate_0}\times 100\%

The percentage move in an exchange rate between two points in time.

Currency & ForexIntermediate

Cross Rate

Rate_{A/C} = Rate_{A/B} \times Rate_{B/C}

Derive the exchange rate between two currencies via a common third currency.

Currency & ForexAdvanced

Purchasing Power Parity

S = \dfrac{P_{domestic}}{P_{foreign}}

The exchange rate that would equalize the price of an identical basket of goods across countries.

Currency & ForexAdvanced

Real Exchange Rate

RER = S \times \dfrac{P_{foreign}}{P_{domestic}}

The nominal rate adjusted for price levels, measuring relative purchasing power.

Currency & ForexAdvanced

Forward Exchange Rate

F = S \times \dfrac{1 + i_d}{1 + i_f}

The agreed future exchange rate implied by interest-rate differentials (covered interest parity).

Everyday MathBasic

Percentage Change

\%\Delta = \frac{new - old}{old}\times 100

Relative change between two values.