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22 results for “term”

Formulae (21)

Discriminant

\Delta = b^2 - 4ac

Determines the nature of the roots of a quadratic equation.

AlgebraIntermediate

Binomial Theorem

(a+b)^n = \sum_{k=0}^{n} \binom{n}{k} a^{n-k} b^k

Expands any power of a binomial into a sum of terms.

AlgebraBasic

Arithmetic Series Sum

S_n = \frac{n}{2}(a_1 + a_n)

Sum of the first n terms of an arithmetic sequence.

AlgebraBasic

Arithmetic nth Term

a_n = a_1 + (n-1)d

The nth term of an arithmetic sequence.

AlgebraIntermediate

Geometric Series Sum

S_n = a_1 \frac{1 - r^n}{1 - r}

Sum of the first n terms of a geometric sequence (r ≠ 1).

AlgebraIntermediate

Finite Geometric Series

S_n = a\frac{1-r^n}{1-r}

Sum of the first n terms of a geometric series.

Geometry & TrigonometryIntermediate

Tangent Identity

\tan\theta = \frac{\sin\theta}{\cos\theta}

Defines tangent in terms of sine and cosine.

CalculusAdvanced

L'Hôpital's Rule

\lim_{x\to c}\frac{f(x)}{g(x)} = \lim_{x\to c}\frac{f'(x)}{g'(x)}

Evaluates indeterminate limits 0/0 or ∞/∞.

CalculusIntermediate

Second Derivative Test

f''(x) > 0 \Rightarrow \text{min}

Concavity determines local minima and maxima.

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.

Data Science & MLIntermediate

TF-IDF Weight

w_{t,d} = tf_{t,d} \times \log\frac{N}{df_t}

Term importance: frequency in a document scaled by rarity across documents.

Linear AlgebraIntermediate

Determinant (2×2)

\det\begin{pmatrix} a & b \\ c & d \end{pmatrix} = ad - bc

Determinant of a 2×2 matrix.

Linear AlgebraAdvanced

Determinant (3×3)

\det = a(ei-fh) - b(di-fg) + c(dh-eg)

Determinant of a 3×3 matrix by cofactor expansion.

Linear AlgebraAdvanced

Determinant of a Product

\det(AB) = \det(A)\det(B)

The determinant of a product is the product of determinants.

PhysicsAdvanced

Terminal Velocity

v_t = \sqrt{\frac{2mg}{\rho A C_d}}

Constant fall speed when drag balances gravity.

Aviation & AeronauticsIntermediate

Crosswind Component

XW = V_w\sin\theta

Crosswind component determines whether landing is within aircraft limits.

Finance & InterestIntermediate

Current Ratio

CR = \frac{\text{Current Assets}}{\text{Current Liabilities}}

Liquidity measure of short-term solvency.

Finance & InterestBasic

Working Capital

WC = \text{Current Assets} - \text{Current Liabilities}

Short-term financial health of a business.

AccountingIntermediate

Current Ratio

CR = \dfrac{Current\ Assets}{Current\ Liabilities}

A liquidity measure of whether a firm can cover its short-term obligations with short-term assets.

AccountingIntermediate

Working Capital

WC = Current\ Assets - Current\ Liabilities

The short-term capital available to run day-to-day operations.

Number TheoryBasic

Fibonacci Recurrence

F_n = F_{n-1} + F_{n-2}

Each term is the sum of the two before it.

Math Tricks (1)

FOIL for Binomial Products

Multiply two binomials by combining First, Outer, Inner, Last terms.

View trick