Fundamental formulas in mathematics

 Here are some fundamental formulas in mathematics:

Algebra

1. *Linear Equation*: ax + by = c

2. *Quadratic Equation*: ax^2 + bx + c = 0

3. *Polynomial Equation*: a_n x^n + a_(n-1) x^(n-1) + ... + a_1 x + a_0 = 0

Geometry

1. *Pythagorean Theorem*: a^2 + b^2 = c^2

2. *Circle Area*: A = πr^2

3. *Circle Circumference*: C = 2πr

Trigonometry

1. *Sine*: sin(A) = opposite side / hypotenuse

2. *Cosine*: cos(A) = adjacent side / hypotenuse

3. *Tangent*: tan(A) = opposite side / adjacent side

Calculus

1. *Derivative*: f'(x) = lim(h → 0) [f(x + h) - f(x)]/h

2. *Integral*: ∫f(x) dx = F(x) + C

Statistics

1. *Mean*: μ = (Σx_i) / n

2. *Median*: M = middle value of data set

3. *Standard Deviation*: σ = √[(Σ(x_i - μ)^2) / (n - 1)]

Other Formulas

1. *Exponential Growth*: A = P(1 + r)^t

2. *Logarithm*: log_b(a) = x ⇔ b^x = a

3. *Permutation*: P(n, r) = n! / (n - r)!

4. *Combination*: C(n, r) = n! / (r!(n - r)!)