MathML

Arithmetisches Mittel

\overline{x} = \frac{1}{n} \sum_{i = 1}^{n} x_{i} = \frac{x_{1} + x_{2} + … + x_{n}}{n}

Binomische Formel

{(a + b)}^{2} = a^{2} + 2 a b + b^{2}

Eulers Identität

e^{i π} + 1 = 0

Fourier-Transformormation

X_{k} = \frac{1}{N} \sum_{n = 0}^{N - 1} x_{n} e^{i 2 π k \frac{n}{N}}

To find the energy at a particular frequency, spin your signal around a circle at that frequency, and average a bunch of points along that path.

Integralrechnung

\int_{0}^{π} \sin x ⅆ x = {[- \cos x]}_{0}^{π} = - (- 1) - (- 1) = 2

Kombination

(\binom{n}{k}) = \frac{n!}{(n - k)! \cdot k!}

(\binom{49}{6}) = \frac{49!}{(49 - 6)! \cdot 6!} = 13983816

Lösungsformel der quadratischen Gleichung

Zur Lösung einer quadratischen Gleichung der Form $x^{2} + p x + q = 0$ dient folgende Formel:

x_{1,2} = - \frac{p}{2} \pm \sqrt{{(\frac{p}{2})}^{2} - q}

Standardnormalverteilung

φ (x) = \frac{1}{\sqrt{2 π}} e^{- \frac{1}{2} x^{2}}

Zeitdilatation

T ′ = T_{0} \frac{1}{\sqrt{1 - {(\frac{v}{c})}^{2}}}

WirisQuizz (05.01.2023)

\frac{2^{20} + 4^{10} + 4^{11} + 8^{8}}{2^{21} + 8^{7} + 4^{12}}

= \frac{2^{20} + {(2^{2})}^{10} + {(2^{2})}^{11} + {(2^{3})}^{8}}{2^{21} + {(2^{3})}^{7} + {(2^{2})}^{12}}

= \frac{2^{20} + 2^{20} + 2^{22} + 2^{24}}{2^{21} + 2^{21} + 2^{24}}

= \frac{2^{20} (1 + 1 + 4 + 16)}{2^{20} (2 + 2 + 16)}

= \frac{22}{20}

= \frac{11}{10}