Translate exercise 10.

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Kremitzl 2021-07-20 21:06:25 +02:00
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6 changed files with 19 additions and 18 deletions

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\begin{minted}{latex} \begin{minted}{latex}
% Fallbeschleunigung in Deutschland % Gravitational acceleration in Germany
$$9,81\,\frac{m}{s^2}$$ $$9,81\,\frac{m}{s^2}$$
% pq-Formel % pq formula
$$x_{1,2} = - \frac{p}{2} \pm \sqrt{\left(\frac{p}{2}\right)^2 - q}$$ $$x_{1,2} = - \frac{p}{2} \pm \sqrt{\left(\frac{p}{2}\right)^2 - q}$$
% Mitternachtsformel % Quadratic formula
$$x_{1,2} = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ $$x_{1,2} = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$
% Catalansche Zahlen % Catalan numbers
\begin{equation*} \begin{equation*}
C_n = \frac{1}{n+1} {2n \choose n} = \frac{(2n)!}{(n+1)!n!} C_n = \frac{1}{n+1} {2n \choose n} = \frac{(2n)!}{(n+1)!n!}
\end{equation*} \end{equation*}
% Definition der Fakultät % Definition of a factorial
$$n! = \prod_{i=1}^{n} i$$ $$n! = \prod_{i=1}^{n} i$$
% Menge aller ungeraden natürlichen Zahlen % Set of all odd natural numbers
$$\{ x \mid x \in \mathds{N}, \mathrm{ungerade}(x) \}$$ $$\{ x \mid x \in \mathds{N}, \mathrm{odd}(x) \}$$
% Elimination $\neg\exists x$ % Elimination $\neg\exists x$
$$\neg\exists x . p(x) \Leftrightarrow \forall x . \neg p(x)$$ $$\neg\exists x . p(x) \Leftrightarrow \forall x . \neg p(x)$$
\end{minted} \end{minted}

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% Ersetzt diese Grafik durch die entsprechenden Formeln: % Replace this graphic by the corresponding formulas:
\includegraphics{graphics/math-formulas.rend-crop.pdf} \includegraphics{graphics/math-formulas.rend-crop.pdf}

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\hrule \hrule
\begin{center} \begin{center}
\textbf{Fallbeschleunigung in Deutschland} \textbf{Gravitational acceleration in Germany}
$$9,81\,\frac{m}{s^2}$$ \\ $$9,81\,\frac{m}{s^2}$$ \\
~ \\ ~ \\
\textbf {pq-Formel} \textbf {\textit{pq} formula}
$$x_{1,2} = - \frac{p}{2} \pm \sqrt{\left(\frac{p}{2}\right)^2 - q}$$ \\ $$x_{1,2} = - \frac{p}{2} \pm \sqrt{\left(\frac{p}{2}\right)^2 - q}$$ \\
~ \\ ~ \\
\textbf{Mitternachtsformel} \textbf{Quadratic formula}
$$x_{1,2} = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ \\ $$x_{1,2} = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ \\
~ \\ ~ \\
\textbf{Catalansche Zahlen} \textbf{Catalan numbers}
\begin{equation*} C_n = \frac{1}{n+1} {2n \choose n} = \frac{(2n)!}{(n+1)!n!} \end{equation*} \\ \begin{equation*} C_n = \frac{1}{n+1} {2n \choose n} = \frac{(2n)!}{(n+1)!n!} \end{equation*} \\
~ \\ ~ \\
\textbf{Definition der Fakultät} \textbf{Definition of a factorial}
$$n! = \prod_{i=1}^{n} i$$ \\ $$n! = \prod_{i=1}^{n} i$$ \\
~ \\ ~ \\
\textbf{Menge aller ungeraden natürlichen Zahlen} \textbf{Set of all odd natural numbers}
$$\{ x \mid x \in \mathds{N}, \mathrm{ungerade}(x) \}$$ $$\{ x \mid x \in \mathds{N}, \mathrm{odd}(x) \}$$
~ \\ ~ \\
\textbf{Elimination $\neg\exists x$} \textbf{Elimination $\neg\exists x$}

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Setzt die folgenden Formeln und beachtet dabei die Größe der Klammern. Use \LaTeX{} math mode to typeset the following formulas.
Pay attention to the size of brackets.
\exercisematerial{exercises/maths/math-formulas} \exercisematerial{exercises/maths/math-formulas}

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