Translate exercise 10.
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\begin{minted}{latex}
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\begin{minted}{latex}
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% Fallbeschleunigung in Deutschland
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% Gravitational acceleration in Germany
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$$9,81\,\frac{m}{s^2}$$
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$$9,81\,\frac{m}{s^2}$$
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% pq-Formel
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% pq formula
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$$x_{1,2} = - \frac{p}{2} \pm \sqrt{\left(\frac{p}{2}\right)^2 - q}$$
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$$x_{1,2} = - \frac{p}{2} \pm \sqrt{\left(\frac{p}{2}\right)^2 - q}$$
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% Mitternachtsformel
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% Quadratic formula
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$$x_{1,2} = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$
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$$x_{1,2} = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$
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% Catalansche Zahlen
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% Catalan numbers
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\begin{equation*}
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\begin{equation*}
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C_n = \frac{1}{n+1} {2n \choose n} = \frac{(2n)!}{(n+1)!n!}
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C_n = \frac{1}{n+1} {2n \choose n} = \frac{(2n)!}{(n+1)!n!}
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\end{equation*}
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\end{equation*}
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% Definition der Fakultät
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% Definition of a factorial
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$$n! = \prod_{i=1}^{n} i$$
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$$n! = \prod_{i=1}^{n} i$$
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% Menge aller ungeraden natürlichen Zahlen
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% Set of all odd natural numbers
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$$\{ x \mid x \in \mathds{N}, \mathrm{ungerade}(x) \}$$
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$$\{ x \mid x \in \mathds{N}, \mathrm{odd}(x) \}$$
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% Elimination $\neg\exists x$
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% Elimination $\neg\exists x$
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$$\neg\exists x . p(x) \Leftrightarrow \forall x . \neg p(x)$$
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$$\neg\exists x . p(x) \Leftrightarrow \forall x . \neg p(x)$$
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\end{minted}
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\end{minted}
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% Ersetzt diese Grafik durch die entsprechenden Formeln:
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% Replace this graphic by the corresponding formulas:
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\includegraphics{graphics/math-formulas.rend-crop.pdf}
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\includegraphics{graphics/math-formulas.rend-crop.pdf}
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\hrule
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\hrule
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\begin{center}
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\begin{center}
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\textbf{Fallbeschleunigung in Deutschland}
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\textbf{Gravitational acceleration in Germany}
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$$9,81\,\frac{m}{s^2}$$ \\
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$$9,81\,\frac{m}{s^2}$$ \\
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~ \\
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~ \\
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\textbf {pq-Formel}
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\textbf {\textit{pq} formula}
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$$x_{1,2} = - \frac{p}{2} \pm \sqrt{\left(\frac{p}{2}\right)^2 - q}$$ \\
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$$x_{1,2} = - \frac{p}{2} \pm \sqrt{\left(\frac{p}{2}\right)^2 - q}$$ \\
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~ \\
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~ \\
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\textbf{Mitternachtsformel}
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\textbf{Quadratic formula}
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$$x_{1,2} = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ \\
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$$x_{1,2} = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ \\
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~ \\
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~ \\
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\textbf{Catalansche Zahlen}
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\textbf{Catalan numbers}
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\begin{equation*} C_n = \frac{1}{n+1} {2n \choose n} = \frac{(2n)!}{(n+1)!n!} \end{equation*} \\
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\begin{equation*} C_n = \frac{1}{n+1} {2n \choose n} = \frac{(2n)!}{(n+1)!n!} \end{equation*} \\
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~ \\
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~ \\
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\textbf{Definition der Fakultät}
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\textbf{Definition of a factorial}
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$$n! = \prod_{i=1}^{n} i$$ \\
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$$n! = \prod_{i=1}^{n} i$$ \\
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~ \\
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~ \\
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\textbf{Menge aller ungeraden natürlichen Zahlen}
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\textbf{Set of all odd natural numbers}
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$$\{ x \mid x \in \mathds{N}, \mathrm{ungerade}(x) \}$$
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$$\{ x \mid x \in \mathds{N}, \mathrm{odd}(x) \}$$
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~ \\
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~ \\
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\textbf{Elimination $\neg\exists x$}
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\textbf{Elimination $\neg\exists x$}
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Setzt die folgenden Formeln und beachtet dabei die Größe der Klammern.
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Use \LaTeX{} math mode to typeset the following formulas.
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Pay attention to the size of brackets.
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\exercisematerial{exercises/maths/math-formulas}
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\exercisematerial{exercises/maths/math-formulas}
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