User:Covada/Sandbox

This is my own subpage used as a Sandbox.

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Example 1 $$ \begin{align} t &= \dfrac{s}{v} \qquad h =\dfrac{gt^{2}}{2} \\ 2 \cdot h &= gt^2 \qquad \frac{2 \cdot h}{g} = t^2 \qquad t = \sqrt{\dfrac{2 \cdot h}{g}} \\ \dfrac{s}{v} &= \sqrt{\dfrac{2 \cdot h}{g}} \\ v &= \dfrac{s}{\sqrt{\dfrac{2\cdot h}{g}}} \\ v &= s \cdot \sqrt{\dfrac{g}{2 \cdot h}} \qquad v = s \cdot \sqrt{\dfrac{9,81}{2 \cdot h}} \end{align} $$ Example 2 $$ \begin{align} \tau = R \cdot C \\ 1-e^{-1} \end{align} $$ Example 3 $$ B = \mu_0\dfrac{N\cdot I}{l} $$ Example 4 $$ \begin{align} E_k&=\dfrac{1}{2}mv^2 \qquad E_{opgeslagen}=\dfrac{1}{2}CU^2 \qquad v = s \cdot \sqrt{\dfrac{g}{2 \cdot h}} \\ \\ \eta &=\dfrac{E_k=\dfrac{1}{2}mv^2}{E_{opgeslagen}=\dfrac{1}{2}CU^2}\cdot 100\% \\ \eta &=\dfrac{mv^2}{CU^2}\cdot 100\% \\ \eta &=\dfrac{m \cdot \left (s \cdot \sqrt{\dfrac{g}{2 \cdot h}}\right)^2}{CU^2}\cdot 100\% \\ \eta &=\dfrac{m \cdot s^2 \cdot \dfrac{g}{2 \cdot h}}{CU^2} \cdot 100\% \\ \eta &=\dfrac{m \cdot g \cdot s^2}{2\cdot h \cdot CU^2} \cdot 100\% \\ \end{align} $$