Updated spacing between @ latex expressions

astrosander edited
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revision #10581 parent #9973 GitHub c702ebe ← older newer →
en/1.3.3.md +2 −2
@@ -80,14 +80,14 @@
$$ \frac{x}{\cos{\alpha}} = \frac{g \cdot \sin{\alpha} \cdot t^2}{2} $$
Therefore, expressing from $(1)$ $x$, we obtain from the last equation:
$$ t^2 = \frac{2h}{g \cdot \sin{\alpha} \cdot \cos{\alpha} (\tan{\alpha} + \tan{\varphi})} $$
−The time will be minimal if $\xi=g \cdot \sin{\alpha} \cdot \cos{\alpha} (\tan{\alpha} + \tan{\varphi})$ is maximal.
+The time will be minimal if $\xi =g \cdot \sin{\alpha} \cdot \cos{\alpha} (\tan{\alpha} + \tan{\varphi})$ is maximal.
$$ \xi = \frac{\sin{\alpha}}{\cos{\varphi}} \sin{(\alpha + \varphi)} $$
$$ \xi = \frac{1}{2 \cos{\varphi}} (\cos{\varphi} - \cos{(2\alpha + \varphi)}) $$
This expression will be maximal when $\cos{(2\alpha + \varphi)}$ is minimal, and therefore equal to $-1$. Then $2\alpha + \varphi = \pi$, whence:
$$ \alpha = \frac{\pi}{2} - \frac{\varphi}{2} $$
The angle of the gutter to the vertical is:
−$$ \beta = \frac{\pi}{2} - \alpha $$
+$$ \beta = \frac{\pi}{2} - \alpha$$
$$ \fbox{$\beta =\frac{\varphi}{2}$} $$
unchanged lines 20