Initial program 13.4
\[w0 \cdot \sqrt{1 - {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2} \cdot \frac{h}{\ell}}\]
Simplified13.0
\[\leadsto \color{blue}{\sqrt{1 - \frac{\frac{M \cdot D}{2 \cdot d} \cdot \frac{M \cdot D}{2 \cdot d}}{\frac{\ell}{h}}} \cdot w0}\]
- Using strategy
rm Applied div-inv13.0
\[\leadsto \sqrt{1 - \frac{\frac{M \cdot D}{2 \cdot d} \cdot \frac{M \cdot D}{2 \cdot d}}{\color{blue}{\ell \cdot \frac{1}{h}}}} \cdot w0\]
Applied times-frac8.1
\[\leadsto \sqrt{1 - \color{blue}{\frac{\frac{M \cdot D}{2 \cdot d}}{\ell} \cdot \frac{\frac{M \cdot D}{2 \cdot d}}{\frac{1}{h}}}} \cdot w0\]
- Using strategy
rm Applied clear-num8.1
\[\leadsto \sqrt{1 - \frac{\color{blue}{\frac{1}{\frac{2 \cdot d}{M \cdot D}}}}{\ell} \cdot \frac{\frac{M \cdot D}{2 \cdot d}}{\frac{1}{h}}} \cdot w0\]
- Using strategy
rm Applied associate-/l/8.1
\[\leadsto \sqrt{1 - \color{blue}{\frac{1}{\ell \cdot \frac{2 \cdot d}{M \cdot D}}} \cdot \frac{\frac{M \cdot D}{2 \cdot d}}{\frac{1}{h}}} \cdot w0\]
- Using strategy
rm Applied add-sqr-sqrt8.1
\[\leadsto \sqrt{\color{blue}{\sqrt{1 - \frac{1}{\ell \cdot \frac{2 \cdot d}{M \cdot D}} \cdot \frac{\frac{M \cdot D}{2 \cdot d}}{\frac{1}{h}}} \cdot \sqrt{1 - \frac{1}{\ell \cdot \frac{2 \cdot d}{M \cdot D}} \cdot \frac{\frac{M \cdot D}{2 \cdot d}}{\frac{1}{h}}}}} \cdot w0\]
Applied rem-sqrt-square8.1
\[\leadsto \color{blue}{\left|\sqrt{1 - \frac{1}{\ell \cdot \frac{2 \cdot d}{M \cdot D}} \cdot \frac{\frac{M \cdot D}{2 \cdot d}}{\frac{1}{h}}}\right|} \cdot w0\]
Simplified8.8
\[\leadsto \left|\color{blue}{\sqrt{1 - \left(\frac{\frac{D}{2 \cdot d} \cdot M}{\ell} \cdot \left(\frac{D}{2 \cdot d} \cdot M\right)\right) \cdot h}}\right| \cdot w0\]
Final simplification8.8
\[\leadsto \left|\sqrt{1 - \left(\frac{\frac{D}{2 \cdot d} \cdot M}{\ell} \cdot \left(\frac{D}{2 \cdot d} \cdot M\right)\right) \cdot h}\right| \cdot w0\]
