Initial program 13.5
\[w0 \cdot \sqrt{1 - {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2} \cdot \frac{h}{\ell}}\]
Simplified13.5
\[\leadsto \color{blue}{\sqrt{1 - \left(\frac{M \cdot D}{2 \cdot d} \cdot \frac{M \cdot D}{2 \cdot d}\right) \cdot \frac{h}{\ell}} \cdot w0}\]
- Using strategy
rm Applied div-inv13.5
\[\leadsto \sqrt{1 - \left(\frac{M \cdot D}{2 \cdot d} \cdot \frac{M \cdot D}{2 \cdot d}\right) \cdot \color{blue}{\left(h \cdot \frac{1}{\ell}\right)}} \cdot w0\]
Applied associate-*r*10.2
\[\leadsto \sqrt{1 - \color{blue}{\left(\left(\frac{M \cdot D}{2 \cdot d} \cdot \frac{M \cdot D}{2 \cdot d}\right) \cdot h\right) \cdot \frac{1}{\ell}}} \cdot w0\]
- Using strategy
rm Applied associate-*l*8.7
\[\leadsto \sqrt{1 - \color{blue}{\left(\frac{M \cdot D}{2 \cdot d} \cdot \left(\frac{M \cdot D}{2 \cdot d} \cdot h\right)\right)} \cdot \frac{1}{\ell}} \cdot w0\]
- Using strategy
rm Applied associate-*l*8.0
\[\leadsto \sqrt{1 - \color{blue}{\frac{M \cdot D}{2 \cdot d} \cdot \left(\left(\frac{M \cdot D}{2 \cdot d} \cdot h\right) \cdot \frac{1}{\ell}\right)}} \cdot w0\]
- Using strategy
rm Applied div-inv8.0
\[\leadsto \sqrt{1 - \frac{M \cdot D}{2 \cdot d} \cdot \left(\left(\color{blue}{\left(\left(M \cdot D\right) \cdot \frac{1}{2 \cdot d}\right)} \cdot h\right) \cdot \frac{1}{\ell}\right)} \cdot w0\]
Final simplification8.0
\[\leadsto w0 \cdot \sqrt{1 - \left(\left(\left(\frac{1}{2 \cdot d} \cdot \left(D \cdot M\right)\right) \cdot h\right) \cdot \frac{1}{\ell}\right) \cdot \frac{D \cdot M}{2 \cdot d}}\]
