Initial program 13.7
\[w0 \cdot \sqrt{1 - {\left(\frac{M \cdot D}{2 \cdot d}\right)}^{2} \cdot \frac{h}{\ell}}\]
Simplified13.4
\[\leadsto \color{blue}{\sqrt{1 - \frac{\frac{M \cdot D}{2 \cdot d} \cdot \frac{M \cdot D}{2 \cdot d}}{\frac{\ell}{h}}} \cdot w0}\]
- Using strategy
rm Applied div-inv13.4
\[\leadsto \sqrt{1 - \frac{\frac{M \cdot D}{2 \cdot d} \cdot \frac{M \cdot D}{2 \cdot d}}{\color{blue}{\ell \cdot \frac{1}{h}}}} \cdot w0\]
Applied times-frac8.5
\[\leadsto \sqrt{1 - \color{blue}{\frac{\frac{M \cdot D}{2 \cdot d}}{\ell} \cdot \frac{\frac{M \cdot D}{2 \cdot d}}{\frac{1}{h}}}} \cdot w0\]
- Using strategy
rm Applied add-cube-cbrt8.5
\[\leadsto \sqrt{1 - \frac{\frac{M \cdot D}{2 \cdot d}}{\ell} \cdot \frac{\frac{M \cdot D}{2 \cdot d}}{\color{blue}{\left(\sqrt[3]{\frac{1}{h}} \cdot \sqrt[3]{\frac{1}{h}}\right) \cdot \sqrt[3]{\frac{1}{h}}}}} \cdot w0\]
Applied associate-/r*8.5
\[\leadsto \sqrt{1 - \frac{\frac{M \cdot D}{2 \cdot d}}{\ell} \cdot \color{blue}{\frac{\frac{\frac{M \cdot D}{2 \cdot d}}{\sqrt[3]{\frac{1}{h}} \cdot \sqrt[3]{\frac{1}{h}}}}{\sqrt[3]{\frac{1}{h}}}}} \cdot w0\]
Final simplification8.5
\[\leadsto \sqrt{1 - \frac{\frac{D \cdot M}{2 \cdot d}}{\ell} \cdot \frac{\frac{\frac{D \cdot M}{2 \cdot d}}{\sqrt[3]{\frac{1}{h}} \cdot \sqrt[3]{\frac{1}{h}}}}{\sqrt[3]{\frac{1}{h}}}} \cdot w0\]
