((10 $\sqrt{\2}$ /9.8)-1/2)
You asked:
Evaluate the expression: \(\frac{10 \sqrt{2}}{9.8} - \frac{1}{2}\)
MathBot Answer:
\[\frac{10 \sqrt{2}}{9.8} - \frac{1}{2} = - \frac{1}{2} + \frac{50 \sqrt{2}}{49} \approx 0.94307506364601535592009053490786\]
\[\begin{aligned}\frac{10 \sqrt{2}}{9.8} - \frac{1}{2}& = 10 \cdot \sqrt{2} \cdot \frac{1}{9 + \frac{8}{10}} - \frac{1}{2}\\& = 10 \cdot \sqrt{2} \cdot \frac{1}{9 + \frac{4}{5}} - \frac{1}{2}\\& = 10 \cdot \sqrt{2} \cdot \frac{1}{\frac{49}{5}} - \frac{1}{2}\\& = 10 \cdot \frac{5}{49} \cdot \sqrt{2} - \frac{1}{2}\\& = \frac{50}{49} \cdot \sqrt{2} - \frac{1}{2}\\& = - \frac{1}{2} + \frac{50}{49} \cdot \sqrt{2}\end{aligned}\]