2×3.14√6.4×10^6/9.8

asked by guest
on Nov 26, 2024 at 2:41 am



You asked:

Evaluate the expression: \(\frac{2 \cdot 3.14 \cdot \sqrt{6.4} \cdot {10}^{6}}{9.8}\)

MathBot Answer:

\[\frac{2 \cdot 3.14 \cdot \sqrt{6.4} \cdot {10}^{6}}{9.8} = \frac{25120000 \sqrt{10}}{49} \approx 1621151.32292713650652677971094183448096\]

\[\begin{aligned}\frac{2 \cdot 3.14 \cdot \sqrt{6.4} \cdot {10}^{6}}{9.8}& = 2 \cdot \left(3 + \frac{14}{100}\right) \cdot \sqrt{6 + \frac{4}{10}} \cdot 10^{6} \cdot \frac{1}{9 + \frac{8}{10}}\\& = 2 \cdot \left(3 + \frac{7}{50}\right) \cdot \sqrt{6 + \frac{4}{10}} \cdot 10^{6} \cdot \frac{1}{9 + \frac{8}{10}}\\& = 2 \cdot \frac{157}{50} \cdot \sqrt{6 + \frac{4}{10}} \cdot 10^{6} \cdot \frac{1}{9 + \frac{8}{10}}\\& = 2 \cdot \frac{157}{50} \cdot \sqrt{6 + \frac{2}{5}} \cdot 10^{6} \cdot \frac{1}{9 + \frac{8}{10}}\\& = 2 \cdot \frac{157}{50} \cdot \sqrt{\frac{32}{5}} \cdot 10^{6} \cdot \frac{1}{9 + \frac{8}{10}}\\& = 2 \cdot \frac{157}{50} \cdot \frac{4}{5} \cdot \sqrt{10} \cdot 10^{6} \cdot \frac{1}{9 + \frac{8}{10}}\\& = 2 \cdot \frac{157}{50} \cdot \frac{4}{5} \cdot \sqrt{10} \cdot 1000000 \cdot \frac{1}{9 + \frac{8}{10}}\\& = 2 \cdot \frac{157}{50} \cdot \frac{4}{5} \cdot \sqrt{10} \cdot 1000000 \cdot \frac{1}{9 + \frac{4}{5}}\\& = 2 \cdot \frac{157}{50} \cdot \frac{4}{5} \cdot \sqrt{10} \cdot 1000000 \cdot \frac{1}{\frac{49}{5}}\\& = 2 \cdot \frac{157}{50} \cdot \frac{4}{5} \cdot \sqrt{10} \cdot \frac{5000000}{49}\\& = \frac{157}{25} \cdot \frac{4}{5} \cdot \sqrt{10} \cdot \frac{5000000}{49}\\& = \frac{628}{125} \cdot \sqrt{10} \cdot \frac{5000000}{49}\\& = \frac{25120000}{49} \cdot \sqrt{10}\end{aligned}\]

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