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: 2⋅3.146.4⋅1069.8\frac{2 \cdot 3.14 \sqrt{6.4} \cdot {10}^{6}}{9.8}

MathBot Answer:

2⋅3.146.4⋅1069.8=251200001049≈1621151.32292713650652677971094183448096\frac{2 \cdot 3.14 \sqrt{6.4} \cdot {10}^{6}}{9.8} = \frac{25120000 \sqrt{10}}{49} \approx 1621151.32292713650652677971094183448096

2⋅3.146.4⋅1069.8=2⋅(3+14100)⋅6+410⋅106⋅19+810=2⋅(3+750)⋅6+410⋅106⋅19+810=2⋅15750⋅6+410⋅106⋅19+810=2⋅15750⋅6+25⋅106⋅19+810=2⋅15750⋅325⋅106⋅19+810=2⋅15750⋅45⋅10⋅106⋅19+810=2⋅15750⋅45⋅10⋅1000000⋅19+810=2⋅15750⋅45⋅10⋅1000000⋅19+45=2⋅15750⋅45⋅10⋅1000000⋅1495=2⋅15750⋅45⋅10⋅500000049=15725⋅45⋅10⋅500000049=628125⋅10⋅500000049=2512000049⋅10\begin{aligned}\frac{2 \cdot 3.14 \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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