5.3(39.87)+0.16((39.87-39.9)/(-0.24))^(3/2)

asked by guest
on Mar 16, 2025 at 5:34 am



You asked:

Evaluate the expression: 5.3⋅39.87+0.16(39.87−39.9−0.24)325.3 \cdot 39.87 + 0.16 {\left( \frac{39.87 - 39.9}{-0.24} \right)}^{\frac{3}{2}}

MathBot Answer:

5.3⋅39.87+0.16(39.87−39.9−0.24)32=2200+2113111000≈211.318071067811865475244008443621055.3 \cdot 39.87 + 0.16 {\left( \frac{39.87 - 39.9}{-0.24} \right)}^{\frac{3}{2}} = \frac{\sqrt{2}}{200} + \frac{211311}{1000} \approx 211.31807106781186547524400844362105

5.3⋅39.87+0.16(39.87−39.9−0.24)32=(5+310)⋅(39+87100)+16100⋅((39+87100−(39+910))⋅1−24100)32=5310⋅(39+87100)+16100⋅((39+87100−(39+910))⋅1−24100)32=5310⋅3987100+16100⋅((39+87100−(39+910))⋅1−24100)32=2113111000+16100⋅((39+87100−(39+910))⋅1−24100)32=2113111000+16100⋅((39+87100−39910)⋅1−24100)32=2113111000+16100⋅((3987100−39910)⋅1−24100)32=2113111000+16100⋅(−3100⋅1−24100)32=2113111000+16100⋅(−3100⋅1−625)32=2113111000+16100⋅(18)32=2113111000+16100⋅132⋅2=2113111000+425⋅132⋅2=2113111000+1200⋅2\begin{aligned}5.3 \cdot 39.87 + 0.16 {\left( \frac{39.87 - 39.9}{-0.24} \right)}^{\frac{3}{2}}&=\left(5 + \frac{3}{10}\right) \cdot \left(39 + \frac{87}{100}\right) + \frac{16}{100} \cdot \left(\left(39 + \frac{87}{100} - \left(39 + \frac{9}{10}\right)\right) \cdot \frac{1}{- \frac{24}{100}}\right)^{\frac{3}{2}}\\&=\frac{53}{10} \cdot \left(39 + \frac{87}{100}\right) + \frac{16}{100} \cdot \left(\left(39 + \frac{87}{100} - \left(39 + \frac{9}{10}\right)\right) \cdot \frac{1}{- \frac{24}{100}}\right)^{\frac{3}{2}}\\&=\frac{53}{10} \cdot \frac{3987}{100} + \frac{16}{100} \cdot \left(\left(39 + \frac{87}{100} - \left(39 + \frac{9}{10}\right)\right) \cdot \frac{1}{- \frac{24}{100}}\right)^{\frac{3}{2}}\\&=\frac{211311}{1000} + \frac{16}{100} \cdot \left(\left(39 + \frac{87}{100} - \left(39 + \frac{9}{10}\right)\right) \cdot \frac{1}{- \frac{24}{100}}\right)^{\frac{3}{2}}\\&=\frac{211311}{1000} + \frac{16}{100} \cdot \left(\left(39 + \frac{87}{100} - \frac{399}{10}\right) \cdot \frac{1}{- \frac{24}{100}}\right)^{\frac{3}{2}}\\&=\frac{211311}{1000} + \frac{16}{100} \cdot \left(\left(\frac{3987}{100} - \frac{399}{10}\right) \cdot \frac{1}{- \frac{24}{100}}\right)^{\frac{3}{2}}\\&=\frac{211311}{1000} + \frac{16}{100} \cdot \left(- \frac{3}{100} \cdot \frac{1}{- \frac{24}{100}}\right)^{\frac{3}{2}}\\&=\frac{211311}{1000} + \frac{16}{100} \cdot \left(- \frac{3}{100} \cdot \frac{1}{- \frac{6}{25}}\right)^{\frac{3}{2}}\\&=\frac{211311}{1000} + \frac{16}{100} \cdot \left(\frac{1}{8}\right)^{\frac{3}{2}}\\&=\frac{211311}{1000} + \frac{16}{100} \cdot \frac{1}{32} \cdot \sqrt{2}\\&=\frac{211311}{1000} + \frac{4}{25} \cdot \frac{1}{32} \cdot \sqrt{2}\\&=\frac{211311}{1000} + \frac{1}{200} \cdot \sqrt{2}\end{aligned}

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