90+7(-2ln(0.4753)^0.5)sin(6.28*0.8741)

asked by guest
on Nov 25, 2024 at 9:25 am



You asked:

Evaluate the expression: \(90 + 7 \cdot -\left( 2 {\ln\left( 0.4753 \right)}^{0.5} \right) \cdot \sin\left( 6.28 \cdot 0.8741 \right)\)

MathBot Answer:

\[90 + 7 \cdot -\left( 2 {\ln\left( 0.4753 \right)}^{0.5} \right) \cdot \sin\left( 6.28 \cdot 0.8741 \right) = 90 - 14 \sqrt{\log{\left(\frac{4753}{10000} \right)}} \sin{\left(\frac{1372337}{250000} \right)}\]

\[\begin{aligned}90 + 7 \cdot -\left( 2 {\ln\left( 0.4753 \right)}^{0.5} \right) \cdot \sin\left( 6.28 \cdot 0.8741 \right)& = 90 + 7 \cdot -1 \cdot 2 \cdot \log{\left(\frac{4753}{10000} \right)}^{\frac{5}{10}} \cdot \sin{\left(\left(6 + \frac{28}{100}\right) \cdot \frac{8741}{10000} \right)}\\& = 90 + 7 \cdot -1 \cdot 2 \cdot \sqrt{\log{\left(\frac{4753}{10000} \right)}} \cdot \sin{\left(\left(6 + \frac{28}{100}\right) \cdot \frac{8741}{10000} \right)}\\& = 90 + 7 \cdot -1 \cdot 2 \cdot \sqrt{\log{\left(\frac{4753}{10000} \right)}} \cdot \sin{\left(\left(6 + \frac{7}{25}\right) \cdot \frac{8741}{10000} \right)}\\& = 90 + 7 \cdot -1 \cdot 2 \cdot \sqrt{\log{\left(\frac{4753}{10000} \right)}} \cdot \sin{\left(\frac{157}{25} \cdot \frac{8741}{10000} \right)}\\& = 90 + 7 \cdot -1 \cdot 2 \cdot \sqrt{\log{\left(\frac{4753}{10000} \right)}} \cdot \sin{\left(\frac{1372337}{25} \cdot \frac{1}{10000} \right)}\\& = 90 + 7 \cdot -1 \cdot 2 \cdot \sqrt{\log{\left(\frac{4753}{10000} \right)}} \cdot \sin{\left(\frac{1372337}{250000} \right)}\\& = 90 - 7 \cdot 2 \cdot \sqrt{\log{\left(\frac{4753}{10000} \right)}} \cdot \sin{\left(\frac{1372337}{250000} \right)}\\& = 90 + -14 \cdot \sqrt{\log{\left(\frac{4753}{10000} \right)}} \cdot \sin{\left(\frac{1372337}{250000} \right)}\\& = 90 - 14 \cdot \sqrt{\log{\left(\frac{4753}{10000} \right)}} \cdot \sin{\left(\frac{1372337}{250000} \right)}\end{aligned}\]

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