6.112*EXP((17.67*23.89)/(23.89+243.5))

asked by guest
on Oct 23, 2024 at 3:29 am



You asked:

Evaluate the expression: \(6.112 \cdot {e}^{\frac{17.67 \cdot 23.89}{23.89 + 243.5}}\)

MathBot Answer:

\[6.112 \cdot {e}^{\frac{17.67 \cdot 23.89}{23.89 + 243.5}} = \frac{764 e^{\frac{1407121}{891300}}}{125} \approx 29.63579362679439316403068535750468\]

\[\begin{aligned}6.112 \cdot {e}^{\frac{17.67 \cdot 23.89}{23.89 + 243.5}}& = \left(6 + \frac{112}{1000}\right) \cdot e^{\left(17 + \frac{67}{100}\right) \cdot \left(23 + \frac{89}{100}\right) \cdot \frac{1}{23 + \frac{89}{100} + 243 + \frac{5}{10}}}\\& = \left(6 + \frac{14}{125}\right) \cdot e^{\left(17 + \frac{67}{100}\right) \cdot \left(23 + \frac{89}{100}\right) \cdot \frac{1}{23 + \frac{89}{100} + 243 + \frac{5}{10}}}\\& = \frac{764}{125} \cdot e^{\left(17 + \frac{67}{100}\right) \cdot \left(23 + \frac{89}{100}\right) \cdot \frac{1}{23 + \frac{89}{100} + 243 + \frac{5}{10}}}\\& = \frac{764}{125} \cdot e^{\frac{1767}{100} \cdot \left(23 + \frac{89}{100}\right) \cdot \frac{1}{23 + \frac{89}{100} + 243 + \frac{5}{10}}}\\& = \frac{764}{125} \cdot e^{\frac{1767}{100} \cdot \frac{2389}{100} \cdot \frac{1}{23 + \frac{89}{100} + 243 + \frac{5}{10}}}\\& = \frac{764}{125} \cdot e^{\frac{1767}{100} \cdot \frac{2389}{100} \cdot \frac{1}{23 + \frac{89}{100} + 243 + \frac{1}{2}}}\\& = \frac{764}{125} \cdot e^{\frac{1767}{100} \cdot \frac{2389}{100} \cdot \frac{1}{\frac{2389}{100} + 243 + \frac{1}{2}}}\\& = \frac{764}{125} \cdot e^{\frac{1767}{100} \cdot \frac{2389}{100} \cdot \frac{1}{\frac{26689}{100} + \frac{1}{2}}}\\& = \frac{764}{125} \cdot e^{\frac{1767}{100} \cdot \frac{2389}{100} \cdot \frac{1}{\frac{26739}{100}}}\\& = \frac{764}{125} \cdot e^{\frac{1767}{100} \cdot \frac{2389}{26739}}\\& = \frac{764}{125} \cdot e^{\frac{1407121}{891300}}\end{aligned}\]

\(e\) is Euler's number, a mathematical constant that is approximately \(2.71828\).

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