((0.9^2/34+1.1^2/34)^2)/(1/33)*(0.9^2/34)^2+(1/33)*(1.1^2/34)^2

asked by guest
on Oct 21, 2024 at 4:47 am



You asked:

Evaluate the expression: \(\frac{{\left( \frac{{0.9}^{2}}{34} + \frac{{1.1}^{2}}{34} \right)}^{2}}{\frac{1}{33}} \cdot {\left( \frac{{0.9}^{2}}{34} \right)}^{2} + \frac{1}{33} \cdot {\left( \frac{{1.1}^{2}}{34} \right)}^{2}\)

MathBot Answer:

\[\frac{{\left( \frac{{0.9}^{2}}{34} + \frac{{1.1}^{2}}{34} \right)}^{2}}{\frac{1}{33}} \cdot {\left( \frac{{0.9}^{2}}{34} \right)}^{2} + \frac{1}{33} \cdot {\left( \frac{{1.1}^{2}}{34} \right)}^{2} = \frac{10472537339}{100225200000000} \approx 0.00010449006177089195132561471566\]

\[\begin{aligned}\frac{{\left( \frac{{0.9}^{2}}{34} + \frac{{1.1}^{2}}{34} \right)}^{2}}{\frac{1}{33}} \cdot {\left( \frac{{0.9}^{2}}{34} \right)}^{2} + \frac{1}{33} \cdot {\left( \frac{{1.1}^{2}}{34} \right)}^{2}& = \left(\left(\frac{9}{10}\right)^{2} \cdot \frac{1}{34} + \left(1 + \frac{1}{10}\right)^{2} \cdot \frac{1}{34}\right)^{2} \cdot \frac{1}{\frac{1}{33}} \cdot \left(\left(\frac{9}{10}\right)^{2} \cdot \frac{1}{34}\right)^{2} + \frac{1}{33} \cdot \left(\left(1 + \frac{1}{10}\right)^{2} \cdot \frac{1}{34}\right)^{2}\\& = \left(\frac{81}{100} \cdot \frac{1}{34} + \left(1 + \frac{1}{10}\right)^{2} \cdot \frac{1}{34}\right)^{2} \cdot \frac{1}{\frac{1}{33}} \cdot \left(\left(\frac{9}{10}\right)^{2} \cdot \frac{1}{34}\right)^{2} + \frac{1}{33} \cdot \left(\left(1 + \frac{1}{10}\right)^{2} \cdot \frac{1}{34}\right)^{2}\\& = \left(\frac{81}{3400} + \left(1 + \frac{1}{10}\right)^{2} \cdot \frac{1}{34}\right)^{2} \cdot \frac{1}{\frac{1}{33}} \cdot \left(\left(\frac{9}{10}\right)^{2} \cdot \frac{1}{34}\right)^{2} + \frac{1}{33} \cdot \left(\left(1 + \frac{1}{10}\right)^{2} \cdot \frac{1}{34}\right)^{2}\\& = \left(\frac{81}{3400} + \left(\frac{11}{10}\right)^{2} \cdot \frac{1}{34}\right)^{2} \cdot \frac{1}{\frac{1}{33}} \cdot \left(\left(\frac{9}{10}\right)^{2} \cdot \frac{1}{34}\right)^{2} + \frac{1}{33} \cdot \left(\left(1 + \frac{1}{10}\right)^{2} \cdot \frac{1}{34}\right)^{2}\\& = \left(\frac{81}{3400} + \frac{121}{100} \cdot \frac{1}{34}\right)^{2} \cdot \frac{1}{\frac{1}{33}} \cdot \left(\left(\frac{9}{10}\right)^{2} \cdot \frac{1}{34}\right)^{2} + \frac{1}{33} \cdot \left(\left(1 + \frac{1}{10}\right)^{2} \cdot \frac{1}{34}\right)^{2}\\& = \left(\frac{81}{3400} + \frac{121}{3400}\right)^{2} \cdot \frac{1}{\frac{1}{33}} \cdot \left(\left(\frac{9}{10}\right)^{2} \cdot \frac{1}{34}\right)^{2} + \frac{1}{33} \cdot \left(\left(1 + \frac{1}{10}\right)^{2} \cdot \frac{1}{34}\right)^{2}\\& = \left(\frac{101}{1700}\right)^{2} \cdot \frac{1}{\frac{1}{33}} \cdot \left(\left(\frac{9}{10}\right)^{2} \cdot \frac{1}{34}\right)^{2} + \frac{1}{33} \cdot \left(\left(1 + \frac{1}{10}\right)^{2} \cdot \frac{1}{34}\right)^{2}\\& = \frac{10201}{2890000} \cdot \frac{1}{\frac{1}{33}} \cdot \left(\left(\frac{9}{10}\right)^{2} \cdot \frac{1}{34}\right)^{2} + \frac{1}{33} \cdot \left(\left(1 + \frac{1}{10}\right)^{2} \cdot \frac{1}{34}\right)^{2}\\& = \frac{10201}{2890000} \cdot 33 \cdot \left(\left(\frac{9}{10}\right)^{2} \cdot \frac{1}{34}\right)^{2} + \frac{1}{33} \cdot \left(\left(1 + \frac{1}{10}\right)^{2} \cdot \frac{1}{34}\right)^{2}\\& = \frac{10201}{2890000} \cdot 33 \cdot \left(\frac{81}{100} \cdot \frac{1}{34}\right)^{2} + \frac{1}{33} \cdot \left(\left(1 + \frac{1}{10}\right)^{2} \cdot \frac{1}{34}\right)^{2}\\& = \frac{10201}{2890000} \cdot 33 \cdot \left(\frac{81}{3400}\right)^{2} + \frac{1}{33} \cdot \left(\left(1 + \frac{1}{10}\right)^{2} \cdot \frac{1}{34}\right)^{2}\\& = \frac{10201}{2890000} \cdot 33 \cdot \frac{6561}{11560000} + \frac{1}{33} \cdot \left(\left(1 + \frac{1}{10}\right)^{2} \cdot \frac{1}{34}\right)^{2}\\& = \frac{336633}{2890000} \cdot \frac{6561}{11560000} + \frac{1}{33} \cdot \left(\left(1 + \frac{1}{10}\right)^{2} \cdot \frac{1}{34}\right)^{2}\\& = \frac{2208649113}{33408400000000} + \frac{1}{33} \cdot \left(\left(1 + \frac{1}{10}\right)^{2} \cdot \frac{1}{34}\right)^{2}\\& = \frac{2208649113}{33408400000000} + \frac{1}{33} \cdot \left(\left(\frac{11}{10}\right)^{2} \cdot \frac{1}{34}\right)^{2}\\& = \frac{2208649113}{33408400000000} + \frac{1}{33} \cdot \left(\frac{121}{100} \cdot \frac{1}{34}\right)^{2}\\& = \frac{2208649113}{33408400000000} + \frac{1}{33} \cdot \left(\frac{121}{3400}\right)^{2}\\& = \frac{2208649113}{33408400000000} + \frac{1}{33} \cdot \frac{14641}{11560000}\\& = \frac{2208649113}{33408400000000} + \frac{1331}{34680000}\\& = \frac{10472537339}{100225200000000}\end{aligned}\]

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