1) \(3\frac{2}{5} \cdot 2 - 5\frac{3}{4} : 1\frac{11}{12}\) : 3\(\frac{1}{6}\) - 4\(\frac{4}{5}\) : 9 + 2\(\frac{2}{3}\); 2) [40 - \(4.25 \cdot 7.08 + 6.768 : 0.75\)] \(\cdot\) 2050.

Решение:

1. Первое выражение: \( \left( 3\frac{2}{5} \cdot 2 - 5\frac{3}{4} : 1\frac{11}{12} \right) : 3\frac{1}{6} - 4\frac{4}{5} : 9 + 2\frac{2}{3} \)
• \( 3\frac{2}{5} \cdot 2 = \frac{17}{5} \cdot 2 = \frac{34}{5} = 6\frac{4}{5} \)
• \( 5\frac{3}{4} : 1\frac{11}{12} = \frac{23}{4} : \frac{23}{12} = \frac{23}{4} \cdot \frac{12}{23} = \frac{12}{4} = 3 \)
• \( 6\frac{4}{5} - 3 = 3\frac{4}{5} \)
• \( 3\frac{4}{5} : 3\frac{1}{6} = \frac{19}{5} : \frac{19}{6} = \frac{19}{5} \cdot \frac{6}{19} = \frac{6}{5} = 1\frac{1}{5} \)
• \( 4\frac{4}{5} : 9 = \frac{24}{5} : 9 = \frac{24}{5} \cdot \frac{1}{9} = \frac{8}{15} \)
• \( 1\frac{1}{5} - \frac{8}{15} = \frac{6}{5} - \frac{8}{15} = \frac{18}{15} - \frac{8}{15} = \frac{10}{15} = \frac{2}{3} \)
• \( \frac{2}{3} + 2\frac{2}{3} = \frac{2}{3} + \frac{8}{3} = \frac{10}{3} = 3\frac{1}{3} \)
2. Второе выражение: \( \left[ 40 - \left( 4.25 \cdot 7.08 + 6.768 : 0.75 \right) \right] \cdot 2050 \)
• \( 4.25 \cdot 7.08 = 30.09 \)
• \( 6.768 : 0.75 = 9.024 \)
• \( 30.09 + 9.024 = 39.114 \)
• \( 40 - 39.114 = 0.886 \)
• \( 0.886 \cdot 2050 = 1816.3 \)

Ответ: 1) \( 3\frac{1}{3} \); 2) \( 1816.3 \).