58 Найдите неизвестный член пропорции: 1 2 1 a) 3:2=2:t; 27 3 1 6 б) 3: s = 4:1; 3 7 2 1 B) y: = 8:2; 3 6 5 7 г) : = z:12

a) $$\frac{3\frac{1}{2}}{2\frac{1}{2}} = \frac{2\frac{1}{3}}{t}$$

$$\frac{\frac{7}{2}}{\frac{5}{2}} = \frac{\frac{7}{3}}{t}$$

$$\frac{7 \cdot 2 \cdot 3 \cdot t}{2 \cdot 5 \cdot 7 \cdot 3} = 1$$

$$\frac{t}{5} = 1$$

$$t = 5$$

б) $$\frac{3\frac{1}{3}}{s} = \frac{4\frac{6}{7}}{1\frac{1}{6}}$$

$$\frac{\frac{10}{3}}{s} = \frac{\frac{34}{7}}{\frac{7}{6}}$$ $$\frac{10 \cdot 7 \cdot 6}{3 \cdot s \cdot 34 \cdot 7} = 1$$

$$\frac{60}{34s} = 1$$

$$34s = 60$$

$$s = \frac{60}{34} = \frac{30}{17} = 1\frac{13}{17}$$

в) $$\frac{y}{\frac{2}{3}} = \frac{8\frac{1}{2}}{2\frac{1}{6}}$$ $$\frac{y}{\frac{2}{3}} = \frac{\frac{17}{2}}{\frac{13}{6}}$$ $$\frac{6 \cdot y \cdot 2 \cdot 13}{3 \cdot 17 \cdot 2 \cdot 13} = 1$$

$$y = \frac{17}{3} = 5\frac{2}{3}$$

г) $$\frac{\frac{5}{7}}{z} = \frac{7}{12}$$ $$\frac{5 \cdot 12}{7 \cdot z \cdot 7} = 1$$

$$z = \frac{60}{49} = 1\frac{11}{49}$$

Ответ: a) t = 5, б) $$s = 1\frac{13}{17}$$, в) $$y = 5\frac{2}{3}$$, г) $$z = 1\frac{11}{49}$$