3.58 Найдите неизвестный член пропорции: 1 a) 3:2 = 2:t; 2: t; 7 6) б) 3:8 = 4:1; B) y: 2 = 8:2 3 6 )5:윽-2:

а) $$3:2\frac{1}{2} = 2\frac{1}{7} : t$$

$$3 : \frac{5}{2} = \frac{15}{7} : t$$

По основному свойству пропорции:

$$3 \cdot t = \frac{5}{2} \cdot \frac{15}{7}$$

$$3t = \frac{75}{14}$$

$$t = \frac{75}{14} : 3$$

$$t = \frac{75}{14} \cdot \frac{1}{3}$$

$$t = \frac{25}{14} = 1\frac{11}{14}$$

б) $$3:8 = 4\frac{1}{2} : t$$

$$3:8 = \frac{9}{2} : t$$

По основному свойству пропорции:

$$3 \cdot t = 8 \cdot \frac{9}{2}$$

$$3t = 36$$

$$t = 36:3$$

$$t = 12$$

в) $$y:\frac{2}{3} = 8 : 2\frac{1}{6}$$

$$y:\frac{2}{3} = 8 : \frac{13}{6}$$

По основному свойству пропорции:

$$y \cdot \frac{13}{6} = \frac{2}{3} \cdot 8$$

$$y \cdot \frac{13}{6} = \frac{16}{3}$$

$$y = \frac{16}{3} : \frac{13}{6}$$

$$y = \frac{16}{3} \cdot \frac{6}{13}$$

$$y = \frac{32}{13} = 2\frac{6}{13}$$

г) $$5\frac{1}{7} : \frac{6}{7} = z:\frac{12}{17}$$

$$\frac{36}{7} : \frac{6}{7} = z:\frac{12}{17}$$

По основному свойству пропорции:

$$\frac{36}{7} \cdot \frac{12}{17} = \frac{6}{7} \cdot z$$

$$\frac{6}{7} z= \frac{36}{7} \cdot \frac{12}{17}$$

$$z = (\frac{36}{7} \cdot \frac{12}{17}) : \frac{6}{7}$$

$$z = (\frac{36}{7} \cdot \frac{12}{17}) \cdot \frac{7}{6}$$

$$z = \frac{36}{6} \cdot \frac{12}{17} = 6 \cdot \frac{12}{17} = \frac{72}{17} = 4\frac{4}{17}$$

Ответ: а) $$t = 1\frac{11}{14}$$; б) $$t = 12$$; в) $$y = 2\frac{6}{13}$$; г) $$z = 4\frac{4}{17}$$