3) так как в периоде должно быть 0,(90)
20 * 4 = 80 км - длина всего пути
80 * 5/16 = 25 км прошел турист в первый день
25 - 20 = на 5 км больше турист прошел в первый день, чем планировал
№ 78
1) 3/4 : 5/7 = 3/4 * 7/5 = 21/20 = 1 1/20
2) 5/18 : 25/27 = 5/18 * 27/25 = 1/2 * 3/5 = 3/10
3) 9/16 : 3/64 = 9/16 * 64/3 = 3/1 * 4/1 = 3/4
4) 25/72 : 45/63 = 25/72 * 63/45 = 5/8 * 7/9 = 35/72
№ 79
8 : 4/5 = 8/1 * 5/4 = 2 * 1 = 2
1 : 7/16 = 1/1 * 16/7 = 16/7 = 2 2/7
8/15 : 24 = 8/15 * 1/24 = 1/15 * 1/3 = 1/45
12 1/2 : 3 3/4 = 25/2 : 15/4 = 25/2 * 4/15 = 5/1 * 2/3 = 10/3 = 3 1/3
1 3/5 : 5 1/3 = 8/5 : 16/3 = 8/5 * 3/16 = 1/5 * 3/2 = 3/10 = 0,3
2 5/8 : 7/32 = 21/8 : 7/32 = 21/8 * 32/7 = 3/1 * 4/1 = 12
№ 80
1) 2 1/4 : 3/8 : 1/ 2 = 9/4 * 8/3 * 2/1 = 3/1 * 2/1 * 2/1 = 12
2) 2 1/4 : (3/8 : 1/2) = 9/4 : (3/8 * 2/1) = 9/4 : 6/8 = 9/4 * 8/6 = 3/1 * 2/2 = 3
3) (6 3/4 - 5 1/8 : 1 9/32) : 2 1/5 = 5/4 = 1 1/4
1) 5 1/8 : 1 9/32 = 41/8 : 41/32 = 41/8 * 32/41 = 1/1 * 4/1 = 4
2) 6 3/4 - 4 = 6 3/4 - 3 4/4 = 5 7/4 - 3 4/4 = 2 3/4
3) 2 3/4 : 2 1/5 = 11/4 : 11/5 = 11/4 * 5/11 = 5/4
4) (3 1/4 + 2 1/6) : 2 3/5 - 2/3 : 4/9 = 11
1) 3 1/4 + 2 1/6 = 3 3/12 + 2 2/12 = 5 5/12
2) 5 5/12 : 2 3/5 = 65/12 : 13/5 = 65/12 * 5/13 = 5/12 * 5/1 = 25/2
3) 2/3 : 4/9 = 2/3 * 9/4 = 1/1 * 3/2 = 3/2
4) 25/2 - 3/2 = 22/2 = 11
№ 81
1) 6/5х = 3/5
х = 3/5 : 6/5
х = 3/5 * 5/6
х = 1/2
2) 4/7х = 1
х = 1 : 4/7
х = 7/4 = 1 3/4
3) 3/4х = 12
х = 12 : 3/4
х = 12/1 * 4/3
х = 16
4) 3х = 2/3
х = 2/3 : 3
х = 2/3 * 1/3
х = 2/9
5) х : 7/15 = 15/28
х = 15/28 * 7/15
х = 1/4
6) 5 1/4 : х = 7/8
х = 5 1/4 : 7/8
х = 21/4 : 7/8
х = 21/4 * 8/7
х = 3/1 * 2/1
х = 6
*-умножение, cos^2-квадрат
Рассмотрим левую часть:
16sin^4a-(sin^2a-3cos^2a)^2=16sin^4-(sin^4a-2*sin^2a*3cos^2a+9cos^4a)=16sin^4a-sin^4a+6sin^2a*cos^2a-9cos^4a=15sin^4a+6sin^2acos^2a-9cos^4a=
т.к сos^2+sin^2=1, то cos^2=1-sin^2 значит
=15sin^4a+6sin^2a(1-sin^2a)-9(1-sin^2a)^2=15sin^4a+6sin^2a-6sin^4a-9(1-2sin^2+sin^4a)=15sin^4a+6sin^2a-6sin^4a-9+18sin^2a-9sin^4a=24sin^2a-9
т.о 24sin^2a-9=24sin^2a-9 ч.т.д