1) 1/ 3 ÷ 1 /9 = 1 /3 × 9/ 1 = 1·9/3·1 = 9/ 3 = 3 · 3 /3 = 3 = 3
2)3/ 8 ÷ 1 /2 = 3 /8 × 2/ 1 = 3·2 /8·1 = 6/ 8 = 3 · 2/ 4 · 2 = 3/ 4 = 0.75
3)4 /9 ÷ 8 /9 = 4 /9 × 9/ 8 = 4·9/ 9·8 = 36 /72 = 1 · 36 /2 · 36 = 1 /2 = 0.5
4)1 /12 ÷ 1/ 6 = 1/ 12 × 6/ 1 = 1·6/ 12·1 = 6 /12 = 1 · 6 /2 · 6 = 1 /2 = 0.5
5)3 /5 ÷ 1 /25 = 3 /5 × 25/ 1 = 3·25/ 5·1 = 75/ 5 = 15 · 5/ 5 = 15
6)2 /7 ÷ 3 /7 = 2 /7 × 7 /3 = 2·7 /7·3 = 14/ 21 = 2 · 7 /3 · 7 = 2 /3
7)1 /10 ÷ 1 /10 = 1 /10 × 10/ 1 = 1·10/ 10·1 = 10/ 10 = 1
8)3 /4 ÷ 5 /8 = 3 /4 × 8 /5 = 3·8 /4·5 = 24 /20 = 6 · 4/ 5 · 4 = 6/ 5 = 1·5 + 1 /5 = 1 / 1 5 = 1.2
всё)
2) KL² =NL*LM² NL =x LM=MN -NL =25 -x;
144 =x(25 -x) ;
x² -25x +144 =0;
x = 9
x=16 (по рисунку NL < LM )
ΔKLN : NK² =NL²+ LK²
NK =3*5 =15 (9 =3*3; 12=3*4; 3*5=15)..
ΔKLM : KM² =KL² +LM²
KM =4*5 =20 (12 =4*3; 16=4*4 ;4*5 =20)
3) KE² =EM*EL
EM =KE²/EL =6²/8 =9/2 =4,5
KL² =KE² +EL² =6² +8² =100 =10²
KL =10.
KL² =ML*EL
ML =KL²/EL =100/8 =12,5.;
( 5/EM = ML --EL =12,5 -8 =4,5)
MK² =ML*ME;
MK² =12,5*4,5 =25*0,5*0,5*9;
MK =5*0,5*3 =7,5.
4) MN² =MK² +KN² =5² +²12² =25 +144 =169 =13²;
MN =13;
MK² =MN*MT ;
MT =MK²/MN=5²/13 =25/13.
NT =MN -MT =13 -25/13 =144/13;
KT² =MT*NT=25/13*144/13 =(5*12/13)² ;
KT =5*12/13 =60/13.
или из ΔMTK :
KT² =MK² -MT²² =5² -(25/13)² =(5 -25/13)(5+25/13) =40/13*90/13 =(2*3*10/13)²;
KT =2*3*10/13 =60/13 .
1) 1/ 3 ÷ 1 /9 = 1 /3 × 9/ 1 = 1·9/3·1 = 9/ 3 = 3 · 3 /3 = 3 = 3
2)3/ 8 ÷ 1 /2 = 3 /8 × 2/ 1 = 3·2 /8·1 = 6/ 8 = 3 · 2/ 4 · 2 = 3/ 4 = 0.75
3)4 /9 ÷ 8 /9 = 4 /9 × 9/ 8 = 4·9/ 9·8 = 36 /72 = 1 · 36 /2 · 36 = 1 /2 = 0.5
4)1 /12 ÷ 1/ 6 = 1/ 12 × 6/ 1 = 1·6/ 12·1 = 6 /12 = 1 · 6 /2 · 6 = 1 /2 = 0.5
5)3 /5 ÷ 1 /25 = 3 /5 × 25/ 1 = 3·25/ 5·1 = 75/ 5 = 15 · 5/ 5 = 15
6)2 /7 ÷ 3 /7 = 2 /7 × 7 /3 = 2·7 /7·3 = 14/ 21 = 2 · 7 /3 · 7 = 2 /3
7)1 /10 ÷ 1 /10 = 1 /10 × 10/ 1 = 1·10/ 10·1 = 10/ 10 = 1
8)3 /4 ÷ 5 /8 = 3 /4 × 8 /5 = 3·8 /4·5 = 24 /20 = 6 · 4/ 5 · 4 = 6/ 5 = 1·5 + 1 /5 = 1 / 1 5 = 1.2
всё)
2) KL² =NL*LM² NL =x LM=MN -NL =25 -x;
144 =x(25 -x) ;
x² -25x +144 =0;
x = 9
x=16 (по рисунку NL < LM )
ΔKLN : NK² =NL²+ LK²
NK =3*5 =15 (9 =3*3; 12=3*4; 3*5=15)..
ΔKLM : KM² =KL² +LM²
KM =4*5 =20 (12 =4*3; 16=4*4 ;4*5 =20)
3) KE² =EM*EL
EM =KE²/EL =6²/8 =9/2 =4,5
KL² =KE² +EL² =6² +8² =100 =10²
KL =10.
KL² =ML*EL
ML =KL²/EL =100/8 =12,5.;
( 5/EM = ML --EL =12,5 -8 =4,5)
MK² =ML*ME;
MK² =12,5*4,5 =25*0,5*0,5*9;
MK =5*0,5*3 =7,5.
4) MN² =MK² +KN² =5² +²12² =25 +144 =169 =13²;
MN =13;
MK² =MN*MT ;
MT =MK²/MN=5²/13 =25/13.
NT =MN -MT =13 -25/13 =144/13;
KT² =MT*NT=25/13*144/13 =(5*12/13)² ;
KT =5*12/13 =60/13.
или из ΔMTK :
KT² =MK² -MT²² =5² -(25/13)² =(5 -25/13)(5+25/13) =40/13*90/13 =(2*3*10/13)²;
KT =2*3*10/13 =60/13 .