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, , . ISBN 978-960-381-362-0
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7x + 3 + 2y + = ( + ) = ( ) . . ) 3 x + 5 x = (3 + 5) x = 8 x ) 5 + 7 = (5 1 + 7) = 11 ) y + 13 y + 5 = (1 + 13) y + 5 = 14 y + 5 , (.) . () . 7x 3y 7 x 3 y 51 (3x 2y) 51 (3 x 2 y)
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: ) 5 3 + 18 = (5 3 + 18) = 20 ) x + 3x 7x 10x = (1 + 3 7 + 10) x = 7x ) 4 + 5x + 2x = (4 1) + (5 + 2) x = 3 + 7x ) y 3 8y + 6 2 = (1 8) y + (3 + 6) 2 = 7y + 3 2
2) = 2 (x 2y + 1) 3(2x y 3) 4x x = 1 y = 1 : = 2 (x 2y + 1) 3 (2x y 3) 4x = 2x 4y + 2 6x + 3y + 94x = (2 6 4)x + (4 + 3)y + 11 = 8x y +11 O x = 1 y = 1 : = 8 (1) 1 + 11 = 8 1 + 11 = 18 3) = 17 [5 + 3 + ( + 9)] + = 12 = 17 (5 + 3 + ( + 9) = = 17 (5 + 3 + 9) = = 17 + 5 + 3 + 9 = = ( + ) = ( 12) = 12 4) ,
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: 7 (x + 5) = 2(x 1) 3 7x + 35 = 2x 2 3 ( ) 7x 2x = 2 3 35 ( ) 5x = 40 ( ) ( ) x = 8 3) : : =3 ( , = 3) (y + 1) ( 2y + 1) = 21 y + 1 2y 1 = 21 ( ) y 2y = 21 1 + 1 ( ) y = 21 ( ) ( ) y = 21 4) : :
24
3 (3x 1) 2 (2x 5) = 1 (5x + 1) 9x 3 4x + 10 = 5x + 5 9x 4x 5x = 5 + 3 10 0x = 2
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25
, . : = 0 = 0 = 0 . : (x 2) (3x 5) (7 + 4x) = 0 x 2 = 0 3x 5 = 0 7 + 4x = 0 x=2 3x = 5 4x = 7
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33
9. i) m ii) r 10. V = V0(1 + a ) . 11. F = 1,8C + 32, F C . C C F = 73,4. 12. = 2(x + y), x y . x y. : ) x 56cm y = 10cm ) T y 148cm x = 46cm.
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217
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94,2 = 2 3,14 94,2 =6,28 =
= 15cm
= 2 = 3,14 152 = 3,14 225 = 706,5cm2. 2) To 50,24cm2. . : E = 2 50,24 = 3,14 2 2 = = = 4cm. : L= 2 = 2 3,14 4 = 25,12cm. 3) 50m. 4m. m2 . 1 = 4m 2=50m 2=25m .. = .. = 3,14 (252-42) .. = 3,14 (225 16)=3,14 209=656,26m2 2 = 16
3
25m 4m
1) : L 2cm 25,12cm 153,86cm2
t t t t t
2) . , :
225
: 2 : 4 : 8 : . 3) L, : : : : :
. 4) 4 cm, : : = 2 L : = 4L : E = L : = .
t t t t t
1. 1256 cm2. 2. 81,64m. 3. (,) = 3 cm. (,).
4. .
5cm
3cm
A
5. . (=4 cm = 3 cm)
4cm M 3cm B
226
6. 32cm2. .
7. 16cm. . 8. 615,44cm2 . .
3
9. . R .
R
10. .
8cm
u
3.6 O Y E
ttt0
.
A
B
.. : .. = rad : .. =
227
. , = =
0 A B
t t t t t
1) 94,2 cm, 120. : L = 2 94,2 = 2 3,14 94,2 = 6,28 = = 15cm
: .. = 2) . : =
10cm A 90 10cm B
228
3
= 78,5 50 = 28,5cm2A 12cm
3) . .
3cm E2 6cm
E1
E3
B
12cm
3cm
=12 cm, 1 6 cm
= 6cm, 2 3cm
3
E = 1 + 2 + 3 = 56,52 + 14,13 + 108 = 178,65 cm2.
t t t t t
1) 16cm. 45 : : 8 (cm2) B: 16 (cm2) : 24 (cm2) : 32 (cm2) . 2) 4,71cm2 3cm, : : 90 : 45 : 60 : 120 3) , :
229
: 4
:
:
: 2
4) () () . ) ) ) 2x A 1 0 x 2 B
) 1 = 2 )
1. .
t t t t t
.
2. 120 84,78cm2. . 3. 1519,76cm2. 72. 4. 30 L
.
5. 12 cm = 60. N : ) ) ) .A
60 12cm B
230
6. (,10cm) = 60.
A 60 0
3
7. 1 = 5cm 2 = 12cm. .
0 A 60
8. .(A = 10cm, = 4cm).A 10cm A 4cm
9.
A
10. , 10 cm.
11. ( = 90) = = 6 cm. .
A
231
12. . : ) . ) . ) .
5cm 5cm
5cm 5cm
13. .
5cm 5cm 5cm
5cm
14. 8 cm.
15. ( = ) = 120, = 3 cm. = . ) . ) .
3cm
3cm
232
1
t t t t t
1 ) ; ) , ; ) : 90 360 180 60 45 2 . . x + 10
3
A x + 20
0 2x + 10
3 62,8 cm. . ;A
4 12cm. .
233
2 1 ) ; ) : 72 3 6
t t t t t
140
2 x, y, z :A 120 100 50 x z y y x 60 z 0 40
3 . , 10m2 1 ;
10m
30m
50m
234
4 = 6 cm. 6 cm .
) ) . ) .
A 6cm 6cm 6cm
3
235
4
4
4.1 , , . (p, q, r).
p
. p , , p.
, . . , .p q p q
: . . 1 2 , :
239
, . 1//2. , . , . 1 2 .
2 1 p 2 p 1
2 1
q, : , q. , q. , q. , . q, , q. .
q
A
B
q
q
p
A
q
240
p q, p q.
p
4
q
6cm 3cm
1) .
3cm
4cm
, 2 = 2 + 2 2 = 62 + 42 2 = 36 + 16 2 = 52 = , 2=2+2 2=32+ 2=9+52 2=61 = 2) : ) ) ) 5cm 8cm
6cm
) , : 2 = 2 + 2 2 = 82 + 62 2 = 64 + 36 2 = 100 = = 10cm. ) : 2 = 2 + 2 2 = 52 + 102 2 = 25 + 100 2=125 = 11,18 cm.
241
) :
() (): 1) . 2) . 3) . 4) , , . 5) . 6) . 7) p, .
1. : ) ) ) .
3cm 4cm
2. .
242
12cm
3. , q =17 cm =12cm. =12 cm, .
4
q
4. : ) ) )
8cm 12cm
9cm
5. . . , , .
6m 5m 4m
6. . ( = 18cm, = 10cm, = 28cm)
4.2 , , . ,
243
. , . . , , ... , , ...
. = ( ) () . = + 2
, . . . , .
0
0
244
, : = 2 : = + 2 = 2 = 22
p
4
p
A
1) , =9 cm, =12cm 10cm.
9cm
12cm
10cm
: 2 = 2 + 2 2 = 92 + 122 2 = 81 + 144 2 = 225 = 15 cm : = ( ) () = (9+12+15) 10 = 36 10 = 360 cm2 = + 2 = 360 + 2 = 360 + 108 = 468 cm2.
245
2) . 5m 3m.
5cm 30cm 5cm
, : = 2 = 2 3,14 5 30 = 942cm2 = 0,0942m2 : = 5 3 = 15m2 : 15 : 0,0942 159 .
: 1) : ) : 5 : 6 : 7 ) : 8 : 6 : 9 ) : 12 : 9 : 6 2) 8cm 5cm. 9cm, : ) : : 117cm2 : 162cm2 : 234cm2 ) : : 314cm2 : 242cm2 : 157cm2 3) 10cm 10cm. ) : : 314cm2 : 942cm2 : 628cm2 ) : : 1256cm2 : 628cm2 : 1884cm2
246
1. 80cm, 40cm 30cm. 2. 25m , 15m 2,5m . : ) ) 25cm 0,30. 3. =192cm2 8cm. .
4
4. ( ) . , 1m2 15.0,4m
45cm 0,8m 60cm 1,2m 0,4m
5. 16cm 8cm. 6. 50,24cm 20cm. . 7. , 50 , 1,50m 0,20m 3 1m2. 8. , : ) 4m 3m. ) 37,68cm 12cm. ) 78,5 cm2 10cm.
247
9. 1000 1,2m 80cm. , 10% 1m2 1,5; 10. 30cm 60cm. ) . ) 10m 18m. .
4.3 , . (m3), 1m. : m3 dm3 cm3 mm3 1dm3 = 0,001m3 1cm3 = 0,000001m3 1mm3 = 0,000000001m3
(1L=1dm3) m (1ml=1cm3). . V= ( ) ()
248
.
V= ( ) () V= 2
4
1) 8cm 12cm. = 8cm, = 4cm. : V=2 = 3,14 42 12 = 602,88cm3. 2) 87,92 cm 10cm. L = 2 87,92 = 2 3,14 87,92 = 6,28 = =14cm. V = 2 = 3.14 142 10 = 6.154,4cm3. 3) = 6cm, = 8cm 20cm. : ) ) ) ) . ) : 2 = 2 + 2 2 = 62 + 82 2 = 36 + 64 2 = 100 = = 10cm. ,
249
, . ==10 =5cm. ) : V = 2 = 3,14 52 20 = 1570 cm3. ) : V = ( ) () V= ) : V = 1570 480 = 1090cm3.
1) , , . 25cm2 4cm 144cm3 16cm2 50cm 160dm3
2) , , . 25 cm2 8cm 294 cm3 49 cm2 4cm 314cm3
250
3) () (). ) ) ) V = 2
1. . 135cm3, : ) ) . 2. = 12cm = 16cm . : ) ) ) . 3. . = 2m, = 24cm, = 50cm 2m = 30cm. : ) 50cm =24cm ) 30cm ) .
4
4. ( = = 5cm) 4cm. 15cm, : ) ) . 5. : ) 30 cm 0,8m ) 942mm 0,4m. 6. 452,16cm2 24cm. . 7. .
251
70mm 100mm. , . 8. , 10cm. 9. 8m. , 3m 2,5dm.
4.4 O I I , . . . , , , K
. . . , , . , . , .
252
, , . .
: = ( ) ()
4
= + :
V=
( ) ()K
- , , .
1) 8cm. 12cm, . = = ( ) ()
(8 8) 12=384cm2.K
2) .
8cm 5cm 5cm
253
: 2 = 2 + 2 82 = 2 + 2,52 2 = 64 6,25 2 = 57,75 = : = ( ) () = (4 5) 7,6 = 76cm2.
: = + = 76 + 52 = 101cm2. : 2=2+2 2 = 52 + 52 2 = 50 = = =3,55cm.
: 2 = 2 + 2 82 = 2 + 3,552 2 = 64 12,6025 2 = 51,3975 = : V= ( ) ()= 52 7,2=60cm.
1) () (). ) . ) . ) . ) . ) .
254
) , .
4
1. 15cm 20cm. . 2. 12cm 10cm. . 3. 10cm 12cm. : ) ) ) . 4. . 384cm3 8cm 10cm 12cm 12cm 240cm2 10cm
5. 16cm 17cm. 6. 5cm. ( ). : ) ) , 4,1cm. 7. . .
255
8. 8cm 10cm. : ) ) ) ) . 9. = 12cm, , . .
= 8cm
10. : ) ) .
4.5 . . = . p , 0 . . . : 2 = 2 + 2 :
256
=
: = + = + 2 : V= V= 2
4
( ) ()
1) = 15cm 9cm. : V= 2 . 2 = 2 + 2 152 = 92 + 2 2 = 152 92 2 = 225 81 2 = 144 = = 12cm. : V = 3,14 122 9 = 1.356,48cm3.
2) 50,24cm2 5cm. : ) ) . ) : = 2 50,24 = 3,14 2 2 = 16 = 4cm. = = 3,14 4 5 = 62,8cm2 ) 2 = 2 + 2 2 = 2 2 2 = 52 42 2 = 25 16 2 = 9 = =3cm. : V= 2 = 3,14 42 3 = 50,24cm3.
257
3) : ) ) ) ) .
p
) : 2 = 2 + 2 = 2 = 36 = 6cm. p = 2 = 18 + 18
= 2 + 32 2 = 18 9 ) 2 = 2 + p2 2 = 9 = 3cm ) : Eo = + = p + p2 = 3,14 3 28,26cm2 = 28,26 ) : V= p2 = 3,14 32 3 = 28,26cm3. + 3,14 32 = 28,26 +
() (). ) 2 = 2 2. ) . ) V= 2. ) . ) . ) .
258
) . ) .
4
1. 8cm 6cm. 2. To 226,08 m2 = 9 m. .30
3. .p = 3cm
4. 18,84dm. = 5dm. : ) ) .50cm
5. . : ) ) .
5cm 20cm 25cm 20cm
6. . ) . ) 30 m2, 50
12cm
10cm
7. . 19,625m3 3 m. .
259
8.
-
9 cm. (dm3 ). 9. 20 cm . .20cm 20cm
20cm
20cm
10. 6 cm 10cm 15 cm . .
4.6 I I , p (,) . p p . (,). .
p
p
A
260
p
, , . , . . E = 4p2 : V = p3
4
1) = 10cm. . = 10cm, = 4p2 = 4 3,14 52 = 314cm2 V = p3 = 3,14 53 = 523,33cm3
2) 305,08 cm3. :
p3 = 729 p3 = 93 p = 9cm
261
: = 4p2 = 4 3,14 92 = 1017,36cm2. 3) 12cm . . = 12cm, : V = , : V = 123 = 1728cm3 : V = V V= 1728 904,32 = 823,68cm3. 4) 153,86 cm2. . = p2 : 153,86 = 3,14 2 2 = : V = 2 =49
() () 1) . 2) . 3) 4) , .
262
5) , . 6) , .
4
1. = 8cm. . 2. 50,24cm. : ) ) ) . 3. 2cm 3cm. 4. 113,04dm3. N . 5. 18m, m2 5. 6. 1256cm2. . 7. 6cm. 8. 30cm. . 9. = 25cm. : ) ) . 10. = 30cm . :
263
) ) ) 11. = 8cm . .
4.7 , . . 90 90 . () (S). . ( . ) , () (W). 180 180 . . ( ) . ( ) . . , (W) (), () (S).
264
1 1 ) . ) . ) . 2 : ) ) x 12cm 4cm 3cm
4
3 = 6cm = 8cm = 15cm. : ) ) . 4 15cm 16cm. : ) ) .
2 1 ) ; ; ) ; ) . ) . 2 7m 0,4m. , 150 . 3
265
502,4cm2 20cm. : ) ) ) . 4 20cm. .
266
-
11.1 1) 2 4 6 3 , , , t t t t t
1
2) ,
1. ) 5x + 7, x ) = 4x = x2, x ) 3 x, x ) 0,8 x, x ) = 2x + 2(x 5) = 4x 10, x ) x + 10, x
t t t t t
2. ) 9x 4y ) 22 27 ) 2 + 3 ) 3,1x 2,8y ) x 3. ) = 5x 12 + 6x + 8 + 4x = 15x 4 x = 3 = 15 ( 3) 4 = 49 ) = 7 14 6 6 + 5 = 20 + 5 = 7 = 1 = 7 20 ( 1) + 5 = 32 ) = 19 2 + 2 2 + x 12 = 3 + x + 7 x = 5 = 6 = 3 ( 6) + 5 + 7 = 30
269
~
4. ) = 5 10 6 + 9 + 7 = + 7 + = 8 = ( 8) + 7 = 15 ) = x + 6x 2y 4y + 12 + x = 6x 6y + 12 x y = = 6 (x y) + 12 = 6 + 12 = 1 + 12 = 13
) = 3 + x y + + 1 = x y + 4 x + y = 11 = ( 11) + 4 = 15 5. = 2 + 2 = 3 = = 1
= 3(
)(
)1
=
6. = 3x 4y + 5x 7y + 10 9x + 8y = x 3y + 10 = ( 10) 3( = 21 7. ) x = 20 x ) = x(20 x) = 20x x2 x = 10, ) + 10 y=
8. M = x (x ) (x ) = x x + x + = + x
1.2 1) ) 8 ) ) ) ) ) ) 6 ) iv i v ii ) 7 ) ) 69 ) ) 5 ) ) 5 )t t t t t
270
1. ) x = 4 ) x = 3 ) x = 2 ) x = 21 2. ) x = 4 ) y = 1 ) x = ) = 3. ) x [3 + (x x 3)] = 5 x=5 ) x ( 3x 1 5) = 2x 2 x + 3x + 1 + 5 = 2x 2 6x = 8 x=
t t t t t
1
) {2(x 4) 3(x + 1) + [10 2(x + 1) 60]} = 15(x + 1) ( 8 3x 3 + 10 2 60) = 15x + 15 8 + 3x + 3 10 + 2 + 60 = 15x + 15 3x 15x = 15 + 10 8 3 2 60 12x = 48 x=4 4. ) 2(3x + 2) = 3(4x 5) 6x + 4 = 12x 15 6x = 19 ) 21x + 63 15 = 10 40x 61x = 38
) 15x + 15 = 12x 8 27x = 23
271
~
5.
2(6x 4) = 7(1 + 3x) 14x 12x 8 = 7 + 21x 14x 5x = 15 x=3
3(x + 3) 6x + 30 = 2(2x + 2) 3x + 9 6x + 30 = 4x + 4 7x = 35 x=5
3x + 3 2x 30 = 6x 2 5x = 25 x= 5
20x 15 21x 14 = 2 x 140 x = 109
4x 2 5 = 4x + 4 11 0x = 0
6.
3 (3x + 3) + 2(2 2x) = 5x 5 9x + 9 + 4 4x = 5x 5 18x = 18 x=1
5(3y 1) + 5 = 2(y 2) + 5(2y + 5) 15y 5 + 5 = 2y 4 + 10y + 25 3y = 21 y=7
272
13(1 ) + 4(2 4) = 2( + 11) 3 3 + 8 16 = 2 + 22 3 = 35 = 3 + 2( + 3) = 5 + 6 3 + 2 + 6 = 5 + 6 =
7.
144 4 2x = 9 15 18x 12 4 144 8x = 135 18x 48 10x = 57 x = 5,7
4 6 4 + 5 = + 2 24 4 + 5 = + 2 6 = 27
273
~x 10 45 300 = 60x 1 59x = 354
x = 6 8.
2(6x 18) = 30 + 3x 12 12x 36 = 30 + 3x 12 9x = 54 x=6
x 3 9 = 27x + 40 26x = 52 x= 2
274
120 3(5x 1) 2(x + 5) = 144 3(3x + 1) 4(2x + 1) 120 15x + 3 2x 10 = 144 9x 3 8x 4 0x = 24
1
9.
15x 15(2x 1) = 10x + 6 2 15x 30x + 15 = 10x + 12 5x = 3
18 + 6 = 34 6 = 16 =
80x 8 = 66 11x 91x = 72
x=
275
~
7x 3 36x + 12 = 3(7x 15) 7x 3 36x + 12 = 21x 45 7x 36x 21x = 3 12 45 50x = 54
10. ) =
= 20
4 (2x 6) 20 = 5(3x 6) 8x 24 20 = 15x 30 7x = 14 x= 2
) =
276
4x (5x 12) = 12 x 4x 5x + 12 = 12 x x =
1
) =
2 x + 6x 10 = 3x + 18 2x 4x = 26 x=
11. ) (5x 7)(3x + 12) (x 2) = 0 5x 7 = 0 3x + 12 = 0 x= x= 4
x2=0 x=2
) ( x + 3)( 2x 13)(7x + 3) = 0 x + 3 = 0 2x 13 = 0 x=3 x=
7x + 3 = 0 x=
) (x 2) (x2 + 5) = 0 x 2 = 0 x2 + 5 = 0 x=2 x2 = 5
12. (1 x) + 3 = 2x + 5 + ) = 5 : 5(1 x) + 3 = 2x + 5 + 5 5 5x + 3 = 2x + 10 7x = 2 x= ) x = 3, (1 ( 3)) + 3 = 2( 3) + 5 +
277
~
+ 3 + 3 = 6 + 5 + 3 = 4 = ) = 2, 2(1 x) + 3 = 2x + 5 2 2 + 2x + 3 = 2x + 3 0x = 2 13. 7x + 5 = x + (7 )x = 5 ) : = 7 = 5 ) : = 7 = 5 14. ) = 2 ) = 5 ) = 1 ) = 1 15. : 16. : = 3y 5 = 3 y 4y = 8 y = 2 : 2 = 2 + 2 102 = 2 + 62 2 = 100 36 2 = 64 = 8 cm 5x 2 = 8 5x = 10 x = 10 3x + 10 = 4x 10 x = 20 x 20
1.31.t t t t t
278
2. i)
ii)
3. i)
ii)
1
11.
F = 73,4o
12.
279
~
1.4 1) . 2) .t t t t t
1. x , : 5x 5 = 4x + 9 x = 13 2. x , : x + (x + 2) + (x + 4) = 69 3x = 63 x = 21 : 21, 23, 25 3. x , : = 12
t t t t t
4x + 3x = 1092 7x = 1092 x = 156 4. x , x + 18 , 5x = 2x + 36 3x = 36 x = 12
12 18. 5. x , : 125 = x 17 + 6 17 x = 125 6 x=7
17 x = 119
280
6. x , 20 x, : 6x 3(20 x) = 75 6x 60 + 3x = 75 9x = 135 x = 15 7. x , 4x, x + 4x = 90 5x = 90 x = 18 18 4 18 = 72 8. x , 3x 2 (3x) = 6x. : 6x + 3x + x = 400 10x = 400 x = 40 6 40 = 240, 3 40 = 120 40. 9. x , x + 27. : x + (x + 27) + (x + 27) = 180 3x + 54 = 180 3x = 126 x = 42A x
1
B
x + 27 x + 27
10. x , : (x + 2) x = x2 + 50 x2 + 2x = x2 + 50 2x = 50 x = 25 cm 11. x , 60 x , : x(60 x) = (x 10)(60 x + 10) 100 60x x2 = (x 10) (70 x) 100 60x x2 = 70x x2 700 + 10x 100 20x = 800 x = 40 = 40 cm = 20 cm
281
~
12. x , 50 x, : x + 8 = 2(50 x + 8) x + 8 = 100 2x + 16 3x = 108 x = 36 36 14 . 13. x . 48 + x = 2 (18 + x) 48 + x = 36 + 2x x = 12 x = 12 14. x y , x 5 = 2(y 5) x = 2y 10 + 5 x = 2y 5 (x + 10) = y + 10
5x + 50 = 7y + 70
2y 5 = 10y 25 = 7y 20 3y = 45 y = 15 x = 2 15 5 = 25 25 15 . 15. x , 13 x . : 2,5x = 4(13 x) 2,5x = 52 4x 6,5x = 52 x = 8 8 2,5 = 20Km. 16. x , 80 (x + 1) = 100 x 80x + 80 = 100 x
282
20x = 80 x = 4 1.. 512 400 = 112Km . 17. x , :
1
x = 1.800 720
630
450
18. x , x 7. : 2x + 2(x 7) = 66 2x + 2x 14 = 66 4x = 80 x = 20 = 20cm = 13cm. 19. x , 3x. : 240 = 4x 10 40x = 240 x = 6cm 6cm 3 6 = 18cm
283
~
20. x , 48 x. : 2 x + 3(48 x) = 114 2x + 144 3x = 114 x = 30 x = 30 48 30 = 18 . 21. x , 12 x . : 1,5 x + 3 (12 x) = 30 1,5x + 36 3x = 36 1,5x = 6 x=4 4 12 4 = 8. 22. x, 2x 6 : 2x 6 = 3(x 6) 2x 6 = 3x 18 x = 12 12 24 . 23. 8 , 1 .
6 , . x , EK = 24
4x 3x = 24 x = 24 . 24. x , :
284
1x + 2x + 3x = 6 6x = 6 x = 1 . 25. x , 12(x + 0,5) = 14 x + 1 12x + 6 = 14 x + 1 2x = 5 x = 2,5 26. x ,
400 + 60 = 8x 460 = 8x x = 57,5% 27. x , :
24 .
x = 24
28. x , 16 x. : 5 x = 3 (16 x) 5x = 48 3x 8x = 48 x=6 6 .
285
~
1.5 1) ) x 2 10 )t t t t t
)
2) ) 3) . . ) ) i ii ii i
)
)
)
)
)
)
)
)
1. ) x 4 0 18 0 0 0 3 0
t t t t t
+ 4 +
) x < 18
) x >3
+
) x 6
+ 6 +
286
) x
2. ) x >1
0 1
+
) y > 3
3 0
+
1
) 6
0 6
+
) x 3
0 3
+
) x 0
0
+
3. ) x3
+
) x 3
0 3
+
) x 8
0 8
+
+ 0
)
)
+ 0
4. ) 3{x 5[ x (x + 2)]} < 15( x 3) 3[x 5( x x 2)] < 15x 45 3(x + 5x + 5x + 10)< 15x 45
287
~
3(11x + 10) < 15x 45 33x 30 < 15x 45 18x < 15 33x+15x x + 6 9x > 16 0
+
5. )
36x 4(10x 5) 3 (15x + 15) 24x 36x 40x + 20 45x + 45 24x 36x 40x 45x + 24x 45 20 25x 25 x 1
+ 1 0
)
2(2x + 30) 12x < 50 5x 3(x + 6) + 54 4x + 60 12x < 50 5x 3x 18 + 54 4x 12x + 5x + 3x < 50 18 + 54 60 0x < 26 x. 0 +
289
~
) 4 2( + 1) 8 3(3 )> 0 4 2 2 8 3 + > 0 3 > 13 0
+
)
18 + 3(x 2) + 2(x + 1) > 3(x + 5) 18 + 3x 6 + 2x + 2 > 3x + 15 2x > 1 0
+
)
14(2x 26) 21(3x + 5) 6 (2x 4) 210 28x 364 63x 105 12x 24 210 28x 63x 12x 364 + 105 24 210 47x 235 x55 0
+
6. )
290
2(x + 1) + 5x 10x + 20 (3x 4) 2x + 2 + 5x 10x + 20 3x + 4 0x 22 x. ) 5x + 1 3(3x 1) 2(5 2x) 5x + 1 9x + 3 10 4x 0x 6 . ) x + 2 4x > (3x 1) x 4x + 3x > 1 2 0x > 1 x. ) x 3 + 4(x 1) > 5(2 + x) x 3 + 4x 4 > 10 + 5x 0x > 17 . 7. ) x 7 < 2 5 x < 2 x < 9 x > 3 0 3 9 +
1
3 < x < 9 ) 2(x + 3) 3(x + 1) 2(x 1) 2x + 6 3x 3 2x + 2 x 1 1 0 8
3(x 3) + 7 < 2(x + 3) 3x 9 + 7 < 2x + 6 x 3x 24 2x + 3x 21 < 8 2x 1 6x 2 + 15x 40 > 3x 24
291
~
7x < 28 x 18 x >1+ 1 4
1 < x < 4 )
4x 8 + 14 < 3x 15 x < 21 21 0
9x 10 > 8x + 6 x > 16+ 16
) 3x 2 < 13 2(x 3) > 2 3x 5(x 1) 1 3x < 15 2x 6 > 2 3x 5x 5 1 x 4 2x 6 x>2 x3 + 0 2 3 5
3 x < 5
) x>3 6 3 0 2
x6
x2+
3 < x 2 8. ) 11 3x + 2 < 29 11 2 3x < 29 2 9 3x < 27 3xx> 3 ) 9 8x + 1 13 8 8x 12 1x
3 0 1
+
1
0 1
+
9. < 0 5( 2) 30 < 0 5 10 30 < 0 5 < 40 (4 2) 28 5 + 2 > 2 7 > 30
11. x , : 0,40 x > 10 x > 25 25 . 12. x . A x = 13 + 7 () . : 55 < x < 65 55 < 13 + 7 < 65 48 < 13 < 58 3,692 < < 4,46. = 4
x = 13 4 + 7 = 59. 13. x . 3x > 750
293
~
x > 250 x < 252 250 < x < 252 x = 251 251 . 14. x .
x + 16 + 51 + 72 + 76 + 20 > 18 14 x + 235 > 252 x > 17 15. x 2 , 100 + 0,5 x >150 + 0,3 x 0,5x 0,3x > 150 100 0,2x > 50 x > 250
1 1 . ( ) . ) ) ) 2 ) x = 3 . x > .
t t t t t
)
) x > 1
)
4 x
294
5x + 3x + x = 5 180 9x = 900 x = 100
1t t t t t
2 1 ) 2 . x = 7 3 . . = 10 >5 ) ) ) )
. = 2
4 26 .
295
22.1 t t t t t
2
1) ) , ) , ) , ) , ) , ) , ) , ) , ) , ) 2)
3) 4) 5) 6)
1.
t t t t t
2. ) 24 3. = =
) 38
)
) 19 3x 15 0 2 6x 0 x5 x 1/3
297
~4.
= 5x9
x 5 0 6x+54 0 x 5 x 9
5. x = 6,
y = 13,
z = 1,
= 25,
=8
6. ) x = 6 x = 6 ) x = x=
) ) x = 13 x = 13 7. = 2 8. = 40m 9. = 15cm E = 120cm2 10. = 17cm, = 4 17 = 68cm 11. = 24cm = 1008cm2 12. = 24cm = 26cm 13. x , : x2 8 = 14. = 3, 2x2 16 = x2 x2 = 16 x = 4 = 4, = 8, x=6
2.2 1) ) , 2) : ) , ) , ) , ) t t t t t
298
:
1.
t t t t t
2
2. 3.
1
0
1
2
3
4
5
6
7
4. ) x = ) x =
x= x=
)
) x = 1 x = 1
5. x cm . : x2 + x2 = 82 x2 = 32 x = x = 5,65cm
6. =
. = 18cm2
7. = 6,92cm E = 27,68 cm2 8. = 45 .
, = = 4cm : 2 = 42 + 42 2 = 32 = 5,65cm . =
45 4cm
299
~
. = 8= = 2,83cm
9. 2 = 62+122 2 = 180 = 13,41cm = 2 13,41 = 26,82cm 10. . = 16cm . 2 = 2 + 2 162 = 2 + 82 2 = 192 = = 13,85cm = 2 = 2 13,85 = 27,7cm E. = 11. :16cm 16cm
60 16cm 16cm
0
= 16cm 12. = 6cm . : 2 = 2 + 2 = 6,7cm = 6+6+9+6,7 = 27,7cm6m 18m 3m 6m
300
2.31. = 8,696m 2. x = 3cm (1 : 5cm) x= (2 : 5cm 4cm.t t t t t
2
3. 2 = 2 2 2 = 202-162 2 = 144 = 12cm AB2 = 2 + 2 2 = 362+122 2 = 1440 = 37,947cm 4. xcm , x+ = 12,07 2,41x = 12,07 x = 5cm = 20cm = 52 = 25cm2 5. 10 . 6. x2+(3x)2 = 302 x2+9x2 = 900 10x2 = 900 x2 = 90 = 5 x2 = 5 90 = 450cm2 7. 2 = 2 2 2 = 292 212 2 = 400 = 20cm . = 21 20 = 420cm2 8. 2 = 2 2 2 = 1296 = 36cm.
=21,6cm.
9. AB = 8 + 20 + 8 = 36cm 2 = 82 + 82 2 = 128 = =11,31cm 45 A
20cm 8cm 8cm
45 8cm
8cm
301
~
10. 2 = 22 + 42 2 = 20 = 2 = 22 + 42 2 = 20 =
2 = 22 + 62 2 = 40 = 2 = 2 + 2 . . 11. =50m = = 150 50 = 7.500m2 7,5 . 50 7,5 = 375 .
1 1 . ( ) . i) . ( ) 2 ) x 3 ) x 4 3 ) =8cm ii)
t t t t t
) =120cm2
4 = 15m =76m 12 76 = 912 .
2 1 ) . 7 ) . 4 ) . ) . 4 ) .
t t t t t
302
2 ) 125 ) 23 ) 153 ) 3 = = 4 x = 4cm, y = 6cm, =
2
303
33.1 1) ) y = 1,1x 2) ) y =x 4000 3) ) 4) ) = 20 + 5xt t t t t
3
1. x y 2. x y 3. x y 3 30 1 12 0 6 2 0 5 6 2 5 1 1 0 3 1 1 2 5 1 2 0 1 1 3 4 4
t t t t t
4. y = 1,19 x 5. y = 200 + 0.5 x x y 100 250 200 300 300 350 500 450
305
~
6. E = 4x2 7. ) y = 25 x. x = 8 y = 17 ) x = 15 y = 16
8. ) y = 1,05 x x y 900 945 1000 1400 1500 1050 1470 1575
9. y = 2x 3 x y 5 7 2 7 2 1 6 9
10. ) S = 3 450 = 1350 ) S =450 t ) 2.250 = 450 t t = 5 .
3.2 1) (3,4), 2) (3, 7) (5, 6) (1, 4) (8, 10) xx (3, 7) (5, 6) (1, +4) (8, 10) yy (3, 7) (5, 6) (1, 4) (8, 10) 0 (3, 7) (5, 6) (1, 4) (8, 10)t t t t t
(0,3),
(4,3),
(25),
(1,2)
306
3) ) < 4) ) : = 90
3
) : = ) : =2 ) : = 5 .. 5) ) y = 4, ) y = 2, ) y = 1, ) y = 0, ) y = 2, ) y = 3
1. y 3 (4,2 2 (0,2) 1 x 4 3 2 1 0 1 2 2,7 3 4 y 1 2 3 3,5 4
t t t t t
Z(5,0) 5
x 6
E(3,5, 2,7)
2. ) (7,2)
) (7,2)
307
~3.
) (7,2)
) 2 = 2 + 2 20 = 10 + 10 20 = 20 )
4. A (5,2) (-2,4) (-1,0) 5.
xx 2 4 0
yy 5 2 1
6. y = 2x2 x y 2 8 1 2 0 0 1 2 2 8
308
)
y 8 7 6 5 4 3 2 1
)
y 8 7 6 5 4 3 2 1
3
x
2 1 1 y
x 1 2
x
2 1 1 y
x 1 2
x
x
7. (3,15) y = 2x2 + : 15 = 2(3)2 + 15 = 18 + =3 3
8. , 500 , 500 : 400= 1,25 1 1 .4 (3,4)
9. 90 ) 86 80 7768 70 60 50 41 32 20 10
>
>
> > >
>
>
>> 5
10 15 20 25 30
> > > > c
) 10 C F 50 ) 77 F C 25
309
~
10. ) y(Kg)90 81 76,5 72 67,5 63 > > > > > > > > > > > 160 170 180 190 200 210 175 185 > > >
) 175 cm 67,5 ) 76,5 185 cm.x(cm)
3.3 1) ) x y 3 4 6 8 9 12 12 16 )t t t t t
2) : 3) : y= 3x 4) ) 2, ) 1, ) 1, ) 2, ) 1
y
t t t t t
1. )
x y
2 3
4 6
6 9
8 12
)3
310
)
x y
2
x
2. x y
y = 3x 0 0 1 3 x y
y = 5x 0 0y 5 4 3 2 1 x 3 2 1 1 2 3 4 5 y y = 5x y = 2x x 1 2 3 4 y = 3x
y = 2x 1 x y 0 0 1 2
5
3
3.y y = 2x 2 1 x 3 2 1 1 2 y x 1 2 3
y = 2x x y 0 0 1 2 x y 0 0 2 1
.
4. y=x, 6 = (4) = 5. y = 6. 1 : y = 2 : y = y =
311
~
7. t S
S=8t 0 0 1 8
S () S=8t
24 16 8 1 2 3
t ()
8. y= x (3,6) : 6 = 3 = 2 = 2 9. ) y=1,05 x ) x = 850 y = 1,05 850=892,5 ) y = 945 945=1,05 x x = 900 10. ) y =5x ) 52,5 ) 9 11. ) ) =
3.4 1) : y = 7x + 3 2) : (3,0) 3) : (0,7) 4) : 3x 2y = 6 5) ) : ) : (6,0) ) : (0,2)t t t t t
312
1.5 4 3 2 1 x 3 2 1 1 2 3 4 5 y x 1 2 3 4 y 2: y = 2x+3 1: y = 2x 3: y = 2x 2
t t t t t
3
1: y = 2x
x y x y x y
0 0 0 3 0 2
1 2
2: y = 2x + 3
0 1 0
3: y = 2x 2
2. )y 3 2 1 x 1 2 y y =5x+3 1 3 x
)y 3 2 1 x 3 2 1 1 2 y (x 0) x 1 2 3
(x )
313
~
)18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 x 3 2 1 1 2 3 4 5 6 7 8 9 10 11 12 (3 x 3
y
x 1 2 3
y
314
3. 1: y = (5 2)x + 3 2: y = ( + 2)x 9 , : 5 2 = + 2 4 = 4 =1
4. : 5. ) (2,1) (2,4)
3
) (2,1) 3x + 4y = 10 : 3(2) + 4 1 = 10 3x + 4y = 10 (2,4) 3x + 4y = 10 : 3 2 + 4 4 = 10 3x + 4y = 10 6. 4x 3y = 12 xx (3,0) yy (0,4). x 0 (3,0) (0,4) y y
x
7. )
2x + y = 4 x y 0 4 2 0x 0 4
y
2
x
) = 2 ) 8. ) (5,1) ) = (2,1) (2,3) (5,3)
y
315
~
9. y = 5x7, , = 5. y = 2x + y = 5x + . (3,1) ; 1 = 5(3) + = 16. y = 5x + 16. 10. ) y = 0,05x + 800 ) y = 1200 : 1200 = 0,05 x + 800 0,05x = 400 x = 8.000 y )1600 1200 800 400 x y 1000 2000 3000 4000 5000 6000 7000 8000 9000 x y = 0,05x + 800
11. ) y = 80 x 1200
)400 x 400 800 1200
y y = 80 x 1200 x
5
10
15
20
25
y
12. ) t = 0 S=600 80 0 = 600Km ) S = 0 0 = 600 80 t t = 7, 5 ) S600
0
7,5
t
316
13. ) (2,2) : 2 = (3 + 1) 2 + 2 = 6 + 2 + 2 6 = 6 = 1 ) = 1 : y = 2x + 2 x y 0 2 1 0x 2 1 3 2 1 1 2 y x 1 2 3 y
3
14. () y = 5x + 7 2 + 1 = 5 = 3 (1,6) : 6 = [2 (3) + 1] (1) + 3 2 6 = 5 (1) + 3 2 3 = 3 =1 = 3 = 1
3.5 1) ), ), ) 2) ) , ) , ) , ) t t t t t
1. ) x y 6 3 1 1 3 1 3 3 1 6
t t t t t
317
~
y
)3 2 x 6 5 4 3 2 1 1 1 1 2 3 y 2 3 4 5 6 x
2. x y 5 4 2 2 5 4 2,5 5 2y 9 8 7 6 5 4 3 2 1 x 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 x
x y
5 2
4 2,5
2 5
2
4
5
2 2,5 5
5 2,5 2
318
y
3.
x y x y x y
4
2 1
1 2 1 4 3 4
1 2 1 4 3 4
2 1 2 2 4 3
4
3
4 1 6 2
2 2 4 3
4 1 6 2
y
x 0
x
y
4. )
:
3 = 25 ) = 1
2 = 2
=1
319
~
y
x 0
x
y
5. 12 (20 5) = 10 x
x = 18
6. 150 (10 4) = (150 x) 9 900 = 1350 9x 9x = 450 x = 50 .()
7. ) = ) 80 3 60 4 40 6 20 12
12 8 6 4 3 0 10 20 30 40 50 60 70 80 ()
8. ) ) x = 4 ) y = 6 6= 12 x = 8 .
320
1 1 ), ) ( ) 2 y =5x2 7 3 (1,3) x y 0 7 2 13 1 2 4 73 5 118
t t t t t
3
(7,9)
4 (2,2) y = : = 0 x y 4 8 3 2 2y 1 x 5 4 3 2 1 1 2 3 4 5 6 7 8 9 y 1 2 3 4 5 x
x2 +
=0
1
0 0
1
2 2
3
4 8
321
~
2 1 ), ) ( )
t t t t t
2 y = x (3,15) : 15 = (3) = 5 y = 5x 3 ) xx (3,0) yy (0,7) ) =
) 4 , : 6 10 = x 15 60 = 15 x x = 4
3 1 . . ( ) 2 ) y = 1,08 x ) x = 120 : y = 1,08 120 = 129,6 ) y = 216 : 216 = 1,08 x x = 200
t t t t t
322
3 ) y = x
:
3
)
4 y = x + (0,3), 3 = + 12 = 3 + 0 y = 4x = =4 (3,12),
323
44.1 1. ) 2. ) 3. )t t t t t
4
t t t t t
1. ) 130 ) 45 ) 167 ) 18 ) 8 2. ) 3,5 ) 24 ) 56 ) 208 ) 450 3. ) 40% ) 400% ) 100% ) 80% 4. ) 165 5. 40% 60% . 6. "" : 0,3 30%
"" :
0,45 45%
"" :
0,25 25%
7. ) :
0,7 70% 0,35 35%
) :
8. . , . 9. . 200 . .
325
~
4.2 1. ) . 100 ) . 20 ) . 65 ) . 65 ) . 0t t t t t
) . 10%
t t t t t
1. ) : 4.000 + 4.500 + 3.5 00+ 7.000 + 6.000 = 25.000 . ) 2005 : )( ) 8000 7000 6000 5000 4000 3000 2000 1000 2002 2003 2004 () 2005 2006
0,28 28%.
2. ) : :
:
126 72 54 108
:
326
:
) : 3.(gr) 180 250 200 150 100 40 50 A
()
4
: : : :
( )
75 12520
50 90
: :
4. ) 6 + 32 = 38 ) 10 2 ) 10 + 2 = 12 2 ) 64%
327
~
)
36 32 28 24 20 16 12 10 8 6 4 2 0 1 2 3
) 0 : 1 :
1
0
2 :
43,2 230,4 14,4 3 72
2
3 :
5. : 90 : 270
4.3 1) ) . 20 ) . 5 ) . ) .t t t t t
) .
328
2)
40 16 32 48 24 160
. (%) 25 10 20 30 15 100
4
1. 1 2 3 4 5 6 2 4 6 5 2 1 20
t t t t t
. (%) 10 20 30 25 10 5 100
2.
6 2 8 10 8 6 40
. (%) 15 5 20 25 20 15 100
329
~
3. )
. . (%) 26 27 28 29 30 4 6 3 2 1 16 25 37,5 18,75 12,5 6,25 100
) 3 + 2 + 1 = 6 28 ) 4 + 6 + 3 = 13 28 4. ) 0 1 2 3 4 5 6 )(. )
I II III IIII IIII III I
1 2 4 4 5 3 1 20
. (%) 5 10 20 20 25 15 5 100
5 4 3 2 1 0 1 2 3 4 5 5
) 1+2+4+4=11 3 . ) 20% 5 .
330
5. ) . % 30 15 5 50 60 30 10 100 216 108 36 360
4
)30 (. ) 25 20 15 10 5 0 216 108 36
6. + 2 + 126 + 3 + 126 + 72 = 360 3 = 162 = 54 40 60 70 30 200 . (%) 20 30 35 15 100 72 108 126 54 360
331
~
7.
. 0 1 2 3 4
12 10 18 7 3 50
. (%) 24 20 36 14 6 100 56%
) : 28
) : 40
80%
) : 10
20%
) 2 3 : 25
50%
4.4 1) 1. . 4 2. . 14 3. . 8 4. . 20%t t t t t
1. ) = 18 3 = 15 =
t t t t t
332
) 36 69 9 12 12 15 15 18 )10 8 6 4 2 0 3 6 9 12 15 18
IIII IIII III IIII III IIII IIII IIII IIII
4 8 8 10 10 40
. (%) 10 20 20 25 25 100
4
2. ) 33 30 22 15 0 20 30 40 50 60
)
. .
. (%)
20 30 30 40 40 50 50 60
22 30 33 15 100
22 30 33 15 100
) 33% + 15% = 48% 40 .
333
~
3. ) () 50 55 55 60 60 65 65 70 ) 8 . % 7 6 4 3 2 0 50 55 60 65 70
III IIII IIII II IIII I
3 4 7 6 2040 35 30 20 15 10 0
. (%) 15 20 35 30 100
50 55 60 65 70
4. ) () . % 86 () 80 64 60 40 30 20 0 0 50 100 150 200
0 50 15% 30
50 100 43% 86
100 150 32% 64
150 200 10% 20
) 64 + 20 = 84 100 . ) 30 + 86 + 64 = 180 150 .
334
5. ) 8 + 12 + 14 + 10 + 6 = 50 ) 12% 16
4
)
54% .
4.5 1) . 6 4) . 24 2) . 567 3) ) . 25 ) . 27 ) . 23 5) . 360 fit t t t t
1. 2. 3. x , 2x,
t t t t t
35 = 29 + 3x 3x = 6 x = 2 2 4. 4. ) ) : 172, 175, 177, 183, 189, 190, 193, 195
)
335
~
5. 02 24 46 68 8 10 1 3 5 7 9 . 8 12 10 6 4 40 ( ) () 8 36 50 42 36 172
6. :
7. : 1.150 (v + 5) = 1.200v + 5.000 1.150v + 5.750 = 1.200v + 5000 50v = 750 = 15 . 8. y 2 = 14 y = 16
126 = 19x + 88 19x = 38
x=2
336
9. ) 25 35 45 55 ( . . % ) () 15 20 10 5 50 30 40 20 10 100 375 700 450 275 1800
4
20 30 30 40 40 50 50 60
IIII IIII IIII IIII IIII IIII IIII IIII IIII IIII
)
1 1 ), ) ( ) 2 ) 56,25% .
t t t t t
) 3 )
33,33% .
13 14 15 16 17 18 19 20
2 1 3 3 4 2 3 2 20
. . % 10 5 15 15 20 10 15 10 100
337
(. )
~
)5 4 3 2 1 13 14 15 16 17 18 19 19
()
) 2 + 1 + 3 + 3 = 9 16. ) 20% + 10% + 15% + 10% = 55% 17. 4 ) ) : 168, 169, 170, 171, 172, 175, 175, 177, 180, 183
2 1 ), ) ( ) 2 3 )
t t t t t
)
+ 9 + 4 = 19 5 .
338
4 ) : f1 + f2 + 0,3 + f4 = 1 f2 = 2f1 f1 = 2f4 2f4 + 4f4 + 0,3 + f4 = 1 7f4 = 0,7 f4 = 0,1. f1 = 0,2 f2 = 0,4 ) 167 0,2 + 173 0,4 + 179 0,3 + 185 0,1 = = 33,4 + 69,2 + 53,7 + 18,5 =174,8cm.
4
339
11.11. ) 1= 36 ) 1=18 ) 1= 9 2. 2=42 2=21 2=10,5t t t t t
1
3.
1.2 1) 1. B. 450mm2 2. B. 51000cm2 3. . 0,00039dm2 4. . 0,072m2 2) 1. 2,7Km2 = 2.700.000m2 = 2.700 2. 46m2 = 4.600dm2 = 460.000cm2 = 46.000.000mm2 3. 528dm2 = 5,28m2 = 0,00528 4. 7903mm2 = 79,03cm2 = 0,7903dm2 0,007903m2t t t t t
1. 25m2 = 250.000cm2 2,16 Km2 = 21.600.000.000cm2
t t t t t
341
B~
143dm2 = 14.300cm2 5779mm2 = 57,79cm2 712m2 = 7.120.000cm2 2. 498cm2 = 0,0498m2 111dm2 = 1,11m2 12,7Km2 = 12.700.000m2 13.534mm2 = 0,013534m2 607dm2 = 6,07m2 3. 456m2 = 456.000.000mm2 82,7dm2 = 827.000mm2 0,571cm2 = 57,1mm2 0,0025m2 = 2.500mm2 4. 914m2 = 0,000914Km2 4832dm2 = 0,00004832Km2 17075m2 = 0,017075Km2 103 = 0,103Km 5. 72564m = 72,564 3,4Km = 3400 137920dm = 1,3792 45m = 0,045 6. m 98,3 7,56 3,2103 0,738019 dm 9.830 756 321,03 73,8019 cm 983.000 75.600 32103 7380,19 mm 98.300.000 7.560.000 3.210.300 738.019
342
1.3 1) 1. 2. 2) 1. 2. 3. 3. 4. 4. 5. 5. 6. 7. 8. t t t t t
1
1. . . = : 144 = 122 = = 12cm : 4 12 = 48cm.
t t t t t
2. xm , 2x m . : 2 x + 2 2x = 162 2x + 4x = 162 6x = 162 x =27 27m 2 27 = 54m. . = () () = 54 27 = 1458m. 3. , : . = 2 16 25 = 800cm 127 : 127 800 = 101.600cm. 4. . = 46 20 = 920m 300 920 = 276.000g = 276Kg. 2 276 = 552 . 5. . = 8 7 = 56cm = . = 2 8 + 2 7 = 30cm = . . 2 10 + 2 x = 30 2x = 10 x= 5cm 10 1 = 56 5 2 = 56 1 = 5,6cm 2 = 11,2cm. 6. x , 2x :
343
B~
3x 6 = 72
3x = 12
x=4
= 4cm, = 8cm. 7. . () = 18 = 324cm () = 324 = 81cm, (AKB) = 18 x = 162 E() = 324 = 54cm, () = 18 y = 108 81 = x = 9cm
54 = y = 6cm
() = () () () = 324 81 54 =189cm. 8. () = () 4 () = 32 18 4 9. ) : = 1 = 2 () = ) = = () = = = 576 288 = 288cm.
3 = 1 = 2 () = () = () () = 10. ) x = 81 ) 5 x = 60 ) ) () x = 9cm x = 12cm x = 6cm x = 64 x = 8cm
= 24 = 32
344
11. ) 24,5cm 12. () =
) 300cm
) 228cm
) 70cm
) 169cm
1
() = 4 30 = 120m 975 120 = 855m 13. () = 1024 = 1024 = 32cm () = 676 = 676 = 26cm E() = ( = = 26cm = = 32 26 = 6cm). 14. () = () () E() = 80 = 6400 300 300 = 5.800m
5,8 : 5,8 12.000 = 69.600 . 15. ) = = 9 + 2,25 = 11,25cm
) () = () () () ()= =85 = 40 6,25 5 5,25 = 23,5cm 16. () = () () E
=
() = () () () = ()
, . () = () + ()
345
B~
1.4 1) 1. (x = 6cm) 2. A(x = 13cm) 3. (x = 24cm) 2) 1. 2. 3. 4. 5. t t t t t
1. ) 26 =242 + 10 676 = 576 + 100 676 = 676 ) 29=20 + 21 841 = 400 + 441 841 = 841
t t t t t
) 6 = 5 + 4 36 = 25 + 16 36 = 41
2. =12 + 9 = 144 + 81 = 225 = =15cm = = 15 =225cm 3. .. 8 = + 4 64 = + 16 = 64 16 = 48 = = 48cm
9cm
12cm
8cm 4cm
8cm
4cm
4. ) .. . : = 40 + 30 = 2500 = 50m = 4 50 = 200m ) 15 200 = 3000
40m 30m 0 30m 40m
346
5. = 21 + 20 = 441 + 400 = 841 = 29Km 6. AB = 8 + 15 AB = 64 + 225 AB = 289 AB = 17 AB = 17cm6cm8cm 8cm
1
15cm 6cm
7. .., 150 = 75 + 130 22500 = 5625 + 16900 22500 = 22525 . 8. ) = 10 8 = 100 64 = 36 = 6 = 21 6 = 15 x = 8 + 15 x = 289 x= 17 ) .. : = + 10 = + 8 = 100 64 = 36 = 6 = + = 6+9 = 15 x = + x= 15 + 8 x = 289 x = 17 ) .. : = + 10 = + 8 = 36 = 6 = + 17 = 8 + = 289 64 = 225 = 15 x = 6 + 15 = 21 x 10 8 21 x 10 9
8
x 17
8
10
347
B~
9. ) = =
= 40cm 40cm 40cm
) .. : = + 40 = + 24 1600 = + 574 = 1600 574 = 1024 = 32cm ) () = ) () = = 768cm 768 =
24cm 24cm 48cm
40 = 1536 = 38,4cm
10. = xcm, = 8 x cm .. : = + = 9 + x = 81 + x (1) .. : = + = 7 + (8 x) = 49 + (8 x) (2) = (1) : 81 + x = 49 + (8x) 81 + x = 49 + (8x) (8x) 81 +x = 49 + 64 + 8x 8x + x 16x = 32 x = 2cm. = 2cm. 11. .. : = + 10 = + 8 = 36 = 6cm = =3cm .. : = 8 + 3 = 73 = = 73cm 12. () = 136 = .. . EBZ : = +
10cm
8cm
348
136 = 6 + x x = 100 x = 10cm 10 + 6 = 16cm () = 16 = 256cm.
1
1 1 . . ( ) 2 = 20cm . = 20 14 = 280cm 3 ) ) ) 4 ) 16cm
t t t t t
) = 20cm
) 240cm
) 1 = 15cm
2 1 . ( ) . ) x = 5cm ) x = 7cm
t t t t t
2 27 15 = 12cm : 1 = = 20cm 2 = = 25cm
3 ) (7 x2)+(6x4) + 4x = 96 17x = 102 x=6
349
B~
: = 40cm, KM = 32cm = 24cm ) = + 40 = 32 + 24 1600 = 1600 .., . KM 4 . ..: = + 17 = + 8 = 289 64 = 225 = 15cm =
17cm 8cm
10cm
17cm
10cm 26cm
8cm
= 270cm
350
22.1 1) 1. 2) 1. 2. 2. 3. 3. 4. 4. 5. 6. 7. t t t t t
2
1. ) 40 = ) 50 = ) 48 = ) 60 = 0,839 = 1,192 = 1,111 = 1,732 = x = 0,839 5 x= x=
t t t t t
x = 4,195cm x = 5 cm
x = 1,732 15 x = 25,98cmy
2. x OA = 5cm oy = 3cm. =
B 3cm 0 5cm A x
3. 20 = 50 =
0,364 = 1,192 =
=
13,736 cm.
16,37 cm
x = + = 5 + 16,37 = 21,37cm.
351
B~
4. 25 = 42 =
0,466 = 0,9 =
= =
25,75m. 13,33m.
= = 25,75 13,33 = 12,42m.
5. 23 = 41 =
0,424 = 0,869 =
= 0,424 30 = 12,72m. = 0,869 30 = 26,07m.
x = = 26,07 12,72 = 13,35m. 6. = = = 0,08. 0,08 = A 350m 8%
B
= 0,08 350 = 28m. 7.
A
4cm
1,95 cm. 0,487 = =
64 B
26 =
8,21 cm.
= 1,95 + 8,21 = 10,16 cm. 8. = 2
= 2 , .
352
x
y
9. = 2x + 2y 19 = 2x + 2y 9,5 = x + y (1)
y 42 A x
2
B
42 =
0,9 =
y = 0,9 x
(2)
(1) (2) 9,5 = x + 0,9 x 9,5 = 1,9x x = x = 5 cm. y = 0,9 5 = 4,5 cm. = x y = 5 4,5 = 22,5 cm2 10. =
=
}) )
= 2 .
2.2 1) ) 2) : 3) ), ), ), ) . 4) ) , ) , ) , ) , ) , ) 5) ) 2 + 2 = 1 ) 2 + 2 = 1 ) = ) = ) = ) t t t t t
t t t t t
1. ) .. 2 = 2 2 2 = 2,52 1,52 2 = 6,25 2,25 2 = 4 = 2 cm.
353
B~
) 2 = 212 + 202 2 = 841 = 29cm
) 2 =202 162 2 = 144 = 12cm
2. 2 + 2 =1
2 =
=
=
=
3. 2 + 2 = 1 =
=
354
4. ) 5 3 > 2 3 > 3 < 1 ) < 1 7 < 7 7 + 4 < 11 < 1 4 < 4 ) 6 + 3 < 9 3 < 3 < 1 ) < 1 2 < 2 2 + 3 < 5 < 1 3 >
>
>
> B
>
}
(+) >
11. ), )F2 = 20N F F1 = 15N
)
2
12. ) ) ) (1) (2)
(1) (2)
2.7 1) : 8 2) : 17t t t t t
1.
t t t t t
367
B~
2.
,
3.
4.
5.
35 = 320 0,819 = 262,08
1 1 ), ) () 2 ) 30 =
t t t t t
x = 4cm
) 45 =
x = 3 cm
) 60 = 3
x = 15 cm
368
=
= 0,15 520 = 78m
4
2
2 1 ), ) () ) i) 37 < 43 ii) 56 > 16 iii) 17 > 52 iv) 89 > 1 v) 40 = 50 2 30 = x = 75cm
t t t t t
30 =
45 =
3 = = 700m
.. 2 = 2 + 2 2 = 7002 + 702 2 = 490000 + 4900 2 = 494.900
369
B~
4
3 1 () 2 5 4 = 0
t t t t t
2 + 2 = 1
+ 2 = 1
+ 2 = 1 2 = 1 2 =
=
=
3 ) .. : 2 = 52 + 122 2 = 25 + 144 2 = 169 = 13cm
A 5cm B O 12cm
370
)
2
) = 5cm . , 4
371
33.1 1) ) : 55, ) : 110, ) : 35 2) ) . 40, ) . 120, ) . 115, ) . 65 3) ) , ) , ) , ) t t t t t
3
1.
t t t t t
2. 3. 6x 10+ 2x +30 = 180 8x = 160 x = 20 4. 5. 6. 7. 8.
373
B~
9. 10.
11. . 12. , .
3.2 1. . 36 2. . 120 3. . 24 4. . 30 5. . 3 6. . 135 7. . 72 8. . 90 9. ) ) ) ) t t t t t
1. 4 5 8 12 90 108 135 150
t t t t t
90 72 45 30
374
2.
120 160 108 140
30 20 72 40
3
3.
= 12
4.
v =
O 40 B
5. (O,) . 6. ) v = ( )
)
= 180 140 = 40 v =
=9
.
375
B~
B
7. . .
8. 5 (,) 72. . 72. . 9. = 18 +72 = 90 .72 72
1 0 72 1
72 B
72 72
72
36
36 B 18 72 18 72
72
72
3.3 1. o o L 6cm 37,68cm 0,8m 5,024m 8cm 50,24cmt t t t t
18cm 113,04m
376
2. ) ,
) ,
)
1. L = 56,52 cm 2. p = 13 cm 3. L1 L2 = 26 21 2 2 = 26 (1 2) = 26 1 2 = 1 2 =
t t t t t
3
1 2 4,14cm.
4. ) 1 2 = 8 2 1 22 = 8 1 2 = 4cm ) L1 L2 = 1 2 = ( 1 2) = 3,14 8 = 25,12cm 5. L = 3,14 68 = 213,52cm = 2,1352m . 3.500 2,1352 = 7.473,2m = 7,4732m. 6. .. : = + = 12 + 16 = 400 = 20cm L = 3,14 20 = 62,8cm. 7. =2 = 2 45 = 90o . AOB . .. : = + 2 2 2 = + 2 = 18 L = 3,14 2 3=18,84cm.
2 = 9
= 3cm.
8. 24 24 . : L = 2 3,14 1,2 = 7,536cm L = 2 3,14 2 = 12,56cm 9. L = 3,14 70 = 219,8m 2 110 = 220m = 220.000m 220.000 : 219,8 1000 .
377
B~
3.4 1. 30 60 90 120 135 150 240 ) : 2L 2. ) : = 60t t t t t
1. 45 30 75 48
t t t t t
225
330
2. ) L = 2 50,24 = 2 3,14 =
= 8 cm.
378
) L =
= 12,56 cm.
3.
L
4cm 30o
5m 45o
4cm 270
3
2,09cm 3,925m
6cm
4.
62,8 cm.
5.
12 cm.
6. 6(x-2) + 3 = 4x 1
6x 12 + 3 = 4x 1 2x = 8
x = 4cm. O = 4cm = 2cm
7. : L
=
= 6,28cm
L
=
= 3,14 cm
L
= +L
= 9,42 cm +L = 6,28 + 3,14 + 9,42 = 18,84cm
=L
8. L =
= 7,85 cm
L = 3 (2 3,14 8) = 150,72 cm 7,85 + 150,72 = 158,57 cm.
379
B~
3.5 1) L 2cm 12,56cm 12,56cm2 4cm 25,12cm 7cm 43,96cmt t t t t
50,24cm2 153,86cm2
2) : 4 3) : = 4) : = L
1. = : 1256 = 2 = = 400 = 20 cm
t t t t t
L = 2 3,14 20 = 125,6 cm 2. L = 2 : 81,64 = 2 3,14 = 13 m = = 3,14 13 = 530,66 m. 3. 1 = 1 = 3,14 3 = 28,26 cm, 2 2 = 8 1 = 8 28,26 = 226,08 cm 2 = 2 226,08 = 3,14 2 2= 72 2 = 4. E. = 3,14 (52 32) = 3,14 16 = 50,24 cm. 5. .. = + = 3 + 4 = 25 = 5 cm L = 2 3,14 5 = 31,4 cm = 5 = 3,14 25 = 78,5 cm.
380
6. . = 32 = . . .. = + = + = 32 + 32 = 64 = 8cm = 4cm L = 8 3,14 = 25,12cm = 3,14 4 = 50,24cm.
0 B
3
7. = 16 cm = 8cm L= 16 3,14 = 50,24cm = 3,14 8 = 200,96cm. 8. = : 615,44 = 3,14 = 196 = 14cm 2 = 2 14 = 28cm = 4 28 = 112cm. 9. : = (R ) = R = = = 3,14 (5 ) = 157cm 157 = R 157 3,14 R = 314 R = 100 R = 10cm. 10. = = 2 = 2 3,14 = 3,14 4 = 8 =
3.6 1) : 8 (cm) 2) : 60 3) : 2 4) ) , ) ,t t t t t
) ,
) ,
)
381
B~
1. = 36 2. .. = 84,78 =
t t t t t
= 81 = 9cm L = 2 = 2 3,14 9 = 56,52cm. 3. = 1519,76 = 3,14 = 484 = 22cm .. = 4. L = = 303,952cm
= 4cm 4,18cm
.. =
5. )
=
= 75,36cm
) .. OAB: 122 = 2 + 36 144 = 2 +36 2 = 108 = = = 75,36 = 75,36 62,35 = 13,01cm
) = .. 7. =
= 104,66cm
8. () =
=
=
382
= 75,36 13,08 = 62,28 cm
9. . =
= 39,25 14,13 6,28 = 18,84cm
3
. = 3,14 5 + 3,14 3 + 3,14 2 = 3,14 (5 + 3 + 2) = 3,14 10 = 31,4cm 10. .. . = + = = 10cm = . = . 2 .. . = = 5cm.
= 50 39,25 = 10,75cm.
11. .. . = + 10 = + 5 = 75 = . = 2 ..
= 8,66cm
12. AB ( = = 45 = 14,13cm
= 90 = )
=
= 18cm2
. = 18 14,13 = 3,87cm .. : = + = 6 + 6 = 72 =
8,48cm
383
B~
L
=
= 4,71cm = 6 + (8,48 6) + 4,71 = 13,19cm
. = + +L
13. ) H M .. . (A2 = 2 + 2 2 = (10 = 400 = )2 + (10 )2 = 10cm
= 20cm
R = ) = 3,14 2
= 157cm
= 3,14 10 = 314cm ) = 314 157 = 157cm 14. . = 10 4 = 100 78,5 = 21,5cm
15. . = 2 + 2 = 8 = 64cm = = 25,12cm
=
= 33,49 27,71 = 5,78cm . = 64 2 25,12 + 2 5,78 = 25,32cm 16. )
) . =
.. 7,65 4,71 = 2,94cm
384
1 1 ), ) () ) 180 90 360 45 2 2x + 10 = 90 x = 40. = 50 = 130. = 85,
t t t t t
3
= 60, = 90,
= 120, = 95 = 90.
3 . = 4 62,8 = 4 = 15,7 cm = = 15,7 = 246,49 cm L = 2 62,8 = 2 3,14 = 10 cm = = 3,14 10 = 314 cm . 4 . = 4 12 +2
= 48 + 37,68 = 85,68cm
. = 2 ( ) = 2
= 61,92 cm.
2 1 ) () ) v 3 60 120 5 108 72 6 120 60
t t t t t
9 140 40
385
B~
2 ) ) = 110, = 20, = 50, = 25, = 60 = 135 = 70 = 45
3 . = 50 30 3,14 5 = 1500 78,5 = 1421,5cm 1421,5 : 10 = 142,15 4 ) L =L =L = +L +L = 6,28cm = 3 6,28 = 18,84cm
) = L
= .
+ 3 =
= 15,3 + 3(18,84 15,3) = 15,3 + 3 3,54 = 25,92 cm ) . = 25,92 15,3 = 10,62 cm.
386
44.1 1) , 2) , 3) , 4) , 5) , 6) , 7) t t t t t t t t t t
4
1. ) , , ) , , , ) , , ,
2. = 3 + 4 = 25 = 5cm = + = 12 + 5 = 144 + 5 = 169 = 13 cm 3. = 12 + (17 12) = 144 + 5 = 144 + 25 = 169 = 13 cm 4. ) = + = 12 + 9 = 144 +81 = 225 = 15cm ) = + = 8 + 15 = 64 + 225 = 289 = 17 cm ) = = 0,533,
5. = + = 6 + 4 = 52 = = + = 52 + 25 =77 = AE = + BE = 6 + 5 = 61 = 6. = + = 18 + 14 = 520 22,8cm. = 0,438, =24
387
~
4.2 1) ) : 5 2) ) : 234 cm 3) ) : 628 cm ) : 6 ) :314 cm ) : 1256 cm ) : 9 t t t t t
t t t t t
1. = + 2 = (2 80 +2 40) 30 + 2 80 40 = 13.600cm 2. ) = + = (2 25 + 2 15) 2,5 + 25 15 = 575m ) = 25 = 625 cm = 0,0625 m 575 : 0,0655 = 9.200 9.200 0,30 = 2760 3. = ( ) () 192 = 3 8 = =8cm
. . = + 2 = 192 + 2 27,71 = 247,42cm 4. = = + 2 = (0,8 + 0,6 + 0,45 + 0,45 + 0,6) 1,2 + 2 0,56 = 4,6m 4,6 15 = 69. 5. = 2 3,14 8 16 + 2 3,14 8 = 1205,76cm 6. = 50,24 20 = 1004,8 cm L = 2 50,24 = 2 3,14 = 8cm = + 2 = 1004,8 + 2 3,14 8 = 1406,72 cm
388
7. = 2 3,14 0,10 1,50 = 0,942 m 50 0,942 = 47,1 m 3 47,1 = 141,3 . 8. ) = 2 3,14 4 3 = 75,36 m = 75,16 + 2 3,14 4 = 175,64 m ) = 6cm = 452,16 cm = 678,24 cm ) = 5 cm = 314 cm = 471 cm 9. = + 2 = 2 3,14 0,4 1,2 + 2 3,14 0,4 = 4,0192m 1000 1000 4,0192 = 4019,2m 10% 4019,2 : 0,9 = 4465,77m 1,5 4.465,77 = 6698,65 . 10. ) = 2 3,14 0,15 0,6 = 0,5652m . ) = 10 18 = 180 m 180 : 0,5652 = 319 .
4
4.3 1) 2) 3) ) , ) , 25 cm2 8 200 cm3 ) 49 cm2 6cm 294 cm3 78,5cm2 4cm 314cm3 25cm2 4cm 100cm2 16cm2 9cm 144cm3 32dm 50cm 160dm3t t t t t
389
~
t t t t t
1. ) , : V = V = 5 V = 53 135 = 5 3 3 = 27 3 = 33 = 3cm. ) = + 2 = 4 5 + 2 2 = 20 32 + 2 32 = 198cm2 2. ) = + = 12 +16 = 400 =20 cm ) = + 2 = 4
) V = () () =
20 = 1.920cm3
3. ) .. : = 24 + 10 = 676 = 26cm. = = 26 cm. ) = (2 0,26 + 0,3) 2 + 2 ) V = 2 = 0,192m3
= 1,832m
4. ) .. . : = = 5 4 = 9 = 3cm. = 2 3 = 6cm = + 2 = (5 + 5 + 6) 15 + 2 ) V = 15 = 180cm3
5cm 4cm
5cm
= 264cm
5. ) V = 3,14 0,32 0,8 = 0,22608m3 = 226,08dm3 ) = 150mm = 0,15m V = 3,14 0,15 0,4 = 0,02826m3 = 28,26dm3 6. = 2 452,16 = 2 3,14 24 = = 3cm.
390
V = = 3,14 3 24 = 678,24cm3.
7. V = 3,14 3,5 10 = 384,65cm3 V = 2 384,65 = 769,3cm3 8. = 1 = 3,14 10 = 314 cm2 = 2 314 = 2 3,14 = 100 = 10cm. V = 3,14 10 5 = 1570 cm3 9. V = V V = 3,14 1,75 8 3,14 1,5 8 = 20,41m3
4
4.4 1) ) , ) , ) , ) , ) , ) t t t t t
1. V = 15 20 = 1500cm3
t t t t t
2. =
( ) ()
=
5 12 10 = 300cm
3. ) =
(4 10) 12 = 240 cm
) = + = 240 + 10 = 340 cm ) .. . : = +
391
~
12 = + 5 = 144 25 = 119 = V = 10 10,9 = 545cm3
10cm 10cm
4. . . 9,16cm 8cm 10cm 160cm2 195,41cm3 8cm 12cm 10cm 240cm2 384cm3 10cm 13,26cm 12cm 318,24cm2 1758,276cm3
5. .. () () 17 = + 8 = 289 64 = 225 = 15cm 15 = + 8 = 225 64 = 161 V = 16 12,68 = 1623,04cm3
6. ) .. : 5 = + 2,5 = 18,75 =
5cm 5cm
5cm
= ) V =
(3 5 ) 4,33 = 32,475cm
2
(. ) () =
4,1 = 14,79cm3
7.
392
V2 = 4 V1
8. ) = 10 4 = 84 = ) = (6 8) 9,16 = 219,84cm2
9,16cm
4
) .. , . = 8 4 = 64 16 = 48 = = 166,08cm2
= + = 219,84 + 166,08 = 385,92cm2 ) = 10 8 = 36 = 6cm V = 166,08 6 = 332,16cm3.
9. .. = 8 + 6 = 100 = 10cm () = 5 12 + (4 12) 10 = 960cm2
V = V V = 123 10. ) )
12 8 = 1344cm3
4.5 1) ) , ) , ) , ) , ) , ) ,t t t t t
) , )
t t t t t
1. = + ( = + = 8 + 6 = 100 = 10cm) = 3,14 6 10 + 3,14 6 = 301,44cm2
393
~
2. = 226,08 = 3,14 9 = 8cm = = 3,14 8 = 200,96cm2 3. 30 = = 6cm
30 =
= + = 3,14 3 6 + 3,14 3 = 84,78cm2. V = = 3,14 3 5,19 = 48,89cm3
4. ) L= 2 18,84 = 2 3,14 = 3dm. = 3,14 3 5 + 3,14 3 = 75,36 cm2 ) = + 5 = + 3 = 25 9 = 16 = 4dm V= = 3,14 3 4 = 37,68dm3
5. ) = + =50 + 10 = 2500 + 100 = 2.600 = .. = = 3,14 10 51 = 1601,4 cm2 .. = 2 = 2 3,14 12,5 5 = 392,5cm2 = 1601,4 + 392,5 + (3,14 12,5 3,14 10) = = 1993,9 + 3,14 (156,25 100) = 1993,9 + 176,625= = 2170,525cm2 ) V = = 3,14 10 50 = 5233,33cm3
V = = 3,14 12,5 5 = 2453,125cm3 V = 5233,33 + 2453,125 = 7686,455cm3. 6. ) V = = 3,14 10 10 =1046,66cm3
V = = 3,14 10 12 = 3768cm3 V = 1046,66 + 3768 = 4814,66 cm3. ) .. = 2 = 2 3,14 10 12 = 753,6 cm2 = + = 10 + 10 = 200
394
=
14,1cm
.. = = 3,14 10 14,1 = 442,74cm2 = 753,6 + 442,74 = 1196,34 cm2 50 50 1196,34 = 59817 cm2 = = 5,9817 m 30 5,9817 = 179,451 . 7. 19,625 = 3,14 3 = 6,25 = 2,5m = ( = + = 3 + 2,52 = 15,25 = 3,9m) = 3,14 2,5 3,9 = 30,615 m . 8. = =9,
4
= 9 29 20 = 180 9 = 180 = 20cm = 29cm = + 29 = + 20 = 841 400 = 441 = 21cm V = = 3,14 20 21 = 8792cm3 = 8,792dm3 ()
9. .. : =20 + 20 = 800 = = = 14,14cm
= 2 E = 2 = 2 3,14 14,14 20 = 1775,984cm V = 2 V = 2 V = V1 V2 = = 2 3,14 14,14 14,14 = 5918,15cm3
3,14 6 15
3,14 6 10 = 188,4cm3.
395
~
4.6 1) , 2) , 3) , 4) , 5) , 6) t t t t t
1. = 4 = 4 3,14 8 = 803,84cm V = 2. ) L = 2 50,24 = 2 3,14 ) = 803,84cm ) V = 2143,57cm3 3.
t t t t t
= 8cm
4. V = 113,04 = 3,14 3
:
3 = 27
3 = 33
= 3cm
= 4 = 4 3,14 3 = 113,04cm 5. = 4 = 4 3,14 9 = 1017,36m 5 1017,36 = 5086,8 . 6. = 1256 = 3,14 = 400 = 20cm.
396
V =
3 =
3,14 203 33493,33cm3.
4
7. = 4 = 4 3,14 6 = 452,16cm2. 8. V = 3 = 3,14 153 = 14130cm3 = 14,13 .
9. ) =
+ = 3 = 3 3,14 25 = 5887,5cm
) V =
3,14 253 = 32708,33cm3
10. ) V =
3 =
3,14 153 = 14130cm3
) V = 3 = 303 = 27000cm3 ) V = 27000 14130 = 12870 cm3 11. 1 , .. 8 =1 + 4 1 = 64 16 1 = 48 1 = E = 1 = 3,14 48 = 150,72cm.
1 1 ), ), ), () 2 ) = 4 + 3 = 25 = 5cm ) x =
t t t t t
3 ) = + = 6 + 8 = 100 = 10cm.
397
~
= E + 2 = (6 + 8 + 10) 15 + 2 ) V = 4 ) E = (4 16) 15 = 480cm 15 = 360cm3
= 408cm
) .. : 15 = + 8 = 15 8 = 225 64 = 161 = 12,68cm V = 16 12,68 = 3246cm
2 1 ), ), ), ) ()
t t t t t
2 V = = 3,14 0,4 7 = 3,5168m3 150 3,5168 = 527,52 . 3 ) E = 502,4 = 3,14 20 = 8 cm ) = + 20 = + 8 = 400 64 = 336 = 18,33cm ) V = = 3,14 8 18,33 = 1227,86cm3
4 V = V V = 203
3,14 103 = 8000 4186,66 = 3813,34cm3.
398
O 1
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200 0 200 1 200 2 200 3
427
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: 1,5 : 33+30+12+5=80% 2 : 6+14+33+30=83% : 1,5 : 27+33+16+8=84% 2 : 4+12+27+33=76%
4.3 O
1.
429
O OO O
2.
1.
2.
430
200 0 200 1 200 2 200 3 200 4
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431
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437
O OO O
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1. 2.
1. 2. ) 12 m2 = 120.000 cm2, ) 175 dm2 = 17.500 cm2, ) 456 m2 = 4.560.000 cm2,) 136 m2 = 1.360.000 cm2, ) 3 km2 = 30.000.000.000 cm2, ) 1750 m2 = 17,5 cm2, ) 256 km2 = 2.560.000.000.000 cm2 ) 17 dm2 = 170.000 mm2, ) 236 cm2 = 23.600 mm2
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5.
6. 1.3 O
1.
438
O 1
1. 2. 3. 4.x x x
x
x
5.
6. 7.
8.
439
O OO O
9.
10.
11. 12.
13.
14.
15. 16.
440
O 1
17.
400 cm2. 200 cm2 100 cm2.
1.4 O
1.
2.
3.
4.
1. 2.
441
O OO O
3.
4.
5. 6. 7.
8.
442
O 1
9.
443
O OO O
O 2o2.1 O
1.
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3.
1.
2.7 cm
10 cm
3.
444
O 2
4.
5.
6.
7.
445
O OO O
2.2 O
1. 6. 7.
2.
3.
4.
5.
1.
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:
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2. = 3cm = 5 cm. .. : 2 2 = 2 + 2 2 = 52 32 3 cm 5 cm
= 16 = 4 cm.
4 = = 5
446
O 2
2.3 , O
1.
2.
1.
2.
447
O OO O
3.
4.
5.
6.
7.
8. = 6.371 383.795 km. 0,0166
448
O 2
2.4 O 30, 45 60 O
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1.
2.
3.51
449
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Z
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452
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