3306 Likf ger x 28 = 36 42 28 x = 36⋅ = 24 cm 42 3314a Likf ger x 12 = 32 19 12 x = 32⋅ = 20,2 cm 19 3315a Likf ger x 7,2 = 4,8 3,6 7,2 x = 4,8 ⋅ = 9,6 cm 3,6 3316a Likf ger x 150 = 32 105 150 x = 32⋅ = 46 m 105 3318b Likf ger y 12 = 24 30 12 y = 24⋅ = 9,6 cm 30 LÖSNINGAR DEL B Likf ger y 28 = 52 42 28 y = 52⋅ = 35 cm 42 z = 110 Likf ger y 12 = 24 19 12 y = 24⋅ = 15,2 cm 19 3315b Likf ger y 6,4 = 18,0 12,0 6,4 y = 18,0 ⋅ = 9,6 cm 12,0 3316b Likf ger x 36 = 128 96 36 x = 128⋅ = 48 cm 96 3320a Likf ger x 8 = 8 10 8 x = 8⋅ = 6,4 cm 10 3310 Likf ger x 42 = 260 54 42 x = 260⋅ = 202 cm 54 3314b Likf ger x 6,4 = 9,0 8,0 6,4 x = 9,0 ⋅ = 7,2 cm 8,0 3315c Likf ger z 2,6 = 11,7 7,8 2,6 z = 11,7 ⋅ = 3,9 cm 7,8 3317 Likf ger x 84 = 84 119 84 x = 84⋅ = 59 cm 119 3320b Likf ger x 6 = 6 8 6 x = 6⋅ = 4,5 cm 8 3311 Likf ger 57 x 36 = 45 48 36 x = 45⋅ = 34 cm 48 Likf ger y 6,4 = 12,0 8,0 6,4 y = 12,0 ⋅ = 9,6 cm 8,0 3315d Likf ger x 9,6 = 45 21,5 9,6 x = 45⋅ = 20,1 cm 21,5 3318a Likf ger x 12 = 12 30 12 x = 12⋅ = 4,8 cm 30 3320c Likf ger x 6 = 6 10 6 x = 6⋅ = 3,6 cm 10
3320d Likf ger 10 − x 9 = ( kors mult) 9 10 10(10 − x) = 9⋅9 10(10 −x) −9⋅ 9 = 0 100 −10x − 81 = 0 − 10x + 19 = 0 x − 1, 9 = 0 ( flytta om) x = 1, 9 3323b Likf ger + 6,2 4,1 ( flytta) ( div − 10) z + 5,3 10,3 = ( kors mult ) 5,3 4,1 4,1( z + 5,3) = 5,3 ⋅10,3 4,1( z + 5,3) = 5,3 ⋅10,3 4,1z + 21,73 −54,59 = 0 4,1z − 32,86 = 0 ( div 4,1) z − 8,0 = 0 ( flytta om) z = 8, 0 cm LÖSNINGAR DEL B 3322a Likf ger 3+ 6 x 9 = 8 6 9 x = 8⋅ = 12 cm 6 3324a Likf ger 9− x 7,5 = ( kors mult ) 9 12 12(9 − x) = 7,5 ⋅9 12(9 −x) −7,5 ⋅ 9 = 0 108 −12x − 67,5 = 0 − 12x + 40,5 = 0 ( div) x − 3, 4 = 0 ( flytta om) x = 3, 4 cm 3325 Antag att CE är x cm, då blir AE 12 – x cm. Se figur. 12-x 12 E x A 6 D B 15 C (cm) ( flytta) 3322b Likf ger z 8 = 4 5 8 z = 4⋅ = 6,4 cm 5 3324b Likf ger 5−2 y 3 = ( kors mult ) 6 5 5y= 3⋅6 5y= 18 18 y = = 3, 6 cm 5 Likf ger 12 − x 6 = ( kors mult ) 12 15 15(12 − x) = 6⋅12 15(12 −x) −6⋅ 12 = 0 180 −15x − 72 = 0 − 15x + 108 = 0 x − 7,2 = 0 ( flytta om) x = 7,2 CE = 7,2 cm ( flytta) ( div − 15) 3323a Likf ger x 5 = x + 7 11 5+ 6 58 ( kors mult) 5( x+ 7) = 11x 5( x+ 7) − 11x= 0 5x+ 35− 11x= 0 − 6x+ 35= 0 x − 5,8 = 0 x = 5,8 cm ( flytta om) ( div − 6) ( flytta om)
- Page 1 and 2:
NÅGRA KOMMENTARARER TILL LÖSNINGA
- Page 3 and 4:
1109a x tan 41 = 67 ( mult 67) 67
- Page 5 and 6:
1129c cos64 x = 97 ( mult 97) 97
- Page 7 and 8: 1146a Sätt sidan AB till x cm x c
- Page 9 and 10: 1149b 1150 1202 tan35 h = 43 ( mul
- Page 11 and 12: 1209a Antag att byggnadens höjd ä
- Page 13 and 14: LÖSNINGAR DEL B 1215 Antag att den
- Page 15 and 16: 1221 1222a 16 cosv = 21 −1 ⎛16
- Page 17 and 18: 1227 1228 Beräkna tringelns sidor
- Page 19 and 20: 1233 Antag att bisektrisen CD är x
- Page 21 and 22: 2102a 13 + −8 13 − 8 5 ( ) 2103
- Page 23 and 24: 2125a 3 310 ⋅ 30 = = 4 410 ⋅ 40
- Page 25 and 26: 2131a 2 ⎛ 1⎞ ⎛ 5 ⎛ 3 ⎞⎞
- Page 27 and 28: 2144b 3 3 4/2 − (4/2) 3 3 4/2−2
- Page 29 and 30: 2154a 3969 / -49 −81 ( ) 2155a 63
- Page 31 and 32: 2219a ( ) 2 3 10 49 + 4⋅ 125 −5
- Page 33 and 34: 2234a 1,890 2234b 0,845 LÖSNINGAR
- Page 35 and 36: 2349 Antag att grillen kostade A kr
- Page 37 and 38: 2415a x 2 = 2⋅2 x 2 = 2 ⋅2 x 2
- Page 39 and 40: 2433a 1 1 0,01 = = = 100 10⋅10 1
- Page 41 and 42: 2447a-b Antag att sidan är x m x
- Page 43 and 44: 2556a s = v⋅t (2547) meter 11 s
- Page 45 and 46: 2611a 2 x + + 4 y 2 3+ + 4 −2 3
- Page 47 and 48: 2640a A= 3b 3b= A 3b A = 3 3 A b =
- Page 49 and 50: 2671a 9 −( x − 3) = 20 9 −( x
- Page 51 and 52: 2705c 2r⋅ 4r = 8r 2 hela 2 ⋅
- Page 53 and 54: 2725a Antag att vattnet står x m h
- Page 55 and 56: 2748a 2400 12 pris per bok ⋅ 20 =
- Page 57: LÖSNINGAR DEL B 3129a Enligt randv
- Page 61 and 62: LÖSNINGAR DEL B 3338 Antag att den
- Page 63 and 64: 3355 Antag att hypotenusan i stora
- Page 65 and 66: 4229a 2 ab( a −b) −a( ab −b)
- Page 67 and 68: 4239d 3 −( − 5m+ 8) = 36 −(1
- Page 69 and 70: 4245a A1+ A2 2 2 (2x + 20 x) + (2x
- Page 71 and 72: 4302a ( x+ 3)( x−3) 2 2 x − 3 2
- Page 73 and 74: 2 LÖSNINGAR DEL B 4308c 2 2 ( x+ 4
- Page 75 and 76: 4329a Pytagoras sats ger ( x+ 18) =
- Page 77 and 78: LÖSNINGAR DEL B 4334 Antag att dom
- Page 79 and 80: 4410a 2 x − 3x+ 2= 0 3 x = ∓ 2
- Page 81 and 82: 4415 x x− = x+ + x(2x−1) − (
- Page 83 and 84: 4608 Antagande se figur 4609a 25 =
- Page 85 and 86: 4613 LÖSNINGAR DEL B a) Antag att
- Page 87 and 88: 4631a 4631b Antagande se figur LÖS
- Page 89 and 90: 5113a (3,7) (2,2) (8,4) d d a b
- Page 91 and 92: 5116 Det finns 2 punkter på x-axel
- Page 93 and 94: 5206 5207 5208a Sträckan = Hastigh
- Page 95 and 96: 5220 5223 5303a y= 3x−2 y= x+ −
- Page 97 and 98: 5314a P = (0,0) 1 } } 3 Δy k = 4
- Page 99 and 100: 5328 Genom R R ST ( −3,6) (2,
- Page 101 and 102: 5340a Enpunktsformen ger (5,4) k
- Page 103 and 104: 5354e − 3x+ 3y− 15= 0 3y= 3x+ 1
- Page 105 and 106: 5366 VL HL y = 5 −2 x (1.1,2.7)
- Page 107 and 108: 5375 2 y = 2 ax+ a (1,8) x y 2 8=
- Page 109 and 110:
5407a ⎧4x− 3z = 6 ⎨ ⎩z −
- Page 111 and 112:
5420c ⎧2m− 5n= 1 ⎨ ⎩3m+ n=
- Page 113 and 114:
5424a ⎧6 − ( x+ y+ 1) = x ⎨
- Page 115 and 116:
5429a ⎧x = 3 ⎪ ⎨2x+ y = 5 ⎪
- Page 117 and 118:
5431a ⎧x+ 3y− z = 4 ⎪ ⎨2x+
- Page 119 and 120:
5453 Antagande se figur LÖSNINGAR
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LÖSNINGAR DEL B 120