NÅGRA KOMMENTARARER TILL LÖSNINGARNA

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1121a 24 tan v = 45 −1 ⎛24 ⎞ v = tan ⎜ ⎟ ⎝45 ⎠ −1 tan (24 45) v = 28,1 1123 1126a 8 sin v = 10 6 cosv = 10 1128a sin37 x = 68 ( mult 68) 68⋅ sin37 = 68 ⋅ 68sin37 = x x = 68sin37 68sin(37) x = 41 cm x 68 LÖSNINGAR DEL B 1121b 35 tan v = 12 −1 ⎛35 ⎞ v = tan ⎜ ⎟ ⎝12 ⎠ −1 tan (35 12) v = 71,1 1126b 16 sin v = 34 30 cosv = 34 1122a 3a tan v = 1a 3 a tan v = 1a v tan ⎛3⎞ ⎝1⎠ −1 = ⎜ ⎟ −1 tan (3 1) v = 71,6 42,9 tan v = 70,0 −1 ⎛42,9 ⎞ v = tan ⎜ 70,0 ⎟ ⎝ ⎠ −1 tan (42.9 70.0) v = 31,5 1128b 18 sin33 = ( mult x) x 18 x⋅ sin33 = x ⋅ x xsin33 = 18 div ( sin 33) x sin33 sin33 18 = sin33 18 x = sin33 18 sin(33) x = 33 cm 1127a 24 sin A = 26 10 cos A = 26 1129a 49 cos58 = ( mult x) x 49 x⋅ cos58 = x ⋅ x xcos58 = 49 div ( cos 58 ) x cos58 cos58 49 = cos58 49 x = cos58 49 cos(58) x = 92 cm 1122b 57a tan v = 76a 57 a tan v = 76 a v tan ⎛57 ⎞ ⎝76 ⎠ −1 = ⎜ ⎟ −1 tan (57 76) v = 36,9 1127b 66 sin A = 130 112 cos A = 130 1129b 25 sin 42 = ( mult x) x 25 x⋅ sin 42 = x ⋅ x xsin 42 = 25 div ( sin 42 ) x sin 42 sin 42 25 = sin 42 25 x = sin 42 25 sin(42) x = 37 cm 3
1129c cos64 x = 97 ( mult 97) 97 ⋅ cos64 = 97 ⋅ 97cos64 = x x = 97cos64 97cos(64) x = 43 cm x 97 1131a 234 cos38,7 = ( mult x) x 234 x⋅ cos38,7 = x ⋅ x xcos38,7 = 234 div ( cos 38, 7 ) x cos38,7 cos38,7 234 = cos38,7 234 x = cos38,7 234 cos(38.7) x = 300 cm 1138a 17 sin v = 36 −1 ⎛17 ⎞ v = sin ⎜ ⎟ ⎝36 ⎠ −1 sin (17 36) v = 28 1129d sin 49 LÖSNINGAR DEL B x = 67 ( mult 67) 67 ⋅ sin 49 = 67 ⋅ 68sin 49 = x x = 68sin 49 68sin(49) x = 51 cm 1138b 31 cosv = 52 −1 ⎛31⎞ v = cos ⎜ ⎟ ⎝52 ⎠ −1 cos (31 52) v = 53 x 67 1130a sin55 x = 72 ( mult 72) 72⋅ sin55 = 72 ⋅ 72sin55 = x x = 72sin55 72sin(55) x = 59 cm x 72 1131b 15,1 cos76,5 = ( mult x) x 15,1 x⋅ cos76,5 = x ⋅ x xcos76,5 = 15,1 div ( cos 76, 5 ) x cos76,5 cos76,5 15,1 = cos76,5 15,1 x = cos76,5 15,1 cos(76.5) x = 64,7 cm 1139a 52 sin v = 65 −1 ⎛52 ⎞ v = sin ⎜ ⎟ ⎝65 ⎠ −1 sin (52 65) v = 53 (tan eller cos går också bra) 1130b x cos71 = 39 ( mult 39) 39⋅ cos71 = 39 ⋅ 39cos71 = x x = 39cos71 39cos71 x = 13 cm 1139b 51 sin v = 85 −1 ⎛51⎞ v = sin ⎜ ⎟ ⎝85 ⎠ −1 sin (51 85) v = 37 x 39 (tan eller cos går också bra) 4
Page 1 and 2: NÅGRA KOMMENTARARER TILL LÖSNINGA
Page 3: 1109a x tan 41 = 67 ( mult 67) 67
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 and 58:
LÖSNINGAR DEL B 3129a Enligt randv
Page 59 and 60:
3320d Likf ger 10 − x 9 = ( kors
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 =
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4613 LÖSNINGAR DEL B a) Antag att
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4631a 4631b Antagande se figur LÖS
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5113a (3,7) (2,2) (8,4) d d a b
Page 91 and 92:
5116 Det finns 2 punkter på x-axel
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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,
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5340a Enpunktsformen ger (5,4) k
Page 103 and 104:
5354e − 3x+ 3y− 15= 0 3y= 3x+ 1
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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 ⎨
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5429a ⎧x = 3 ⎪ ⎨2x+ y = 5 ⎪
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5431a ⎧x+ 3y− z = 4 ⎪ ⎨2x+
Page 119 and 120:
5453 Antagande se figur LÖSNINGAR
Page 121 and 122:
LÖSNINGAR DEL B 120
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NÅGRA KOMMENTARARER TILL LÖSNINGARNA

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