1140a a sin v = 4a 1a sin v = 4 a v ⎛1⎞ ⎝4⎠ −1 = sin ⎜ ⎟ −1 sin (1 4) v = 14 1144a 36 sin v = 60 48 cosv = 60 36 tan v = 48 1145a tan19 x = 750 ( mult 750) 750⋅ tan19 = 750 ⋅ 750tan19 = x x = 750tan19 750tan(19) x = 258 m x 750 LÖSNINGAR DEL B 1140b 10a cosv = 11a 10 a cosv = 11a v cos ⎛10 ⎞ ⎝11⎠ −1 = ⎜ ⎟ −1 cos (10 11) v = 25 1144b 25 sin v = 65 60 cosv = 65 25 tan v = 60 1141a 1,52 x cosv = 2,41x 1,52 x cosv = 2,41 x v ⎛1,52 ⎞ ⎝2,41 ⎠ −1 = cos ⎜ ⎟ −1 cos (1.52 2.41) v = 51 1145b 98 tan 63 = ( mult x) x 98 x⋅ tan 63 = x ⋅ x x tan 63 = 98 div ( tan 63 ) x tan 63 tan 63 98 = tan 63 98 x = tan 63 98 tan(63) x = 50 m 1141b 3,52 y sin v = 5,35 y 3,52 y sin v = 5,35 y v ⎛3,52 ⎞ ⎝5,35 ⎠ −1 = sin ⎜ ⎟ −1 sin (3.52 5.35) v = 41 5
1146a Sätt sidan AB till x cm x cos35,8 = 23,4 ( mult 23,4) 23,4 ⋅ cos35,8 = 23,4 ⋅ 23,4cos35,8 = x x = 23,4cos35,8 23.4cos(35.8) x = 19,0 cm 1147a Sätt sidan AC till x cm 42,6 cos 27,5 = ( mult x) x 42,6 x⋅ cos 27,5 = x ⋅ x xcos 27,5 = 42,6 div x 23,4 ( cos 27, 5 ) x cos 27,5 cos 27,5 42,6 = cos 27,5 42,6 x = cos 27,5 42.6 cos(27.5) x = 48,0 cm 1148a tan37 x = 43 ( mult 43) 43⋅ tan37 = 43 ⋅ 43tan37 = x x = 43tan37 43tan(37) x = 32 m x 43 LÖSNINGAR DEL B 43 cos37 = y ( mult y) 43 y⋅ cos37 = y ⋅ y y cos37 = 43 ( div cos 37 ) y cos37 cos37 43 = cos37 43 y = cos37 43 cos(37) y = 54 m 1146b Sätt sidan AB till x cm x sin59,3 = 67,9 ( mult 67,9) 67,9 ⋅ sin59,3 = 67,9 ⋅ 67,9sin59,3 = x x = 67,9sin59,3 67.9sin(59.3) x = 58,4 cm 1147b 98,5 sin 76,4 = x 98,5 x⋅ sin 76,4 = x ⋅ x xsin 76,4 = 98,5 div ( mult x) ( sin 76,4 ) x sin 76,4 sin 76,4 98,5 = sin 76,4 98,5 x = sin 76,4 98.5 sin(76.4) x = 101 cm 1148b 27 tan 29 = ( mult x) x 27 x⋅ tan 29 = x ⋅ x x tan 29 = 27 div ( tan 29 ) x tan 29 tan 29 27 = tan 29 27 x = tan 29 27 tan(29) x = 49 m x 67,9 27 sin 29 = y ( mult y) 27 y⋅ sin 29 = y ⋅ y ysin 29 = 27 ( div sin 29 ) y sin 29 sin 29 27 = sin 29 27 y = sin 29 27 sin(29) y = 56 m 6
- Page 1 and 2: NÅGRA KOMMENTARARER TILL LÖSNINGA
- Page 3 and 4: 1109a x tan 41 = 67 ( mult 67) 67
- Page 5: 1129c cos64 x = 97 ( mult 97) 97
- 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 =
- 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
- Page 121 and 122:
LÖSNINGAR DEL B 120