NÅGRA KOMMENTARARER TILL LÖSNINGARNA
NÅGRA KOMMENTARARER TILL LÖSNINGARNA NÅGRA KOMMENTARARER TILL LÖSNINGARNA
1106a x 15 = 2 ( mult 2) 215 ⋅ = 2⋅ 30 = x x = 30 x 2 1107a 500 20 = ( mult x) x 500 x⋅ 20 = x ⋅ x 20x = 500 ( div 20) 20 x 500 = 20 20 x = 25 1108a x 17 = a ( mult a) a⋅ 17 = a ⋅ 17a= x x= 17a x a LÖSNINGAR DEL B 1106b x a = ( mult b) b x b⋅ a= b ⋅ b ab = x x= ab 1107b d c = x ( mult x) x⋅ c= x ⋅ cx = d c x d = c c d x = c d x ( div c) 1108b x tan v = 32 ( mult 32) 32⋅ tan v = 32 ⋅ 32tan v= x x= 32tan v x 32 1106c x tan v = 7 ( mult 7) 7⋅ tanv= 7 ⋅ 7tanv= x x= 7tanv x 7 1107c 30 tan v = ( mult x) x 30 x⋅ tan v= x ⋅ x xtan v= 30 xtan v 30 = tan v tan v 30 x = tan v 1108c c 20 = x ( mult x) x⋅ 20 = x ⋅ 20x= c 20 x c = 20 20 c x = 20 ( div tan v) c x ( div 20) 1106d x tan v = a ( mult a) a⋅ tan v= a ⋅ atan v= x x= atan v 1107d a tan v = ( mult x) x a x⋅ tan v= x ⋅ x xtan v= a xtan v a = tan v tan v a x = tan v x a ( div tan v) 1108d d tan v = ( mult x) x d x⋅ tan v= x ⋅ x xtan v= d xtan v d = tan v tan v d x = tan v ( div tan v) 1
1109a x tan 41 = 67 ( mult 67) 67 ⋅ tan 41 = 67 ⋅ 67 tan 41 = x x = 67 tan 41 67 tan(41) x = 58 m 1111a 3 tan v = 5 3 = 0,6 5 1113a tan 28 x = 85 ( mult 85) 85⋅ tan 28 = 85 ⋅ 85tan 28 = x x = 85tan 28 85tan(28) x = 45 m 1120a 5 tan v = 12 −1 ⎛ 5 ⎞ v = tan ⎜ ⎟ ⎝12 ⎠ −1 tan (5 12) v = 22,6 x 67 x 85 1109b tan36 LÖSNINGAR DEL B x = 75 ( mult 75) 75⋅ tan36 = 75 ⋅ 75tan36 = x x = 75tan36 75tan(36) x = 54 m 1111b 4 tan v = 2 tan v = 2 2 1113b 27 tan34 = ( mult x) x 27 x⋅ tan34 = x ⋅ x x tan34 = 27 div x 75 ( tan34 ) x tan34 tan34 27 = tan34 27 x = tan34 27 tan(34) x = 40 m 1120b 43 tan v = 51 −1 ⎛43 ⎞ v = tan ⎜ ⎟ ⎝51⎠ −1 tan (43 51) v = 40,1 1110a 65 tan 44 = ( mult x) x 65 x⋅ tan 44 = x ⋅ x x tan 44 = 65 div ( tan 44 ) x tan 44 tan 44 65 = tan 44 65 x = tan 44 65 tan(44) x = 67 m 1112a 15 tan A = 8 8 tan B = 15 1114a 94 tan57 = ( mult x) x 94 x⋅ tan57 = x ⋅ x x tan57 = 94 div ( tan57 ) x tan57 tan57 94 = tan57 94 x = tan57 94 tan(57) x = 61 m 1120c 14 tan v = 48 −1 ⎛14 ⎞ v = tan ⎜ ⎟ ⎝48 ⎠ −1 tan (14 48) v = 16,3 1110b 52 tan31 = ( mult x) x 52 x⋅ tan31 = x ⋅ x x tan31 = 52 div ( tan31 ) x tan31 tan31 52 = tan31 52 x = tan31 52 tan(31) x = 87 m 1112b 20 tan A = 21 21 tan B = 20 1114b tan 65 x = 35 ( mult 35) 35⋅ tan 65 = 35 ⋅ 35tan 65 = x x = 35tan 65 35tan(65) x = 75 m 1120d 85 tan v = 81 −1 ⎛85 ⎞ v = tan ⎜ ⎟ ⎝81⎠ −1 tan (85 81) v = 46,4 x 35 2
- Page 1: NÅGRA KOMMENTARARER TILL LÖSNINGA
- 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 ⋅
1109a<br />
x<br />
tan 41 =<br />
67<br />
( mult 67)<br />
<br />
67 ⋅ tan 41 = 67 ⋅<br />
<br />
67 tan 41 = x<br />
<br />
x = 67 tan 41<br />
67 tan(41)<br />
x = 58 m<br />
1111a<br />
3<br />
tan v =<br />
5<br />
3<br />
= 0,6<br />
5<br />
1113a<br />
tan 28<br />
<br />
x<br />
=<br />
85<br />
( mult 85)<br />
<br />
85⋅ tan 28 = 85 ⋅<br />
<br />
85tan 28 = x<br />
<br />
x = 85tan 28<br />
85tan(28)<br />
x = 45 m<br />
1120a<br />
5<br />
tan v =<br />
12<br />
−1<br />
⎛ 5 ⎞<br />
v = tan ⎜ ⎟<br />
⎝12 ⎠<br />
−1<br />
tan (5 12)<br />
v = 22,6<br />
<br />
x<br />
67<br />
x<br />
85<br />
1109b<br />
tan36<br />
LÖSNINGAR DEL B<br />
<br />
x<br />
=<br />
75<br />
( mult 75)<br />
<br />
75⋅ tan36 = 75 ⋅<br />
<br />
75tan36 = x<br />
<br />
x = 75tan36<br />
75tan(36)<br />
x = 54 m<br />
1111b<br />
4<br />
tan v =<br />
2<br />
tan v = 2<br />
2<br />
1113b<br />
27<br />
tan34 = ( mult x)<br />
x<br />
27<br />
x⋅ tan34 = x ⋅<br />
x<br />
x tan34 = 27 div<br />
x<br />
75<br />
<br />
( tan34 )<br />
<br />
x tan34<br />
tan34 <br />
27<br />
= <br />
tan34<br />
27<br />
x = <br />
tan34<br />
27 tan(34)<br />
x = 40 m<br />
1120b<br />
43<br />
tan v =<br />
51<br />
−1<br />
⎛43 ⎞<br />
v = tan ⎜ ⎟<br />
⎝51⎠ −1<br />
tan (43 51)<br />
<br />
v = 40,1<br />
1110a<br />
65<br />
tan 44 = ( mult x)<br />
x<br />
65<br />
x⋅ tan 44 = x ⋅<br />
x<br />
x tan 44 = 65 div<br />
<br />
( tan 44 )<br />
<br />
x tan 44<br />
tan 44 <br />
65<br />
= <br />
tan 44<br />
65<br />
x = <br />
tan 44<br />
65 tan(44)<br />
x = 67 m<br />
1112a<br />
15<br />
tan A =<br />
8<br />
8<br />
tan B =<br />
15<br />
1114a<br />
94<br />
tan57 = ( mult x)<br />
x<br />
94<br />
x⋅ tan57 = x ⋅<br />
x<br />
x tan57 = 94 div<br />
<br />
( tan57 )<br />
<br />
x tan57<br />
tan57 <br />
94<br />
= <br />
tan57<br />
94<br />
x = <br />
tan57<br />
94 tan(57)<br />
x = 61 m<br />
1120c<br />
14<br />
tan v =<br />
48<br />
−1<br />
⎛14 ⎞<br />
v = tan ⎜ ⎟<br />
⎝48 ⎠<br />
−1<br />
tan (14 48)<br />
v = 16,3<br />
<br />
1110b<br />
52<br />
tan31 = ( mult x)<br />
x<br />
52<br />
x⋅ tan31 = x ⋅<br />
x<br />
x tan31 = 52 div<br />
<br />
( tan31 )<br />
<br />
x tan31<br />
tan31 <br />
52<br />
= <br />
tan31<br />
52<br />
x = <br />
tan31<br />
52 tan(31)<br />
x = 87 m<br />
1112b<br />
20<br />
tan A =<br />
21<br />
21<br />
tan B =<br />
20<br />
1114b<br />
tan 65<br />
<br />
x<br />
=<br />
35<br />
( mult 35)<br />
<br />
35⋅ tan 65 = 35 ⋅<br />
<br />
35tan 65 = x<br />
<br />
x = 35tan 65<br />
35tan(65)<br />
x = 75 m<br />
1120d<br />
85<br />
tan v =<br />
81<br />
−1<br />
⎛85 ⎞<br />
v = tan ⎜ ⎟<br />
⎝81⎠ −1<br />
tan (85 81)<br />
v = 46,4<br />
<br />
x<br />
35<br />
2
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