さくらの個別指導 ( さくら教育研究所 ) A 2 P Q 3 R S T R S T P Q ( ) ( ) m n m n m n n n
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- やすもり あみおか
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1 A 2 P Q 3 R S T R S T P Q m n m n m n n n n
2 A B 1, 2 a b c a b A i j c d i, j , 2 2 1, 3 3 3, 3 B A B A B A B i, j A B A B 2 a b p q A B c d r s A B a p, b q, c r, d s 1.3 x y z w 4 3 2z w 2x + y x 3y 5 6 x 3y 4
3 A 2 A B A B i, j i, j A B A + B A B i, j i, j A B A B 2 2 a b p q a + p b + q + c d r s c + r d + s a b p q a p b q c d r s c r d s 1.2 A A + B A B B
4 4 1 A A 2 a b a b A A c d c d 1.5 A A A + A A 2 A O B 1 A + B B + A 2 A + B + C A + B + C 3 A + A O 4 A + O A 2 3 A + B + C A + B A B A A O
5 C k A k ka 2 a b ka kb k k c d kc kd 1.7 A A A 3 3A 4 1A
6 6 1 1A A 1A A 0A O ko O k l 1 kla kla 2 k + la ka + la 3 ka + B ka + kb a b p q 1.8 A B k 2 l 3 c d r s 1 kla, kla 2 k + la, ka + la 3 ka + B, ka + kb A B
7 A 3 6 X B A + X A + 3B 2A + X A + 3B 2X A + 3B X 1 A + 3B 2 { A B 3 2 X } 1 2A + 3X B 2 3A + X X + 2B
8 A a b x c d y a b x ax + by a b c d y cx + dy c d a b 1 2 P Q c d R 2 S 3 P Q R x y x y S P Q ax + by cx + dy ax + by cx + dy
9 B 2 2 a b p q ap + br aq + bs c d r s cp + dr cq + ds a c a c b p d r b p d r q ap + br s cp + dr q ap + br s cp + dr aq + bs cq + ds aq + bs cq + ds
10 10 1 C A l m B m n AB A i B j i, j l n A B A B x x + 2y + 3z y 4x + 5y + 6z z 7x + 8y + 9z x y z
11 A 1 ABC ABC } 2 A + BC AC + BC AB + C AB + AC 3 kab AkB kab k 1 3 A B C ABC 3 kab kab kab 2 a b p q x y 1.13 A B C k 3 c d r s z w 1 ABC, ABC 2 A + BC, AC + BC 3 AB + C, AB + AC
12 kab, AkB, kab B AB BA A B AB BA A B AB BA 1.6 A B AB BA A B A B x x A B
13 C E 0 1 a b E 2 A c d AE EA A E E 3 B 3 BE EB B 2 3 A A E O AE EA A AO OA O E O 1 0
14 14 1 a 0, b 0 ab 0 A O B O AB O A B AB O A B 4 a a b AB O a b D A AA A 2 AAA A 3 A n A n A 1 0 A A 3 A A
15 A 1 A 4 2 A 5 3 A A A 2 A 3 A A A
16 A a 0 0 b a b 1.2 A A A 2 a b a b a 2 ab + b a 2 ab + b { a ab + b a ±2 a 2 2 b 1 a 2 2 b 3 a 2, b 1 a 2, b 3 a b
17 1.19 A a 3 2 b A a b a A A b 0 8 a b a b
18 18 1 E 2 a b A c d A 2 a + da + ad bce O A 2 + ad bce a + da A 2 a b a b a 2 + bc ab + bd c d c d ac + cd bc + d 2 ad bc 0 ad bce 0 ad bc A 2 aa + d ba + d + ad bce ca + d da + d a b a + d c d a + da A 2 a + da + ad bce O
19 1.21 A a c b d 1 a + d 0, ad bc 0 A 2 O a + d 0, ad bc 1 A 2 E A B C A 3B + C 2 2A + B B 3C
20 A + B 2 A 2 + 2AB + B 2 2 A + E 2 A 2 + 2A + E E
21 A a a 1 A 2 E 2 AX XA E X X A A`1 AA`1 A`1 A E A`1`1 A a b A c d a + da A 2 ad bce d b B a + de A c a AB BA ad bce 1 1 ad bc 0 1 B A ad bc 2 ad bc 0 1 AB O A AB O A 1 A 1 AB O B O A 1 ABEBB a b c d 0 A O X AX E A A 2 a b A ad bc c d 0 A A`1 1 c a 0 A d b
22 A 2 B A A B A B C
23 a a a 0 aa a 2 2a 3 a + 1a 3 a + 1a 3 0 a 1, a a 4 a a + 2 B AX B X 2 A B AX B X A AX B A 1 A 1 AX A 1 B A 1 AX EX X A AX B X X A`1 B A Y A B Y A 1 Y BA 1
24 A 7 2 B X A A A AX B X X A B AX B A B AX B X Y A B Y
25 A 1 { ax + by p 1 cx + dy q 1 a b x p 2 c d y q 2 A a c b X d x y P p q 2 AX P 3 A { { 2x + 3y 4 x + 2y x + 4y 3 4x 7y 6 A 3 A 1 X A 1 P 1 a b x p A X P A c d y q AX P X X A 1 P x y A
26 { 5x + 2y 8 3x + y x y x y x 4 y { 2x + y 3 1 5x + 3y
27 2 { 3x + 7y 10 x + 4y B 25 3 A { 2x + 3y 1 4x + 6y { 2x + 3y 1 2x + 3y x + 3y 1 x y { 2x y 1 4x 2y x y 1 4x 2y 2 3
28 28 1 { 3x + y kx x + 4y ky k x 0 y 0 x y 1 { 3 kx + y 0 3 k 1 x 0 2x + 4 ky k y 0 x 0 y k4 k k 2 7k k 2, 5 k 2k 50 1 k 2 x + y 0 x y k 5 2x y 0 x y { 2x + 2y kx x y ky k x 0 y 0
29 A 2 x, y x, y x x, y { x x y y y x, y { x 1 x + 0 y y 0 x + 1 y O x, y x x 1 0 x y 0 1 y 1.28 x, y x, y 1 y y x, y x, y x, y 2 x, y y, x O x 3 y x y, x x, y y x
30 30 1 B 1 1 P Q Q P f g f Px, y y Qx, y Px, y a b c d { f x ax + by 1 y cx + dy Qx, y f 1 O x x a b x 1 y 1 f c d y a b 1 c d x y y x x y y x , , 15
31 , 2 2 4, , , 4 a 1.30 c b d 1 1 1, 0 a, c 2 0, 1 b, d
32 32 1 C P P a b c d a c b d 1 0, , 0 2, 4 0, 1 1, 5 1 A a b A c d a b 1 2 a c d 0 4 c a 2, c 4, b 1, d A 4 5 b d , 0 a, c 0, 1 b, d 1 a b c d , 0 2, 3 0, 1 1, 4 1
33 p, r a, c q, s b, d 1 p a q b A A A r c s d p q a b A r s c d 1.6 2, 1 4, 2 5, 3 7, 1 1 A A A , 0 2, 5 3, 4 6, 7 1 A
34 y 2x f 1 f 2 P Q l l PQ y 2x l l Px, y y l y 2x Qx, y Px, y PQ l PQ l Qx, y 2 y y x x 1 y + y 2 x + x O x 2 2 { x + 2y x + 2y 2x + y 2x y x y x y x y x y f x y x y
35 y 3x f 1 f
36 f g A B f Px, y Qx, y y g Qx, y Rx, y Px, y x x x x A, B g f Rx, y y y y y f g O x Qx, y x x x B A BA y y y BA Px, y Rx, y 1 f g g f 1 f g A B g f 1 g f BA f g A B g f BA
37 f g A B g f 2 f g 3 f f B 1 f Px, y Qx, y f A A 1 x x x A y y y A 1 x y A 1 Qx, y Px, y 1 f f `1 y O Px, y f 1 f Qx, y 1 f A A f f 1 f 1 A 1 x
38 f A f Q2, P A A A f f 1 A P 2, f g 1 f 1 g 1 2 f Q4, 1 P
39 A Px, y O θ 1 y P Qx, y Qx OP r OP x, y α x r cos α, y r sin α 1 Q O θ r α Px, y x x r cosα + θ, y r sinα + θ x rcos α cos θ sin α sin θ y rsin α cos θ + cos α sin θ 1 { x x cos θ y sin θ y x sin θ + y cos θ x y cos θ sin θ sin θ cos θ O θ O θ 1 cos θ sin θ sin θ cos θ x y 1 θ II
40 A P2, 4 Q 3 cos 30 sin 30 1 A 2 2 sin 30 cos Q 3 2, A P0, 2 Q
41 B θ 1 f y f 1 θ 1 f 1 cos θ sin θ sin θ cos θ O cos θ sin θ sin θ cos θ Q θ f 1 P x cos θ sin θ sin θ cos θ 1 cos θ sin θ sin θ cos θ f f 1
42 42 1 x y θ l h P l P Q P Q θ θ Q P Q P O Q x θ y f x g θ P f 1 h O f 1 g f Q l x x h 1 cos θ sin θ 1 0 cos θ sin θ sin θ cos θ 0 1 sin θ cos θ cos θ sin θ cos θ sin θ sin θ cos θ sin θ cos θ cos 2 θ sin 2 θ 2 sin θ cos θ 2 sin θ cos θ sin 2 θ cos 2 θ cos 2θ sin 2θ sin 2θ cos 2θ
43 A B AB AB 1 B 1 A f g A B f g 2, 3 6 P3, 1 x Q Q 150 R R
44 ABB 1 A 1 E B 1 A 1 AB E 5 5, , A cos θ sin θ sin θ cos θ cos θ sin θ sin θ cos θ
45 A A 2 + xa + ye O x y 1 5 E 2 O A B A B A 1 B 1 AB A E A ke k
46 , 2 7, 4 2, 1 4, 3 1 A 3 a 6 A 1 f f f b a A a b , 4
47 1.3.2 B 8 2 A B A + B A 2 B A B x 3 9 A A 2 7A + 12E O x y 2 y E 2 O 2 10 A x 1 3 y 4 A 3 A x y
48 E 1 A XA Y A X Y 2 A 2 2A + E O A E 12 A f f 1 2 f f f f 1 A 3
49 A B 10 A 1 A A 2 E 12 f x 8 y 17 [ A 2 + xa + ye x + y 16 2x 8 + x x + y ] 7 + 3x + y x x x + y 0 3 A 1 B AB A B 4 k 2 [ A ke k k [ 1 2 A A a 2 b ] k4 k ] A 2 A 9 + ab 3 3a a 2 a 3b ab b ab + a 2 a , [ cos 30 sin 30 sin 30 cos ]
50 50 1 [ 2A 2B A B ] 9 x 1 y 6 x 6 y 1 [ x 3 A 2 y ] x 2 7x y 2 7y x + y x 2 y 2 x 2 y 6 A A [ A 1 A A 2 E, A A x 2 3 x y + 4 3x + 3y y [ a b 2 A c d A 2 a + da ] + ad bce O a + d 2 ad bc A [ ] cos 60 sin 60 1 A sin 60 cos 60 ]
2 (1) a = ( 2, 2), b = (1, 2), c = (4, 4) c = l a + k b l, k (2) a = (3, 5) (1) (4, 4) = l( 2, 2) + k(1, 2), (4, 4) = ( 2l + k, 2l 2k) 2l + k = 4, 2l
ABCDEF a = AB, b = a b (1) AC (3) CD (2) AD (4) CE AF B C a A D b F E (1) AC = AB + BC = AB + AO = AB + ( AB + AF) = a + ( a + b) = 2 a + b (2) AD = 2 AO = 2( AB + AF) = 2( a + b) (3) CD = AF = b (4) CE
A(6, 13) B(1, 1) 65 y C 2 A(2, 1) B( 3, 2) C 66 x + 2y 1 = 0 2 A(1, 1) B(3, 0) P 67 3 A(3, 3) B(1, 2) C(4, 0) (1) ABC G (2) 3 A B C P 6
1 1 1.1 64 A6, 1) B1, 1) 65 C A, 1) B, ) C 66 + 1 = 0 A1, 1) B, 0) P 67 A, ) B1, ) C4, 0) 1) ABC G ) A B C P 64 A 1, 1) B, ) AB AB = 1) + 1) A 1, 1) 1 B, ) 1 65 66 65 C0, k) 66 1 p, p) 1 1 A B AB A 67
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熊本県数学問題正解
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.1 n.1 1 A T ra A A a b c d A 2 a b a b c d c d a 2 + bc ab + bd ac + cd bc + d 2 a 2 + bc ba + d ca + d bc + d 2 A a + d b c T ra A T ra A 2 A 2 A A 2 A 2 A n A A n cos 2π sin 2π n n A k sin 2π cos 2π
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高等学校学習指導要領解説 数学編
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HITACHI 液晶プロジェクター CP-AX3505J/CP-AW3005J 取扱説明書 -詳細版- 【技術情報編】
B A C E D 1 3 5 7 9 11 13 15 17 19 2 4 6 8 10 12 14 16 18 H G I F J M N L K Y CB/PB CR/PR COMPONENT VIDEO OUT RS-232C LAN RS-232C LAN LAN BE EF 03 06 00 2A D3 01 00 00 60 00 00 BE EF 03 06 00 BA D2 01
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取扱説明書 -詳細版- 液晶プロジェクター CP-AW3019WNJ
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2/8 一次二次当該 42 AX 変圧器 なし 43 AY 変圧器 なし 44 BA 変圧器 なし 45 BB 変圧器 なし 46 BC 変圧器 なし
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０４年度LS民法Ⅰ教材改訂版.PDF
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HITACHI 液晶プロジェクター CP-EX301NJ/CP-EW301NJ 取扱説明書 -詳細版- 【技術情報編】 日本語
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数学Ⅲ立体アプローチ.pdf
Ⅲ Ⅲ DOLOR SET AMET . cos x cosx = cos x cosx = (cosx + )(cosx ) = cosx = cosx = 4. x cos x cosx =. x y = cosx y = cosx. x =,x = ( y = cosx y = cosx. x V y = cosx y = sinx 6 5 6 - ( cosx cosx ) d x = [
BD = a, EA = b, BH = a, BF = b 3 EF B, EOA, BOD EF B EOA BF : AO = BE : AE, b : = BE : b, AF = BF = b BE = bb. () EF = b AF = b b. (2) EF B BOD EF : B
2000 8 3.4 p q θ = 80 B E a H F b θ/2 O θ/2 D A B E BD = a, EA = b, BH = a, BF = b 3 EF B, EOA, BOD EF B EOA BF : AO = BE : AE, b : = BE : b, AF = BF = b BE = bb. () EF = b AF = b b. (2) EF B BOD EF :
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5. F(, 0) = = 4 = 4 O = 4 =. ( = = 4 ) = 4 ( 4 ), 0 = 4 4 O 4 = 4. () = 8 () = 4
... A F F l F l F(p, 0) = p p > 0 l p 0 P(, ) H P(, ) P l PH F PF = PH PF = PH p O p ( p) + = { ( p)} = 4p l = 4p (p 0) F(p, 0) = p O 3 5 5. F(, 0) = = 4 = 4 O = 4 =. ( = = 4 ) = 4 ( 4 ), 0 = 4 4 O 4 =
x () g(x) = f(t) dt f(x), F (x) 3x () g(x) g (x) f(x), F (x) (3) h(x) = x 3x tf(t) dt.9 = {(x, y) ; x, y, x + y } f(x, y) = xy( x y). h (x) f(x), F (x
[ ] IC. f(x) = e x () f(x) f (x) () lim f(x) lim f(x) x + x (3) lim f(x) lim f(x) x + x (4) y = f(x) ( ) ( s46). < a < () a () lim a log xdx a log xdx ( ) n (3) lim log k log n n n k=.3 z = log(x + y ),
1/68 A. 電気所 ( 発電所, 変電所, 配電塔 ) における変圧器の空き容量一覧 平成 31 年 3 月 6 日現在 < 留意事項 > (1) 空容量は目安であり 系統接続の前には 接続検討のお申込みによる詳細検討が必要となります その結果 空容量が変更となる場合があります (2) 特に記載
1/68 A. 電気所 ( 発電所, 変電所, 配電塔 ) における変圧器の空き容量一覧 平成 31 年 3 月 6 日現在 < 留意事項 > (1) 空容量は目安であり 系統接続の前には 接続検討のお申込みによる詳細検討が必要となります その結果 空容量が変更となる場合があります (2) 特に記載のない限り 熱容量を考慮した空き容量を記載しております その他の要因 ( 電圧や系統安定度など ) で連系制約が発生する場合があります
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0. =. =. (999). 3(983). (980). (985). (966). 3. := :=. A A. A A. := := 4 5 A B A B A B. A = B A B A B B A. A B A B, A B, B. AP { A, P } = { : A, P } = { A P }. A = {0, }, A, {0, }, {0}, {}, A {0}, {}.
(1.2) T D = 0 T = D = 30 kn 1.2 (1.4) 2F W = 0 F = W/2 = 300 kn/2 = 150 kn 1.3 (1.9) R = W 1 + W 2 = = 1100 N. (1.9) W 2 b W 1 a = 0
1 1 1.1 1.) T D = T = D = kn 1. 1.4) F W = F = W/ = kn/ = 15 kn 1. 1.9) R = W 1 + W = 6 + 5 = 11 N. 1.9) W b W 1 a = a = W /W 1 )b = 5/6) = 5 cm 1.4 AB AC P 1, P x, y x, y y x 1.4.) P sin 6 + P 1 sin 45
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yoshi@image.med.osaka-u.ac.jp http://www.image.med.osaka-u.ac.jp/member/yoshi/ II Excel, Mathematica Mathematica Osaka Electro-Communication University (2007 Apr) 09849-31503-64015-30704-18799-390 http://www.image.med.osaka-u.ac.jp/member/yoshi/
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122 6 A 0 (p 0 q 0 ). ( p 0 = p cos ; q sin + p 0 (6.1) q 0 = p sin + q cos + q 0,, 2 Ox, O 1 x 1., q ;q ( p 0 = p cos + q sin + p 0 (6.2) q 0 = p sin
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dynamics-solution2.dvi
1 1. (1) a + b = i +3i + k () a b =5i 5j +3k (3) a b =1 (4) a b = 7i j +1k. a = 14 l =/ 14, m=1/ 14, n=3/ 14 3. 4. 5. df (t) d [a(t)e(t)] =ti +9t j +4k, = d a(t) d[a(t)e(t)] e(t)+ da(t) d f (t) =i +18tj
n Y 1 (x),..., Y n (x) 1 W (Y 1 (x),..., Y n (x)) 0 W (Y 1 (x),..., Y n (x)) = Y 1 (x)... Y n (x) Y 1(x)... Y n(x) (x)... Y n (n 1) (x) Y (n 1)
D d dx 1 1.1 n d n y a 0 dx n + a d n 1 y 1 dx n 1 +... + a dy n 1 dx + a ny = f(x)...(1) dk y dx k = y (k) a 0 y (n) + a 1 y (n 1) +... + a n 1 y + a n y = f(x)...(2) (2) (2) f(x) 0 a 0 y (n) + a 1 y
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Gmech08.dvi
145 13 13.1 13.1.1 0 m mg S 13.1 F 13.1 F /m S F F 13.1 F mg S F F mg 13.1: m d2 r 2 = F + F = 0 (13.1) 146 13 F = F (13.2) S S S S S P r S P r r = r 0 + r (13.3) r 0 S S m d2 r 2 = F (13.4) (13.3) d 2
, = = 7 6 = 42, =
http://www.ss.u-tokai.ac.jp/~mahoro/2016autumn/alg_intro/ 1 1 2016.9.26, http://www.ss.u-tokai.ac.jp/~mahoro/2016autumn/alg_intro/ 1.1 1 214 132 = 28258 2 + 1 + 4 1 + 3 + 2 = 7 6 = 42, 4 + 2 = 6 2 + 8
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1 (1) ( i ) 60 (ii) 75 (iii) 315 (2) π ( i ) (ii) π (iii) 7 12 π ( (3) r, AOB = θ 0 < θ < π ) OAB A 2 OB P ( AB ) < ( AP ) (4) 0 < θ < π 2 sin θ
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