) 9 81
|
|
- なおみ いんそん
- 4 years ago
- Views:
Transcription
1 ) 9 81
2 natural numbers 1, 2, 3, 4, 4.2, 3, 2, 1, 0, 1, 2, 3, integral numbers integers 1, 2, 3,, 3, 2, ( ) m, n m 0 n m 82
3 rational numbers m 1 ( ) 3 = = =
4 ( ) c a, b a 2 + b 2 = c 2 a = 1, b = 1 c c 2 =
5 c 2 = 2 c 2 = irrational numbers real numbers x = 3 c 2 = 2 4 I p
6 x = x = 3 x = x = 3 3x = x = 5 yes ax + b = 0 5 a, b x = b a 5 2x + 3 x = 5 86
7 ax + b = 0 a 0 a, b ax 2 + bx + c = 0 ( a 0) c 2 = 2 x 2 2 = 0 x = ax + b = 0 ax + b = 0 ( a 0) 87
8 x = = = = = (1) (2) 1 7 (3)
9 < = r < b 7 10 x = x = x = 9 x = 1 1 =
10 ( ) ( ) ( ) a > = 0, b > = 0 a < b a < b 1 < 2 <
11 = 1. 0, 1, 2, 3, 4, 5, 6, 7, 8, , 1.1, 1.2,, 1.9 (1.0) 2 = 1, (1.1) 2 = 1.21,, (1.4) 2 = 1.96, (1.5) 2 = < 2 < = =
12 2 = 3 = 5 = ( ) 1, 2, 3, 0 { 1, 2, 3, 2 3 2, π 1 2 = = = = =
13 1 3 1 = = = 1. 1 ( ) ( ) 46 7 a a + 1 a (01 ( )) ( ) 0 ( a 0 86 ax + b = 0, (a 0) a 0 93
14 a b = x b x = a a b x b x a 0 0 x = a x 0 x = 0 a 0 x a = 0 0 x = a b = x b + x = a a b a + ( b) a b = a + ( b) b b a b = a 1 b
15 ( ) 1 a, b a + b = b + a, ab = ba 2 a, b, c (a + b) + c = a + (b + c), (ab)c = a(bc) 3 a a + 0 = a, a 1 = a 11 4 a a + ( a) = 0, a 1 a = 1 ( a 0 ) 12 5 a, b, c a(b + c) = ab + ac a = a 0 + a = a, 1 a = a 0 + a = a + 0 = a a + 0 = a 12 a + ( b) = a b a + ( a) = a a 13 (a + b)c = ac + bc 24 a(b + c) = ab + ac (a + b)c = ac + bc 95
16 15 a 0 a = 0 a = b = a c = b c = 0 (0 + 0) a = 0 a 0 a + 0 a = 0 a 0 a 96
17 0 + 0 = 0 (0 + 0) a = 0 a 0 a + 0 a = 0 a 0 a 0 a = 0 14 ( ) 25 ( 1)a = a 1 + ( 1) = 0 26 ( 1) ( 1) = ( 1) = 0 ( ) (1) ab = 0 a = 0 b = 0 (2) a 0 b 0 ab 0 (1) 2 (2) 2 1 (3) ( ) 97
18 4.8.2 ( ) a a > 0, a = 0, a < 0 ( ) a > 0 a a < 0 a ( ) 0 a b 0 ( ) a b > 0, a b = 0, a b < 0 a > b, a = b, a < b a > b a = b a > = b a < b a = b a < = b 17 ( ) 14 0 a 15 a > b a b b a 16 a = b = a c = b c (a c) (b c) = a c b + c = a b a b = 0 (a c) (b c) = 0 a c = b c 17 a > = b a b a < = b a b 98
19 ( ) a > 0, b > 0 a + b > 0, ab > 0 ( ) 1 a > b, b > c a > c 2 a > b a + c > b + c, a c > b c 3 a > b, c > 0 ac > bc, a c > b c 4 a > b, c < 0 ac < bc, a c < b c 5 a > b, c > d a + c > b + d 6 a > = b a < = b a = b a > b, b > c a b > 0, b c > 0 (a b) + (b c) > 0 a c > 0 a > c 3 a > b a b > 0 (a b)c > ac bc > 0 ac > bc 1 c 0 1 c = 0 c 1 = 1 0 c < 0 c 1 < 0 c > 0 1 c > 0 18 a c = a 1 c 19 a c > b c ( ) 27 a > 0 a < A A A 1 c = 0 B 1 c < 0 C 1 > 0 c 19 99
20 ( ) a a O E O E E O O E O 0 E 1 OE 21 O OE OE 1cm OE 1cm cm m cm m 100
21 ( ) P x P P(x) O ( ) 47 A, B, C D(2.5), E( 2) D, E C B A ( ) a { a ( a > a = = 0 ) a ( a < 0) a ( ) (1) 1 (2) O a A a
22 (3)? a 2 { a ( a > a 2 = = 0 ) a ( a ) ( ) a a = a 2 a 2 = a 2 ( ) 3 = 3, 4 = 4, 0 = 0 ( ) 48 (1) 5 (2) 2.4 (3) 3 4 x = 2 x x2 = 2 x 2 = 4 x = ±2 x = 2 x ( ) 102
23 ( x = a ) a > = 0 x = a x ±a x = a x x = a x = ±a 0 a < 0 ( ) 16 x 2 = 3 x 2 = ±3 x 2 = 3 x 2 = 3 x 2 = ±3 x = 5, 1 ( ) ( ) 49 (1) x + 3 = 5 (2) 3x 1 = 6 ( ) 1 a > = 0 1 a = 0 a = 0 2 ab = a b, a = a b b b 0 3 a = a 4 a + b < = a + b 2 ab = (ab) 2 = a 2 b 2 = a 2 b 2 = a b 103
24 ( ) ( ) ( ) 2 A(a) B(b) d d = b a ( ) AB b a a b 3 a b = (a b) = a + b = b a ( ) A(2) B(5) d C(3) D( 1) d d = 5 3 = 2 = 2 d = 1 3 = 4 = 4 ( ) 50 A(3) B(9) C( 3) AB BC CA
25 ) (
26
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
More information> > <., vs. > x 2 x y = ax 2 + bx + c y = 0 2 ax 2 + bx + c = 0 y = 0 x ( x ) y = ax 2 + bx + c D = b 2 4ac (1) D > 0 x (2) D = 0 x (3
13 2 13.0 2 ( ) ( ) 2 13.1 ( ) ax 2 + bx + c > 0 ( a, b, c ) ( ) 275 > > 2 2 13.3 x 2 x y = ax 2 + bx + c y = 0 2 ax 2 + bx + c = 0 y = 0 x ( x ) y = ax 2 + bx + c D = b 2 4ac (1) D >
More information04年度LS民法Ⅰ教材改訂版.PDF
?? A AB A B C AB A B A B A B A A B A 98 A B A B A B A B B A A B AB AB A B A BB A B A B A B A B A B A AB A B B A B AB A A C AB A C A A B A B B A B A B B A B A B B A B A B A B A B A B A B A B
More information48 * *2
374-1- 17 2 1 1 B A C A C 48 *2 49-2- 2 176 176 *2 -3- B A A B B C A B A C 1 B C B C 2 B C 94 2 B C 3 1 6 2 8 1 177 C B C C C A D A A B A 7 B C C A 3 C A 187 187 C B 10 AC 187-4- 10 C C B B B B A B 2 BC
More information140 120 100 80 60 40 20 0 115 107 102 99 95 97 95 97 98 100 64 72 37 60 50 53 50 36 32 18 H18 H19 H20 H21 H22 H23 H24 H25 H26 H27 1 100 () 80 60 40 20 0 1 19 16 10 11 6 8 9 5 10 35 76 83 73 68 46 44 H11
More information2 (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
More information7 27 7.1........................................ 27 7.2.......................................... 28 1 ( a 3 = 3 = 3 a a > 0(a a a a < 0(a a a -1 1 6
26 11 5 1 ( 2 2 2 3 5 3.1...................................... 5 3.2....................................... 5 3.3....................................... 6 3.4....................................... 7
More information行列代数2010A
a ij i j 1) i +j i, j) ij ij 1 j a i1 a ij a i a 1 a j a ij 1) i +j 1,j 1,j +1 a i1,1 a i1,j 1 a i1,j +1 a i1, a i +1,1 a i +1.j 1 a i +1,j +1 a i +1, a 1 a,j 1 a,j +1 a, ij i j 1,j 1,j +1 ij 1) i +j a
More informationPSCHG000.PS
a b c a ac bc ab bc a b c a c a b bc a b c a ac bc ab bc a b c a ac bc ab bc a b c a ac bc ab bc de df d d d d df d d d d d d d a a b c a b b a b c a b c b a a a a b a b a
More informationkoji07-01.dvi
2007 I II III 1, 2, 3, 4, 5, 6, 7 5 10 19 (!) 1938 70 21? 1 1 2 1 2 2 1! 4, 5 1? 50 1 2 1 1 2 2 1?? 2 1 1, 2 1, 2 1, 2, 3,... 3 1, 2 1, 3? 2 1 3 1 2 1 1, 2 2, 3? 2 1 3 2 3 2 k,l m, n k,l m, n kn > ml...?
More information漸化式のすべてのパターンを解説しましたー高校数学の達人・河見賢司のサイト
https://www.hmg-gen.com/tuusin.html https://www.hmg-gen.com/tuusin1.html 1 2 OK 3 4 {a n } (1) a 1 = 1, a n+1 a n = 2 (2) a 1 = 3, a n+1 a n = 2n a n a n+1 a n = ( ) a n+1 a n = ( ) a n+1 a n {a n } 1,
More information5 n P j j (P i,, P k, j 1) 1 n n ) φ(n) = n (1 1Pj [ ] φ φ P j j P j j = = = = = n = φ(p j j ) (P j j P j 1 j ) P j j ( 1 1 P j ) P j j ) (1 1Pj (1 1P
p P 1 n n n 1 φ(n) φ φ(1) = 1 1 n φ(n), n φ(n) = φ()φ(n) [ ] n 1 n 1 1 n 1 φ(n) φ() φ(n) 1 3 4 5 6 7 8 9 1 3 4 5 6 7 8 9 1 4 5 7 8 1 4 5 7 8 10 11 1 13 14 15 16 17 18 19 0 1 3 4 5 6 7 19 0 1 3 4 5 6 7
More information1
005 11 http://www.hyuki.com/girl/ http://www.hyuki.com/story/tetora.html http://www.hyuki.com/ Hiroshi Yuki c 005, All rights reserved. 1 1 3 (a + b)(a b) = a b (x + y)(x y) = x y a b x y a b x y 4 5 6
More information, 1. x 2 1 = (x 1)(x + 1) x 3 1 = (x 1)(x 2 + x + 1). a 2 b 2 = (a b)(a + b) a 3 b 3 = (a b)(a 2 + ab + b 2 ) 2 2, 2.. x a b b 2. b {( 2 a } b )2 1 =
x n 1 1.,,.,. 2..... 4 = 2 2 12 = 2 2 3 6 = 2 3 14 = 2 7 8 = 2 2 2 15 = 3 5 9 = 3 3 16 = 2 2 2 2 10 = 2 5 18 = 2 3 3 2, 3, 5, 7, 11, 13, 17, 19.,, 2,.,.,.,?.,,. 1 , 1. x 2 1 = (x 1)(x + 1) x 3 1 = (x 1)(x
More information1 12 ( )150 ( ( ) ) x M x 0 1 M 2 5x 2 + 4x + 3 x 2 1 M x M 2 1 M x (x + 1) 2 (1) x 2 + x + 1 M (2) 1 3 M (3) x 4 +
( )5 ( ( ) ) 4 6 7 9 M M 5 + 4 + M + M M + ( + ) () + + M () M () 4 + + M a b y = a + b a > () a b () y V a () V a b V n f() = n k= k k () < f() = log( ) t dt log () n+ (i) dt t (n + ) (ii) < t dt n+ n
More informationO E ( ) A a A A(a) O ( ) (1) O O () 467
1 1.0 16 1 ( 1 1 ) 1 466 1.1 1.1.1 4 O E ( ) A a A A(a) O ( ) (1) O O () 467 ( ) A(a) O A 0 a x ( ) A(3), B( ), C 1, D( 5) DB C A x 5 4 3 1 0 1 3 4 5 16 A(1), B( 3) A(a) B(b) d ( ) A(a) B(b) d AB d = d(a,
More information行列代数2010A
(,) A (,) B C = AB a 11 a 1 a 1 b 11 b 1 b 1 c 11 c 1 c a A = 1 a a, B = b 1 b b, C = AB = c 1 c c a 1 a a b 1 b b c 1 c c i j ij a i1 a i a i b 1j b j b j c ij = a ik b kj b 1j b j AB = a i1 a i a ik
More information2002.N.x.h.L.......g9/20
1 2 3 4 5 6 1 2 3 4 5 8 9 1 11 11 12 13 k 14 l 16 m 17 n 18 o 19 k 2 l 2 m 21 n 21 o 22 p 23 q 23 r 24 24 25 26 27 28 k 28 l 29 m 29 3 31 34 42 44 1, 8, 6, 4, 2, 1,2 1, 8 6 4 2 1, 8, 6, 4, 2, 1,2 1, 8
More information76 3 B m n AB P m n AP : PB = m : n A P B P AB m : n m < n n AB Q Q m A B AQ : QB = m : n (m n) m > n m n Q AB m : n A B Q P AB Q AB 3. 3 A(1) B(3) C(
3 3.1 3.1.1 1 1 A P a 1 a P a P P(a) a P(a) a P(a) a a 0 a = a a < 0 a = a a < b a > b A a b a B b B b a b A a 3.1 A() B(5) AB = 5 = 3 A(3) B(1) AB = 3 1 = A(a) B(b) AB AB = b a 3.1 (1) A(6) B(1) () A(
More informationad bc A A A = ad bc ( d ) b c a n A n A n A A det A A ( ) a b A = c d det A = ad bc σ {,,,, n} {,,, } {,,, } {,,, } ( ) σ = σ() = σ() = n sign σ sign(
I n n A AX = I, YA = I () n XY A () X = IX = (YA)X = Y(AX) = YI = Y X Y () XY A A AB AB BA (AB)(B A ) = A(BB )A = AA = I (BA)(A B ) = B(AA )B = BB = I (AB) = B A (BA) = A B A B A = B = 5 5 A B AB BA A
More information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
1 1.1 1.1.1 A 2 P Q 3 R S T R S T P 80 50 60 Q 90 40 70 80 50 60 90 40 70 8 5 6 1 1 2 9 4 7 2 1 2 3 1 2 m n m n m n n n n 1.1 8 5 6 9 4 7 2 6 0 8 2 3 2 2 2 1 2 1 1.1 2 4 7 1 1 3 7 5 2 3 5 0 3 4 1 6 9 1
More information(1) θ a = 5(cm) θ c = 4(cm) b = 3(cm) (2) ABC A A BC AD 10cm BC B D C 99 (1) A B 10m O AOB 37 sin 37 = cos 37 = tan 37
4. 98 () θ a = 5(cm) θ c = 4(cm) b = (cm) () D 0cm 0 60 D 99 () 0m O O 7 sin 7 = 0.60 cos 7 = 0.799 tan 7 = 0.754 () xkm km R km 00 () θ cos θ = sin θ = () θ sin θ = 4 tan θ = () 0 < x < 90 tan x = 4 sin
More information70 : 20 : A B (20 ) (30 ) 50 1
70 : 0 : A B (0 ) (30 ) 50 1 1 4 1.1................................................ 5 1. A............................................... 6 1.3 B............................................... 7 8.1 A...............................................
More information1 (1) vs. (2) (2) (a)(c) (a) (b) (c) 31 2 (a) (b) (c) LENCHAR
() 601 1 () 265 OK 36.11.16 20 604 266 601 30.4.5 (1) 91621 3037 (2) 20-12.2 20-13 (3) ex. 2540-64 - LENCHAR 1 (1) vs. (2) (2) 605 50.2.13 41.4.27 10 10 40.3.17 (a)(c) 2 1 10 (a) (b) (c) 31 2 (a) (b) (c)
More informationuntitled
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/
More information0.6 A = ( 0 ),. () A. () x n+ = x n+ + x n (n ) {x n }, x, x., (x, x ) = (0, ) e, (x, x ) = (, 0) e, {x n }, T, e, e T A. (3) A n {x n }, (x, x ) = (,
[ ], IC 0. A, B, C (, 0, 0), (0,, 0), (,, ) () CA CB ACBD D () ACB θ cos θ (3) ABC (4) ABC ( 9) ( s090304) 0. 3, O(0, 0, 0), A(,, 3), B( 3,, ),. () AOB () AOB ( 8) ( s8066) 0.3 O xyz, P x Q, OP = P Q =
More informationさくらの個別指導 ( さくら教育研究所 ) A 2 2 Q ABC 2 1 BC AB, AC AB, BC AC 1 B BC AB = QR PQ = 1 2 AC AB = PR 3 PQ = 2 BC AC = QR PR = 1
... 0 60 Q,, = QR PQ = = PR PQ = = QR PR = P 0 0 R 5 6 θ r xy r y y r, x r, y x θ x θ θ (sine) (cosine) (tangent) sin θ, cos θ, tan θ. θ sin θ = = 5 cos θ = = 4 5 tan θ = = 4 θ 5 4 sin θ = y r cos θ =
More information1 29 ( ) I II III A B (120 ) 2 5 I II III A B (120 ) 1, 6 8 I II A B (120 ) 1, 6, 7 I II A B (100 ) 1 OAB A B OA = 2 OA OB = 3 OB A B 2 :
9 ( ) 9 5 I II III A B (0 ) 5 I II III A B (0 ), 6 8 I II A B (0 ), 6, 7 I II A B (00 ) OAB A B OA = OA OB = OB A B : P OP AB Q OA = a OB = b () OP a b () OP OQ () a = 5 b = OP AB OAB PAB a f(x) = (log
More informationH27 28 4 1 11,353 45 14 10 120 27 90 26 78 323 401 27 11,120 D A BC 11,120 H27 33 H26 38 H27 35 40 126,154 129,125 130,000 150,000 5,961 11,996 6,000 15,000 688,684 708,924 700,000 750,000 1300 H28
More information学習の手順
NAVI 2 MAP 3 m 17 13 19 12 17 24 1 20 18 23 18 12 1 12 17 11 14 16 19 22 m 12 16 A 16 20 B 20 24 24 28 C 20 AC 40 cm AD A 0.20 12 0.300 B 0.200 0.12 12 C D 40 1.000 20 2 2 0 20 30 cm 14 1 1 160 160 16
More information68 A mm 1/10 A. (a) (b) A.: (a) A.3 A.4 1 1
67 A Section A.1 0 1 0 1 Balmer 7 9 1 0.1 0.01 1 9 3 10:09 6 A.1: A.1 1 10 9 68 A 10 9 10 9 1 10 9 10 1 mm 1/10 A. (a) (b) A.: (a) A.3 A.4 1 1 A.1. 69 5 1 10 15 3 40 0 0 ¾ ¾ É f Á ½ j 30 A.3: A.4: 1/10
More informationA (1) = 4 A( 1, 4) 1 A 4 () = tan A(0, 0) π A π
4 4.1 4.1.1 A = f() = f() = a f (a) = f() (a, f(a)) = f() (a, f(a)) f(a) = f 0 (a)( a) 4.1 (4, ) = f() = f () = 1 = f (4) = 1 4 4 (4, ) = 1 ( 4) 4 = 1 4 + 1 17 18 4 4.1 A (1) = 4 A( 1, 4) 1 A 4 () = tan
More information.1 A cos 2π 3 sin 2π 3 sin 2π 3 cos 2π 3 T ra 2 deta T ra 2 deta T ra 2 deta a + d 2 ad bc a 2 + d 2 + ad + bc A 3 a b a 2 + bc ba + d c d ca + d bc +
.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
More informationEPSON VP-1200 取扱説明書
4020178-01 w p s 2 p 3 4 5 6 7 8 p s s s p 9 p A B p C 10 D p E 11 F G H H 12 p G I s 13 p s A D p B 14 C D E 15 F s p G 16 A B p 17 18 s p s 19 p 20 21 22 A B 23 A B C 24 A B 25 26 p s p s 27 28 p s p
More informationII
II 16 16.0 2 1 15 x α 16 x n 1 17 (x α) 2 16.1 16.1.1 2 x P (x) P (x) = 3x 3 4x + 4 369 Q(x) = x 4 ax + b ( ) 1 P (x) x Q(x) x P (x) x P (x) x = a P (a) P (x) = x 3 7x + 4 P (2) = 2 3 7 2 + 4 = 8 14 +
More informationB. 41 II: 2 ;; 4 B [ ] S 1 S 2 S 1 S O S 1 S P 2 3 P P : 2.13:
B. 41 II: ;; 4 B [] S 1 S S 1 S.1 O S 1 S 1.13 P 3 P 5 7 P.1:.13: 4 4.14 C d A B x l l d C B 1 l.14: AB A 1 B 0 AB 0 O OP = x P l AP BP AB AP BP 1 (.4)(.5) x l x sin = p l + x x l (.4)(.5) m d A x P O
More information6 2 2 x y x y t P P = P t P = I P P P ( ) ( ) ,, ( ) ( ) cos θ sin θ cos θ sin θ, sin θ cos θ sin θ cos θ y x θ x θ P
6 x x 6.1 t P P = P t P = I P P P 1 0 1 0,, 0 1 0 1 cos θ sin θ cos θ sin θ, sin θ cos θ sin θ cos θ x θ x θ P x P x, P ) = t P x)p ) = t x t P P ) = t x = x, ) 6.1) x = Figure 6.1 Px = x, P=, θ = θ P
More informationTaro13-第6章(まとめ).PDF
% % % % % % % % 31 NO 1 52,422 10,431 19.9 10,431 19.9 1,380 2.6 1,039 2.0 33,859 64.6 5,713 10.9 2 8,292 1,591 19.2 1,591 19.2 1,827 22.0 1,782 21.5 1,431 17.3 1,661 20.0 3 1,948 1,541 79.1 1,541 79.1
More information17 ( ) II III A B C(100 ) 1, 2, 6, 7 II A B (100 ) 2, 5, 6 II A B (80 ) 8 10 I II III A B C(80 ) 1 a 1 = 1 2 a n+1 = a n + 2n + 1 (n = 1,
17 ( ) 17 5 1 4 II III A B C(1 ) 1,, 6, 7 II A B (1 ), 5, 6 II A B (8 ) 8 1 I II III A B C(8 ) 1 a 1 1 a n+1 a n + n + 1 (n 1,,, ) {a n+1 n } (1) a 4 () a n OA OB AOB 6 OAB AB : 1 P OB Q OP AQ R (1) PQ
More information1 θ i (1) A B θ ( ) A = B = sin 3θ = sin θ (A B sin 2 θ) ( ) 1 2 π 3 < = θ < = 2 π 3 Ax Bx3 = 1 2 θ = π sin θ (2) a b c θ sin 5θ = sin θ f(sin 2 θ) 2
θ i ) AB θ ) A = B = sin θ = sin θ A B sin θ) ) < = θ < = Ax Bx = θ = sin θ ) abc θ sin 5θ = sin θ fsin θ) fx) = ax bx c ) cos 5 i sin 5 ) 5 ) αβ α iβ) 5 α 4 β α β β 5 ) a = b = c = ) fx) = 0 x x = x =
More information1 2 3 4 5 6 X Y ABC A ABC B 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 13 18 30 P331 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 ( ) 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59
More information26 2 3 4 5 8 9 6 7 2 3 4 5 2 6 7 3 8 9 3 0 4 2 4 3 4 4 5 6 5 7 6 2 2 A B C ABC 8 9 6 3 3 4 4 20 2 6 2 2 3 3 4 4 5 5 22 6 6 7 7 23 6 2 2 3 3 4 4 24 2 2 3 3 4 4 25 6 2 2 3 3 4 4 26 2 2 3 3 27 6 4 4 5 5
More informationmogiJugyo_slide_full.dvi
a 2 + b 2 = c 2 (a, b, c) a 2 a 2 = a a a 1/ 78 2/ 78 3/ 78 4/ 78 180 5/ 78 http://www.kaijo.ed.jp/ 6/ 78 a, b, c ABC C a b B c A C 90 a 2 + b 2 = c 2 7/ 78 C a b a 2 +b 2 = c 2 B c A a 2 a a 2 = a a 8/
More informationEPSON エプソンプリンタ共通 取扱説明書 ネットワーク編
K L N K N N N N N N N N N N N N L A B C N N N A AB B C L D N N N N N L N N N A L B N N A B C N L N N N N L N A B C D N N A L N A L B C D N L N A L N B C N N D E F N K G H N A B C A L N N N N D D
More informationありがとうございました
- 1 - - 2 - - 3 - - 4 - - 5 - 1 2 AB C A B C - 6 - - 7 - - 8 - 10 1 3 1 10 400 8 9-9 - 2600 1 119 26.44 63 50 15 325.37 131.99 457.36-10 - 5 977 1688 1805 200 7 80-11 - - 12 - - 13 - - 14 - 2-1 - 15 -
More informationEPSON エプソンプリンタ共通 取扱説明書 ネットワーク編
K L N K N N N N N N N N N N N N L A B C N N N A AB B C L D N N N N N L N N N A L B N N A B C N L N N N N L N A B C D N N A L N A L B C D N L N A L N B C N N D E F N K G H N A B C A L N N N N D D
More information公務員人件費のシミュレーション分析
47 50 (a) (b) (c) (7) 11 10 2018 20 2028 16 17 18 19 20 21 22 20 90.1 9.9 20 87.2 12.8 2018 10 17 6.916.0 7.87.4 40.511.6 23 0.0% 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2.0% 4.0% 6.0% 8.0%
More informationQ1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 A B (A/B) 1 1,185 17,801 6.66% 2 943 26,598 3.55% 3 3,779 112,231 3.37% 4 8,174 246,350 3.32% 5 671 22,775 2.95% 6 2,606 89,705 2.91% 7 738 25,700 2.87% 8 1,134
More information橡hashik-f.PDF
1 1 1 11 12 13 2 2 21 22 3 3 3 4 4 8 22 10 23 10 11 11 24 12 12 13 25 14 15 16 18 19 20 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 144 142 140 140 29.7 70.0 0.7 22.1 16.4 13.6 9.3 5.0 2.9 0.0
More information198
197 198 199 200 201 202 A B C D E F G H I J K L 203 204 205 A B 206 A B C D E F 207 208 209 210 211 212 213 214 215 A B 216 217 218 219 220 221 222 223 224 225 226 227 228 229 A B C D 230 231 232 233 A
More information1
1 2 3 4 5 (2,433 ) 4,026 2710 243.3 2728 402.6 6 402.6 402.6 243.3 7 8 20.5 11.5 1.51 0.50.5 1.5 9 10 11 12 13 100 99 4 97 14 A AB A 12 14.615/100 1.096/1000 B B 1.096/1000 300 A1.5 B1.25 24 4,182,500
More information05[ ]戸田(責)村.indd
147 2 62 4 3.2.1.16 3.2.1.17 148 63 1 3.2.1.F 3.2.1.H 3.1.1.77 1.5.13 1 3.1.1.05 2 3 4 3.2.1.20 3.2.1.22 3.2.1.24 3.2.1.D 3.2.1.E 3.2.1.18 3.2.1.19 2 149 3.2.1.23 3.2.1.G 3.1.1.77 3.2.1.16 570 565 1 2
More information/9/ ) 1) 1 2 2) 4) ) ) 2x + y 42x + y + 1) 4) : 6 = x 5) : x 2) x ) x 2 8x + 10 = 0
1. 2018/9/ ) 1) 8 9) 2) 6 14) + 14 ) 1 4 8a 8b) 2 a + b) 4) 2 : 7 = x 8) : x ) x ) + 1 2 ) + 2 6) x + 1)x + ) 15 2. 2018/9/ ) 1) 1 2 2) 4) 2 + 6 5) ) 2x + y 42x + y + 1) 4) : 6 = x 5) : x 2) x 2 15 12
More informationネットショップ・オーナー2 ユーザーマニュアル
1 1-1 1-2 1-3 1-4 1 1-5 2 2-1 A C 2-2 A 2 C D E F G H I 2-3 2-4 2 C D E E A 3 3-1 A 3 A A 3 3 3 3-2 3-3 3-4 3 C 4 4-1 A A 4 B B C D C D E F G 4 H I J K L 4-2 4 C D E B D C A C B D 4 E F B E C 4-3 4
More information2003 10 2003.10.21 70.400 YES NO NO YES YES NO YES NO YES NO YES NO NO 20 20 50m 12m 12m 0.1 ha 4.0m 6.0m 0.3 ha 4.0m 6.0m 6.0m 0.3 0.6ha 4.5m 6.0m 6.0m 0.6 1.0ha 5.5m 6.5m 6.0m 50m 18 OK a a a a b a
More information1990 IMO 1990/1/15 1:00-4:00 1 N N N 1, N 1 N 2, N 2 N 3 N 3 2 x x + 52 = 3 x x , A, B, C 3,, A B, C 2,,,, 7, A, B, C
0 9 (1990 1999 ) 10 (2000 ) 1900 1994 1995 1999 2 SAT ACT 1 1990 IMO 1990/1/15 1:00-4:00 1 N 1990 9 N N 1, N 1 N 2, N 2 N 3 N 3 2 x 2 + 25x + 52 = 3 x 2 + 25x + 80 3 2, 3 0 4 A, B, C 3,, A B, C 2,,,, 7,
More information新たな基礎年金制度の構築に向けて
[ ] 1 1 4 60 1 ( 1 ) 1 1 1 4 1 1 1 1 1 4 1 2 1 1 1 ( ) 2 1 1 1 1 1 1 1996 1 3 4.3(2) 1997 1 65 1 1 2 1/3 ( )2/3 1 1/3 ( ) 1 1 2 3 2 4 6 2.1 1 2 1 ( ) 13 1 1 1 1 2 2 ( ) ( ) 1 ( ) 60 1 1 2.2 (1) (3) ( 9
More information高等学校学習指導要領解説 数学編
5 10 15 20 25 30 35 5 1 1 10 1 1 2 4 16 15 18 18 18 19 19 20 19 19 20 1 20 2 22 25 3 23 4 24 5 26 28 28 30 28 28 1 28 2 30 3 31 35 4 33 5 34 36 36 36 40 36 1 36 2 39 3 41 4 42 45 45 45 46 5 1 46 2 48 3
More information0 (18) /12/13 (19) n Z (n Z ) 5 30 (5 30 ) (mod 5) (20) ( ) (12, 8) = 4
0 http://homepage3.nifty.com/yakuikei (18) 1 99 3 2014/12/13 (19) 1 100 3 n Z (n Z ) 5 30 (5 30 ) 37 22 (mod 5) (20) 201 300 3 (37 22 5 ) (12, 8) = 4 (21) 16! 2 (12 8 4) (22) (3 n )! 3 (23) 100! 0 1 (1)
More informationエンジョイ北スポーツ
28 3 20 85132 http://www.kita-city-taikyo.or.jp 85 63 27 27 85132 http://www.kita-city-taikyo.or.jp 2 2 3 4 4 3 6 78 27, http://www.kita-city-taikyo.or.jp 85132 3 35 11 8 52 11 8 2 3 4 1 2 4 4 5 4 6 8
More informationAC-2
AC-1 AC-2 AC-3 AC-4 AC-5 AC-6 AC-7 AC-8 AC-9 * * * AC-10 AC-11 AC-12 AC-13 AC-14 AC-15 AC-16 AC-17 AC-18 AC-19 AC-20 AC-21 AC-22 AC-23 AC-24 AC-25 AC-26 AC-27 AC-28 AC-29 AC-30 AC-31 AC-32 * * * * AC-33
More informationPart y mx + n mt + n m 1 mt n + n t m 2 t + mn 0 t m 0 n 18 y n n a 7 3 ; x α α 1 7α +t t 3 4α + 3t t x α x α y mx + n
Part2 47 Example 161 93 1 T a a 2 M 1 a 1 T a 2 a Point 1 T L L L T T L L T L L L T T L L T detm a 1 aa 2 a 1 2 + 1 > 0 11 T T x x M λ 12 y y x y λ 2 a + 1λ + a 2 2a + 2 0 13 D D a + 1 2 4a 2 2a + 2 a
More information繖 7 縺6ァ80キ3 ッ0キ3 ェ ュ ョ07 縺00 06 ュ0503 ュ ッ 70キ ァ805 ョ0705 ョ ッ0キ3 x 罍陦ァ ァ 0 04 縺 ァ タ0903 タ05 ァ. 7
30キ36ヲ0 7 7 ュ6 70キ3 ョ6ァ8056 50キ300 縺6 5 ッ05 7 07 ッ 7 ュ ッ04 ュ03 ー 0キ36ヲ06 7 繖 70キ306 6 5 0 タ0503070060 08 ョ0303 縺0 ァ090609 0403 閨0303 003 ァ 0060503 陦ァ 06 タ09 ァ タ04 縺06 閨06-0006003 ァ ァ 04 罍ァ006 縺03 0403
More informationさくらの個別指導 ( さくら教育研究所 ) 1 φ = φ 1 : φ [ ] a [ ] 1 a : b a b b(a + b) b a 2 a 2 = b(a + b). b 2 ( a b ) 2 = a b a/b X 2 X 1 = 0 a/b > 0 2 a
φ + 5 2 φ : φ [ ] a [ ] a : b a b b(a + b) b a 2 a 2 b(a + b). b 2 ( a b ) 2 a b + a/b X 2 X 0 a/b > 0 2 a b + 5 2 φ φ : 2 5 5 [ ] [ ] x x x : x : x x : x x : x x 2 x 2 x 0 x ± 5 2 x x φ : φ 2 : φ ( )
More informationall.dvi
5,, Euclid.,..,... Euclid,.,.,, e i (i =,, ). 6 x a x e e e x.:,,. a,,. a a = a e + a e + a e = {e, e, e } a (.) = a i e i = a i e i (.) i= {a,a,a } T ( T ),.,,,,. (.),.,...,,. a 0 0 a = a 0 + a + a 0
More information熊本県数学問題正解
00 y O x Typed by L A TEX ε ( ) (00 ) 5 4 4 ( ) http://www.ocn.ne.jp/ oboetene/plan/. ( ) (009 ) ( ).. http://www.ocn.ne.jp/ oboetene/plan/eng.html 8 i i..................................... ( )0... (
More information広報さっぽろ 2016年8月号 厚別区
8/119/10 P 2016 8 11 12 P4 P6 P6 P7 13 P4 14 15 P8 16 P6 17 18 19 20 P4 21 P4 22 P7 23 P6 P7 24 25 26 P4 P4 P6 27 P4 P7 28 P6 29 30 P4 P5 31 P5 P6 2016 9 1 2 3 P4 4 P4 5 P5 6 7 8 P4 9 10 P4 1 b 2 b 3 b
More informationuntitled
351 351 351 351 13.0 0.0 25.8 1.0 0.0 6.3 92.9 0.0 80.5 0.0 1.5 15.9 0.0 3.5 13.1 0.0 30.0 54.8 18.0 0.0 27.5 1.0 0.0 2.5 94.7 0.0 91.7 0.0 1.3 14.7 0.0 3.8 14.4 0.0 25.0 50.5 16.0 0.0 27.5 2.0 0.0 2.5
More informationuntitled
2010824 1 2 1031 5251020 101 3 0.04 % 2010.8.18 0.05 % 1 0.06 % 5 0.12 % 3 0.14 % 2010.8.16 5 0.42 % 2010.7.15 25 5 0.42 % 0.426% 2010.6.29 5 0.496 % 2010.8.12 4 0.85 % 2010.8.6 10 0.900 % 2010.8.18 2.340
More informationDVIOUT-HYOU
() P. () AB () AB ³ ³, BA, BA ³ ³ P. A B B A IA (B B)A B (BA) B A ³, A ³ ³ B ³ ³ x z ³ A AA w ³ AA ³ x z ³ x + z +w ³ w x + z +w ½ x + ½ z +w x + z +w x,,z,w ³ A ³ AA I x,, z, w ³ A ³ ³ + + A ³ A A P.
More informationR R 16 ( 3 )
(017 ) 9 4 7 ( ) ( 3 ) ( 010 ) 1 (P3) 1 11 (P4) 1 1 (P4) 1 (P15) 1 (P16) (P0) 3 (P18) 3 4 (P3) 4 3 4 31 1 5 3 5 4 6 5 9 51 9 5 9 6 9 61 9 6 α β 9 63 û 11 64 R 1 65 13 66 14 7 14 71 15 7 R R 16 http://wwwecoosaka-uacjp/~tazak/class/017
More information18 ( ) I II III A B C(100 ) 1, 2, 3, 5 I II A B (100 ) 1, 2, 3 I II A B (80 ) 6 8 I II III A B C(80 ) 1 n (1 + x) n (1) n C 1 + n C
8 ( ) 8 5 4 I II III A B C( ),,, 5 I II A B ( ),, I II A B (8 ) 6 8 I II III A B C(8 ) n ( + x) n () n C + n C + + n C n = 7 n () 7 9 C : y = x x A(, 6) () A C () C P AP Q () () () 4 A(,, ) B(,, ) C(,,
More information高校生の就職への数学II
II O Tped b L A TEX ε . II. 3. 4. 5. http://www.ocn.ne.jp/ oboetene/plan/ 7 9 i .......................................................................................... 3..3...............................
More informationx = a 1 f (a r, a + r) f(a) r a f f(a) 2 2. (a, b) 2 f (a, b) r f(a, b) r (a, b) f f(a, b)
2011 I 2 II III 17, 18, 19 7 7 1 2 2 2 1 2 1 1 1.1.............................. 2 1.2 : 1.................... 4 1.2.1 2............................... 5 1.3 : 2.................... 5 1.3.1 2.....................................
More information......1201-P1.`5
2009. No356 2/ 5 6 a b b 7 d d 6 ca b dd a c b b d d c c a c b - a b G A bb - c a - d b c b c c d b F F G & 7 B C C E D B C F C B E B a ca b b c c d d c c d b c c d b c c d b d d d d - d d d b b c c b
More informationlinearal1.dvi
19 4 30 I 1 1 11 1 12 2 13 3 131 3 132 4 133 5 134 6 14 7 2 9 21 9 211 9 212 10 213 13 214 14 22 15 221 15 222 16 223 17 224 20 3 21 31 21 32 21 33 22 34 23 341 23 342 24 343 27 344 29 35 31 351 31 352
More informationab c d 6 12 1:25,000 28 3 2-1-3 18 2-1-10 25000 3120 10 14 15 16 7 2-1-4 1000ha 10100ha 110ha ha ha km 200ha 100m 0.3 ha 100m 1m 2-1-11 2-1-5 20cm 2-1-12 20cm 2003 1 05 12 2-1-13 1968 10 7 1968 7 1897
More informationii-03.dvi
2005 II 3 I 18, 19 1. A, B AB BA 0 1 0 0 0 0 (1) A = 0 0 1,B= 1 0 0 0 0 0 0 1 0 (2) A = 3 1 1 2 6 4 1 2 5,B= 12 11 12 22 46 46 12 23 34 5 25 2. 3 A AB = BA 3 B 2 0 1 A = 0 3 0 1 0 2 3. 2 A (1) A 2 = O,
More information