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最佳解答:
1. (a) (3y - 2x)/(x - 4y) = 2 3y - 2x = 2x - 8y -4x = -11y x : y = 11 : 4 (b) x ; y = 11 : 4 Let x = 11k and y = 4k √(x + y) : √(x - y) = √(11k + 4k) : √(11k - 4k) = √15 : √7 2. (a) (m - 1)/n = 5/3 3m - 3 = 5n 3m = 5n + 3 m = (5n + 3)/3 (b) Let m - 1 = 5k and n = 3k Then, m = 5k + 1 3m + 4n = 57 3(5k + 1) + 4(3k) = 57 k = 2 Hence, m = 5(2) + 1 = 11 and n = 3(2) = 6 3. (a) 5a = 4b a : b = 4 : 5 3b = 5c b : c = 5 : 3 Hence, a : b : c = 4 : 5 : 3 Let a = 4k, b = 5k, c = 3k (2a + 3b - 4c) : (3a - 4b + 4c) = [2(4k) + 3(5k) - 4(3k)] : [3(4k) - 4(5k) + 4(3k)] = 11 : 4 (b) a + b + c = 48 4k + 5k + 3k = 48 k = 4 Hence, b = 5(4) = 20 4. (a) Since 2x = 3y, then y = 2x/3 Since 2x = 4z, then z = x/2 x : y : z = x : 2x/3 : x/2 x : y : z = 6 : 4 : 3 (b) Let x = 6k, y = 4k, z = 3k (6k)2 + 2(4k)2 + 3(3k)2 = 95 k2 = 1 k = 1 or k = -1 Then, x = 6 or x = -6 5. (a) 6x2 - 11xy + 4y2 = 0 (3x - 4y)(2x - y) = 0 3x = 4y or 2x = y x/y = 4/3 or x/y = 1/2 (b) When x/y = 4/3 Let x = 4k, y = 3k (x2 + 3xy + y2)/(x2 - 3xy + y2) = [(4k)2 + 3(4k)(3k) + (3k)2]/[(4k)2 - 3(4k)(3k) + (3k)2] = (61k2)/(-11k2) = -61/11 When x/y = 1/2 Let x = m, y = 2m (x2 + 3xy + y2)/(x2 - 3xy + y2) = [(m)2 + 3(m)(2m) + (2m)2]/[(m)2 - 3(m)(2m) + (2m)2] = (11m2)/(-m2) = -11 6. (a) water : alcohol = 25% : (1 - 25%) = 1 : 3 (b) (213 L) : alcohol = 1 : 3 Volume of alcohol = 639 L 7. (a) R.F. = 6 cm : 12 km = 6 cm : (12 x 1000 x 100 cm) = 1 : 200000 (b) Actual area = (4 x 200000 cm)2 = (800000 cm)2 = (8 km)2 = 64 km2 8. (a) Let the angles be ko, 2ko and 3ko. k + 2k + 3k = 180 k = 30 The angles of the triangle are 30o, 60o and 120o (b) By sine law, Ratio of the sides of the triangle = sin 30o : sin60o : sin90o = 1/2 : (√3)/2 : 1 = 1 : √3 : 2 9 (a) (i) Speed of car A = 210/3 km/h = 70 km/h Speed of car B = 200/2.5 km/h = 80 km/h (ii) Speed of car A = (70 x 1000 m)/ (3600 s) = [19 and (4/9)] m/s Speed of car B = (80 x 1000 m)/ (3600 s) = [22 and (2/9)] m/s (b) Time taken by car A = (280/70) h = 4 h Time taken by car B = (280/80) h = 3.5 h =
其他解答:0D7DAC4E7B8CAAC5
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最佳解答:
1. (a) (3y - 2x)/(x - 4y) = 2 3y - 2x = 2x - 8y -4x = -11y x : y = 11 : 4 (b) x ; y = 11 : 4 Let x = 11k and y = 4k √(x + y) : √(x - y) = √(11k + 4k) : √(11k - 4k) = √15 : √7 2. (a) (m - 1)/n = 5/3 3m - 3 = 5n 3m = 5n + 3 m = (5n + 3)/3 (b) Let m - 1 = 5k and n = 3k Then, m = 5k + 1 3m + 4n = 57 3(5k + 1) + 4(3k) = 57 k = 2 Hence, m = 5(2) + 1 = 11 and n = 3(2) = 6 3. (a) 5a = 4b a : b = 4 : 5 3b = 5c b : c = 5 : 3 Hence, a : b : c = 4 : 5 : 3 Let a = 4k, b = 5k, c = 3k (2a + 3b - 4c) : (3a - 4b + 4c) = [2(4k) + 3(5k) - 4(3k)] : [3(4k) - 4(5k) + 4(3k)] = 11 : 4 (b) a + b + c = 48 4k + 5k + 3k = 48 k = 4 Hence, b = 5(4) = 20 4. (a) Since 2x = 3y, then y = 2x/3 Since 2x = 4z, then z = x/2 x : y : z = x : 2x/3 : x/2 x : y : z = 6 : 4 : 3 (b) Let x = 6k, y = 4k, z = 3k (6k)2 + 2(4k)2 + 3(3k)2 = 95 k2 = 1 k = 1 or k = -1 Then, x = 6 or x = -6 5. (a) 6x2 - 11xy + 4y2 = 0 (3x - 4y)(2x - y) = 0 3x = 4y or 2x = y x/y = 4/3 or x/y = 1/2 (b) When x/y = 4/3 Let x = 4k, y = 3k (x2 + 3xy + y2)/(x2 - 3xy + y2) = [(4k)2 + 3(4k)(3k) + (3k)2]/[(4k)2 - 3(4k)(3k) + (3k)2] = (61k2)/(-11k2) = -61/11 When x/y = 1/2 Let x = m, y = 2m (x2 + 3xy + y2)/(x2 - 3xy + y2) = [(m)2 + 3(m)(2m) + (2m)2]/[(m)2 - 3(m)(2m) + (2m)2] = (11m2)/(-m2) = -11 6. (a) water : alcohol = 25% : (1 - 25%) = 1 : 3 (b) (213 L) : alcohol = 1 : 3 Volume of alcohol = 639 L 7. (a) R.F. = 6 cm : 12 km = 6 cm : (12 x 1000 x 100 cm) = 1 : 200000 (b) Actual area = (4 x 200000 cm)2 = (800000 cm)2 = (8 km)2 = 64 km2 8. (a) Let the angles be ko, 2ko and 3ko. k + 2k + 3k = 180 k = 30 The angles of the triangle are 30o, 60o and 120o (b) By sine law, Ratio of the sides of the triangle = sin 30o : sin60o : sin90o = 1/2 : (√3)/2 : 1 = 1 : √3 : 2 9 (a) (i) Speed of car A = 210/3 km/h = 70 km/h Speed of car B = 200/2.5 km/h = 80 km/h (ii) Speed of car A = (70 x 1000 m)/ (3600 s) = [19 and (4/9)] m/s Speed of car B = (80 x 1000 m)/ (3600 s) = [22 and (2/9)] m/s (b) Time taken by car A = (280/70) h = 4 h Time taken by car B = (280/80) h = 3.5 h =
其他解答:0D7DAC4E7B8CAAC5
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