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maths questions
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simplify : a) sin2(90° - a) cos(270° - a) / tan2(270° + a) = cos2a (-sin a) / [sin2(270° + a) / cos2(270° + a)] = cos2a (-sin a) sin2a / cos2a = -sin3a b) [sin(90° + a) / cos(180° - a)] - [cos(360° - a) / tan(270° + a)] - sin a = [cos a/ (-cos a)] - [cos a / (-cot a)] - sin a = -1 + [cos a / (cos a / sin a)] - sin a = -1 + sin a - sin a = -1 ===== solve: a) 2sin a + 3cos a = 0 2sin a = -3cos a sin a / cos a = -3/2 tan a = -3/2 a = (180 - 56.31)°, (360 - 56.31)° a = 123.69°, 303.69° b) 2sin a = -[3^(1/3)]tan a 2sin a = -[3^(1/3)](sin a / cos a) 2sin a cos a = -[3^(1/3)]sin a 2sin a cos a + [3^(1/3)]sin a = 0 sin a [2 cos a + 3^(1/3)] = 0 sin a = 0 or cos a = -3^(1/3) / 2 a = 0°, 180°, 360° or a = (180 - 43.85)°, (180 + 43.85)° a = 0°, 136.15°, 180°, 223.85°, 360° If the equation is : 2sin a = -[3^(1/2)]tan a The answers will be : a = 0°, 150°, 180°, 210°, 360° c) 4^x + 2^(2x+1) = 48 4^x + 2*(2^2x) = 48 4^x + 2*(4^x) = 48 3*(4^x) = 48 4^x = 16 4^x = 4^2 x = 2 d) 5^x - 5^(x - 1) = 60 + 8[5^(x - 2)] 5^2[5^(x - 2)] - 5[5^(x - 2)] = 60 + 8[5^(x - 2)] 25[5^(x - 2)] - 5[5^(x - 2)] - 8[5^(x - 2)] = 60 (25 - 5 - 8)[5^(x - 2)] = 60 12[5^(x - 2)] = 60 5^(x - 2) = 5 x - 2 = 1 x = 3 ===== simplify with + index : a) [x^(-4/3) * y^(2/5)]^(-1/2) / [x^(7/12) * y^(-1/5)]^4 = [x^(2/3) * y^(-1/5)] / [x^(7/3) * y^(-4/5)] = x^[(2/3) - (7/3)] * y^[(-1/5) - (-4/5)] = x^(-5/3) * y^(3/5) = y^(3/5) / x^(5/3) b) √[x^5 * √(x^3 * √x)] = √[x^5 * √(x^3 * x^(1/2))] = √[x^5 * √(x^(7/2))] = √[x^5 * (x^(7/2))^(1/2)] = √[x^5 * x^(7/4)] = √[x^(27/4)] = [x^(27/4)]^(1/2) = x^(27/8)
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maths questions
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a in all questions starts for thetasimplify:a) sin^2(90-a)cos(270-a) / tan^2(270+a)b)sin(90+a)/cos(180-a) - cos(360-a)/tan(270+a) - sin asolve:a) 2sin a + 3cos a = 0b) 2sin a= - (3^1/3) tan ac) 4^x+2^(2x+1)=48d) 5^x-5^(x-1)=60+8(5^(x-2))simplify with + index :a) (x^-4/3*y^2/5)^-1/2 / (x^7/12... 顯示更多 a in all questions starts for theta simplify: a) sin^2(90-a)cos(270-a) / tan^2(270+a) b)sin(90+a)/cos(180-a) - cos(360-a)/tan(270+a) - sin a solve: a) 2sin a + 3cos a = 0 b) 2sin a= - (3^1/3) tan a c) 4^x+2^(2x+1)=48 d) 5^x-5^(x-1)=60+8(5^(x-2)) simplify with + index : a) (x^-4/3*y^2/5)^-1/2 / (x^7/12 * y^-1/5)^4 b) √ (x^5*√ (x^3*√ x))最佳解答:
simplify : a) sin2(90° - a) cos(270° - a) / tan2(270° + a) = cos2a (-sin a) / [sin2(270° + a) / cos2(270° + a)] = cos2a (-sin a) sin2a / cos2a = -sin3a b) [sin(90° + a) / cos(180° - a)] - [cos(360° - a) / tan(270° + a)] - sin a = [cos a/ (-cos a)] - [cos a / (-cot a)] - sin a = -1 + [cos a / (cos a / sin a)] - sin a = -1 + sin a - sin a = -1 ===== solve: a) 2sin a + 3cos a = 0 2sin a = -3cos a sin a / cos a = -3/2 tan a = -3/2 a = (180 - 56.31)°, (360 - 56.31)° a = 123.69°, 303.69° b) 2sin a = -[3^(1/3)]tan a 2sin a = -[3^(1/3)](sin a / cos a) 2sin a cos a = -[3^(1/3)]sin a 2sin a cos a + [3^(1/3)]sin a = 0 sin a [2 cos a + 3^(1/3)] = 0 sin a = 0 or cos a = -3^(1/3) / 2 a = 0°, 180°, 360° or a = (180 - 43.85)°, (180 + 43.85)° a = 0°, 136.15°, 180°, 223.85°, 360° If the equation is : 2sin a = -[3^(1/2)]tan a The answers will be : a = 0°, 150°, 180°, 210°, 360° c) 4^x + 2^(2x+1) = 48 4^x + 2*(2^2x) = 48 4^x + 2*(4^x) = 48 3*(4^x) = 48 4^x = 16 4^x = 4^2 x = 2 d) 5^x - 5^(x - 1) = 60 + 8[5^(x - 2)] 5^2[5^(x - 2)] - 5[5^(x - 2)] = 60 + 8[5^(x - 2)] 25[5^(x - 2)] - 5[5^(x - 2)] - 8[5^(x - 2)] = 60 (25 - 5 - 8)[5^(x - 2)] = 60 12[5^(x - 2)] = 60 5^(x - 2) = 5 x - 2 = 1 x = 3 ===== simplify with + index : a) [x^(-4/3) * y^(2/5)]^(-1/2) / [x^(7/12) * y^(-1/5)]^4 = [x^(2/3) * y^(-1/5)] / [x^(7/3) * y^(-4/5)] = x^[(2/3) - (7/3)] * y^[(-1/5) - (-4/5)] = x^(-5/3) * y^(3/5) = y^(3/5) / x^(5/3) b) √[x^5 * √(x^3 * √x)] = √[x^5 * √(x^3 * x^(1/2))] = √[x^5 * √(x^(7/2))] = √[x^5 * (x^(7/2))^(1/2)] = √[x^5 * x^(7/4)] = √[x^(27/4)] = [x^(27/4)]^(1/2) = x^(27/8)
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