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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3191118

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Calculating Area Triangle ABC and Length AN ÷ Length NC. Let AB equal x. a = (3*x)/(3+4) a = ⅐(3x) units. a is AT = AN. b = (4*x)/(3+4) b = ⅐(4x) units. b is TB = MB. c = a+4 c = ⅐(3x)+4 c = ⅐(3x+28) units. c is AC. d = b+4 d = ⅐(4x)+4 d = ⅐(4x+28) units. d is BC. Calculating x. (4*x)+(4*⅐(3x+28))+(4*⅐(4x+28)) = ⅐(4x+28)*⅐(3x+28) 4x+⅐(12x)+⅐(112)+⅐(16x)+⅐(112) = ((4x+28)(3x+28))/49 196x+84x+784+112x+784 = 12x²+196x+784 84x+784+112x = 12x² 12x²-196x-784 = 0 3x²-49x-196 = 0 It impl...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3191035

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Calculating Blue Area. Blue Area is; 2(area circle of radius 1 unit - 2(2(area sector of radius 1 unit and angle 60°) - area equilateral triangle of two side length 1 unit and angle 60°)) = 2(π - 2(2(π/6) - ¼(√(3)))) = 2(π - 2(⅓(π) - ¼(√(3)))) = 2(π - ⅔(π) + ½(√(3))) = 2π - ⅓(4π) + √(3) = ⅓(6π - 4π + 3√(3)) = ⅓(2π + 3√(3)) square units. = 3.82644590997 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3191023

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Sir Mike Ambrose is the author of the question. Calculating Area Green ÷ Area Rectangle. Area rectangle is; 9x8 = 72 square units. Area green is; Area trapezoid with two parallel lengths (5+2-¾) units and height 5 units - Area sector of radius 5 units and angle (tan–¹(4/3))°. = ½(7-¾)*5 - (tan–¹(4/3)*25π÷360) = (125/8) - (5πtan–¹(4/3)/72) = (1125-5πtan–¹(4/3))/72 = (7875 - 110tan–¹(4/3))/504 square units. = 4.02914432746 square units. Therefore; Area Green ÷ Area Rectangle is; = ((...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3190116

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Calculating Blue Area. Let x be the radius of the ascribed half circle. a²+7² = (2x)² a = √(4x²-49) units. b = a-4 b = (√(4x²-49)-4) units. It implies; Calculating x. √(4x²-49) ~ x 2x ~ (√(4x²-49)-4) Cross Multiply. 2x² = 4x²-49-4(√(4x²-49) 4(√(4x²-49) = 2x²-49 16(4x²-49) = (2x²-49)² 64x²-784 = 4x⁴-196x²+2401 4x⁴-260x²+3185 = 0 It implies; x² = 48.6245 Or  x² = 16.3755 Therefore; x ≠ √(16.3755) units. x = √(48.6245) units. x = 6.97312698866 units. Again, x is the radius of the half...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3189445

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Calculating Area Inscribed Yellow Square. Let the inscribed yellow square side length be x. Calculating x. a = (8-x) units. b = (8-2x) units. It implies; 8² = (8-2x)²+(8-x)² 64 = 64-32x+4x²+64-16x+x² 5x²-48x+64 = 0 (x-⅕(24))² = -⅕(64)+(-⅕(24))² (x-⅕(24))² = (576-320)/25 x = ⅕(24)±⅕√(256) x = ⅕(24)±⅕(16) x = ⅕(24±16) It implies; x ≠ ⅕(40) units. x = ⅕(8) units. Again, x is the side length of the inscribed yellow square. Therefore, area inscribed yellow square is...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3189442

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Calculating Green Area. Notice. The composite plane shape is not drawn to scale. Let x be the width of the ascribed rectangle. Therefore; x = the diameter of the inscribed small half circle, and also the radius of the inscribed quarter circle. b = (1+x) units. b is the length of the ascribed rectangle, and also the diameter of the big inscribed half circle. c = ½(b) c = ½(1+x) units. c is the radius of the big inscribed half circle. d = ½(x) units. d is the radius of the small inscribe...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3188286

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Calculating Area Yellow. Let y be each of the two equal lengths that makes the length of the ascribed rectangle. Calculating Yellow Area. a = 14+18 a = 32 units. a is the width of the ascribed rectangle. b = 2y units. b is the length of the ascribed rectangle. c² = 32²+y² c = √(1024+y²) units. d² = 14²+(2y)² d = √(196+4y²) units. e² = 18²+y² e = √(324+y²) units. Therefore; √(324+y²)² = √(196+4y²)²+√(1024+y²)²-2√(1024+y²)*√(196+4y²)cosx 324 = 4y²+1220-2√(1024+...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3188284

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Sir Mike Ambrose is the author of the question. Let the two equal length of the inscribed isosceles triangle (red area) be 2 units. Therefore; Area blue will be; Area triangle with lengths 1 unit and ⅔ units, and angle 60°, the angle they form. = ½(1*⅔sin60) = (√(3)/6) square units. Area red will be; 2(area triangle with height 1 unit and base √(3) units). = 2x½(1x√(3)) = √(3) square units. Area green will be; 2(area triangle with height 2 units and base ⅔(√(3)) units). = 2x½(2x⅔(√...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3186898

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Calculating square area. tana = (k+2k)/k a = atan(3)° b = 90-a b = atan(⅓)° tanc = 3k/2k c = atan(3/2)° d = 180-a-c d = 180-atan(3)-atan(3/2) d = 52.1250163489° e = 180-a e = (90+atan(⅓))° f = 180-e-b f = 180-(90+atan(⅓))-atan(⅓) f = (90-2atan(⅓))° f = 53.1301023542° g = 180-f-d g = 180-(90-2atan(⅓))-52.1250163489 g = 74.7448812969° h² = (3k)²+k² h = √(10)k units. (2k/sin(53.1301023542)) = (j/sin(90+atan(⅓))) j = 2.37170824512k units. l = h-j l = 0.7...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3186821

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Calculating Blue Inscribed Square Area. Let a be the side length of the inscribed blue square. b = a+½(a) b = ½(3a) units. 6² = 2c² c² = ½(36) c = √(18) c = 3√(2) units. Notice. b = c ½(3a) = 3√(2) 3a = 6√(2) a = ⅓(6√(2)) a = 2√(2) units. Therefore, area blue inscribed square is; a² = (2√(2))² = 8 square units.
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