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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3193649

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Calculating Area Inscribed yellow Circle. Let x be the area of the ascribed circle. a*12 = 5*9 a = (45/12) a = ¼(15) units. a = 3.75 units. b = ½(a+12) b = ½(15.75) b = 7.875 units. c = 12-b c = 12-7.875 c = 4.125 units. d = ½(5+9) d = 7 units. It implies; e² = 7²+4.125² e = √(66.015625) e = 8.125 units. e is the radius of the ascribed circle. Calculating x. f = e-2x f = (8.125-2x) units. It implies; 8.125² = (8.125-2x)²+7² 66.015625 = 66.015625...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3193643

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Calculating Area Blue. a = ½(4) a = 2 units. a is the radius of the inscribed half circle. b = (2+x) units. x is the radius of the inscribed circle. c = (4-x) units. It implies; d²+x² = (4-x)² d² = 16-8x+x²-x² d = √(16-8x) units. e = (2-x) units. Calculating x. (2+x)² = (2-x)²+√(16-8x)² 4+4x+x² = 4-4x+x²+16-8x 16x = 16 x = 1 units. Again, x is the radius of the inscribed circle. Therefore, Blue Area is; Area quarter circle with radius 4 units-Area half circle with radius 2 units-Area...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3192494

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Calculating R, radius of the circle. R² = 8²+5²-2*8*5cosx R² = 89-80cosx --- (1). a = (90-x)° R² = 5²+12²-2*5*12cos(90-x) R² = 169-120cos(90-x) R² = 169-120(cos90cosx-sin90sinx) R² = 169-120sinx --- (2). At (1). R² = 89-80cosx 80cosx = 89-R² cosx = (89-R²)/80 --- (3). At (3). (89-R²) is adjacent. 80 is hypotenuse. Calculating opposite. Opposite = √(80²-(89-R²)²) Opposite = √(6400-7921+178R²-R⁴) Opposite = √(-1521+178R²-R⁴) units. Therefore; sinx = √(-...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3192444

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Calculating angle x. Let CD = 1 unit. (1/sin30) = (a/sin(180-20-20-30)) a = 1.87938524157 units. a is BC. cos20 = (½(BC))/b cos20 = (0.5*1.87938524157)/b b = 0.93969262079/cos20 b = 1 unit. b is OC.  Notice. CD = OC = 1 unit, making inscribed triangle OCD an isosceles triangle. Angle x is; x = ½(180-20) x = ½(160) x = 80°

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3192283

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Calculating Area Ascribed Square. Let x be the radius of the red inscribed circle. a = (x-4) cm. b = (x-6) cm. It implies; Calculating x. (x-4)*(x-4) = x*(x-6) (x-4)² = x(x-6) x²-8x+16 = x²-6x -8x+16 = -6x 8x-6x = 16 2x = 16 x = 8 cm. Again, x is the radius of the inscribed red circle. c = 2x c = 2*8 c = 16 cm. c is the diameter of the inscribed red circle and also the side length of the ascribed square. Area Square is; c² = 16² = 256 cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3192258

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Calculating Green Area. tana = 6/3 a = atan(2)° b = 180-a b = (180-atan(2))° (6/sin(180-atan(2)) = (3/sinc) c = 26.5650511771° d = 180-sin(180-atan(2))-c d = 36.8698976458° e = 2d e = 73.7397952916° e' = 90-e e' = 16.2602047084° f² = 2(6)²-2(6)²cos16.2602047084 f = 1.69705627486 units. g = 90-2atan(½) g = 36.8698976458° sin(0.5*36.8698976458) = (0.5*1.69705627486)/h h = 2.68328157302 units. Area green is; (½*6²sin36.8698976458)-(½*2.68328157302²sin36.8698976458) = 10.8-2.16 = 8.64...

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...
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