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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2743954

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Let a be the side length of the square. b² = 13²+a² b = √(169+a²) units. c² = 2a² c = √(2)a units. d²+5² = a² d = √(a²-25) units. e = b-d e = (√(169+a²)-√(a²-25)) units. Calculating a. 13² = (√(169+a²)-√(a²-25))²+5² 169-25 = (√(169+a²)-√(a²-25))² 144 = (√(169+a²)-√(a²-25))² 12 = (√(169+a²)-√(a²-25)) (12+√(a²-25))² = 169+a² 144+24√(a²-25)+a²-25 = 169+a² 144+24√(a²-25) = 194 24√(a²-25) = 50 12√(a²-25) = 25 144(a²-25) = 625 144a² = 625+(144*25) 144a² = 4225 a =...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2743143

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b = √(625-a²) units. c = √(a²-256) units. Where a is the diameter of the blue circle. Calculating a. b² = c²+9² √(625-a²)² = √(a²-256)²+9² 625-a² = a²-256+81 625-a² = a²-175 2a² = 800 a² = 400 a = 20 units. Again, a is the diameter of the blue circle. Therefore, radius of the blue circle is; ½(a) = 10 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2743132

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Calculating angle x. x = 180-½(360-100-160) x = 180-½(360-260) x = 180-½(100) x = 180-50 x = 130°

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2743126

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a² = 4²+1² a = √(17) units. a is the diameter of the circle. b = ½(a) b = 0.5√(17) units. b is the radius of the circle. Area circle is; π(b²) = π(0.5√(17))² = ¼(17π) square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2741817

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a = 1+3 a = 4 cm² b² = 4 b = 2 cm. 0.5*2c = 1 c = unit. d² = 1²+2² d = √(5) units. It implies; √(5) - 1 1 - e Cross Multiply. e = 1/√(5) e = ⅕√(5) units. f = d+e f = √(5)+⅕√(5) f = ⅕(6√(5)) units. Again; √(5) - 1 2 - g Cross Multiply. g = ⅕(2√(5)) units. Therefore, Blue Area is; Area square with side ⅕(6√(5)) units - Area triangle with height ⅕√(5) units and base ⅕(2√(5)) units - 3 cm² = (⅕(6√(5)))²-(½*⅕√(5)*⅕(2√(5)))-3 = ⅕(36)-⅕-3 = ⅕(...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2741632

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Let the radius of the ascribed semi circle be 1 unit. a² = 2(1)² a = √(2) units. b = ½(a) b = 0.5√(2) units. b is AM = CM. c² = 1²+1²-2*1*1cos(0.5*90) c = 0.7653668647 units. c is CN. d = ½(180-45) d = ½(135) d = 67.5° d is angle OCN. e = 45+d e = 112.5° e is angle MCN. f² = (0.5√(2))²+0.7653668647²-2*0.5√(2)*0.7653668647cos112.5 f = 1.2247448714 units. f is MN. (1.2247448714/sin112.5) = (0.7653668647/sing) g = 35.264389682° g is angle CMN. h = 90-g h =...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2741560

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Let the single side length of the green square be x. Therefore; x ~ √(9-x²) 2 ~ 3 Cross Multiply. 3x = 2√(9-x²) 9x² = 4(9-x²) 9x² = 36-4x² 13x² = 36 x² = 36/13 Therefore the area of the inscribed green square, x² is; (36/13) square unit.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2741533

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Sir Mike Ambrose is the author of the question. Let the width of the rectangle be x and the length be y. Let the unknown inscribed length of the rectangle be z. Calculating z. √(74)²+√(58)²=√(34)²+z² Therefore z is; z = √(98) units. Calculating x (width). x² = 156-2√(98)*√(58)cos68.2 x² = 100.003444042 x = 10.0001722006 units. Calculating y (length). y = √(34)cos30.9651378262 + √(58)cos23.199577149 y = 11.999876013 units. Therefore area rectangle is; xy...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2741527

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r = 5√(145)/8 unit. Please, move the above question one time, right/left to review the solution. Thank you.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2740746

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Let a be the radius of the circle. b = (a-1) units. 7² = a²+b²-2abcosc --- (1). 11² = a²+b²+2abcosc --- (2). At (1). 7² = a²+b²-2abcosc 2abcosc = a²+b²-49 --- (3). Substituting (3) in (2). 11² = a²+b²+a²+b²-49 121 = 2a²+2b²-49 2a²+2b² = 170 a²+b² = 85 --- (4). And b = a-1 Therefore; a²+(a-1)² = 85 a²+a²-2a+1 = 85 2a²-2a-84 = 0 a²-a-42 = 0 a²-7a+6a-42 = 0 a(a-7)+6(a-7) = 0 (a+6)(a-7) = 0 It implies; a ≠ -6 a = 7 units. Again, a is the radius of t...
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