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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3238777

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Sir Mike Ambrose is the author of the question. Calculating Area purple ÷ Area brown exactly. Area purple is; Area trapezium with two parallel side length (58/15) cm and (46/5) cm, and height 4 cm. = ½((58/15)+(46/5))*4 = (392/15) cm² Area brown is; Area triangle with height 8 cm and base 12 cm - Area triangle with height (14/5) cm and base (56/15) cm. = ½(8*12) - ½((14/5)*(56/15)) = 48 - (392/75) = (3208/75) cm² It implies; Area purple ÷ Area brown exactly...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3238776

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Calculating Angle x. Let the base of the ascribed quadrilateral be 1 unit. (1/sin78) = (a/sin(18+30)) a = 0.75974712295 units. (1/sin78) = (b/sin54) b = 0.82709091529 units. (0.82709091529/sin30) = (c/sin18) c = 0.51117029743 units. d² = 0.51117029743²+0.75974712295-2*0.51117029743*0.75974712295co54 d = 0.61803398875 units. Therefore, the required angle x is; (0.61803398875/sin54) = (0.51117029743/sinx) x = asin(0.66913060636) x = 42°

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3238773

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Calculating Ascribed Square Area. Let the ascribed square side length be x. a² = 5 a = √(5) cm. a is the side length of the inscribed red square. b² = 20 b = √(20) b = 2√(5) units. b is the side length of the inscribed green square. c = a+b c = 3√(5) cm. d² = √(5)²+(2√(5))² d² = 5+20 d = √(25) d = 5 cm. e = (x-5) cm. Calculating x. (x-5) ~ 2√(5) √(5) ~ 5 Cross Multiply  5x-25 = 10 5x = 35 x = 7 cm. Again, x is the side length of the ascribed square. A...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3237963

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Calculating x, the base of the ascribed right-angled triangle. a² = 15²+x² a = √(15²+x²) units. a is the hypotenuse of the ascribed right-angled triangle. Therefore, x is; 3*15+3*x +3√(15²+x²) = 15*3 45+3x+3√(15²+x²) = 15x 3√(15²+x²) = 12x-45 9(225+x²) = 144x²-1080x+2025 2025+9x² = 144x²-1080x+2025 135x² = 1080x 135x = 1080 x = 1080/135 x = 8 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3237960

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Calculating the required angle, let it be x. Let a be the side length of the equilateral triangle. It implies; 6² = a²+10²-2*10*a cosy 36 = a²+100-20acosy 20acosy = a²+64 cosy = (a²+64)/(20a) --- (1). 8² = a²+10²-2*10*acos(60-y) 64 = a²+100-20a(½*cosy+½√(3)siny) 64 = a²+100-10acosy-10√(3)asiny 10acosy+10√(3)asiny = a²+36 --- (2). At (1). cosy = (a²+64)/(20a) Calculating siny. siny = opp/hyp opp = √((20a)²-(a²+64)²) opp = √(400a²-(a⁴+128a²+4096)) opp = √(-a⁴...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3237399

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Calculating Area Circle Green. Let x be the radius of area circle green. a²+2² = x² a = √(x²-4) units. b = a+x b = (x+√(x²-4)) units. Calculating x. (x+√(x²-4)) ~ 2 8 ~ √(x²-4) Cross Multiply. 16 = x√(x²-4)+x²-4 (20-x²)² = x²(x²-4) 400-40x²+x⁴ = x⁴-4x² 400 = 36x² x² = 400/36 x = √(400/36) x = ⅙(20) units. x = 3⅓ units. Again, x is the radius of the green circle. It implies; Area green circle is; πx² = ⅑(100π) square units. = 34.9065850399 square un...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3237395

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Calculating the red length. Let it be x. Notice. AB = CD = 2 units. It implies; AD = 2((AB)+½(AB)) AD = 2*(2+½(2)) AD = 2(2+1) AD = 6 units. a²+(2+1)² = 6² a² = 36+9 a = √(27) a = 3√(3) units. Or sin60 = a/6 ½√(3) =a/6 a = 3√(3) units. b = a-2 b = (3√(3)-2) units. tanc = (3√(3)-2)/1 c = atan(3√(3)-2)° c = 72.626340873° d = 180-c d = 107.373659127° cos72.626340873 = 1/e e = 3.348938684 units. e is BC. f = ½(e) f = 1.674469342 units. g² = 1....

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3236929

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Calculating Shaded Area. Shaded blue area is  Area quarter of radius 10 cm - Area sector of radius 10 cm and angle 30° - Area equilateral triangle of single side length 5 cm - Area sector of radius 5 cm and angle 120°. = (¼(100π))-((100π)/12)-(¼(25√(3)))-(⅓(25π)) = 25π - ⅓(50π) - ¼(25√(3))  = (300π-200π-75√(3))/12 = (100π-75√(3))/12 cm² = 15.3546212326 cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3236920

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Calculating Area Circle. Radius of the circle r is; r = 5-(√(18-18cos(180-2atan(4/3))) r = 5-3.6 r = 1.4 units. r = (7/5) units. Therefore area of the circle is; πr² = π(7/5)² = (49/25)π square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3236914

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Calculating red area. Red shaded area is; Area square with single side length 3 inches  = 3 * 3 = 9 square inches.
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