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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/3236905

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Sir Mike Ambrose is the author of the question. Calculating Area Orange. Radius of the circle, r is; (5-r)²=18-18cos(180-2atan(4/3)) (5-r)²=12.96 5-r=√(12.96) 5-r=3.6 Therefore; r = 1.4 cm. Area orange is; Area sector with radius 1.4 cm and angle atan(4/3)° - Area triangle with two lengths 1.4 cm and 1.13836187945 cm, and angle ½(atan(4/3))°, the angle they form. = 1.4²π(atan(4/3))/360 - ½(1.4*1.13836187945)sin(½(atan(4/3))) = 0.90874931364 - 0.3563636363...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3236887

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Sir Mike Ambrose is the author of the question. Calculating Area yellow ÷ Area purple. Let the single side length of the regular nonagon be 2 units. Therefore; Area purple is; Area triangle with two equal length 2 units each and angle 140°, the angle they form + Area rectangle with length √(3) units and width 1 unit + Area rectangle with length √(8-8cos140) units and width √(3) units. = ½(4sin140)+(1*√(3))+(√(3)*√(8-8cos140)) = 9.52800747773 square units. Area yellow is;...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3236882

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Sir Mike Ambrose is the author of the question. Calculating exactly, hatched area ÷ orange area. Let the ascribed square side length be 2 units. Therefore, r, radius of the inscribed half circle is 1 unit. a = (b+1) units. b is the height of the inscribed orange area. tanc = 2/1 c = atan(2)° d = 180-2c d = 180-2atan(2) d = 2atan(½)° Calculating b. cosd = 1/(b+1) cos(2atan(½)) = 1/(b+1) ⅗ = 1/(b+1) 3b+3 = 5 b = ⅔ units. Again, b is the height of the inscribed o...
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