Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2541439

a = (1-r) units. b²+r² = (1-r)² b = √(1-2r) units. c = (0.5+r) It implies; (0.5+r)² = r²+√(1-2r)² ¼+r+r² = r²+1-2r 3r = 1-¼ 3r = ¾ r = ¼ units. Or (½+r) = (1-r) Where; AB = BC = 1 unit. AE = BE = ½ units. Therefore; 2r = 1-½ 2r = ½ r = ¼ units. Or r will be; r = ½(½(AB)) r = ¼(AB) And AB = 1 unit. r = ¼(1) r = ¼ unit.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2540565

Let a be the radius of the inscribed sector. b = (2+a) units. Therefore; (2+a)² = a²+6² 4+4a+a² = a²+36 4a = 32 a = 8 units. Again, a is the radius of the inscribed sector. b = (2+a) And a = 8 units. b = 2+8 b = 10 units. c = 6+b And b = 10 units. c = 6+10 c = 16 units. Therefore, Painted Area is; ½(10+16)*8 = 4*26 = 104 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2540051

Let AD = CD = a. Calculating a. b² = 2a² b = √(2)a units. b is AC. c²+3² = a² c = √(a²-9) units. c is DE. a² = d²+7² d = √(a²-49) units. e = c-d e = (√(a²-9)-√(a²-49)) units. e is CB. It implies; b² = e²+10² (√(2)a)² = (√(a²-9)-√(a²-49))²+100 2a² = a²-9-2√((a²-9)(a²-49))+a²-49+100 2√((a²-9)(a²-49)) = 42 √((a²-9)(a²-49)) = 21 (a²-9)(a²-49) = 441 a⁴-49a²-9a²+441 = 441 a⁴-58a² = 0 a² = 58 a = √(58) units. Therefore, Orange Area is; ½(a²) = ½*√(58)² =...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2539465

Calculating blue area. It is; Area square with side length 3 cm + Area semi circle with radius 1 cm + Area semi circle with radius 2 cm. = (3*3)+(π*½*1²)+(π*½*2²) = 9+½(π)+2π = ½(18+π+4π) = ½(18+5π) cm² = 16.853981634 cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2539396

cos30 = a/16 a = 8√(3) cm. cos30 = 10/b b = ⅓(20√(3)) cm. c = a-b c = 8√(3)-⅓(20√(3)) c = ⅓(4√(3)) units. d = 2c d = ⅓(2√(3)) cm. e = b+d e = ⅓(20√(3))+⅓(2√(3)) e = ⅓(22√(3)) cm e = 12.7017059222 cm. f² = 12.7017059222²+8²-16*12.7017059222cos30 f = 7.0237691686 cm. (7.0237691686/sin30) = (8/sing) g = 34.7150039538° h = 180-120-g h = 25.2849960462° tan25.2849960462 = 2/j j = 4.233901974 units. tan30 = k/10 k = ⅓(10√(3)) cm. l = k-j l = 1.5396007179...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2539293

Notice! Radius of the half circle is 9 units. Let the three equal lengths be b. 5² = b²+a²-2bacos45 25 = b²+a²-√(2)ab --- (1). 9² = b²+a²-2abcos135 81 = b²+a²+√(2)ab --- (2). Subtracting (1) from (2). 56 = 2√(2)ab 28 = √(2)ab a = 28/(√(2)b) --- (3). Substituting (3) in (2) to get b. 81 = b²+(28/(√(2)b))²+√(2)(28/(√(2)b))b 81 = b²+(392/b²)+28 53 = b²+(392/b²) 53b² = b⁴+392 Let b² = p. p²-53p +392 = 0 Calculating p. It implies; p = ½(53+√(1241)) p = 44.1139...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2538182

Sir Mike Ambrose is the author of the question. Calculating Yellow Area. It is; Area triangle with height 4sin(atan(⅔)) units and base 8√(13)/9 units - Area triangle with height 1 unit and base ⅔ unit - Area triangle with height ¼ unit and base ⅔ unit = ½*4sin(atan(⅔))*(8√(13)/9) - ½*1*⅔ - ½*¼*⅔ = (32/9)-⅓-(1/12) = (113/36) square units. Area Orange is; Area triangle with height ⅓(10sin(atan(¾))) units and base (5√(13)/9) units. = ½*⅓(10sin(atan(3/2)))*(5√(13)/9) = (25/9) sq...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2538034

a²+2² = 8² a² = 64-4 a = √(60) a= 2√(15) units. a is BD b = ½(a) b = √(15) units. c = ½(AB) c = 4 units. c is the radius of the half circle. cosd = √(15)/4 d = acos(¼√(15))° d is angle ABD. e = 2d e = 2acos(¼√(15))° e is angle ABC. Therefore, the required length, ? (BC) is; Observing CAH, Trigonometry ratio. cos(2acos(¼√(15))) = (BC)/8 BC = 8cos(2acos(¼√(15))) BC = 8*⅞ BC = 7 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2537987

Let the two equal lengths be a units each. a² = 2b² b² = a²/2 b = ½√(2)a unit. It implies; 14+½√(2)a* ½√(2)a = 2a*2a 14+½(a)² = 4a² 14 = 4a²-½(a)² 14 = ½(7)a² 2 = ½(a)² a² = 4 a = 2 units. b = ½√(2)a And a = 2 units. b = ½√(2)*2 b = √(2) units. Therefore; 2a is; = 2*2 = 4 units. c² = 2²+2² c² = 8 c = 2√(2) units. d = b+c d = (√(2)+2√(2)) d = 3√(2) units. Therefore, area blue is; Area square with side 3√(2) units - Blue Area. = (3√(2))²-7 = 18-7...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2537952

a² = 4²+2² a = √(20) a = 2√(5) units. a is the diameter of the circle. b = ½(a) b = √(5) units. b is the radius of the circle. tanc = 4/2 c = atan(2)° d = 180-c d = (180-atan(2))° It implies, the required angle, ? is; Let it be e. Observing Sine Rule. (4/sin(180-atan(2))) = (e/sin45) e = 3.1622776602 units. Again, e is the required length.

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