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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2615207

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Sir Mike Ambrose is the author of the question. Area Blue is; Area triangle with two side length 10½ unit and ((7√(5)sin(atan(3/4)))/(2sin(180-atan(2)-atan(3/4))) unit, and angle (180-2atan(2))°, the angle they form. = ½(21/2)((7√(5)sin(atan(3/4)))/(2sin(180-atan(2)-atan(3/4)))sin(180-2atan(2)) = ¼(21)(378/99) = ½(441/11) = (441/22) square unit.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2615199

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Sir Mike Ambrose is the author of the question. Area Green total, exactly in cm² is; Area triangle with height 24 cm and base 10 cm + Area triangle with height 24 cm and base (24tan15) cm - 2(area triangle with height 10 cm and base (10tan15) cm) = ½*24*10 + ½*24*24tan15 - 2(½*10*10tan15) = 120 + 288(2-√(3)) - 100(2-√(3)) = 120 + 576 - 288√(3) - 200 + 100√(3) = (496 - 188√(3)) cm² = 4(124-47√(3)) cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2615182

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Prime multiples of 243 is; 3*3*3*3*3*3 = 3⁵ in index form. Prime multiples of 27 is; 3*3*3 = 3³ in index form. Prime multiples of 81 is; 3*3*3*3 = 3⁴ in index form. And 3^(x) = 2 Therefore; Substituting 3^(x) = 2 in the expression. It implies; (2⁵/32)+((5*2³)/8)-(2⁴) = (32/32)+((5*8)/8)-16 = 1+5-16 = -10

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2614148

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a = ½(7+13) a = 10 units. a is the radius of the ascribed semi circle. b = 10-7 b = 3 units. Calculating y. 10² = c²+6² c² = 64 c = 8 units. y = b+c y = 11 units. Calculating x. x = 2c-y x = 2*8-11 x = 16-11 x = 5 units. It implies; x = 5 units. y = 11 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2613734

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Let the square side length be a. It implies; Area square is a² Calculating a² (Area of the Square). √(2)² = b²+c² c = √(2-b²) --- (1). √(68)² = (a+b)²+c² 68 = (a+b)²+√(2-b²)² 68 = (a+b)²+2-b² 66 = a²+2ab --- (2). 8² = b²+(c+a)² --- (3). 64 = b²+c²+2ac+a² 64 = b²+(√(2-b²)²+2a√(2-b²)+a² 64 = b²+2-b²+2a√(2-b²)+a² 62 = 2a√(2-b²)+a² (62-a²)² = 4a²(2-b²) 3844-124a²+a⁴ = 8a²-4a²b² 132a²-3844-a⁴= 4a²b² b² = (132a²-3844-a⁴)/(4a²) b = √(132a²-3844-a⁴)/2a --- (3). Substit...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2613584

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a = 180-60 a = 120° (7/sin120) = (3/sinb) b = 21.7867892983° c = 60+b c = 81.7867892983° d = 180-120-b d = 60-21.7867892983 d = 38.2132107017° (7/sin120) = (e/sin38.2132107017) e = 5 units. Therefore, R, radius of the circle is; R² = 5²+7²-2*5*7cos81.7867892983 R = 8 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2613558

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Sir Mike Ambrose is the author of the question. Area rectangle is; 9x8 = 72 square unit. Area green is; Area trapeziod with two parallel lengths (5+2-¾) unit and height 5 unit - Area sector of radius 5 unit 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 unit. = 4.02914432746 square unit. Therefore; Area Green ÷ Area Rectangle exactly in fraction. = ((7875 - 110tan–¹...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2613553

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Blue Area will be; 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 unit. = 3.82644590997 square unit.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2612090

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Sir Mike Ambrose is the author of the question. Let the side length of the square be a. tanb = a/(0.5a) b = atan(2)° c = 180-b-45 c = (135-atan(2))° (0.5a/sin(135-atan(2)) = (d/sin45) d = 0.3726779962a cm. cos(atan(0.5)) = 0.5a/e e = 0.5590169944a cm. Therefore; Calculating a. 0.5*0.3726779962a*0.5590169944a = 10 0.1041666667a² = 10 a² = 96 a = 4√(6) cm. Again, a is the side length of ascribed square. tan(atan(½)) = f/(2√(6)) f = √(6) cm. g = 4√(6)-g g =...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2611915

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Calculating yellow inscribed circle area. a² = 6²+8² a = √(100) a = 10 units. 2b² = 10² b² = 50  b = 5√(2) units. b is the radius of the half circle. (5√(2)/sin45) = (8/sinc) c = 53.1301023542° d = 180-c d = 126.8698976458° e = 180-45-d e = 8.1301023542° (5√(2)/sin45) = (f/sin8.1301023542) f = 1.4142135624 units. f = √(2) units. Let g be the radius of the inscribed yellow circle. h = (5√(2)-g) units. j² = 2g² j = √(2)g units. Calculating g, radius of t...
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