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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2755021

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x²+(x²/(x+1)²) = 3 (x+1)²*x²+x² = 3(x+1)² x²(x²+2x+1)+x² = 3(x²+2x+1) x⁴+2x³+2x² = 3x²+6x+3 x⁴+2x³-x²-6x-3 = 0 It implies; x = ½(1-√(5)) = -0.6180339887 or x = ½(1+√(5)) = 1.6180339887

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2754176

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Let the centre of the circle be N Therefore; N coordinate is; N(2, 4). Point P is; P(-2, (17/2)) Point Q is; Q(x, 0) Gradient of length NP is; (4-(17/2))/(2+2) = -9/8 Notice; Length PQ is a tangent to length NP. Therefore length PQ gradient is; -1/length NP gradient = -1/(-9/8) PQ gradient = 8/9 Calculating x coordinate at point Q. (0-(17/2))/(x+2) = 8/9 -153/2 = 8x + 16 16x + 32 = -152 16x = -185 x = - 185/16 Therefore; Area green exa...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2754172

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πa² = 73π a = √(73) units. a is the radius of the circle. b = 2a b = 2√(73) units. b is the diameter of the circle. c²+7² = (2√(73))² c² = 292-49 c² = 243 c = √(243) c = 9√(3) units. d²+(9√(3))² = 18² d² = 324-243 d = √(81) d = 9 units. Therefore, area yellow triangle is; Area triangle with height and base 9√(3) units and 9 units respectively + Area triangle with height and base 9√(3) units and 7 units respectively. = (0.5*9√(3)*9)+(0.5*9√(3)*7) = ½(81√(3)+63√(3)...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2754168

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Calculating green area. c² = a²+b² c = √(4²+6²) c = √(52) c = 2√(13) units.  c = 7.2111025509 units. d = 90-atan(4/6) d = atan(3/2)° e = 180-2d e = (180-2ata(3/2))° sin(0.5(180-2ata(3/2))) = (0.5*2√(13))/f f = 6.5 units. f is the radius of the half circle. g = 180-2(180-2atan(3/2)) g = 180-360+4atan(3/2) g = (4atan(3/2)-180) g = 45.2397298961° Therefore, green area is; Area sector with radius 6.5 units and angle 45.2397298961° - Area triangle with height 6.5sin...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2754161

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Calculating AB. Notice. 1 unit is the side length of each of the composite plane shape. a = ½*180(6-2) a = 120° a is the single interior angle of the regular hexagon. b = 180(12-2)/12 b = 150° b is the single interior angle of the regular polygon with 12 sides. sin30 = c/1 c = 0.5 units. sin60 = d/1 d = ½√(3) units. sin30 = e/1 e = 0.5 units. Therefore, length AB is; AB = 2c+1+3d+1+e AB = 2(0.5)+1+3(½√(3))+1+0.5 AB = 3.5+0.5(3√(3)) AB = ½(7)+½(3√(3)) AB =...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2753144

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Blue Area is; Area square of single side 4cm - 2(area circle of radius 1cm) - 8(area square of single side 1cm) + 8(area quarter circle of radius 1cm). = 16 - 2π - 8 + ¼(8π) = 8 - 2π + 2π = 8 cm².

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2753110

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Shaded area is; Area circle with radius 1 units - 8(area quarter circle with radius 1 units - area triangle with height and base 1 units each). = π - 8(¼(π)-½) = π - 2π + 4 = (4-π) square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2753087

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Let a be the radius of the quarter circle. b = ½(a) units. tanc = b/a c = atan(½)° d = atan(2)° e = d-c e = (atan(2)-atan(½))° Therefore, the required length, x is; tan(atan(2)-atan(½)) = x/8 x = 8tan(atan(2)-atan(½)) x = 6 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2752584

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Sir Mike Ambrose is the author of the question. Let the side length of the regular hexagon be 1 unit. Therefore; Area green is; Area triangle with height 1 unit and base ⅓√(3) units. = ½(⅓√(3)*1) = √(3)/6 square units. Area yellow is; Area triangle with two length 0.40929915222 units and 1 unit, and angle (90-atan(⅓(2√(3))))° = ½(0.40929915222*1)sin(90-atan(⅓(2√(3)))) = 0.13397459621 square units. It implies; Area yellow ÷ Area green in its exact decimal is; 0.1...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2752566

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Notice; Triangle ABF is isosceles. The height is; 4tan(atan¾) = 3 units. The base, given is 8 units. The two equal side length is; √(4²+3²) = √(25) = 5 units.  Radius, r of the blue circle inscribed triangle ABF is; 2*½(5r)+½(8r)=½(8*3) 5r+4r=12 9r = 12 r = 4/3 units. Therefore; Area inscribed blue circle is; πr = π(4/3)² = 16π/9 square units.
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