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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3434548

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Calculating Area Triangle AED.Let x be CD.Figuring an equilateral triangle OCD considering the strategic given two equal angles, 60°.a = (x-8) units.a is DE.b = (x-10) units.b is OA.cos60 = c/8c = 4 units.c is BC.d = (x-4) units.d is OB.Let AB = AE = y.y² = (x-10)²+(x-4)²-2(x-4)(x-10)cos60y² = x²-20x+100+x²-8x+16-(x²-14x+40)y² = 2x²-28x+116-x²+14x-40y² = x²-14x+76y = √(x²-14x+76) units.Therefore, calculating x, length CD.√(x²-14x+76)² = 10²+(x-8)²-2*10(x-8)cos60x²-14x+76 = 100+x²-16x+64-10x+80-...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3433587

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Calculating Area Blue Square.a = ½(8)a = 4 units.b² = 4²+2²b² = 20b = 2√(5) units.b is the side length of the white inscribed square.c² = 4²+8²c² = 80c = 4√(5) units.c is 2b.Therefore, blue square area is, let it be d².d² = 2b²d² = 2(2√(5))²d² = 2(20)d² = 40 square units.Again, d² is the blue square area.Where d, 2√(10) units is the side length of the blue square.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3432686

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Calculating Green Area.a = ½(3+3+2)a = 4 units.a is the radius of the ascribed half circle.b²+x² = 4²b = √(16-x²) units.Where x is the radius of the green half circle.c = ½(3)c = 1.5 units.d = 3+1.5-4d = 0.5 units.e²+1.5² = x²e = √(x²-2.25) units.Calculating x.b² = d²+e²16-x² = 0.25+x²-2.2516+2 = 2x²2x² = 18x² = 9x = 3 units.Again, x is the radius of the green half circle.Area Green Half Circle is;½*π*x²= ½(9π)= 4.5π square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3431846

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Sir Mike Ambrose is the author of the question.Calculating Area Gold.Area Gold exactly in square cm decimal form is;Area trapezium with two parallel side 6√(13) cm and 14.9769052981 cm, and height 11.6487041207 cm - Area triangle with height 9.6896279025 cm and base 6√(13)sin(atan(1.75)) cm.= (½*11.6487041207(6√(13)+14.9769052981)) - (½*9.6896279025*6√(13)sin(atan(1.75)))= 213.23076923 - 91= 122.23076923 cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3430923

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Calculating Blue Area.Let x be the side length of the blue square.a² = 7²+24²a = √(7²+24²)a = 25 units.b = a+7b = 25+7b = 32 units.c² = b²+24²c = √(32²+24²)c = 40 units.d = ½(c)d = 20 units.d is the radius of the quarter circle.Calculating area square blue.a² = x²+d²Where x² is the area of the blue square.It implies;25² = x²+20²625 = x²+400x² = 625-400x² = 225 square units.Again, x² is blue area.x = 15 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3429972

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Calculating Area Green.Let x be the radius of the half circle.a = ½(8)a = 4 units.x = (4+b) units.Recall, x is the radius of the half circle.c²+4² = (4+b)²c² = 8b+b²c = √(8b+b²) units.d = 2cd = 2√(8b+b²) units.e = b+b+de = (2b+2√(8b+b²)) units.e is the side length of the square.It implies, e is 8 units.Therefore, calculating b.2b+2√(8b+b²) = 8Dividing through by 2.b+√(8b+b²) = 4√(8b+b²) = 4-b8b+b² = (4-b)²8b+b² = 16-8b+b²16b = 16b = 1 unit.Recall.x = (4+b) unitsAnd b = 1 unit.x = 4+1x = 5 units...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3429136

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Calculating Area Red.Let x be the side length of the ascribed square.a = 2+3a = 5 units.b²+5² = x²b = √(x²-25) units.Calculating x.cosc = √(x²-25)/x --- (1).cosc = 3/x --- (2).Equating (1) and (2).√(x²-25)/x = 3/x √(x²-25) = 3x²-25 = 9x² = 34 square units.Where x² is the area of the square.Calculating Shaded Red Area.x² = 34x = √(34) units.Again, x is the side length of the ascribed square.Recall.b = √(x²-25)And x² = 34b = √(34-25)b = 3 units.It implies, red area is;Area ascribed square - 2(are...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3428395

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Calculating Area Green.a = 4+6a = 10 units.a is the diameter of the ascribed half circle.b = ½(a)b = 5 units.b is the radius of the ascribed half circle.c = 5-4c = 1 unit.Let x be the radius of the inscribed half circle.d² = 2x²d = √(2x²)d = √(2)x units.e = 180-45e = 135°Calculating x 5² = 1²+(√(2)x)²-2*1*√(2)xcos13525 = 1+2x²+2x2x²+2x-24 = 0x²+x-12 = 0(x+4)(x-3) = 0It implies;x ≠ -4 units.x = 3 units.Again, x is the radius of the inscribed circle.Therefore, Area Green is;Area half circle with...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3427439

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Calculating Shaded Blue Area.Let x be the radius of the inscribed circle.a = (12+x) units.a is the height of the ascribed triangle.b = (18+x) units.b is the base of the ascribed triangle.c = 12+18c = 30 units.c is the hypotenuse of the ascribed triangle.Calculating x.(18+x)²+(12+x)² = 30²324+36x+x²+144+24x+x² = 9002x²+60x+468 = 9002x²+60x-432 = 0x²+30x-216 = 0(x+15)² = 216+15²(x+15)² = 441x = -15±√(441)x = -15±21It implies;x ≠ -15-21x = -15+21x = 6 units.Again, x is the radius of the inscribed...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3426695

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Calculating Area Red.a = 1+(161/9)+(10/9)a= 1+(171/9)a = 1+19a = 20 units.a is the diameter of the ascribed circle.b = ½(a)b = 10 units.b is the radius of the ascribed circle.Let x be the radius of the inscribed circle.c = (10-x) units.d = 10-1d = 9 units.It implies;(10-x)² = x²+9²-2*9*xcosy100-20x+x² = x²+81-18xcosy81xcosy = 20x-19cosy = (20x-19)/(18x) --- (1).cosy = (161/9)/(2x) --- (2).Calculating x.Equating (1) and (2).(20x-19)/(18x) = (161/9)/(2x)2(20x-19) = (161/9)*1840x-38 = 32240x = 360...
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