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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3611165

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Calculating Alpha.Let it be x.Let a be the radius of the ascribed quarter circle.b = (a-√(2)) units.c = (a-2√(2)) units.Calculating a.a ~ (a-√(2))(a-2√(2)) ~ √(2) Cross Multiply.√(2)a = a²-2√(2)a-√(2)a+4√(2)a = a²-3√(2)a+4a²-4√(2)a+4 = 0(a-2√(2))² = -4+(-2√(2))²(a-2√(2))² = -4+8(a-2√(2))² = 4a-2√(2) = ±2a = 2√(2)±2It implies;a ≠ 2√(2)-2 units.a = 2√(2)+2 units.Again, a is the radius of the ascribed quarter circle.d = a-2√(2)d = 2√(2)+2-2√(2)d = 2 units.It implies;Calculating theta, angle x.sinx...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3611162

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Calculating r, radius of the inscribed circle.Notice.Angle ABD = ¼(60)Angle ABD = 15°tan30 = r/a1/√(3) = r/aa = √(3)r units.b = 2ab = 2√(3)r units.b is the side length of the ascribed regular triangle.(1/sin15) = (√(7)/sinc)c = 43.2175867282°c is angle DAB.d = 180-15-43.217586782d = 121.782413272°d is angle ADB.Calculating r.((2√(3)r)/sin121.782413272) = (1/sin15)r = (sin121.782413272)/(2√(3)sin15)r = 0.94811248631 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3611159

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Calculating the green area x.Notice.5 units is the height of the green triangle and 15 units is the base.It implies, area green (x) is;½*5*15= ½(75)= 37.5 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3610148

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Calculating theta.Let it be x.Let angle BAD be a.b+a+30 = 180b = (150-a)°b is angle ADB.It implies;x+b = 180x+150-a = 180x = (30+a)°Again, a is theta.c = 180-100c = 80°c is the supplementary angle of 100° (angle ACD).Calculating a.It implies;30+x = c30+30+a = 80a = 80-60a = 20°Again, a is angle BAD.Therefore, x, angle theta is;x = 30+aAnd a = 20°x = 30+20x = 50°Or30+x = 180-10030+x = 80x = 80-30x = 50°x is angle theta.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3610140

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Calculating Angle x.a = 90-40a = 50°a is angle EOQ.b = ½(180-a)b = ½(180-50)b = ½(130)b = 65°Therefore the required angle, x is;x = ½(90)+bx = 45+65x = 110°

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3609080

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Calculating x.a = ½(180-60)a = ½(120)a = 60°a is angle DCO = angle COD = angle CDO, making triangle CDO equilateral. b = a-45b = 60-45b = 15°b is angle ECO = angle CEO.c = 180-2bc = 180-2(15)c = 150°c is angle COE.It implies, length x is;x² = 6²+6²-2*6*6cos150x² = 134.353829072x = √(134.353829072)x = 11.5911099154 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3609071

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Calculating Area Blue.a = 8-2a = 6 units.cosb = 6/8b = acos(3/4)°Therefore, blue area is;½*8*8sin(acos(3/4))=½*8*8*0.66143782777= 32*0.66143782777= 21.1660104886 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3609067

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Calculating x.a = (2+x) units. Is the radius of the half circle.b = 2+ab = 2+2+xb = (4+x) units.Therefore, length x is;a²+a² = b²(2+x)²+(2+x)² = (4+x)²2(4+4x+x²) = 16+8x+x²8+8x+2x² = 16+8x+x²8+2x² = 16+x²x² = 8x = √(8)x = 2√(2) units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3608213

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Calculating Shaded Area.Notice.ABCD is a square.Let x be the side length of the square.a²+x² = 40²a = √(1600-x²) units.a is BF.b = x-ab = (x-√(1600-x²)) units.b is AF.It implies;cosc = x/40 --- (1).cosc = (x-√(1600-x²))/10 --- (2).Equating (1) and (2).x/40 = (x-√(1600-x²))/10Cross Multiply.10x = 40(x-√(1600-x²))x = 4(x-√(1600-x²))x = 4x-4√(1600-x²)4√(1600-x²) = 3x16(1600-x²) = 9x²16*1600-16x² = 9x²16*1600 = 25x²x² = 16*64x = √(16*64)x = 4*8x = 32 units.Again, x is the side length of the square....

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3607075

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Calculating L, length of the ascribed regular pentagon.a = (x+8) units.b = ⅕(180(5-2))b = ⅕*180*3b = 108°b is the single interior angle of the regular pentagon.c = 180-bc = 180-108c = 72°Calculating x.cos72 = x/(x+8)x = (cos72)x+8cos72(1-cos72)x = 8cos72x = 8cos72/(1-cos72)x = ⅕(8√(5)) units.x = 3.577708764 units.Recall.a = (x+8)And x = 3.577708764 units.a = 3.577708764+8a = 11.577708764 units.It implies, length L is;L²+3.577708764² = 11.577708764²L² = 11.577708764²-3.577708764²L = √(121.243340...
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