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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...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3606806

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Calculating R, radius of the circle.a = (7-R) units.b²+R² = a²b²+R² = (7-R)²b² = 49-14R+R²-R²b = √(49-14R) units.c = (R-1) units.Therefore R, radius of the circle is;b²+c² = R²√(49-14R)²+(R-1)² = R²49-14R+R²-2R+1 = R²49-14R-2R+1 = 050 = 16R25 = 8RR = ⅛(25) units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3605706

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Calculating r, radius of the inscribed circle.Notice.The ascribed plane shape is a trapezium.a = 2r units.a is the diameter of the inscribed circle.b²+(2r)² = 10²b = √(100-4r²) units.c²+(2r)² = 17²c = √(289-4r²) units.d = b+3+cd = (√(100-4r²)+3+√(289-4r²)) units.d is AD.Calculating r.½(3r)+½(10r)½(17r)+½((√(100-4r²)+3+√(289-4r²))r) = ½(3+(√(100-4r²)+3+√(289-4r²)))*2r½(33r+√(100-4r²)r+√(289-4r²)r) = ½(6r+2r√(100-4r²)+6r+2r√(289-4r²))33r+√(100-4r²)r+√(289-4r²)r = ½(6r+2r√(100-4r²)+6r+2r√(289-4r²)...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3604873

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Calculating the required inscribed orange triangle area.a = ½(3)a = 1.5 units.a is the radius of the inscribed circle.tanb = 3/4b = atan(3/4)°tan(atan(3/4)) = c/1.53/4 = c/1.54c = 4.5c = 1.125 units.d = (180-atan(4/3))°e = a-ce = 1.5-1.125e = 0.375 units.(1.5/sin(180-atan(4/3))) = (0.375/sinf)f = 11.5369590328°g = 180-2fg = 180-2(11.5369590328)g = 156.926081934°h² = 2(1.5)²-2(1.5)²cos156.926081934h = 2.93938769134 units.h is the longest length of the inscribed orange triangle.j = (180-atan(4/3)...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3604589

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Calculating length d.Notice.3 units is the radius of the inscribed green circle.6 units is the radius of the inscribed purple circle.9 units is the radius of the ascribed blue circle.a = 6-3a = 3 units.b =9+9-3-6b = 9 units.c²+3² = 9²c² = 81-9c = √(72)c² = 6√(2) units.x ~ 6√(2)6 ~ 9Cross Multiply.9x = 36√(2)x = 4√(2) units.4√(2) ~ 6√(2)e ~ 32 ~ 3e ~ 3Cross Multiply.3e = 6e = 2 units.f = 3+ef = 5 units.g²+5² = 9²g² = 81-25g = √(56)g = 2√(14) units.Therefore, length d is;d = 2gd = 2*2√(14)d = 4√(...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3603745

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Calculating Area Yellow (Triangle CDE).Let BE be x.Calculating x.½(9+6)*x = 8715x = 174x = (174/15) cm.a = x+ya = ((174/15)+y)a is BC, y is CE.Calculating y.9 ~ 6((174/15)+y) ~ yCross Multiply.9y = 6((174/15)+y)9y = ⅕(348)+6y3y = ⅕(348)y = ⅕(116) cm.Again, y is CE.It implies, area yellow is;½*DE*CE= ½*6*⅕(116)= ⅗(116) cm²= ⅕(348) cm²= 69.6 cm²
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