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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3726990

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Calculating Blue Area.Let x be the radius of the inscribed circle.a = 12+18a = 30 units.b = (x+12) units.c = (x+18) units.Calculating x.a² = b²+c²30² = (x+12)²+(x+18)²900 = x²+24x+144+x²+36x+324900 = 2x²+60x+4682x²+60x-432 = 0x²+30x-216 = 0x²+36x-6x-216 = 0x(x+36)-6(x+36) = 0(x-6)(x+36) = 0It implies;x ≠ -36x = 6 units.Again, x is the radius of the inscribed circle.Therefore, area blue is;Area square with side 6 units - Area quarter circle with radius 6 units.(6*6) - (¼*6*6π)= 36-9π= 9(4-π) squ...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3726042

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Calculating r, radius of the quarter circle.a = r+ra = 2r units.a is diameter.x ~ 158 ~ 2rCross Multiply.x = 60/r units.b²+x² = 8²b² = 64-(3600/r²)b = √(64-(3600/r²)) units.c² = r²+b²c² = r²+√(64-(3600/r²))²c² = r²+64-(3600/r²)c = √((r⁴+64r²-3600)/r²)d = r+xd = r+(60/r)d = (r²+60)/r units.Calculating r.8²+c² = d²64+√((r⁴+64r²-3600)/r²)² = ((r²+60)/r)²64+(r⁴+64r²-3600)/r² = (r⁴+120r²+3600)/r²64r²+r⁴+64r²-3600 = r⁴+120r²+360064r²+64r²-3600 = 120r²+3600128r²-120r² = 72008r² = 7200r² = 900r = 30 un...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3725060

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Calculating area of the half circle.Notice.8π cm² is the area of the red inscribed circle.πr² = 8πr = √(8)r = 2√(2) cm.r is the radius of the red inscribed circle.Let x be that radius of the half circle.a = x+ra = (x+2√(2)) cm.b = x-rb = (x-2√(2)) cm.Calculating x.a² = b²+x²(x+2√(2))² = (x-2√(2))²+x²x²+4√(2)x+8 = x²-4√(2)x+8+x²4√(2)x = x²-4√(2)x8√(2)x = x²x = 8√(2) cm.Again, x is the radius of the half circle.Therefore, area half circle is;½(πx²)= ½*π*(8√(2))²= ½*π*64*2= 64π cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3724099

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Calculating Green Area - Yellow Area.5² = 3²+a²a = √(25-9)a = 4 units.tanb = 3/4b = atan(3/4)°c = 90-bc = atan(4/3)°d = 180-c-45d = (45+atan(3/4))°d = 81.8698976458°tand = 3/ee = 3/tan(81.8698976458)e = 0.42857142857 units.e is the base of the yellow inscribed right-angled triangle.tand = 4/ff = 4/tan(81.8698976458)f = 0.57142857143 units.is the base of the green inscribed right-angled triangle.It implies, green area - yellow area is;(0.5*0.57142857143*4)-(0.5*0.42857142857*3)= 1.14285714286-0....

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3722836

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Calculating y.πr² = πr = 1 cm.r is the radius of the inscribed circle.a = ½(2+y) cm.a is the radius of the ascribed half circle.sin30 = r/b½ = 1/bb = 2 cm.c = a-1c = ½(2+y)-1c = ½(y) cm.d = a-2d = ½(2+y)-2d = ½(y-2)It implies, length y is;c² = b²+d²(½(y))² = 2²+(½(y-2))²¼(y²) = 4+¼(y²-4y+4)y² = 16+y²-4y+44y = 20y = 5 cm.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3721610

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Calculating the area of the quarter circle.Let r be it's radius.Let a be the 3 equal lengths each.b = r-a-a-ab = (r-3a) units.c = a+a+ac = 3a units.d = r+a+a+ad = (r+3a) units.It implies;(r+3a)(r-3a) = 13²r²-9a² = 169r² = 169+9a² --- (1).Therefore;(r+2a)(r-2a) = 17²r²-4a² = 289r² = 289+4a² --- (2).(r+a)(r-a) = 19²r²-a² = 361r² = 361+a² --- (3).Equating (1) and (2).169+9a² = 289+4a²5a² = 120a² = 24a = √(24)a = 2√(6) units.Calculating r.Substituting a in (3).r² = 361+a²And a = 2√(6) units.r² = 36...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3720671

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Calculating the area of the regular pentagon not enclosed by the blue circle.πr² = 288πr² = 288r = √(288)r = 12√(2) cm.r is the radius of the ascribed black circle.a = ⅕*180(5-2)a = 108°a is the single interior angle of the regular pentagon.b = 180-2(½(a))b = 180-108b = 72°c = ½(108)c = 54°sinc = d/rd = 12√(2)sin54d = 13.7294736676 cm.d is the radius of the blue inscribed circle.It implies;Area regular pentagon not enclosed by the blue circle is;5(area triangle with height 12√(2) cm and base 12...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3718647

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Calculating yellow area (area trapezoid).Let x be the height of the yellow area.a = 3-1a = 2 units.b = 1+8b = 9 units.Calculating x.It implies;9 ~ xx ~ 2Cross Multiply.x² = 18x = √(18)x = 3√(2) units.Again, x is the height of the yellow area.Therefore, area yellow is;½(3+1+8)*x= ½*12*3√(2)= 18√(2) square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3717706

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Calculating x.8⁸ = 167772164¹² = 16777216Let 32^(x) = 2^(5x) = a.It implies;a² = 2(16777216)²a = √(2(16777216)²)a = 2²⁴*√(2)a = 2^(24.5)Recall.a = 2^(5x)It implies;2^(5x) = 2^(24.5)5x = 24.5x = 24.5/5x = 4.9

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3716666

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Calculating Area Green Square.a² = 12a = √(12)a = 2√(3) units.a is the side length of the the square.b = a+xb = (x+2√(3)) units.b is the side length of the green square.c = (2√(3)-x) units.Calculating x.2√(3) ~ (x+2√(3))x ~ (2√(3)-x)Cross Multiply.12-2√(3)x = x²+2√(3)xx²+4√(3)x-12 = 0(x+2√(3))² = 12+(2√(3))²(x+2√(3))² = 24(x+2√(3))² = √(24)x = -2√(3)±2√(6)It implies;x = (2√(6)-2√(3)) units.Recall.b = (x+2√(3)) units.b is the side length of the green square.And x = (2√(6)-2√(3)) units.Therefore;...
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