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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...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3426262

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Sir Mike Ambrose is the author of the question.Shaded area coordinates are;Coordinate X is;X(½, (9/4))Coordinate Y is;Y((-3/2), (17/4))Coordinate Z is;Z((5/2), (33/4))Therefore shaded area exactly in square units is;Area trapezoid with parallel side (17/4) unity and (33/4) units, and height 4 units - Area trapezoid with parallel side (17/4) units and (9/4) units, and height 2 units - Area under the curve at coordinate (½, 0) and ((5/2), 0)= ½*4((17/4)+(33/4)) - ½*2((17/4)+(9/4)) - (55/6)= 25 -...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3425962

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Calculating Area of the yellow Hexagon.Let x be the side length of the hexagon.a²+3² = x²a = √(x²-9) cm.b² = 2x²-2x²cos120b = √(3x²)b = √(3)x cm.It implies;Calculating x.sinc = √(x²-9)/x --- (1).sinc = 5/(√(3)x) --- (2).Equating (1) and (2).√(x²-9)/x = 5/(√(3)x)Cross Multiply.5x = √(3)x*√(x²-9)5 = √(3x²-27)25 = 3x²-273x² = 52x² = 52/3x = √(52/3)x = 4.16333199893 cm.Again, x is the side length of the yellow hexagon.Recall.b = √(3)x cm.And x = √(52/3) cm.b = √(3)*√(52/3)b = √(52) cm It implies;Ar...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3425126

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Calculating the blue shaded area.Let x be the radius of the half circle.a = (x-2) cm.Calculating x.It implies;x² = 4²+(x-2)²x² = 16+x²-4x+44x = 20x = 5 cm.Again, x is the radius of the half circle.Or4*4 = 2*(x+(x-2))16 = 2(2x-2)8 = 2x-22x = 10x = 5 cm.Again, x is the radius of the half circle.Recall.a = (x-2) cm.And x = 5 cm.a = 5-2a = 3 cm.tanb = 4/3b = atan(4/3)°Therefore, area shaded blue is;Area sector with radius 5 cm and angle atan(4/3)° - Area right-angled triangle with height 4 cm and...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3424247

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Sir Mike Ambrose is the author of the question.a² = 10²+16²-2*10*16cos120a = 2√(129) units.Where a is length AC.(3√(129)/sin120) = (16/sinb)b = 37.58908946897°c = 90-bc = 52.41091053103° d = 60-bd = 22.41091053103°e = 90-de = 67.58908946897° f = 90-60f = 30°cos37.58908946897 = g/10g = 7.92405815693 units.i = 30+37.58908946897i = 67.58908946897°tan67.58908946897 = j/7.92405815693j = 19.2148198619 units.Where j is the radius of the arc.sin67.58908946897 = 19.2148198619/kk = 20.78460969082 units.l...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3423225

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Calculating x.8 = 2³It implies;2^(3x)+2^(x) =130Let 2^(x) = p.p³+p = 130130 = 1*2*5*13It implies;p = 5Calculating x.Recall.p = 2^(x) And p = 55 = 2^(x)log5 = xlog2x = (log5)/(log2)x = 2.32192809489

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3423223

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Sir Mike Ambrose is the author of the question.The side of area green, inscribed square is;Let it be x.Therefore;1.11496246101x + 0.82101781219x = 27.36726040631.9359802732x = 27.3672604063x = 14.1361256544 cmTherefore;Exact perimeter of green area in decimal cm is;4(14.1361256544)= 56.5445026176 cm

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3422425

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Sir Mike Ambrose is the author of the question.Let the two equal marked lengths of triangle ABC be 2 units.Therefore;Area triangle ABC is;Area triangle with height 5.75877048314 units and base (5.75877048314sin20) units.= 0.5*5.75877048314*5.75877048314sin20= 5.67128181961 space units.Area purple is;Area triangle with height 4 units and base (1.11985686148sin28.334490436) units.= 0.5*4*1.11985686148sin28.334490436= 1.06300877373 space units.It implies;Area Purple ÷ Area ABC to 2 d. p. is;1.0630...
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