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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3514964

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Calculating Area Shaded.Shaded Area is;Area circle with diameter 30 cm - 7(area circle with diameter 10 cm)= π(½(30))² - 7π(½(10))²= π(15)² - 7π(5)²= 225π - 175π= 50π cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3514081

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Sir Mike Ambrose is the author of the question.Let AC be 1 unit.Area smaller pentagon is;½(5)*(1/(2tan(36)))= 1.72047740059 square units.a² = 1²+0.5²-cos108a = 1.24860602048 units.Where a is CD.(1.24860602048/sin108) = (0.5/sinb)b = 22.38617755917°c = 108-22.38617755917c = 85.61382244083°Calculating Area E.It is;0.5*0.5*0.5*1.24860602048sin22.38617755917= 0.05944103227 square units.(a) Area E ÷ Area Smaller Pentagon to 3 decimal places is;0.05944103227 ÷ 1.72047740059= 0.03454915028 ≈ 0.035Calc...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3513115

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Calculating Green Area.Let x be the equal inscribed angles.Let a be the radius of the sector.It implies;b² = 2a²-2a²cosx --- (1).b² = 6²+9²-2*6*9cosxb² = 117-108cosx --- (2).Equating (1) and (2).2a²-2a²cosx = 117-108cosxa²(2-2cosx) = 117-108cosxa² = (117-108cosx)/(2-2cosx) --- (3).c = a+a c = 2a units.It implies;(2a)² = 6²+b²4a² = 36+117-108cosx4a² = 153-108cosxa² = ¼(153-108cosx) --- (4).Calculating x, equating (3) and (4).(117-108cosx)/(2-2cosx) = ¼(153-108cosx)Let cosx = d.(117-108d)/(2-2d)...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3512332

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Sir Mike Ambrose is the author of the question. Area R is;Area triangle with height 4 cm and base (4tan52.5) cm - Area sector with angle 52.5° and radius 4 cm.= ½*4(4tan52.5) - (52.5*4*4π)/360= 8tan52.5 - ⅓(7π)= ⅓(24tan52.5-7π)= 3.09542012435 cm²≈ 3.1 cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3511513

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Calculating Area Yellow.Notice.The ascribed quadrilateral is a square with side 6 units.a² = x²+3²a = √(x²+9) units.b = 2ab = 2√(x²+9) units.c = (6+x) units.Notice.b = cTherefore, calculating x.2√(x²+9) = 6+x4(x²+9) = (6+x)²4x²+36 = 36+12x+x²3x² = 12x3x = 12x = 4 units.d = 6-xd = 6-4d = 2 units.It implies, yellow area is;Area square with side 6 units - Area triangle with height 4 units and base 3 units - Area triangle with height 2 units and base 6 units.= 6²-½(4*3)-½(6*2)= 36-6-6= 36-12= 24 sq...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3510692

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Calculating x, chord of the circle..a² = 1 square units.a = 1 unit.a is the side length of the 3 inscribed equal squares.b = 1+½(1)+yb = (1.5+y) units.c = 1+1c = 2 units.d² = 2²+0.5²d² = 4+0.25d = √(4.25) units.d is r, the radius of the circle.e² = (1.5+y)²+1²e² = 3.25+3y+y²e = √(3.25+3y+y²) units.e is also r, radius of the circle.Calculating y.Equating d and e.√(4.25)² = √(3.25+3y+y²)4.25 = 3.25+3y+y²y²+3y-1 = 0(y+(3/2))² = 1+(3/2)²(y+(3/2))² = (13/4)y = -(3/2)±√(13/4)y = -(3/2)±√(13/4)It impl...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3510033

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Blue area is;Area sector with radius 12 units and angle 30° - Area sector with radius 6 units and angle 60° - Area triangle with height 6 units and base 6sin120 units.= (30π*12²/360) - (60π*6²/360) - (½*6²*sin120)= 12π - 6π - 9√(3)= 6π-9√(3)= 3(2π-3√(3)) square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3509053

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Calculating Length CF.a² = 4²+4²-2*4*4cos150a = 7.72740661031 cm.Where a is BE.b = angle ABE = ½(180-150)b = 15°c = angle AFE = 180-45-15c = 120°(4/sin120) = (d/sin45)d = 3.26598632371 cm.Where d is EF.Notice;EF = CFTherefore;Length CF = 3.26598632371 cm.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3508445

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Calculating Length FG.tan15 = a/4a = 1.07179676972 cm.Where a is AD.b² = 1.07179676972²+4²b = 4.14110472164 cm.Where b is DF.c = 4-1.07179676972c = 2.92820323028 cm.Where c is CD.sin60 = d/2.92820323028 d = 2.53589838487 cm.Where d is DE = BE.e² = 16+16-2*16cos150e = 7.72740661031 cm.Where e is BF.f² = 7.72740661031²+2.53589838487²-2*2.53589838487*7.72740661031cos45f = 6.19925645689 cm.Where f is EF.(6.19925645689/sin45) = (2.53589838487/sing)g = 16.81321456806°Where g is angle BFE.h = 15+gh =...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3507796

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Calculating Shaded Area ( Triangle AEF).a = asin(1/6)b = 2ab = 2(asin(1/6))Where b is angle BAC.sin(2(asin(1/6))) = c/6c = ⅓(√(35)) units.c = 1.97202659437 units.Where c is BE.d = 90-2asin(1/6)d = 70.81186354628°Where d is angle ABE.cos70.81186354628 = e/1.97202659437e = 0.64814814815 unit.Where e is BD.tan70.81186354628 = f/0.64814814815f = 1.86246956135 units.Where f is DE.tan(acos(1/6)) = g/0.64814814815g = 3.83449615572 units.Where g is DF.h = 3.83449615572-1.86246956135h = 1.97202659437 un...
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