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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3585819

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Calculating length c.d = a+bd = 8+9d = 17 units. e = b-ae = 9-8e = 1 unit.It implies;e²+f² = 17²f² = 289-1f = √(288)f = 12√(2) units.cosg = 1/17g = acos(1/17)g = 86.6277133166°h = 180-gh = 180-86.6277133166h = 93.3722866834°j = ½(g)j = ½(86.6277133166)j = 43.3138566583°k = ½(h)k = ½(93.3722866834)k = 46.6861433417°Therefore, length c is;tan43.3138566583 = c/9c = 9tan43.3138566583c = 8.48528137424 units.Or tan46.6861433417 = c/8c = 8tan46.6861433417c = 8.48528137423 units.Or c = ½(f)c = ½(12√(2)...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3584695

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Calculating r+R.Notice.DEFG is a square.DG = (9+R) units.FG = R+1+5+1+rFG = (7+R+r) units.Calculating r.Equating DG = FG.9+R = 7+R+r9 = 7+rr = 9-7r = 2 units.Calculating R.AG = 1+5+RAG = (6+R) units.AD = 9+5+1AD = 15 units.It implies;15² = (9+R)²+(6+R)²225 = 81+18R+R²+36+12R+R²2R²+30R-108 = 0R²+15R-54 = 0R²+18R-3R-54 =0R(R+18)-3(R+18) = 0(R+18)(R-3) = 0Therefore;R ≠ -18R = 3 units.It implies;r+R= 2+3= 5 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3583681

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Calculating Area Blue Circle.Notice.10 units is the side length of the square.a = (10+2x) units.b = ½(a)b = ½(10+2x)b = (5+x) units.b is the radius of the blue circle.c = b-2xc = 5+x-2xc = (5-x) units.d = ½(10)d = 5 units.Calculating x.b² = c²+d²(5+x)² = (5-x)²+5²25+10x+x² = 25-10x+x²+2520x = 25x = 1.25 units.Recall.b = (5+x) And x = 1.25 units.b = 5+1.25b = 6.25 units.Again, b is the radius of the blue circle.Therefore, Area Blue Circle is;πb²= π(6.25)²= 625π/16 square units.= 122.718463031 sq...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3582512

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Calculating perimeter of the blue inscribed square.5² = 7²+8²-2*7*8cosa112cosa = 49+64-25cosa = 88/112a = acos(11/14)a = 38.2132107017°5/sin38.2132107017 = 7/sinbsinb = ⅕(7sin38.2132107017)sinb = 0.86602540378b = asin(0.86602540378)b = 60°c = 180-60c = 120°d = 180-120-38.2132107017d = 21.7867892983°Calculating x, side length of the inscribed blue square.x/sin21.7867892983 = 7/sin120x = (7sin21.7867892983)/(sin120)x = 3 units.There, perimeter of the inscribed blue square is;4xAnd x = 3 units.= 4...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3581617

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Calculating r, radius of the circle.Let the small inscribed right-angled triangle shortest length be x.3 ~ 4x ~ aCross Multiply.3a = 4xa = ⅓(4x) units.a is the big inscribed right-angled triangle shortest length.b²+x² = 3²b = √(9-x²) units.3 ~ 4√(9-x²) ~ cCross Multiply.3c = 4√(9-x²)c = ⅓(4√(9-x²)) units.It implies;3x = x+c3x = x+⅓(4√(9-x²))9x = 3x+4√(9-x²)6x = 4√(9-x²)3x = 2√(9-x²)9x² = 4(9-x²)9x² = 36-4x²13x² = 36x² = 36/13x = √(36/13)x = 6√(13)/13 units.x = 1.66410058868 units.Recall.a = ⅓(4...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3580129

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Calculating x.a² = 9a = √(9)a = 3 units.a is the side length of the inscribed square.b² = 3²+3²b² = 2*3²b = √(2*3²)b = 3√(2) units.b is the radius of the half circle.c = 2bc = 2*3√(2)c = 6√(2) units.c is the diameter of the half circle.d² = 3²+(3√(2))²d² = 9+18d = √(27)d = 3√(3) units.It implies;cose = x/(6√(2)) --- (1).cose = 3√(2)/3√(3)cose = √(2)/√(3) --- (2).Equating (1) and (2).x/(6√(2)) = √(2)/√(3)√(3)x = 12x = 12/√(3)x = 4√(3) units.x = 6.92820323028 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3579049

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Calculating R, radius of the blue circle.a = (R-2) cm.b = ½(20)b = 10 cm.R, radius of the blue circle is;R² = (R-2)²+10²R² = R²-4R+4+1004R = 104R = 26 cm.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3578240

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Calculating Area Red.Let x be the radius of the circle.a = (x-7) cm.Calculating x.x²+(x-7) = 13²x²+x²-14x+49 = 1692x²-14x-120 = 0x²-7x-60 = 0x²-12x+5x-60 = 0x(x-12)+5(x-12) = 0(x-12)(x+5) = 0It implies;x ≠ -5x = 12 cm.Again, x is the radius of the circle.Recall.a = x-7And x = 12 cm.a = 12-7a = 5 cm.Therefore, area red is ;Area quarter circle with radius 12 cm - Area right-angled triangle with height 12 cm and base 5 cm.(¼*12²π) - (½*12*5)= 36π-30= 6(6π-5) cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3577145

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Sir Mike Ambrose is the author of the question.Calculating Area Blue ÷ Area Green to 2 decimal places.Let the side length of the regular pentagon be 1 unit.tan36 = a/0.5a = 0.363271264 unit.b² = 0.363271264²+0.5²b = 0.61803398875 unit.tan72 = c/0.5c = 1.53884176859 units.Area Green is;0.5sin108+0.5*1.53884176859*0.5-0.5*0.5*0.363271264-0.5*0.61803398875*0.61803398875sin36= 0.65716389015 square units.Calculating Area Blue.Let d be the radius of the inscribed blue circle.Calculating d.e = 0.5(90+...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3576039

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Area shaded in pink (area A) is;Notice:The single side length of the square is;3√(2) units.Shaded yellow area height is;Height = 6/(3√(2))= √(2) units.Therefore area A is;Height = 3√(2)-√(2) = 2√(2) units.Base = ⅓(3√(2)) = √(2) units.Area A = ½*√(2)*2√(2)= ½(4)= 2 square units.Area shaded in pink (area A) is;2 square units.
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