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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...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3421550

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Sir Mike Ambrose is the author of the question.Point P coordinate is;P(4, -3)Point R coordinate is;R(0, ⅓(37))Point Q (maximum turning point) coordinate is;Q((-3√(259)/14), (4√(259)/7))Therefore;Area green exactly in square unit decimal form is;Area triangle with height 14.2909320391 units and base (15.8464857653sin(atan(23/6)-atan((8√(259)+42)÷(3√(259)+56))) units.= 0.5*14.2909320391*15.8464857653sin(atan(23/6)-atan((8√(259)+42)÷(3√(259)+56))= 32.7134051364 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3401898

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Sir Mike Ambrose is the author of the question.The side of the square is;6.065425 cmTherefore;Area red in cm² to 2 d. p is;Area triangle with height (2.1tan29.11) cm and base 2.1 cm= 0.5*2.1(2.1tan29.11)= 1.22779137323≈ 1.23 cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3401118

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Sir Mike Ambrose is the author of the question.Calculating Area Green.Area green exactly in cm² is;Area ABCD - Area trapezoid with parallel sides (9-2√(3)) cm and (24√(3)-39) cm, and height 6 cm.= (54-6√(3)) - ½*6((9-2√(3))+(24√(3)-39))= (54-6√(3)) - 3(22√(3)-30)= 54-6√(3)-66√(3)+90= 144-72√(3)= 72(2-√(3)) cm²OrCalculating Area Green.Let a be BC.tan30 = 12/bb = 12√(3) cm.b is the height of the ascribed right-angled triangle.tan30 = a/cc = √(3)a cm.d = 6+cd = (6+√(3)a) cm.tan30 = e/(6+√(3)a)e =...
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