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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3636624

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Calculating length EC.Let it be x.Let y be the radius of the blue inscribed circle.It implies;a = y+y+y+ya = 4y units.a is the diameter of the ascribed circle.b²+(25+4)² = (4y)²b² = 16y²-29²b = √(16y²-841) units.b is BC.Calculating y.25 ~ 29y ~ √(16y²-841)cross Multiply.25√(16y²-841) = 29y25²(16y²-841) = (29y)²10000y²-525625 = 841y²10000y²-841y² = 5256259159y² = 525625y = √(525625/9159)y = 7.57554665261 units.Again, y is the radius of the inscribed circle.tanc = 25/yc = atan(25/7.57554665261)c...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3636623

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Calculating x, length AD.Notice.Plane shape ABC is not drawn to scale.a = 30+30a = 60°b² = 3²+6²-2*3*6cos60b² = 45-18b = √(27)b = 3√(3) units.b is BC.(3√(3)/sin60) = (3/sinc)3sin60 = 3√(3)sincc = asin((3sin60)/(3√(3)))c = asin(½√(3)/√(3))c = asin(½)c = 30°c is angle ACD.d = 180-30-cd = 180-30-30d = 120°d is angle ADC.e = ½(d)e = 60°It implies length AD, x is;sin60 = ½(AB)/x½√(3) = ½(6)/xx√(3) = 6x = 6/√(3)x = ⅓(6√(3))x = 2√(3) units.Orf = 180-60-30f = 90°f is angle ABD.It implies, calculating x...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3636618

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Calculating area red.Let x be the side length of the small square.a = ½(x) cm.b = x+ab = x+½(x)b = ½(3x) cm.It implies;½(x) ~ c½(3x) ~ xTherefore;1 ~ c3 ~ xCross Multiply.3c = xc = ⅓(x) cm.d = c+2√(10)d = (⅓(x)+2√(10)) cm.Notice.d = 2x.Calculating x.It implies;(⅓(x)+2√(10)) = 2xx+6√(10) = 6x5x = 6√(10)x = ⅕(6√(10)) cm.Again, x is the side of the small square.Recall.c = ⅓(x) cm.And x = ⅕(6√(10)) cm.c = ⅓*⅕(6√(10))c = ⅕(2√(10)) cm.tane = c/xe = atan(⅕(2√(10))/⅕(6√(10)))e = atan(⅓)°cose = f/2√(10)...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3636616

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Calculating Length x.Notice.AC = BC.a²+a² = 2²2a² = 4a² = 2a = √(2) units.a is AC = BC.b = a-yb = (√(2)-y)y is the radius of the green circle.c = y+y+xc = (2y+x) units.Where c is equal to a.Calculating y.y²+y² = b²2y² = (√(2)-y)²2y² = 2-2√(2)y+y²y²+2√(2)y-2 = 0(y+√(2))² = 2+√(2)²(y+√(2))² = 4y = -√(2)±√(4)y = -√(2)±2It implies;y ≠ (-√(2)-2) units.y = (2-√(2)) units.Again, x is the radius of the green circle.Recall.c = a = (2y+x) units.And a = √(2) units while y = (2-√(2)) units.Therefore;Calcul...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3635484

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Calculating Area Red (square).Notice.The composite plane shape is not drawn to scale.Let x be the side length of the square.a = (8-x) units.It implies;a²+8² = 10²(8-x)²+64 = 100(8-x)² = 368-x = ±√(36)x = 8±6It implies;x ≠ 8+6 = 14 units.x = 8-6 = 2 units.Therefore, area red square is;x²= 2²= 4 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3635474

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Calculating x.a² = 6²+x²a = √(36+x²) units.a is the diagonal of the rectangle.b = ½(a)b = ½√(36+x²) units.Therefore, length x, the width of the rectangle is;6 ~ ½√(36+x²)x ~ 2Cross Multiply.12 = ½(x√(36+x²))24 = x√(36+x²)24² = x²(36+x²)576 = 36x²+x⁴x⁴+36x²-576 = 0x⁴+48x²-12x²-576 = 0x²(x²+48)-12(x²+48) = 0(x²-12)(x²+48) = 0It implies;x²+48 = 0x² ≠ -48Again;x²-12 = 0x² = 12x = √(12)x = 2√(3) units.OrA smart approach is;x = √(2*6)x = √(12)x = 2√(3) units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3634257

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Calculating Area Circle.Let x be the radius of the circle.a² = 4a = 2 m.a is the side length of the small square.b² = 16b = 4 m.b is the side length of the big square.c = (x-2) units.It implies;(x-2)²+6² = x²x²-4x+4+36 =x²4x = 40x = 10 m.Again, x is the radius of the circle.Ord = (x-4) m.It implies;(x-4)²+8² = x²x²-8x+16+64 = x²8x = 80x = 10 m.x is the radius of the circle.Therefore, area circle is;πx²10²*π= 100π m²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3634250

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Calculating Area BCA.a = x+1+1+2+2a = (6+x) units.a is the height of the triangle.b = x+1+1+2b = (4+x) units.c = (x+1) units.Calculating x.siny = 1/(x+1) --- (1).siny = 2/(x+4) --- (2).Equating (1) and (2).1/(x+1) = 2/(x+4)2(x+1) = x+42x+2 = x+42x-x = 4-2x = 2 units.Recall.a = (6+x) units.And x = 2 units.a = 6+2a = 8 units.Again, a is the height of the triangle.Recall Again.c = (x+1) units.And x = 2 units.c = 2+1 c = 3 units.sind = 1/3d = asin(⅓)°tand = e/atan(asin(⅓)) = e/8e = 8tan(asin(⅓))e =...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3633015

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Calculating Area Blue.Notice.The side lengths of the regular octagon and regular hexagon is 4 units each.a = ⅙*180(6-2)a = 120°a is the single interior angle of the regular hexagon.b = ⅛*180(8-2)b = 135°b is the single interior angle of the regular octagon.c² = 4²+4²-2*4*4cos120c² = 32+16c² = 48c =4√(3) units.tand = 2/(4√(3))d = atan(1/(2√(3))d = 16.102113752°e = 120-30-de =120-30-16.102113752e = 73.897886248°f = 180-ef = 180-73.897886248f = 106.102113752°g = 360-a-bg = 360-120-135g = 105°h = g...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3633012

mathematics-question-and-solution_1785787400KZ2PND.jpg
Calculating length red.Let it be x (length BP).a = ½(2)a = 1 unit.a is the radius of the inscribed circle.b² = 1²+1²b² = 2b = √(2) units.b is half the diagonal of the ascribed square.c = b-ac = (√(2-1) units.d = 2b-cd =2√(2)-(√(2)-1)d = 2√(2)-√(2)+1d = (1+√(2)) units.Calculating x.x² = 2²+(1+√(2))²-2*2(1+√(2))cos45x² = 4+1+2√(2)+2-2(√(2)+2)x² = 5+2√(2)+2-2√(2)-4x² = 3x = √(3) units.Again, x is BP the required red length.Orx² = 2²+(√(2)-1)²-2*2(√(2)-1)cos45x² = 4+2-2√(2)+1-2(2-√(2))x² = 7-2√(2)-...
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