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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3642457

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Calculating h.Let x be the two equal lengths.a = x+xa = 2x units.a is the base of the ascribed right-angled triangle.b²+24² = a²b² = (2x)²-24²b = √(4x²-576) units.c = b-7c = (√(4x²-576)-7) units.Calculating x.√(4x²-576) ~ x2x ~ (√(4x²-576)-7)Cross Multiply.2x² = √(4x²-576)²-7√(4x²-576)7√(4x²-576) = 2x²-57649(4x²-576) = 4x⁴-2304x²+331776196x²-28224 = 4x⁴-2304x²+3317764x⁴-2500x²+360000 = 0x⁴-625x²+90000 = 0Therefore;x ≠ 15 units.x = 20 units.Recall.c = (√(4x²-576)-7) units.And x = 20 units.c = √(...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3642453

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Calculating r, radius of the half circle.Let y be the height of the isosceles triangle.a²+3² = y²a = √(y²-9) units.Calculating y.√(y²-9) ~ y3 ~ 5Cross Multiply.3y = 5√(y²-9)9y² = 25y²-22525y²-9y² = 22516y² = 225y = √(225/16)y = 15/4 units.y = 3.75 units.Again, y is the height of the isosceles triangle.b² = 5²+y²b² = 5²+3.75²b = √(5²+3.75²)b = 6.25 units.It implies, radius of the half circle, r is;r = ½(b)r = ½(6.25)r = 3.125 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3642435

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Calculating Area Blue.a = ⅙*180(6-2)a = 120°a is the interior angle of the ascribed regular hexagon.b² = 5²+5²-2*5*5cos120b² = 50+25b = √(75)b = 5√(3) units.b is the height of the regular hexagon.Therefore, are blue is;Area regular hexagon - 2(area sector with radius 2.5 units and angle 120°)-4(area triangle with height 2.5 units and base 2.5sin60 units)-2(area sector with radius 2.5 units and angle 60°).((5√(3)*5)+(2.5*5√(3)))-2(120π*2.5²/360)-4(0.5*2.5*2.5sin60)-2(60π*2.5²/360)= (25√(3)+12.5√...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3641243

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Calculating a/b.Let r be the equal radius of the inscribed circle and half circle.It implies;r = ½(a) units.c = (a+b) units.c is the radius of the ascribed quarter circle.Let c be 1 unit.d = (1-½(a)) units.Calculating a.(1-½(a))² = a²+(½(a))² 1-a+¼(a²) = a²+¼(a²)a²+a-1 = 0(a+½)² = 1+(½)²a = -½±½√(5)It implies;a ≠ -½-½√(5)a = ½(√(5)-1) units.Calculating b.Recall.a+b = cAnd c = 1 unit.Therefore;a+b = 1And a = ½(√(5)-1) units.It implies;b = 1-ab = 1-½(√(5)-1)b = ½(3-√(5)) units.Therefore a/b is;½(...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3641240

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Calculating Area Blue.Notice.The composite plane shape is not drawn to scale.a² = (3+3)²+(2+2)²-2*6*4cos120a² = 36+16+24a = √(76) units.a = 2√(19) units.a is AC.(2√(19)/sin120) = (6/sinb)b = 36.5867755536°b is angle ACB.c = 90-bc = 90-36.5867755536c = 53.4132244464°d = 180-120-bd = 60-36.5867755536d = 23.4132244464°d is angle BAC.e = 90-de = 90-23.4132244464e = 66.5867755536°cosb = 2/fcos36.5867755536 = 2/ff = 2.49079939631 units.cosd = 3/gcos23.4132244464 = 3/gg = 3.26917420766 units.h = a-f-g...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3641232

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Calculating Area Blue.Let x be the side length of the inscribed regular pentagon.a = ⅕*180(5-2)a = 108°a is the single interior angle of the inscribed regular pentagon.b² = 2x²-2x²cos108b = 1.61803398875x units.c²+(0.5x))² = (1.61803398875x)²c² = 2.61803398875x²-0.25x²c = √(2.36803398875x²)c = 1.53884176859x units.c is the height of the inscribed regular pentagon and also the height of the ascribed isosceles trapezoid.d = 120-90d = 30°cos30 = e/4e = 4cos30e = 2√(3) units.e = 3.46410161514 units...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3639993

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Calculating Area Blue.a = ⅛*180(8-2)a = 45*3a = 135°a is the single interior angle of the ascribed regular octagon.b = ⅙*180(6-2)b = 30*4b = 120°b is the single interior angle of the inscribed regular hexagon.c = a-bc = 135-120c = 15°d² = 4²+4²-2*4*4cos15d = 1.04420953776 units.e = ½(180-c)e = ½(180-15)e = ½(165)e = 82.5°f = a-ef = 135-82.5f = 52.5°g² = 1.04420953776²+4²-2*1.04420953776*4cos52.5g = 3.46482000046 units.(3.46482000046/sin52.5) = (4/sinh)h = 66.3332346534°h' = 180-hh' = 180-66.333...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3639977

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Calculating Area Green.Let x be the side length of the ascribed square.a²+3² = x²a = √(x²-9) units.b = (90-y)°siny = 3/x --- (1).7² = x²+√(x²-9)²-2x√(x²-9)cos(90-y)49 = 2x²-9-2x√(x²-9)siny58 = 2x²-2x√(x²-9)siny29 = x²-x√(x²-9)siny --- (2).Substituting (1) in (2).29 = x²-x√(x²-9)(3/x)29 = x²-3√(x²-9)3√(x²-9) = x²-293²(x²-9) = (x²-29)9x²-81 = x⁴-58x²+841x⁴-67x²+922 = 0(x²-½(67))² = -922+(-½(67))²(x²-½(67))² = 801/4x² = ½(67)±√(801/4)x²= ½(67)±½(3√(89))It implies;x² = ½(67-3√(89))Orx² = ½(67+3√(89...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3639970

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Calculating C, circumference of the circle in terms of π.Let r be the radius of the circle.a = (r-6) units.b = (r+6) units.Calculating r.(r-6)(r+6) = 3*7r²-36 = 21r² = 57r = √(57) units.Therefore, circumference of the circle in terms of π is;2πr= 2√(57)π units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3636632

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Calculating x and y.a = 6+6a = 12 units.a is the diameter of the half circle.sinb = a/13b = asin(12/13)°c²+12² = 13²c² = 169-144c = √(25)c = 5 units.Calculating x.tan(0.5b) = 6/xx = 6/tan(0.5asin(12/13))x = 6/(2/3)x = ½*6*3x = 9 units.Calculating y.It implies;x+y = 13And x = 9 units.9+y = 13y = 13-9y = 4 units.Orx = y+cx is 9 units and c is 5 units.Therefore;9 = y+5y = 9-5y = 4 units.
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