Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3678215

Calculating length x.½*5*a = S5a = 2Sa = ⅕(2S) units.a is CE.x ~ 5b ~ aTherefore;x ~ 5b ~ ⅕(2S)Cross Multiply.⅕(2S)x = 5b2Sx = 25bb = (2Sx)/25 units.b is BC.Calculating x, length AB.½*x*b = 3S+S½*x*((2Sx)/25) = 4Sx²S = 100Sx² = 100x = √(100)x = 10 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3678212

Calculating length x.a = 2+3 = 1+4a = 5 units.a is the radius of the ascribed quarter circle.b = a+3b = 5+3b = 8 units.It implies;c*c = 2*bc² = 2*8c = √(16)c = 4 units.d = c-1d = 4-1d = 3 units.Therefore, length x is;x² = 3²+d²x² = 3²+3²x² = 18x = √(18)x = 3√(2) units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3677686

Calculating x/y.tana = 4/3a = atan(4/3)°b = 180-ab = (180-atan(4/3))°b = 126.869897646°c² = 3²+1²-2*3*1cos126.869897646c = 3.68781778292 units.(1/sind) = (3.68781778292/sin(126.869897646))d = 12.5288077092°e = 90-de = 90-12.5288077092e = 77.4711922908°Calculating x.cose = x/4x = (4cos77.4711922908) units.Calculating y.sine = y/4y = (4sin77.4711922908) units.It implies, x/y is;(4cos77.4711922908)/(4sin77.4711922908)= (cos77.4711922908)/(sin77.4711922908)= 0.22222222222= 2/9

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3677287

Calculating the required angle.Let it be x.Let the square side length be 2 units.a = ½(2)a = 1 unit.tanb = 2/1b = atan(2)°c = 180-bc = (180-atan(2))°(2/sin(180-atan(2))) = (1/sind)d = 26.5650511771°e = 180-(180-atan(2))-de = atan(2)-26.5650511771e = 36.8698976458°f² = 2²+1²-2*2*1cos36.8698976458f = 1.3416407865 units.g² = 1.3416407865²+1²-2*1.3416407865*1cos(atan(2))g = 1.26491106407°Therefore, the required angle x is;(1/sinx) = (1.26491106407/sin(atan(2)))x = asin(0.70710678119)x = 45°Again, x...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3677274

Calculating Area ADPB.Notice.BD = 3 units.CD = 1 unit.a = ½(3)a = 1.5 units.a is AC.b = a+1b = 1.5+1b = 2.5 units.b is OB, the radius of the circle.cosc = a/bc = acos(1.5/2.5)c = 53.1301023542°c is angle OBD.d = 90-cd = 90-53.1301023542d = 36.8698976458°d is angle ABP.cosd = 4/ee = 4/cos36.8698976458e = 5 units.e is AP = BP.It implies, area green (area quadrilateral ADPB) is;Area triangle with height 4 units and base 5 units - Area triangle with height 1 unit and base 5 units.½(4*5)-½(1*5)= 10-...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3676034

Kindly move the question right/left one time to view the analysis.Thank you.Calculating x, angle CHF.a = ½(45)a = 22.5°a is angle OAC.b = 180-2ab = 180-45b = 135°b is angle AOC.c = 180-bc = 45°c is angle COH.It implies, the required angle x is;22.5+45+x+90 = 180x = 90-67.5x = 22.5°Orx = ½(45)x = 22.5°

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3676028

Calculating Area Yellow÷Area Red.Notice.Inscribed blue square area is 8 m².a = √(8)a = 2√(2) m.a = 2.82842712475 m.a is the side length of the inscribed blue square.Let r be the radius of the inscribed yellow circle.b = r-ab = (r-2√(2)) m.Calculating r.b²+b² = r²2(r-2√(2))² = r²2r²-8√(2)r+16 = r²r²-8√(2)r+16 = 0(r-4√(2))² = -16+(-4√(2))²(r-4√(2))² = -16+32r-4√(2) = √(16)r = 4√(2)±4It implies r ≠ (4√(2)-4) m.r = (4√(2)+4) m.r = 4(√(2)+1) m.r = 9.65685424949 units.Again, r is the radius of the in...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3676023

Calculating area ADBC.Let let x be the side length of the small square.a = (2-x) cm.b² = x²+x²b = √(2x²)b = √(2)x cm.b is BD, the diagonal of the small square.c² = x²+a²c² = x²+(2-x)²c² = x²+4-4x+x²c = √(2x²-4x+4) cm.c is AD, the diagonal of the big square.d = 2bd = 2√(2)x cm.d is the side length of the big square.√(2x²-4x+4)² = (2√(2)x)²+(2√(2)x)²2x²-4x+4 = 16x²7x²+2x-2 = 0(x+(1/7))² = (2/7)+(1/7)²(x+(1/7))² = (15/49)x = -(1/7)±√(15/49)x = -(1/7)±(√(15)/7)x = -(1/7)+(√(15)/7)x = ⅐(√(15)-1)x =...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3675194

Calculating Blue Area.It is;Area quarter circle with radius 4 cm - Area triangle with height and base 4 cm respectively.¼*4²π - ½*4²= ¼(16π)-½(16)= 4π-8= 4(π-2) square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3675178

Calculating length CH (x).a = 9+6a = 15 unitsa is AH.b = a+xb = (15+x) units.b is AC.Notice.EF = EH = 6 units.6²+c² = 9²c² = 81-36c = √(45)c = 3√(5) units.c is AF.3√(5) ~ 156 ~ dCross Multiply.3√(5)d = 6*15d = 6√(5) units.d is O1H, the radius of the inscribed yellow half circle.e = c+2de = 3√(5)+2*6√(5)e = 15√(5) units.e is AB, the ascribed of the ascribed half circle.It implies, length x is;3√(5) ~ (15+x)9 ~ 15√(5)Cross Multiply.9(15+x) = 3√(5)*15√(5)15+x = 25x = 25-15x = 10 units.x is CH, the...

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