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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3631954

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Calculating Alpha.Let it be x.Notice.BCDE and ABFG are both square.Let the two equal red lengths be √(2) units each.a²+a² = √(2)²2a² = 2a² = 1a = 1 unit.a is the side length of square BCDE.b = y+ab = (y+1) units.b is length AC.y is the side length of square ABFG.Calculating y.√(2)² = y²+(y+1)²2 = y²+y²+2y+12y²+2y-1 = 0y²+y = ½(y+½)² = ½+(½)²(y+½)² = ¾y = -½±√(¾)y = -½±½√(3)It implies;y ≠ -½(1+√(3)) units.y = ½(√(3)-1) units.y = 0.36602540378 units.Again, y is the side length of square ABFG.Re...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3631933

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Calculating Theta.Let it be x.Notice.ABCD is a square.Let 1 unit be CP = DQ.It implies;a = 180-33-48a = 99°(b/sin99) = (1/sin33)b = 1.81347328615 units.b is the side length of the square.c = b-1c = 1.81347328615-1c = 0.81347328615 units.c is CQ.d = 90-48d = 42°d is angle PCQ.e² = 1²+0.81347328615²-2*0.81347328615cos42e = 0.6728163648 units.Therefore x, angle theta is;(0.81347328615/sinx) = (0.6728163648/sin42)sinx = (0.81347328615sin42)/0.6728163648x = asin(0.80901699437)x = 54°Again, x is angl...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3631012

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Calculating MC ÷ DM.Notice.140 cm² is the area of the the ascribed rectangle.Let x be the length.xy = 140y = 140/x cm.y is the width of the rectangle.½*a*x = 38ax = 76a = 76/x cm.a is the height of the green inscribed triangle area.½*b*y = 46by = 92And y = 140/x cm.b(140/x) = 9270b = 46xb = 46x/70 cm.b is the height of the yellow inscribed triangle.c = 2ac = 2(76/x)c = 152/x units.c is y, the width of the ascribed rectangle.d = a+bd = ((76/x)+(46x/70))d is x, the length of the ascribed rectangl...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3631009

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Calculating length y.Notice.8 cm is the radius of the circle.It implies, length y is;18² = 12²+y²y² = 324-144y² = 180y = √(180)y = 6√(5) cm.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3631001

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Calculating length x.a² = (18+8)²+(4√(14))²a² = 900a = 30 units.a is the diameter of a half circle.b = ½(a)b = ½(30)b = 15 units.b is the radius of the half circle.cosc = (18+8)/ac = acos(26/30)c = acos(13/15)°Therefore, length x is;x² = 8²+15²-2*8*15cos(acos(13/15))x² = 64+225-16*13x² = 289-208x² = 81x = √(81)x = 9 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3630995

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Calculating r, radius of the circle.a = (r-4) units.b = a+rb = (r-4)+rb = 2r-4b = 2(r-2) units It implies;4*2(r-2) = 8*cc = (r-2) units.d = 8+cd = 8+(r-2)d = (6+r) units.Calculating r.11²+(6+r)²-2*11(6+r)cos60 = r²+r²-2*r*rcos120121+36+12r+r²-66-11r = 3r²91+r = 2r²2r²-r-91 = 02r²-14r+13r-91 = 02r(r-7)+13(r-7) = 0(2r+13)(r-7) = 0Therefore;2r+13 = 0r ≠ -½(13) units.It implies;r-7 = 0r = 7 units.Again, r is the radius of the circle.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3630970

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Calculating length x.a² = 7²+12²-2*7*12cos60a² = 49+144-84a = √(193-84)a = √(109)a = 10.4403065089 units.a is the radius of the circle.(10.4403065089/sin60) = (7/sinb)b = asin((7sin60)/10.4403065089)b = 35.4963665447°c = 60-bc = 60-35.4963665447c = 24.5036334553°cosc = d/acos24.5036334553 = d/√(109)d = √(109)sin24.5036334553d = 9.5 units.d is half length x.It implies, length x is;½(x) = dx = 2dAnd d = 9.5 units.x = 2*9.5x = 19 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3629790

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Calculating Area of the Red Rectangle.Let x and y be the length and width of the red rectangle respectively.tana = 4/3a = atan(4/3)°b = 90-ab = atan(3/4)°c = ½(180-a)c = ½(180-atan(4/3))°d = ½(180-b)d = ½(180-atan(3/4))°tan(½(180-atan(4/3))) = 3/ee = 3/tan(½(180-atan(4/3)))e = ½(3)e = (3/2) units.tan(½(180-atan(3/4))) = 4/ff = 4/tan(½(180-atan(3/4)))f = ⅓(4)f = (4/3) units.Therefore;x = 4+(4/3)x = ⅓(16) units.Again, x is the length of the red rectangle.y = 3+(3/2)y = ½(9) units.Again, y is the...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3629783

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Calculating Area S.Let x be the radius of the quarter circle.a²+24² = (2x)²a² = 4x²-576a = √(4x²-576) units.b = a-7b = (√(4x²-576)-7) units.Calculating x.(√(4x²-576)-7) ~ 2xx ~ √(4x²-576)Cross Multiply.2x² = 4x²-576-7√(4x²-576)7√(4x²-576) = 2x²-5767²(4x²-576) = (2x²-576)²49(4x²-576) = 4x⁴-2304x²+331776196x²-28224 = 4x⁴-2304x²+3317764x⁴-2500x²+360000 = 0x⁴-625x²+90000 = 0It implies;x = 20 units.Again, x is the radius of the quarter circle.Recall.a = √(4x²-576) units.And x = 20 units.a = √(4*20²-...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3629778

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Calculating R, radius of the red half circle.a = ½(5+24+22)a = ½(51)a = 25.5 units.a is the radius of the big half circle.b = ½(24)b = 12 units.c²+12² = R²c = √(R²-144) units.d = 25.5-5-12d = 8.5 units.e² = c²+d²e² = √(R²-144)²+8.5²e² = R²-144+72.25e = √(R²-71.75) units.Therefore R, radius of the red half circle is;25.5² = R²+√(R²-71.75)²650.25 = R²+R²-71.752R² = 650.25+71.752R² = 722R² = 361R = √(361)R = 19 units.Again, R is the radius of the red half circle.
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