Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3655310

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/3655307

Calculating x, radius of the circle.sina = 4/16a = asin(¼)°a is angle RTS.b = 90-ab = (90-asin(¼))°b = 75.5224878141°b is angle OTS.It implies x, radius of the circle is;cosb = (½*16)/xcos(75.5224878141) = 8/xx = 8/cos(75.5224878141)x = 32 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3654343

Calculating Area Green Circle.Let r be the radius of the circle.16² = 18²+14²-2*18*14cosaa = acos((18²+14²-16²)/(2*18*14))a = 58.4118644948°a is angle ADE.b = 180-ab = 180-58.4118644948b = 121.588135505°b is angle BDE.(16/sin58.4118644948) = (18/sinc)c = 73.398450401°c is angle AED.d = 180-cd = 180-73.398450401d = 106.601549599°d is angle CED.Calculating r, radius of the circle.tan(0.5b) = r/ee = r/tan(0.5*121.588135505)e = 0.55901699438r units.tan(0.5d) = r/ff = r/tan(0.5*106.601549599)f = 0.7...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3654339

Calculating Alpha.Let it be x.Let 1 unit be the equal lengths of the ascribed right-angled triangle each.a² = 1²+1²a = √(2) units.a is AC.b = 45-15b = 30°b is angle CAD.c = 180-30-15c = 135°c is angle ADC.(d/sin30) = (√(2)/sin135)d = 1 unit.d is CD.It implies, triangle BCD is isosceles.Therefore, Alph (x) angle BDC is;x = ½(180-30)x = ½(150)x = 75°

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3653107

Calculating area inscribed circle and tan x.Notice.Length of arc of the quarter circle is 4π cm.(90/360)*2πr = 4π¼(2πr) = 4π2πr = 16πr = 8 cm.r is the radius of the ascribed quarter circle.Let y be the radius of the inscribed circle.a = r-ya = (8-y) cm.Calculating x.a² = y²+y²(8-y)² = 2y²64-16y+y² = 2y²y²+16y-64 = 0(y+8)² = 64+8²(y+8)² = 128y = -8±√(128)y = -8±8√(2)It implies;y ≠ -8-8√(2)y = (8√(2)-8) cm.y = 8(√(2)-1) cm.y = 3.31370849898 cm.Again, y is the radius of the inscribed circle.Theref...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3653104

Calculating r, radius of the ascribed quarter circle.a² = 8a = 2√(2) cm.a is the side length of the inscribed square.b² = 2a²b² = 2*(2√(2))²b = √(16)b = 4 cm.b is the diagonal of the inscribed square.a² = c²+c²2c² = (2√(2))²c² = ½(8)c = √(4)c = 2 units.It implies, r, radius of the ascribed quarter circle is;2²+4² = r²r² = 4+16r = √(20)r = 2√(5) cm.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3651962

Calculating angle x.Let 2 units be the side length of the ascribed square and also the radius of the inscribed red quarter circle.Notice.BM = CM, meaning point M horizontal shares the both vertical side lengths, OA and BD of the ascribed square to equal halves.a = ½(2)a = 1 unit.a is half the vertical side length, OA and BD of the ascribed square.sinb = ½b = 30°b is angle BOM.c = ½(180-b)c = ½(180-30)c = ½(150)c = 75°c is angle OBM.It implies, angle x (angle BCD) is;Notice again, angle x (angle...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3651955

Calculating the value of alpha(x) ÷ beta(y) (x/y).Calculating alpha (x).x = ⅕*180(5-2)x = ⅕*180*3x = 108°Where x is alpha and also the single interior angle of the regular pentagon.Let 2 units be the side length of the regular pentagon.a = ½(2)a = 1 unit.b² = 1²+2²-2*1*2cos108b = 2.49721204096 units.b is the sum of the radius of the inscribed half circle and the radius of the inscribed 108° sector.(2.49721204096/sin108) = (1/sinc)c = 22.3861775591°d = 180-108-cd = 180-108-22.3861775591d = 49.61...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3650845

Calculating Green Area.a = 12+3a = 15 units.a is the side length of the two congruent squares.cosb = 12/15b = acos(4/5)°c = 90-bc = (90-acos(4/5))°tand = 15/3d = atan(5)°e = c+de = 90-acos(4/5)+atan(5)e = 131.82016988°f² = 15²+3²f = √(225+9)f = √(234) f = 3√(26) units.Therefore, green area is;Area triangle with height 3√(26) units and base 15sin131.82016988 units - Area triangle with height 15 units and base 3 units.0.5*3√(26)*15sin131.82016988 - 0.5*15*3= 85.5 - 22.5= 63 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3650837

Calculating Square Area.Let x be the side length of the square.a = 7+6a = 13 units.6²+b² = x²b = √(x²-36) units.It implies;sinc = x/asinc = x/13 --- (1).sinc = b/xsinc = √(x²-36)/x --- (2).Equating (1) and (2).x/13 = √(x²-36)/xCross Multiply.x² = 13√(x²-36)Notice.x² is the area of the square.Calculating x².It implies;(x²)² = 13²(x²-36)x⁴ = 169x²-6084x⁴-169x²+6084 = 0(x²-½(169))² = -6084+(-½(169))²(x²-½(169))² = 1056.25x² = 84.5±√(1056.25)x² = 84.5±32.5x² ≠ 84.5-32.5x² = 84.5+32.5x² = 117 square...

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