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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3551413

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Calculating Length x.a = ½(6)a = 3 units.a is the radius of the circle.b = (5-c) units.6² = d²+(5-c)²d² = 36-(25-10c+c²)d = √(11+10c-c²) units.e = ½(d)e = ½√(11+10c-c²) units.f = (3-c) units.Calculating c.Notice.f = ½(b)3-c = ½(5-c)6-2c = 5-cIt implies;c = 1 unit.Therefore;For c = 1 unit.e = ½√(11+10c-c²)e = ½√(11+10(1)-1²)e = ½√(20)e = √(5) units.Therefore, length x is;x² = 5²+e²x² = 5²+√(5)²x² = 25+5x = √(30) units.x = 5.47722557505 units.OrCalculating x using a different approach.For c = 1 u...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3550383

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Sir Mike Ambrose is the author of the question. a = ⅛*180(8-2)a = 135°a is the single interior angle of the regular octagon.2² = 2b²b = √(2) units.c = 2+bc = (2+√(2)) units.tand = (2+√(2))/2d = atan(1+½√(2))°tand = 2/e1+½√(2) = 2/ee = 4/(2+√(2)) units.f = c-ef = (2+√(2))-4/(2+√(2))f = ((2+√(2))²-4)/(2+√(2)) units.2/(2+√(2)) = g/((2+√(2))²-4)/(2+√(2))2/(2+√(2)) = g(2+√(2))/((2+√(2))²-4)g(2+√(2))² = 2(2+√(2))²-8g = 2-(8/(2+√(2))²) units.Shaded Area Exactly in square units is;Area rectangle with l...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3549217

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Sir Mike Ambrose is the author of the question.Let CD = 1 units.It implies;DE = 1 units.AD = 2 units.AE = 2 units.1² = 2²+2²-2*2*2cosa1 = 8-8cosacosa = 7/8a = acos(⅞)°b = ½(180-acos(⅞))b = (90-0.5acos(⅞))°sinb = c/2c = 2sin(90-0.5acos(⅞))c = 1.9364916731 units.c = CF.cosb = d/2d = 2cos(90-0.5acos(⅞))d = ½ units.d = EF.AF = AE-EFAF = 2-½AF = ½(3) units.tan(acos(⅞)) = e/AFe = 1.5tan(acos(⅞))e = 0.82992500276 units.e = BFTherefore;BC = CF-BFBC = 1.9364916731-0.82992500276BC = 1.10656667034 units.(...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3548311

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Calculating angle a.Let the length of the ascribed rectangle be 2 units.Therefore it's width is 1 unit.b² = 2²+1²b = √(5) units.b is the diagonal of the ascribed rectangle.tanc = 1/2c = atan(½)°tand = 1/0.5d = atan(2)°e = 2de = 2atan(2)°f = ½(180-2atan(2)°)f = (90-atan(2))°g² = 2(0.5)²-2(0.5)²cos(2atan(2))g = 0.894427191 units.h = 90-f-ch = 90-(90-atan(2))-atan(½)h = (atan(2)-atan(½))°h = 36.8698976458°j² = 0.894427191²+√(5)²-2*0.894427191√(5)cos36.8698976458j = 1.61245154966 units.Therefore, a...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3547390

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Sir Mike Ambrose is the author of the question.Calculating Shaded Area ÷ Circle Area exactly in decimal.Let the side length of the equilateral triangle be 2 units.Calculating r, radius of the circle.cos30 = 1/rr = 1/cos30r = 2/√(3)r = ⅓(2√(3)) units.Area circle is;πr²= π(⅓(2√(3)))²= ⅓(4π) square units.= 4.18879020479 square units.tan30 = a/1a = ⅓√(3) units.b = r-ab = ⅓(2√(3))-⅓√(3)b = ⅓√(3) units.tan60 = ⅓√(3)/cc = ⅓ units.cos60 = (⅓)/dd = ⅔ units.or sin60 = ⅓√(3)/d½√(3) = ⅓√(3)/d½ = (⅓)/dd = ⅔...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3546533

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Calculating Blue Shaded Area.Blue shaded triangle area is;4tan(sin–¹(1÷3))= √(2) square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3545599

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Exact enclosed area R.It is;Area sector with radius 2 units and angle (90-2tan–¹(½)) - Area sector with radius 1 unit and angle (180-4tan–¹(½)) + Area isosceles triangle with two equal lengths 1 unit and angle (180-4tan–¹(½)).=((90-2tan–¹(½))x4π÷360) - ((180-4tan–¹(½))xπ÷360) + 0.5sin(180-4tan–¹(½))= 1.1235011088 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3544731

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Calculating Green Area : Red Area.Let x be the red square side length.Let 2 units be the green square red length.Area green is;2²= 4 square units.Calculating x.a = (2-x) units.b = 90-60b = 30°tan30 = c/xc = x/√(3)c = ⅓(√(3)x) units.d = x-cd = x-⅓(√(3)x)d = ⅓(3-√(3))x units.It implies;x ~ ⅓(3-√(3))x2 ~ (2-x)Cross Multiply.⅔(3-√(3)) = 2-x6-2√(3) = 6-3x3x = 2√(3)x = ⅔√(3) units.Again, x is the side length of the red square.Area red square is;x²= (⅔√(3))²= 4/3 square units.Therefore, Green Area : R...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3543645

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Calculating Angle x.Let 2 units be the radius of the ascribed quarter circle and a be the radius of the inscribed circle.Calculating a.b = (2-a) units.It implies;2a² = (2-a)²2a² = 4-4a+a²a²+4a-4 = 0(a+2)² = 8a = -2±√(8)It implies;a = (2√(2)-2) units.a = 0.82842712475 units.Again, a is the radius of the inscribed circle.tanc = 2/0.82842712475c = 67.4999999999c = 67.5°d = 90-cd = 90-67.5d = 22.5°Therefore, the required angle, x is;x = d+45x = 22.5+45x = 67.5°

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3543012

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Calculating Length EF.Let x be EC = CH, radius of the small inscribed circle.a = (20-x) cm.tanb = 10/20b = atan(½)°c = ½(90-2atan(½))c = ½(atan(2)-atan(½))c = 18.4349488229°Calculating x, radius of the small inscribed circle.tan18.4349488229 = x/(20-x)20tan18.4349488229-xtan18.4349488229 = xx+xtan18.4349488229 = 20tan18.4349488229x = (20tan18.4349488229)÷(1+tan18.4349488229)x = 5 cm.d² = 5²+20²d = 5√(17) cm.d = 20.6155281281 cm.tane = 5/20e = atan(¼)°f = 90-2atan(½)-atan(¼)f = 22.8336541779°It...
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