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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3499443

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Sir Mike Ambrose is the author of the question.Let length AB = 2 units.Therefore;Side length of the square, x is;2x² = 2²x = √(2) units.It implies;Area square is;x²= √(2)²= 2 square units.Area green is;Area triangle with height √(3) units and base 1 unit - Area triangle with height ⅓√(3) units and base 1 unit - Area triangle with height tan15 units and base 1 unit= ½(√(3)*1) - ½(⅓√(3)*1) - ½(tan15*1)= ½√(3) - (√(3)/6) - ½(tan15)= ⅓√(3) - ½(2-√(3))= (5√(3)-6)/6 square units.Therefore;Area Green...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3498160

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Calculating x (AD) the diameter of the half circle.a² = 2²+11²+2*2*11cosya² = 125+44cosy --- (1).a² = x²+7²-2*7*xcosya² = x²+49-14xcosy --- (2).Where a is AC.cosy = 7/x --- (3).Equating (1) and (2).125+44cosy = x²+49-14xcosy76 = x²-14xcosy-44cosy --- (4).Calculating x.Substituting (3) in (4).76 = x²-14x(7/x)-44(7/x)76 = x²-98-(308/x)174 = x²-(308/x)174x = x³-308x³-174x = 308It implies;x = 14 cm.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3497356

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Calculating D, diameter of the ascribed half circle.Let r be the radius of the half circle.a = ½(7)a = 3.5 units.b²+a² = r²b² = r²-3.5²b = √(r²-12.25) units.c = 2bc = 2√(r²-12.25) units.cosx = 7/(2r) --- (1).(2√(r²-12.25))² = 2(3²)+2*3*3cosx4(r²-12.25) = 18+18cosx4r²-49 = 18+18cosx4r²-67 = 18cosxcosx = (4r²-67)/18 --- (2).Equating (1) and (2).7/(2r) = (4r²-67)/187/r = (4r²-67)/9Cross Multiply.63 = 4r³-67rIt implies;r = 4.5 units.Therefore, D, diameter of the half circle is;D = 2rAnd r = 4.5 uni...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3496461

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Sir Mike Ambrose is the author of the question.Let the side let of the square be 2 units.Therefore;Area square is;2²= 4 square units.It implies;Area R is;Area trapezoid with parallel sides 1 unit and 1.44948974279 unit, and height 2 unit - Area square with side 1 unit - Area triangle with base and height 1 unit respectively - Area sector with radius √(2) unit and angle 32.3335306935° - Area triangle with height √(2) unit and base 0.3178372452 unit= (½*2(1+1.44948974279)) - (1*1) - (½*1*1) - (32...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3495549

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Calculating R, radius of the circle.Let alpha be x.a² = 11²+37²-2*11*37cosxa² = 1490-814cosx --- (1).a² = 37²+26²-2*26*37cosxa² = 2045-1924cosx --- (2).Equating (1) and (2) to get alpha (x)1490-814cosx = 2045-1924cosx1924cosx-814cosx = 2045-14901110cosx = 555cosx = 555/1110x (alpha) = 60°It implies, calculating a using (1).a² = 1490-814cos60a = 32.9089653438 units.b = ½(a)b = 16.4544826719 units.Therefore, R, radius of the circle is;sin60 = 16.4544826719/RR = 16.4544826719/sin60R = 19 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3494821

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Calculating R, radius of the circle.a = 30+45a = 75°b = 180-75-60b = 45°8² = 2c²c² = 32c = 4√(2) units.sin30 = 4√(2)/dd = 8√(2) units.e = 2*45°e = 90°Therefore, R, radius of the circle is;2R² = (8√(2))²2R² = 128R² = 64R = 8 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3493886

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Calculating Area Yellow.a = ½(180-30)a = 75°2² = b²+1²b² = 4-1b = √(3) units.Yellow Area is;2(Area triangle with height √(3) units and base 1 unit + Area sector with radius 2 units and angle 60° - Area triangle with height 2 units and base 2sin60 units - Area sector with radius 2 units and angle 30° + Area triangle with height 2 units and base 2sin30 units - Area sector with radius 1 unit and angle 75°)= 2((½*√(3)*1)+(60π*2²/360)-(½*2*2sin60)-(30π*2²/360)+(½*2*2sin30)-(75π/360))= 2((0.5√(3))+(⅔...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3493151

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Sir Mike Ambrose is the author of the question.Let the single side length of the square be 2 units.Therefore;Area square is;2²= 4 square unitsIt implies;Area R is;Area sector with radius 2 units and angle 8.130127545 - Area triangle with height 1.61624318301 unit and base (1.37930921037sin8.130127545) units.= (8.130127545*4π÷360) - (½*1.61624318301*1.37930921037sin8.130127545)= 0.28379498853 - 0.15763573684= 0.12615925169 square units.Therefore;Area Square ÷ Area R to 1 d. p. is4 ÷ 0.126159251...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3492017

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Calculating Length CD.a = 15-11.25 a = 3.75 m.b = atan(3/3.75)°c = 90-atan(3/3.75)c = 51.34019174591° Therefore, Length CD is;tan(51.34019174591) = 15/CDCD = 15/tan(51.34019174591) CD = 12 m.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3491280

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Calculating Blue Area.Area blue is;Area sector with radius 10 cm and angle 2atan(½) - Area triangle with height 10 cm and base 10sin(2atan(½)) cm + Area sector with radius 5 cm and angle 2atan(2) - Area triangle with height 5 cm and base 5sin(2atan(2)) cm - 2(area quarter circle with radius 5 cm - area triangle with height 5 cm and base 5 cm).= (2atan(½)*100π÷360) - (½*100sin(2atan(½))) + (2atan(2)*25π÷360) - (½*25sin(2atan(2))) - 2((¼*25π)-(½*25))= 46.3647609001 - 40 + 27.6787179449 - 10 - 2(1...
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