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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3689029

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Calculating x and R.x*8 = 12*5x = 60/8x = ½(15)x = 7.5 units.a = 180-120a = 60°b² = 8²+5²-2*8*5cos120b = √(129) units.b = 11.3578166916 units.c² = 12²+8²-2*12*8cos60c = 4√(7) units.c = 10.5830052443 units.(11.3578166916/sin120) = (5/sind)d = 22.410910531°(10.5830052443/sin60) = (12/sine)e = 79.1066053497°f = d+ef = 22.410910531+79.1066053497f = 101.517515881°g = 360-2fg = 360-2(101.517515881)g = 156.964968238°h = ½(g)h = 78.482484119°j = ½(12+5)j = ½(17)j = 8.5 units.It implies, R, radius of th...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3688134

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Calculating (ED)² +(DC)².a² = √(3)²+√(3)²a = √(6) units.a is the radius of the ascribed half circle.tanb = √(3)/ab = atan(√(3)/√(6))b = atan(1/√(2))b = atan(½√(2))°b = 35.2643896828°b is angle OBG.c = 180-2bc = 180-2(35.2643896828)c = 109.471220634°c is angle BOC.d = c-45d = 109.471220634-45d = 64.471220634°d is angle COD.e = 90+45-ce = 135-109.471220634e = 25.528779366°e is angle DOE.It implies;(ED)² = 2√(6)²-2√(6)²cos25.528779366(ED)² = 12-12cos25.528779366(ED)² = 1.1715728753 square units.(D...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3687681

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Calculating Area Green ÷ Area Red.Let the two equal lengths be 1 unit each.It implies;Red Area is;½*1*1= ½ square units.a = 1+1a = 2 units.b² = 2²+1²b² = 5b = √(5) units.2 ~ c1 ~ 2Cross Multiply.c = 4 units.It implies;Green Area is;½*a*c= ½*2*4= 4 square units.Therefore, area green/area red is;4/(½)= 8

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3686636

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Calculating length BP.Let it be x.a²+a² = 4²2a² = 16a² = 8a = √(8)a = 2√(2) cm.a is AB, the side length of the square.b = 45-30b = 15°b is angle CAP.tan30 = c/(2√(2))c = 2√(2)tan30c = 1.63299316186 cm.d = a-cd = 2√(2)-1.63299316186d = 1.19543396289 units.e = (90-b)+45e = 90-15+45e = 120°e is angle BCP.f = e-90f = 120-90f = 30°f is angle DCPcos30 = g/dg = 1.19543396289cos30g = 1.03527618041 cm.Therefore length BP, x is;x² = 1.03527618041²+(2√(2))²-2*2√(2)*1.03527618041cos120x = 3.46410161514 cm....

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3685711

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Calculating R, radius of the circle.Let alpha be x.y² = 11²+37²-2*11*37cosxy² = 1490-814cosx --- (1).y² = 26²+37²-2*26*37cosxy² = 2045-1924cosx --- (2).Equating (1) and (2).1490-814cosx = 2045-1924cosx1924cosx-814cosx = 2045-14901110cosx = 555x = acos(555/1110)x = acos(½)x = 60°Again, x is alpha.Recall.At (1).y² = 1490-814cosxAnd x = 60°y² = 1490-407y = √(1490-407)y = 19√(3) units.y = 32.9089653438 units.It implies, R, radius of the circle is;sin60 = (0.5y)/RR = (0.5*32.9089653438)/sin60R = (0....

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3684501

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Calculating Area Green.a = ½(5)a = 2.5 units.a is the radius of the inscribed white quarter circle.b = 180-2atan(2.5/5)b = (180-2atan(½))°Area Green is;Area square with side 5 units - Area quarter circle with radius 2.5 units - Area triangle with height 5 units and base 2.5 units - Area sector with radius 2.5 units and angle (180-2atan(½))° + Area triangle with height 2.5 units and base 2.5(180-2atan(½)) units.5²-¼(2.5²)π-½(5*2.5)-((180-2atan(½))π*2.5²/360)+½(2.5²sin(180-2atan(½))).= 25-1.5625π...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3682742

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Calculating length AK.Notice.CM = 64/17 units.AB = AD = BC = CD = 8 units.r is the radius of the circle.a²+(64/17)² = 8²a² = 64-(4096/289)a² = 14400/289a = √(14400/289)a = 120/17 units.a is BM.b = 2r units.Calculating r.a ~ 2r(64/17) ~ 8It implies;(120/17) ~ 2r(64/17) ~ 8Therefore;15 ~ r8 ~ 4Cross Multiply.8r = 4*15r = ½(15) units.r = 7.5 units.Again, r is the radius of the circle.Or(64/17) ~ (120/17)8 ~ 2rCross Multiply.2r(64/17) = 8(120/17)2r*64 = 8*12064r = 4*12016r = 1202r = 15r = 7.5 units...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3681643

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Calculating the required green area.Notice.OP = AP = r.R = 2r.a² = (2r)²+r²a² = 4r²+r²a = √(5r²)a = √(5)r units.a is CP = OQ.r ~ ab ~ 2rIt implies;r ~ √(5)rb ~ 2rCross Multiply.2r² = √(5)rbb = 2r/√(5) units.b = ⅕(2√(5)r) units.b is OM.c²+b² = r²c² = r²-(2r/√(5))²c² = r²-(4r²/5)c² = ⅕(r²)c = √(⅕(r²))c = ⅕√(5)r units.c is MP.Calculating r.½*b*c = 6½*⅕(2√(5)r)*⅕(√(5)r) = 6⅕(r²) = 6r² = 30r = √(30) units.r = 5.47722557505 units.Recall.R = 2r.r = √(30) units.R = 2√(30) units.Let X be quadrilateral A...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3680805

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Calculating r.a² = 2(2r)²a = √(2(2r)²)a = 2√(2)r unitsa is the diagonal of the inscribed square.b² = 2r²b = √(2)r units.c = a+b+rc = 2√(2)r+√(2)r+rc = (1+3√(2))r units.c is the diagonal of the ascribed square.d² = 2(17)²d = √(2(17)²)d = 17√(2) units.It is also the diagonal of the ascribed square.Calculating r.It implies;c = d(1+3√(2))r = 17√(2)r = 17√(2)/(1+3√(2))r = (6-√(2)) units.r = 4.58578643763 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3680801

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Calculating area triangle BAC.a² = √(7)²+3²a = √(16)a = 4 units.b = a+√(7)b = (4+√(7)) units.b is AB.√(7) ~ 34 ~ cCross Multiply.√(7)c = 12c = ⅐(12√(7)) units.d = 3+cd = 3+⅐(12√(7))d = ⅐(21+12√(7)) units.d is AC.It implies, area BAC is;½* b*d= ½*(4+√(7))*⅐(21+12√(7))= 25.0397743188 square units
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