Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3526250

Calculating Area Blue.Area Blue is;Area semi circle with radius √(2) units - Area quarter circle with radius 2 units + Area triangle with height and base 2 units respectively.= ½(√(2)²)π - ¼(2²)π + ½(2²)= π - π + 2= 2 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3525266

Calculating Area Blue.Area Blue is;Area triangle with height 4 cm and base (4sin150) cm= ½*4*(4sin150)= 2(4sin150)= 8sin150= ½(8)= 4 cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3524456

Calculating x.Dividing through by 9^(x).1+(21^(x))/9^(x)) = (49^(x)/9^(x))1+(7/3)^(x) = (7/3)^(2x)Let (7/3)^(x) = pTherefore;1+p = p²Calculating p.p²-p-1 = 0(p-½)² = 1+(½)²(p-½)² = (5/4)p-½ = ±½√(5)p = ½±½√(5)It implies;p = ½-½√(5)Orp = ½+½√(5)Recall.p = (7/3)^(x)Therefore, calculating x.For p = ½-½√(5)½-½√(5) = (7/3)^(x)Taking log base 10 at both sides of the equality.log(½-½√(5)) = xlog(7/3)x ≠ log(½-½√(5))/log(7/3)For p = ½+½√(5)½+½√(5) = (7/3)^(x)Taking log base 10 at both sides of the equa...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3523658

Calculating r, radius of the 3 congruent circles.x² = (r+1)² - (r-1)²Therefore x = 2√(r) unit.y² = (r+1)² - (2√(r))²Therefore y = √(r²-2r+1)y = √(r-1)²y = (r-1) unitz = (r+1) - yz = (r+1) - (r-1)Therefore z = 2 unitsa = r+rTherefore a = 2r unitsA sincere study and analysis of the composite circles deduced a right-angled triangle with two adjacent sides, 2 units and 2√(r) units respectively, and hypotenuse 2r units.Therefore;Calculating r, the radius of the three congruent circles.(2r)² = 2² + (...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3522531

Calculating x.2^(x)+8^(x) = 722^(x)+2^(3x) = 72Let 2^(x) be p.It implies;p+p³ = 72Using try and error approach to get p.For p = 44+4³ = 4+64 = 68 (less than 72)For p = 55+5³ = 5+125 = 130 (more than 72)It implies, p will be a little above 4.Therefore;p = 4.08 approximately.And 2^(x) = pCalculating x.2^(x) = 4.08Taking log base 10 at both sides of the equality.log(2^(x)) = log(4.08)It implies;xlog(2) = log(4.08)x = log(4.08)/log(2)x = 2.0285691522

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3521607

Sir Mike Ambrose is the author of the question.Let AB be 5 units.Radius, r of the inscribed circle is;5*(2/5)r = 2 units.a = ⅛(180*6)a = 135°2b² = 25b = ½(5√(2)) units.c = 180-0.5(135)-45c = 67.5°sin22.5 = ½(5√(2))/dd = 9.23879532511 units.Where d is the side length of the regular triangle (purple area).Area purple is;0.5*9.23879532511*9.23879532511sin60= 36.95994598698 square units.Calculating Area Shaded.e = 360-135-45-67.5-60e = 52.5°f² = 50-50cos135f = 9.23879532511 units.g = 52.5+0.5(45)g...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3520882

Area R is;Area sector with radius 8 cm and angle 20.16632290743° - Area triangle with height 8 cm and base (4.2sin 20.16632290743) cm= ( 20.16632290743 *64π÷360) - (½*8*4.2sin 20.16632290743)= 11.26299944816 - 5.79174146157 = 5.47125798659 cm²≈ 5.47 cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3519783

Shaded area is;Area sector with radius 10 cm and angle 60°(100π*60)/360= (100π)/6= ⅓(50π) cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3519152

Sir Mike Ambrose is the author of the question.Let the side length of the regular pentagon be 1 unit.tan36 = a/0.5a = 0.363271264 unit.b² = 0.363271264²+0.5²b = 0.61803398875 unit.tan72 = c/0.5c = 1.53884176859 units.Area Green is;0.5sin108+0.5*1.53884176859*0.5-0.5*0.5*0.363271264-0.5*0.61803398875*0.61803398875sin36= 0.65716389015 square units.Calculating Area Blue.Let d be the radius of the inscribed blue circle.Calculating d.e = 0.5(90+36)e =63°(d/tan63) + (d/tan45) = ad = 0.363271264/((1/t...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3518107

Sir Mike Ambrose is the author of the question.Calculating Area Blue.The radius of the inscribed small circle is 2 units.a = 2atan(⅓)°b = 2atan(⅕)°c = 180-a-bc = (180-2atan(⅓)-2atan(⅕))°sin(2atan(⅓)) = d/16d = (48/5) units.cos(2atan(⅓)) = e/16e = (64/5) units.f = (90-2atan(⅓)-2atan(⅕))°tan(90-2atan(⅓)-2atan(⅕)) = g/(48/5)g = (198/35) units.Therefore;Area Blue exactly in square units is;½*(48/5)(198/35)= 4752/175 square units.

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