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...
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°sin...
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)= 11.26...
Shaded area is;Area sector with radius 10 cm and angle 60°(100π*60)/360= (100π)/6= ⅓(50π) cm²
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....
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))...
Area coloured regions is;Half the area of the ascribed square.½(2*2)= 2 square units.
Calculating The Shaded Area.Let x be the three equal lengths.a²+x² = 5²a = √(25-x²) units.a is the height of the ascribed right-angled triangle.Calculating xa ~ x2x ~ xCross Multiply.ax = 2x²2x = a....
Sir Mike Ambrose is the author of the question.Let AC = 2 units.Therefore;AB = ⅖ unit.BC = (8/5) unit.It implies;Area Blue is;Area triangle with height ⅖ unit and base 2sin120 units + Area triangle w...
Sir Mike Ambrose is the author of the question.Let AC be 1 unit.Area smaller pentagon is;½(5)*(1/(2tan(36)))= 1.72047740059 square units.a² = 1²+0.5²-cos108a = 1.24860602048 units.Where a is CD.(1.24...
