Calculating Area Blue.Notice.The ascribed plane shape is a regular octagon.Calculating it's single interior angle.na = 180(n-2)8a = 180(8-2)a = (180*6)/8a = 135°a is the single interior angle of the...
Calculating Inscribed Area Blue Square.Let x be the side length of the blue square.tan60 = x/a√(3) = x/aa = ⅓(√(3)x) units b = a+xb = ⅓(√(3)x)+xb = ⅓(√(3)x+3x) units.Calculating x².10² = x²+(⅓(√(3)x+...
Calculating x (radius of the small inscribed circle)28² + x² = (56-x)²784 + x² = 3136 - 112x + x²112x = 2351x = 21 units.
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...
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
Calculating Area Shaded.Shaded Area is;Area circle with diameter 30 cm - 7(area circle with diameter 10 cm)= π(½(30))² - 7π(½(10))²= π(15)² - 7π(5)²= 225π - 175π= 50π cm²
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...
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)Ther...
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...
