Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3282395

Calculating green area. a = (6+x) units. a is the radius of the circle. b = a-2 b = (6+x)-2 b = (4+x) units. (6+x)² = (4+x)²+c² 36+12x+x² = 16+8x+x²+c² c² = 20+4x c = √(20+4x) units. c' = (6+x)+(4+x) c' = (10+2x) units. d²+x² = (6+x)² d² = 36+12x d = √(36+12x) units. Calculating x. (10+2x) ~ √(36+12x) √(20+4x) ~ x Cross Multiply. (10x+2x²) = √((36+12x)(20+4x)) 100x²+40x³+4x⁴ = 720+144x+240x+48x² 100x²+40x³+4x⁴ = 720+384x+48x² 4x⁴+40x³+52x²-384x-720...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3282393

Let the required angle be x. 5 units, 3 units and 2 units are the radii respectively of each of the circles, decreasingly. Calculating x. a = 5+2 a = 7 units. b = 5-2 b = 3 units. c²+3² = 7² c² = 49-9 c = √(40) c = 2√(10) units. cosd = 3/7 d = 64.6230664748° e = 5+3 e = 8 units. f = 3+2 f = 5 units. 5² = 8²+7²-2*7*8cosg cosg = (8²+7²-5²)/(14*8) g = 38.2132107017° h = ½(180-(d+g)) h = ½(180-64.6230664748-38.2132107017) h = 38.5818614118° j = 90-h j...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3281350

Sir Mike Ambrose is the author of the question. Calculating Area Purple ÷ Area Rectangle. Let the single side length of the three side regular hexagon be 1 unit. Therefore; The width of the rectangle is; 2 units. The length/height of the rectangle is; 4 units. It implies; Area rectangle is; 4*2 = 8 square units. Calculating Area Purple. It is; Area rectangle with length 2 units and width 1.56698729811 units - Area triangle with height 1.56698729811 unit...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3281347

Calculating Length x (AC). Notice. BC = AD = 9 units. a = 9+7 a = 16 units. a is BD. It implies; 9² = 15²+16²-2*15*16cosb 81 = 225+256-480cosb 480cosb = 481-81 cosb = 400/480 b = acos(5/6)° b is angle ABD. Calculating x. x² = 15²+9²-2*15*9cos(acos(5/6)) x² = 225+81-270(5/6) x² = 306-(45*5) x² = 306-225 x² = 81 x = 9 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3280273

Calculating Blue Area. a = (14-x) cm. Calculating x. 10² = x²+(14-x)² 100 = x²+196-28x+x² 2x²-28x+96 = 0 x²-14x+48 = 0 x²-6x-8x+48 = 0 x(x-6)-8(x-6) = 0 (x-6)(x-8) = 0 It implies; x ≠ 8 cm. x = 6 cm. Recall. a = (14-x) cm. And x = 6 cm. a = 14-6 a = 8 cm. b = 20-a b = 12 cm. c = 20-x c = 14 cm. Area Blue is; (½(12+14)*14)-(½*10*10) = ½(26*14)-½(100) = 182-50 = 132 cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3280271

Calculating area of the circle. Let x be the radius of the circle. Method 1. It implies; 2*(4+2) = 6*a 6a = 12 a = 2 units. b = 6+2 b = 8 units. It implies, a cyclic regular quadrilateral (rectangle) is inscribed the circle with length 8 units and width 4 units. c² = 8²+4² c = √(64+16) c = √(80) c = 4√(5) units. c is the diameter of the circle. x = ½(c) x = ½(4√(5)) x = 2√(5) units. Again, x is the radius of the circle. Area circle is; πx² = π(2√(5))²...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3278904

Calculating r, radius of the circle. a = ½(14) a = 7 units. b = (r-7) units. r² = 7²+c² c² = r²-49 c = √(r²-49) units. It implies, 6 units, b and c will make a right-angled triangle where 6 units is the hypotenuse. Calculating r. 6² = (r-7)²+√(r²-49)² 36 = r²-14r+49+r²-49 36 = 2r²-14r r²-7r-18 = 0 r²-9r+2r-18 = 0 r(r-9)+2(r-9) = 0 (r-9)(r+2) = 0 Therefore; r ≠ -2 units. r = 9 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3278891

Calculating angle x. Notice. AC = BC. Let AB be 1 unit. (1/sin(180-70-60-20)) = (a/sin(60+20)) a = 1.96961550602 units. a is AE. (1/sin(180-70-10-60)) = (b/sin60) b = 1.34729635533 units. b is AD. It implies; c² = 1.34729635533²+1.96961550602²-2*1.34729635533*1.96961550602cos10 c = 0.68404028665 units. c is DE. Therefore, angle x is; (0.68404028665/sin10) = (1.34729635533/sinx) x = asin(0.34202014333) x = 20°

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3277868

Calculating the area of the ascribed regular octagon. Let the equal longest length of the both inscribed yellow triangles be x. a = ⅛*180(8-2)) a = ⅛(180*6) a = ½(45*6) a = 135° a is the single interior angle of the ascribed regular octagon. sin(0.5*135) = (0.5x)/b b = 0.54119610015x units. b is the side length of the regular octagon. c = 135-(0.5*45)-½(360-2(135)) c = 135-22.5-45 c = 135-67.5 c = 67.5° c is the second bigger interior angle of inscribed triangle 21 squar...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3277864

Calculating Shaded Area. a = 2+3 a = 5 units. b = 4+3 b = 7 units. tanc = 7/3 c = atan(7/3)° d² = 2(2)² d = 2√(2) units. tane = 5/(3-2) e = atan(5)° f = 180-e f = (180-atan(5))° tang = 3/7 g = atan(3/7)° h = 180-f-g h = 180-(180-atan(5))-atan(3/7) h = (atan(5)-atan(3/7))° h = 55.4914770123° j = 180-45-atan(7/3) j = (45+atan(3/7))° j = 68.1985905136° k = 180-(45+atan(3/7))-(atan(7)-atan(3/7)) k = 180-68.1985905136-55.4914770123 k = 56.3099324741°...

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