Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3349495

Calculating x, length DF. Let a be the radius of the ascribed half circle. b = (a-6) units. c = (a-7) units. 7² = 6²+8²-2*6*8cosd 96cosd = 36+64-49 d = acos((36+64-49)/96) d = 57.9100487437° d is angle ACB. e = 180-d e = 122.089951256° e is angle ACE. Calculating a. a² = 8²+(a-6)²-2*8(a-6)cos122.089951256 a² = 64+a²-12a+36+8.5a-51 3.5a = 49 a = 14 units. Again, a is the radius of the half circle. Recall. c = (a-7) units. And a = 14 units. c = 14-7 c = 7...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3289255

Calculating r, radius of the circle. a = (10-r) units. It implies; r² = (10-r)²+5² r² = 100-20r+r²+25 20r = 125 2r = 12.5 r = 6.25 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3283403

Calculating r, radius of the half circle. a²+9² = 23² a = 8√(7) units. a = 21.1660104885 units. tanb = 8√(7)/8 b = atan(8√(7)/9)° c = (r-5) units. (r-5)² = d²+(½*8√(7))² r²-10r+25 = d²+112 d = √(r²-10r-87) units. e = (9+√(r²-10r-87)) units. Calculating r. (½*8√(7))²+(9+√(r²-10r-87))² = r² 112 +81+18√(r²-10r-87)+r²-10r-87 = r² 106+18√(r²-10r-87)-10r = 0 18√(r²-10r-87) = 10r-106 324(r²-10r-87) = 100r²-2120r+11236 324r²-3240r-28188 = 100r²-2120r+11236...

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/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/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/3253085

Sir Mike Ambrose is the author of the question. Let the side length of the square be 10 units. Area square is; 10² = 100 square units. Therefore; Area R is; Area semi circle with radius 5 units - Area sector with radius 5 units and angle (180-2atan(2))° - Area kite with diagonal lengths √(10²+5²) units and √(200-200cos(2atan(½))) units + Area sector with radius 10 units and angle 2atan(½)° - 2(area quarter circle with radius 5 units - area triangle with height and base 5 un...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3249646

Calculating Area Blue. It implies; A1 = 64π cm², therefore radius A1, x = 8 cm. A2 = 32π cm², therefore radius A1, y = 4√(2) cm. A3 = (16/3)π cm², therefore radius A1, z = 4/√(3) cm. Therefore; Area blue is; Area triangle with two length 10.3094010768 cm and 7.96625532625 cm, and angle 95.85811003° - Area sector with radius (4/√(3)) cm and angle 95.85811003° - Area sector with radius 4√(2) cm and angle 48.6724043189° -Area sector with radius 8 cm and angle 35.4694856511°....

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3243662

Calculating Length EF (x). Let a be the radius of the inscribed blue half circle. b = (4+a) units. Calculating a. 8²+a² = (4+a)² 64+a² = 16+8a+a² 48 = 8a a = 6 units. Again, a is the radius of the blue inscribed half circle. c = 2a c = 2(6) c = 12 units. c is BC, the diameter of the blue inscribed half circle. d = AB+BC+CD d = 4+12+9 d = 25 units. d is AD, the diameter of the ascribed half circle. cose = 8/10 e = acos(4/5)° f = (8+x) units. Calculating x....

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3241832

Calculating yellow area. r, radius of the inscribed circle is; r²=(r-4)²+(r-2)² r²=r²-8r+16+r²-4r+4 r²-12r+20=0 (r-6)²=-20+36 r = 6±√(16) r = 6±4 Therefore; r ≠ 2 units. r = 10 units. Therefore area of the ascribed square is; (2r)² = (2*10)² = 20*20 = 400 square units. It implies; Yellow region area will be; Area of the ascribed square - 4(area green rectangle) - area inscribed circle with radius 10 units. = 400 - 4(4*2) - 100π = 40...

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