Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3284371

Calculating r, radius of the half circle. Let x be the diameter of the half circle. x² = 16²+a² a = √(x²-256) units. b = a-21 b = (√(x²-256)-21) units. c = (x-7) units. Calculating x. 7(x-7) = 21(√(x²-256)-21) 7x-49 = 21√(x²-256)-441 7x+392 = 21√(x²-256) (7x+392)² = 44x²-112896 49x²+5488x+153664 = 441x²-112896 392x²-5488x-266560 = 0 It implies; x ≠ -20 units. x = 34 units. Again, x is the diameter of the half circle. Therefore r, radius of the half circle...

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/3282638

Calculating r, radius of the half circle. a²+14² = (2r)² a = √(4r²-196) units. b = (r-2) units. √(4r²-196)² = 2²+7²-28cosx 4r²-196 = 53+28cosx 28cosx = 4r²-249 cosx = (4r²-249)/28 --- (1). r² = 7²+(r-2)²-14(r-2)cosx 4r-53 = (28-14r)cosx cosx = (4r-53)/(28-14r) --- (2). Calculating r. Equating (1) and (2). (4r²-249)/28 = (4r-53)/(28-14r) 28(4r-53) = (28-14r)(4r²-249) 112r-1484 = 112r²-6972-56r³+3486r 56r³-112r²-3374r+5488 = 0 8r³-16r²-482r+784 =...

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.

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