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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2946125

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Cosine Rule Proof.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2945011

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The radius of the inscribed circle is 2 units. a = 2atan(⅓)° b = 2atan(⅕)° c = 180-a-b c = (180-2atan(⅓)-2atan(⅕))° sin(2atan(⅓)) = d/16 d = (48/5) units. cos(2atan(⅓)) = e/16 e = (64/5) units. f = (90-2atan(⅓)-2atan(⅕))° tan(90-2atan(⅓)-2atan(⅕)) = g/(48/5) g = (198/35) units. Therefore; Area Blue exactly in square units is; ½*(48/5)(198/35) = 4752/175 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2943951

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8 = 4 a = (8-a) Cross multiply. 64-8a = 4a 64 = 12a a = ⅓(16) cm. b = 8-a b = ⅓(8) cm. c = atan(⅔)° d = atan(3/2)° ⅔ = 8/e e = 12 cm ⅔ = f/8 f = ⅓(16) cm. g = 8-f g = ⅓(8) cm. Area Orange exactly in cm² is; Area square units side 8 cm - Area rectangle with length 4 cm and width ⅓(8) cm. = 8² - 4*⅓(8) = 64 - ⅓(32) = ⅓(192-32) = ⅓(160) cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2941833

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Let the side of the green square be x. Therefore; x/(tan(atan¾)) + x + x/(tan(atan(4/3))) = 5 ⅓(4x) + x + ¼(3x) = 5 16x + 12x + 9x = 60 37x = 60 x = (60/37) units. It implies; Area square green is; x² = (60/37)² = 3600/1369 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2940636

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Let AC be 1 unit. Area smaller pentagon is; ½(5)*(1/(2tan(36))) = 1.72047740059 square units. a² = 1²+0.5²-cos108 a = 1.24860602048 units. Where a is CD. (1.24860602048/sin108) = (0.5/sinb) b = 22.38617755917° c = 108-22.38617755917 c = 85.61382244083° Calculating Area E. It is; 0.5*0.5*0.5*1.24860602048sin22.38617755917 = 0.05944103227 square units. (a) Area E ÷ Area Smaller Pentagon to 3 decimal places is; 0.05944103227 ÷ 1.72047740059 = 0.034549...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2940069

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a² = 10²+16²-2*10*16cos120 a = 2√(129) units. Where a is length AC. (3√(129)/sin120) = (16/sinb) b = 37.58908946897° c = 90-b c = 52.41091053103°  d = 60-b d = 22.41091053103° e = 90-d e = 67.58908946897°  f = 90-60 f = 30° cos37.58908946897 = g/10 g = 7.92405815693 units. i = 30+37.58908946897 i = 67.58908946897° tan67.58908946897 = j/7.92405815693 j = 19.2148198619 units. Where j is the radius of the arc. sin67.58908946897 = 19.2148198619/k k = 20....

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2937623

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Sir Mike Ambrose is the author of the question. y = 2^(x) P coordinate is; P(1, 2) dy/dx = 2^(x)In2 For x = 1 dy/dx = 2In2 It implies; Q coordinate is; Q(0, (2-2In2)) Therefore; Shaded area exactly in square units is; (Area under the curve at x = 0 and x = 1) - (Area trapezoid with parallel sides (2-2In2) units and 2 unit, and height 1 units). = (1/(In2)) - (½*1*(2+2-2In2)) = (1/(In2)) - (2-In2) = (In2-1)²/In2 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2936096

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Let the two congruent lengths be 1 unit. tan40 = a/1 a = 0.83909963118 unit. cos40 = 1/b b = 1.30540728933 units. Calculating r, radius of the red inscribed circle. (r/tan(20)) + (r/tan(25)) = 1.30540728933  r = 0.26684617092 units. Red area is: π(0.26684617092)² = 0.22370300775 square units. Calculating Purple Area. cos40 = c/2 c = 1.53208888624 units. sin40 = 1/d d = 1.55572382686  Where c and d is the height and base of the rectangle respectively. t...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2934677

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Let the side of the regular pentagon be 1 unit. Calculating Area Red. a² = 1²+1²-2*1*1cos108 a = 1.61803398875 units. b = 108-36-60 b = 12° (c/sin12) = (1.61803398875/sin96) c = 0.33826121272 units. d = 1-c d = 0.66173878728 units. e = 96-60 e = 36° tan36 = f/0.66173878728 f = 0.48078137139 units. Area Red is; ½(df) = 0.5*0.48078137139*0.66173878728 = 0.15907584083 square units. Calculating Area Lilac. sin36 = 0.48078137139/g g = 0.81795412443 units...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2932593

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a² = 15²+12²-2*12*15cos120 a = 23.43074902772 cm. Where a is the side length of the equilateral triangle ABC. (23.43074902772/sin120) = (12/sinb) b = 26.32950349168° c = 60-b c = 33.67049650832° d² = 15²+15²-2*15*15cos120 d = 25.98076211353 cm. e = atan(7.5/25.98076211353) e = 16.10211375199° f = 90-e f = 73.89788624801° g = 180-f-c g = 72.43161724367° (15/sin72.43161724367) = (h/sin73.89788624801) h = 15.11661227595 cm. i = a-h  i = 8.31413675177 cm. L...
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