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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2856696

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Let the radius of the inscribed half circle be 1 unit. Area rectangle is; 2*1 = 2 square units. Calculating Shaded Area as a single fraction.. It is; ½(1*2) - 1² + ¼(1)²π - ((180-2atan(½))π*1²/360) + (0.5*1²sin(180-2atan(½))) = 1-1+¼(π)-(π(180-2atan(½))/360)+⅖ = (π/4)+⅖-(π(180-2atan(½))/360) = ((5π+8)/20)-(π(180-2atan(½))/360) = (90π+144-180π+2πatan(½))/360 = (144-90π+2πatan(½))/360 square units. Therefore; Area Shaded ÷ Area Rectangle as a single fraction is; ((...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2855166

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Sir Mike Ambrose is the author of the question. The side of area green, inscribed square is; Let it be x. Therefore; 1.11496246101x + 0.82101781219x = 27.3672604063 1.9359802732x = 27.3672604063 x = 14.1361256544 cm Therefore; Exact perimeter of green area in decimal cm is; 4(14.1361256544) = 56.5445026176 cm

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2855149

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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/2853602

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Sir Mike Ambrose is the author of the question. Let the two equal marked lengths of triangle ABC be 2 units. Therefore; Area triangle ABC is; Area triangle with height 5.75877048314 units and base (5.75877048314sin20) units. = 0.5*5.75877048314*5.75877048314sin20 = 5.67128181961 space units. Area purple is; Area triangle with height 4 units and base (1.11985686148sin28.334490436) units. = 0.5*4*1.11985686148sin28.334490436 = 1.06300877373 space units. It implies;...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2853585

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Sir Mike Ambrose is the author of the question. 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;...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2851947

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Sir Mike Ambrose is the author of the question. Area yellow is; Area triangle with two side 8√(2) cm and 2 cm, and angle 45° - Area triangle with height (20/3) cm and base ⅓(20tan(45-2atan(⅓))) cm = ½*2*8√(2)sin45 - ½*(20/3)*⅓(20tan(45-2atan(⅓))) = 8 - (200tan(45-2atan(⅓)))/9 = (72 - 200tan(45-2atan(⅓)))/9 cm² = (2666664 - 1058200)/333333 cm² = 1608464/333333 cm² = (1608464÷5291)/(333333÷5291) = 304/63 cm² = 4.8253968254 cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2851935

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Sir Mike Ambrose is the author of the question. Area red is; Area triangle with two side 4 cm and 8 cm, and angle 110°. = 0.5*4*8sin110 = 15.0350819326 cm² Area blue is; Area triangle with height 4.47952822702 cm and base (4.47952822702tan33.67018696) cm = 0.5*4.47952822702*4.47952822702tan33.67018696 = 6.6836970062 cm² Therefore; Area Blue + Area Red in cm² to 2 d. p. is; 6.6836970062 + 15.0350819326 = 21.7187789388 cm² ≈ 21.72 cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2850252

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Sir Mike Ambrose is the author of the question. Point P coordinate is; P(4, -3) Point R coordinate is; R(0, ⅓(37)) Point Q (maximum turning point) coordinate is; Q((-3√(259)/14), (4√(259)/7)) Therefore; Area green exactly in square unit decimal form is; Area triangle with height 14.2909320391 units and base (15.8464857653sin(atan(23/6)-atan((8√(259)+42)÷(3√(259)+56))) units. = 0.5*14.2909320391*15.8464857653sin(atan(23/6)-atan((8√(259)+42)÷(3√(259)+56)) = 32.7...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2850241

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Sir Mike Ambrose is the author of the question. The side of the square is; 6.065425 cm Therefore; Area red in cm² to 2 d. p is; Area triangle with height (2.1tan29.11) cm and base 2.1 cm = 0.5*2.1(2.1tan29.11) = 1.22779137323 ≈ 1.23 cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2848600

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ac+1 = a ----- (1) bc+1 = 4c ----- (2) 3ab+3 = 7b ---- (3) From (1) ac+1 = a a = 1/(1-c) ----- (4) Sub. (4) in (3) 3ab+3 = 7b 3(1/(1-c))b+3 = 7b 3b/(1-c) = (7b-3) 3b = (1-c)(7b-3) 3b = 7b-3-7bc+3c 7bc+3 = 4b+3c --- (5) Solving (2) and (5) bc+1 = 4c 7bc+3 = 4b+3c It implies; 7bc+7 = 28c 7bc+3 = 4b+3c 4 = 25c-4b -------- (6) b = (25c-4)/4 ----- (7) Sub. (7) in (2). c(25c-4)/4 + 1 = 4c 25c²-4c = 16c-4 25c²-20c+4 = 0 25c²-10c-10c+4 =0 5c(5c-2)-2(5c-2) = 0 (5...
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