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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2671861

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½(ab) = 6 ab = 12 b = (12/a) units. c² = a²+b² c² = a²+(12/a)² c² = a²+(144/a²) c = √(a²+(144/a²)) units. d = 2+b d = (2+(12/a)) units. Calculating a. It implies; d = c (2+(12/a)) = √(a²+(144/a²)) (2+(12/a))² = a²+(144/a²) 4+4(12/a)+(144/a²) = a²+(144/a²) 4+4(12/a) = a² 4a+48 = a³ a³-4a-48 = 0 It implies; a = 4 units. e² = 2²+4² e = √(4+16) e = 2√(5) units. e is AB, the height of triangle ABC. Recall. d = (2+(12/a)) And a = 4 units. d = (2+(12/4)) d...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2670146

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8² = 2a² a² = 32 a = √(32) a = 4√(2) units. a is the side length of the square. c = a+b c = (4√(2)+b) c is the diameter of the circle. d = ½(c) d = ½(4√(2)+b) units. d is the radius of the circle. e = d-b e = ½(4√(2)+b)-b e = ½(4√(2)+b-2b) e = ½(4√(2)-b) units. f = ½(a) f = 2√(2) units. Calculating b. (½(4√(2)+b))² = (2√(2))²+(½(4√(2)-b))² ¼(32+8√(2)b+b²) = 8+¼(32-8√(2)b+b²) 32+8√(2)b+b² = 32+32-8√(2)b+b² 16√(2)b = 32 √(2)b = 2 b = 2/√(2) b = √(2) units....

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2670116

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Calculating a, radius of the small circle. b = c 2a = 3+2c 2a-2c = 3  2c = 2a-3 c = ½(2a-3) --- (1). d = a-½(c) d = ½(2a-c) units. It implies; a² = 1.5²+(½(2a-c))² a² = (9/4)+¼(4a²-4ac+c²) 4a² = 9+4a²-4ac+c² 4ac = 9+c² --- (2). Substituting (1) in (2) to get a, radius of the small circle. 4a(½(2a-3)) = 9+(½(2a-3))² 2a(2a-3) = 9+¼(4a²-12a+9) 16a²-24a = 36+4a²-12a+9 12a²-12a-45 = 0 4a²-4a-15 = 0 Resolving the above quadratic equation via factorization approach...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2670031

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13² = 16²+11²-2*16*11cosa 169 = 256+121-352cosa 352cosa = 377-169 a = acos(208/352) a = 53.7784533802° 9² = 16²+17²-2*16*17cosb 81 = 256+289-544cosb 544cosb = 545-81 cosb = 464/544 b = 31.4669762933° c = a-b c = 53.7784533802-31.4669762933 c = 22.3114770869° Therefore, the required angle, x is; x² = 17²+11²-2*17*11cos22.3114770869 x = 8 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2670022

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tana = 10/6 a = atan(5/3)° b = 180-45-a b = (135-atan(5/3))° Or b = (45+atan(3/5))° It implies; (6/sin(135-atan(5/3))) = (c/sin(atan(5/3))) c = 5.3033008589 units. Therefore, area blue is; 0.5*6*5.3033008589sin45 = 11.25 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2670013

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Area yellow is; Area triangle with two lengths 14 cm and 12.7422688787 cm and angle ½asin(0.9397)° - Area triangle with two lengths 3.05195952611 cm and 7.30994433287 cm and angle ½sin(0.9397)° = 51.1614444441 - 6.39824456324 = 44.7631998809 cm² = 44.8 cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2669737

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Sir Mike Ambrose is the author of the question. Let the single side length of the square be 3 units. Therefore Area square is; 3² = 9 square units. Area green is; ½((1, 2) (7/3, 5/3) (3, 3) (3/5, 12/5) (1, 2)) = ½((-45+30+63)/15) = ½(48/15) = 24/15 = (8/5) square units. = ⅕(8) square units. It implies; Area green ÷ Area square is; (8/5) ÷ 9 = 8/45

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2669724

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Calculating Area Inscribed Green Triangle. Notice. Considering 6 units as the base of the green inscribed triangle, its height will be 6 units as well. Therefore, area inscribed green triangle is; ½(base*height) = ½(6*6) = ½(36) = 18 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2668521

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Notice. 3 units is the radius of the circle. 6² = (6-2a)²+(6-a)² 36 = 36-24a+4a²+36-12a+a² 5a²-36a+36 = 0 5a²-30a-6a+36 = 0 5a(a-6)-6(a-6) = 0 (5a-6)(a-6) = 0 It implies; a ≠ 6 a = ⅕(6) units. a = 1.2 units. b = ½(5-½(a)) b = ½(5-½(1.2)) b = ½(5-0.6 ) b = ½(4.4) b = 2.2 units. cosc = (2.2)/3 c = acos((2.2)/3)° c = 42.8334280661° d = 180-c d =137.1665719339° The required length, y is; y² = 3²+3²-2*3*2cos137.1665719339 y = 5.5856960175 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2668427

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Calculating area of the rectangle. a² = 5²+2² a = √(29) units. a is the width of the rectangle. b = 2+6 b = 8 units. Observing similar plane shape (right-angled) side length ratios to get c, length of the rectangle. 5 - c √(29) - 8 Cross Multiply. √(29)c = 40 c = 40/√(29) units. c = (40√(29))/29 units. Again, c is the length of the rectangle. Area rectangle is; ac = √(29)*(40/√(29)) = 40 square units.
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