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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2709796

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Sir Mike Ambrose is the author of the question. Let the single side length of the small square be 1 unit. Therefore; Area large square is; ((1/tan15)-1)² = 7.46410161514 square units. Area orange is; Area large square - area triangle with height 2.73205080757 units and base 0.73205080757 units - area triangle with height 2 units and base 0.53589838486 units - area triangle with height 2.19615242271 units and base 0.58845726812 units. = 7.46410161514 - ½(2.73205080757*0.732...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2709788

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Sir Mike Ambrose is the author of the question. The width of the rectangle is; (5/2)+(11/2)  = 8 cm Area Rectangle is; 12*8 = 96 cm² Area Green is; ½(7*12)sin((90-atan(5√(3)/11))) = 33 cm² Area green ÷ Area rectangle is; 33 ÷ 96 = 11/32 = 0.34375 = 0.34 to 2 decimal places.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2709264

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Let the square side length be 1 unit. tan15 = a/1 a = 0.2679491924 units. b = 1+a b = 1.2679491924 units. c = 1-a c = 0.7320508076 units. d² = 1²+1² d = √(2) units. e = 90-15 e = 75° f² = √(2)²+1.2679491924²-2√(2)*1.2679491924cos15 f = 0.378937382 units. g² = 0.378937382²+0.7320508076²-2*0.7320508076*0.378937382cos75 g = 0.7320508076 units. Therefore; Since c = g, the required angle, x is; x = 180-2e x = 180-2*75 x = 180-150 x = 30°

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2708447

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Let the length of the two congruent rectangle be 1 units. Let the width be x. Therefore; 1 ~ (1+x) x ~ 1 It implies; 1/x = (x+1)/1 x²+x-1 = 0 (x+½)²=1+¼ x = -½±½√(5) Therefore; x ≠ -½(1+√(5)) x = ½(√(5)-1) units. Let alpha be y. Therefore; Tany = (1+x)/1 Tany = (1+x) And x = ½(√(5)-1) units. Tany = ½(√(5)-1)+1 Tany = ½√(5)-½+1 Tany = ½√(5)+½ Tany = ½(1+√(5))

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2707965

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Let the side length of the blue inscribed equilateral triangle be 1 unit. Area blue equilateral triangle is, 0.5*1²*sin60 = ¼√(3) square units. = 0.4330127019 square units. It implies; ⅓(¼√(3)) = ½*a²*sin60 ⅙ = ½*a² a² = ⅓ a = √(⅓) a = ⅓√(3) units. a is the side length of each of the three congruent red regular triangles. Therefore; b = 2a+1 b = 2*⅓√(3)+1 b = ⅓(2√(3)+3) units. c² = (⅓(2√(3)+3))²+(⅓√(3))²-2*⅓√(3)*⅓(2√(3)+3)cos120 c² = ⅑(12+12√(3)+9)+⅓+⅑(6+3√(3))...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2707956

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Sir Mike Ambrose is the author of the question. The equation of the curve is; Using the points; (4, 4), (2, 0), (12, 0) And, y =ax²+bx+c Therefore; 4=16a+4b+c 0=4a+2b+c 0=144a+12b+c Solving the three equations via matrix determinant approach. It implies; a = -¼, b = ½(7) and c = -6 Substituting a, b and c values in the standard quadratic equation. The equation of the curve is; y = -¼(x²) + ½(7x) - 6 The maximum turning point of the curve is; At y = 6¼...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2707948

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Sir Mike Ambrose is the author of the question. Area BDE is; Area triangle with side 2 units and 3 units, and angle 120° = ¼(6√(3)) = ½(3√(3)) square units. = 2.59807621135 square units. Area yellow is; Area triangle with side 2 units and 3 units, and angle 120° - Area triangle with side 2 units and 1.74355957742 units, and angle (60-atan(3√(3)/7))° + Area triangle with side 1.30766968306 units and 3 units, and angle atan(3√(3)/7)° - Area triangle with side 1 unit and 0.4175747...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2707100

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Sir Mike Ambrose is the author of the question. Let the single side length of the regular hexagon be 2 units. Therefore; Area regular pentagon is; 5(2.12920428618)²÷(4tan(180/5)) = 7.79980303549 square units. Area orange is; Area triangle with side 1.95629520148 units and 1.71576768873 units, and angle 108° + Area triangle with side 2.97412348187 units and 2.09846578712 units, and angle 26.7246503609° = ½(1.95629520148*1.71576768873)sin108 + ½(2.97412348187*2.09846578712)sin...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2706404

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6²+6²-2*6*6cosa = 12²+3²+2*12*3cosa 72-72cosa = 153+72cosa 144cosa = 81 a = acos(9/16) a = 55.7711336722° b = 180-a b = 124.2288663278° 6²+12²-2*6*12cosc = 6²+3²+2*6*3cosc 180-144cosc = 45+36cosc 180cosc = 135 c = acos(3/4) c = 41.4096221093° d = 180-c d = 138.5903778907° e = 180-a-c e = 82.8192442185° (12/sin82.8192442185) = (f/sin55.7711336722) f = 10 units. g = 180-b-c g = 14.3615115629° (6/sin14.3615115629) = (h/sin124.2288663278) h = 20 units. Theref...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2706391

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tana = 5/11 a = atan(5/11)° sin(atan(5/11)) = 5/b b = 12.0830459736 cm. c = b-2.5 c = 9.5830459736 cm. sin(atan(5/11)) = d/9.5830459736 d = 3.9654926392 cm. 5/11 = 3.9654926392/e e = 8.7240838063 cm. Therefore, area inscribed triangle yellow is; de = 0.5*3.9654926392*8.7240838063 = 17.2976450587 cm²
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