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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2898428

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Sir Mike Ambrose is the author of the question. Let the side length of the be 2 units. Therefore; BC = 2 units. It implies; Area orange is; ½(1*2) = 1 square units. Area green is; ½(1*2) + ½(2/√(5))(4/√(5)) = 1 + (4/5) = (9/5) Therefore; Area orange : Area green is; 1 : (9/5) =(5*1) : (5*(9/5)) = 5 : 9 Proved.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2897068

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At point P; x = (π/6)~30° y = √(3)-2 Gradient at point P is; dy/dx = 2/(1+2sinxcosx) At x = (π/6)~30° dy/dx = 8-4√(3) It implies; yQ exactly as a single fraction in terms of π is;  The coordinates are; ((π/6), (√(3)-2)) and (0, yQ) Gradient = 8-4√(3) Therefore; yQ = ⅓((2√(3)-4)π + 3(√(3)-2))

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2897051

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Radius of the circle, r is; r = 5√(5) units. Therefore; Area yellow is; Area sector with radius 5√(5) units and angle (2asin(√(2)/(2√(5))))° - 2(area triangle with height 5 units and base (5√(2)sin135) units). (2asin(√(2)/(2√(5))))*(5√(5))²*π÷360) - 2(½*5*5√(2)*sin135) = 40.2188192996 - 25 = 15.2188192996 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2895581

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Sir Mike Ambrose is the author of the question. Length AD is; AD = 3√(15) cm. Therefore; Area Orange exactly in cm² is; Area triangle with height √(15) cm and base 3√(15) cm + Area triangle with height 5√(6) cm and base ¼√(615)sin(180-atan(3)-atan(5/4)) cm. = ½*3√(15)*√(15) + ½*5√(6)*¼√(615)sin(180-atan(3)-atan(5/4))) = ½(45) + (15√(410)sin(180-atan(3)-atan(5/4)))/8 = ½(45) + (15√(410)sin(57.094757077))/8 = 22.5 + 31.875 = 54.375 cm² = 435/8 cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2895570

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Let the side length of the regular pentagon be 1 unit. tan36 = a/0.5 a = 0.363271264 units. b² = 0.363271264²+0.5² b = 0.61803398875 units. tan72 = c/0.5 c = 1.53884176859 units. Area Green is; 0.5sin108+0.5*1.53884176859*0.5-0.5*0.5*0.363271264-0.5*0.61803398875*0.61803398875sin36 = 0.65716389015 square units. Calculating Area Blue. Let d be the radius of the inscribed blue circle. Calculating d. e = 0.5(90+36) e =63° (d/tan63) + (d/tan45) = a d = 0.3632...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2894623

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Gradient of the curve at x = 3 is; dy/dx = (-19/20) It implies; Area yellow exactly in square units decimal is; Area triangle with height (5/(4sin(atan(19/20)))) units and base (5/(4sin(atan(20/19)))) units. = ½*(5/(4sin43.5311992856))*(5/(4sin46.4688007144)) = ½*1.81488345054*1.72413927802 = 1.56455592105 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2894522

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a = atan(½)° b² = 2(10)² b = 10√(2) units. c = (45-atan(½))° cos(atan(½)) = d/20 d = 17.88854382 units. Area x is; 0.5*17.88854382*10√(2)sin(45-atan(0.5)) = 40 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2894268

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18² = 14²+16²-2*14*16cosa 448cosa = 14²+16²-18² a = acos((14²+16²-18²)/448) a = 73.39845040098° (18/sin73.39845040098) = (14/sinb) b = 48.18968510422° c = 180-48.18968510422-73.39845040098 c = 58.4118644948° cotd = cota+cotb+cotc cotd = 1.80748828181  d = acot(1.80748828181) d = 28.95373454979° e = 58.4118644948-d e = 29.45812994501° f = 180-28.95373454979-73.39845040098 f = 77.64781504923° (14/sin77.64781504923) = (g/sin73.39845040098)  g = 13.73434221224 units....

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2893310

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Let a be the diameter of the semi circle. a² = b²+14² b² = a²-196 b = √(a²-196) It implies; b² = 6²+6²-2*6*6(-cosc) a²-196 = 72+72cosc a²-196-72 = 72cosc 72cosc = a²-268 cosc = (a²-268)/72 --- (1). cosc = 14/a --- (2). Equating (1) and (2). cosc = cosc (a²-268)/72 = 14/a a³-268a = 1008 a³-268a-1008 = 0 Resolving the polynomial equation. a = 18 units. It implies; Radius, r of the semi circle is; ½(a) = ½(18) = 9 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2891801

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Let x the the side length of the inscribed green equilateral triangle. Calculating area green. a = 180-60 a = 120° b = 45-30 b = 15° c = 180-120-15 c = 180-135 c = 45° d = (4+√(6)) units. It implies; (x/sin45) = ((4+√(6))/sin120) x = 5.2659863237109 units. Again, x is the side length of the inscribed green equilateral triangle. Area green inscribed equilateral triangle is; ½(x²)sin60 = 0.5*5.2659863237109²*sin60 = 12.0077072105782 square units. = 12 square...
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