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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2187323

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Sir Mike Ambrose is the author of the question. Area D exactly in cm² is; Area trapezoid with parallel sides 4 cm and 8 cm, and height 4 cm - Area triangle with height 4 cm and base 3 cm - Area sector with radius 4 cm and angle atan(4/3). = (½*4(4+8)) - (½*4*3) - (atan(4/3)*π*4²÷360) = 24 - 6 - (2πatan(4/3))/45 = 18 - (2πatan(4/3))/45 = (810 - (2πatan(4/3)))/45 cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2183313

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Let the side length of the regular hexagon be 1 unit. a² = 1²+1² a = √(2) units. b = 180-120 b = 60° c = 60+45 c = 105° d² = 2+1-2√(2)cos105 d = 1.9318516526 units. (1.9318516526/sin105) = (√(2)/sine) e = 45° f = 180-60-45 f = 75° (1/sin75) = (g/sin60) g = 0.8965754722 units. It implies; Area Green is; 0.5*0.8965754722sin45 = 0.3169872981 square units. = (sin60sin45)/2sin75 square units. h = ½(180-150) h = 15° j = 90-15 j = 75° k = 180-120 k = 60° (1/sin60) = (l/sin45) l = 0.81649...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2181662

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Let the pentagon side length be 1 unit. a = ½(180-108) a = 36° b² = 2-2cos36 b = 0.6180339887 units. Calculating red length (circumference of the inscribed red circle). Let the radius of the re inscribed circle be r. Calculating r. c = ½(180-36) c = 72° Therefore; ½(0.6180339887r+2r) = ½*sin36 2.6180339887r = sin36 r = 0.2245139883 units. Therefore, length red is; 2πr = 2*0.2245139883π = 1.4106629925 units. Calculating blue length. d² = 2-2cos108 d = 1.6180339887 units. 1.618033988...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2180850

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Let the side length of the regular pentagon be 2 units. Therefore; Arc radius is; = 2 units. Calculating Circle Radius. a = 180(3)/5 a =108° b = ½(180-108) b = 36° c = 108-36 c =72° cos72 = 1/d d = 3.2360679775 units. e = 90-72 e = 18° f = 27-18 f =9° sin27 = g/h h = g/sin27 h = 2.2026892646g units. Where g is the radius of the inscribed circle. It implies; (2+g)² = (2.2026892646g)²+3.2360679775²-2*3.2360679775*2.2026892646gcos9 4+4g+g² = 4.8518399964g²+10.472135955-14.0805880855g...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2180105

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Let the square side be 2 units. Area Square is; 2² = 4 square units. tana = 2/1 a = atan(2) b = 180-2a b = (180-2atan(2))° (1/sin(180-2atan(2))) = (c/sin(atan(2))) c = 1.1180339887 units. d² = 1.1180339887²+1²-2*1.1180339887cos(90+atan(2)) d = 2.0615528128 units. e² = 2²+1² e = √(5) e = 2.2360679775 units. f = 2.2360679775+1.1180339887 f = 3.3541019662 units. g² = 3.3541019662²+2²-2*2*3.3541019662cos(atan(0.5)) g = 1.8027756377 units. (1.8027756377/sin(atan(0.5))) = (3.3541019662/sinh...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2179377

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Calculating x, y = 12. y = (8x)/√(2x+4) 12√(2x+4) = 8x 3√(2x+4) = 2x 9(2x+4) = 4x² 18x+36 = 4x² 4x²-18x-36 = 0 2x²-9x-18 = 0 2x²-12x+3x-18 = 0 2x(x-6)+3(x-6) = 0 Therefore; x ≠ -3/2 units. x = 6 units. Calculating gradient of the curve at the tangent at x = 6, observing quotient rule. It implies; Gradient at the tangent, m is; m = 5/4 Calculating n, gradient at the normal. mn = -1 And m = (5/4) Therefore; (5/4)n = -1 n = (-⅘) It implies; (12-0)/(3-a)...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2179361

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Let the red square side be 1 unit. Area Red is; 1² = 1 square units. Calculating Area Blue. (1/sin30) = (a/sin126) a = 1.6180339887 units. a = 2sin126 units. It implies; Area Blue is; 0.5*2sin126sin24 = sin24sin126 square units. Therefore; Area Blue ÷ Area Red exactly is; sin24sin126÷1 = sin24sin126 = 0.3290568565 exactly in decimal. Calculate Alpha to 1 decimal place. b = 180-100  b = 80° c = 126-80 c = 46° (1/sin30) = (d/sin24) d = 0.8134732862 units. (0.8134732862/sin30) = (e/si...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2179197

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AC = 12 cm AB = 10 cm Therefore Area red exactly in cm² is; Area triangle with two side (165/90) cm and √(61) cm, and angle atan(5/6)° = ½*(165/90)*√(61)sin(atan(5/6)) = 4.58333333333 cm² = 4125/900 cm² = 55/12 cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2178578

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Let r be 1 unit. It implies; Radius, R of the ascribed semi circle is; R = 2 units. 2² = a²+(½)² 4-¼ = a² a = √(15/4) a = ½(√(15)) units. 1² = b²+(½)² b² = (3/4) b = ½(√(3)) units. c = a-b c = ½(√(15))-½(√(3)) c = ½(√(15)-√(3)) units. tand = 0.5√(3)/(½) d = atan(√(3)) d = 60° tan60 = (½(√(15)-√(3)))/e √(3) = (½(√(15)-√(3)))/e e = (½(√(15)-√(3)))/√(3) e = ⅙(3√(5)-3) e = ½(√(5)-1) units. Area Green is; ½*½(√(5)-1)*½(√(15)-√(3)) = ⅛(√(75)-√(15)-√(15)+√(3))...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2178357

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Let the side of the regular octagon be 1 unit. Calculating Area Yellow. a = ⅛(180*6)-90 a = 45° b² = 2-2cos45 b = 0.7653668647 units. c = ½(180-45) c = 67.5° d = 135-c d = 135-67.5 d = 67.5° It implies; Area Yellow is; ½*sin45 + ½*0.7653668647sin67.5 = ¼(√(2))+0.3535533906 = 0.7071067812 square units. = ½(√(2)) square units. Calculating Area Blue. e² = 0.7653668647²+1²-2*0.7653668647cos67.5 e = 1 unit. f = 360-135-90 f = 135° g = ½(180-135) g = 22.5° (1/sin22.5) = (h/sin135) h = 1.8...
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