Mathematics Question and Solution

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

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...

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Mathematics Question and Solution

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

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

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

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

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

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...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2177695

Sir Mike Ambrose is the author of the question. Area Blue, in cm² to 1 d. p. is; Half area regular pentagon with side 12 cm - area triangle with height 6 cm and base 6tan24 cm - area triangle with height 12cos36 and base 12sin36 cm. = (½*(60*12)/(4tan(180/5))) - ½(6*6tan24) - ½(12cos36*12sin36) = 123.874372842 - 8.01411633555 - 34.2380345866 = 81.62222192 cm² ≈ 81.6 cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2177527

Area of the shaded region is; Area quarter circle with radius 12 units - Area triangle with height and base 12 units respectively - Area quarter circle with radius 8 units + Area triangle with height and base 8 units respectively + Area quarter circle with radius 8 units - Area triangle with height and base 8 units respectively - Area quarter circle with radius 4 units + Area triangle with height and base 4 units. = ¼(144)π-½(144)-¼(64)π+½(64)+¼(64)π-½(64)-¼(16)π+½(16) = 36π-72-16π+32+...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2176726

Sir Mike Ambrose is the author of the question. (a) Exact radius of the circle is; ½√(2²+4²) = ½√(20) = ½*2√(5) units. = √(5) units. Or Cos(atan(2)) = (1/r) Where r is the radius of the circle. r = 1/cos(atan(2))) r = √(5) units. (b) Area Yellow exactly is; Area triangle with height 2 units and base 2sin(2atan2) units + Area triangle with height ⅕(8√(5)) units and base 8sin(90-asin(√(5)/5)) units - Area triangle with height ⅓(16) units and base 2√(5)sin(asin(√(5)/5)) units....

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