Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3353021

Kindly move the question left/right one time to review the framework/analysis. Thank you amazingly. Calculating angle x. Let 1 unit be the side length of the square. Let y be the equal red lengths. It implies; a = (1-y) units. b² = y²+1² b = √(y²+1) units. c² = 1²+1² c² = 2 c = √(2) units. c is the diagonal of the square. d² = 1²+a² d² = 1²+(1-y)² d² = 1+1-2y+y² d = √(y²-2y+2) units. e = d-y e = (√(y²-2y+2)-y) units. Calculating y. Observing Similar Tr...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3353014

Sir Mike Ambrose is the author of the question. Calculating Red Area Exactly. 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/3353011

Calculating area blue isosceles triangle. (10/sin45) = (6/sina) a = 25.1040902502° b = 180-45-25.1040902502 b = 109.89590975° c = 180-109.89590975 c = 70.10409025° Let r be the radius of the half circle. d = (r-6) units. Calculating r. r² = 10²+(r-6)²-2*10(r-6)cos70.10409025 r² = 100+r²-12r+36-6.80624847494r+40.8374908496 18.80624847494r = 136+40.8374908496 18.80624847494r = 176.83749085 r = 176.83749085/18.80624847494 r = 9.40312423744 units. e = 2r-...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3353007

Calculating the width of the ascribed rectangle. a = 180-60-x a = (120-x)° Let b be the side length of the inscribed regular triangle. cosx = 1/b --- (1). At (1). 1 is adjacent. b is hypotenuse. Calculating c, opposite. c²+1² = b² c = √(b²-1) units. c is the width of the rectangle. Therefore; sinx = √(b²-1)/b --- (2). cos(120-x) = 2/b --- (3). At (3). cos120cosx+sin120sinx = 2/b ½√(3)sinx-½(cosx) = 2/b --- (4). Substituting (2) and (1) in (4)....

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3352233

Calculating Perimeter of the ascribed Hexagon. a = ⅙*180(6-2) a = 120° Let x be the side length of the regular hexagon. b² = 2x²-2x²cos120 b = √(3)x units. sin30 = c/x c = ½(x) units. d = x+2c d = 2x units. e = d-11 e = (2x-11) units. f = ½(a) f = 60° Calculating x. 7² = x²+(2x-11)²-2x(2x-11)cos60 49 = x²+4x²-44x+121-2x²+11x 49 = 3x²-44x+121+11x 3x²-33x+72 = 0 x²-11x+24 = 0 x²-8x-3x+24 = 0 x(x-8)-3(x-8) = 0 (x-8)(x-3) = 0 It implies;...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3351341

Sir Mike Ambrose is the author of the question. Calculating Area R ÷ Area S Exactly. Calculating the equation of the curve. y-b=a(x-4)² ----- (1) At coordinate (8, 0) -b=16a Therefore; a = -b/16 Sub. a in (1) to get the equation of the curve. y-b= (-b/16)(x-4)² It implies; y = (-bx²/16)+(bx/2) ----- (2) Calculating b. The area of the curve at point (8, 0) = 1280/27 It implies; (-32b/3)+16b=1280/27 b = 1280/(16*9) b = 80/9 Therefore sub. b in (2). y = (-(80/9)x²/16)+((80/9)x/...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3351339

Calculating r, radius of the circle. It implies; (45+15)*15 = 20*a a = 45 cm. b = 20+a b = 65 cm. c² = 45²+65² c = 25√(10) cm. c = 79.0569415042 cm. c is the diameter of the circle. It implies, r, radius of the circle is; r = ½(c) r = ½(25√(10)) r = 12.5√(10) cm. r = 39.5284707521 cm.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3350545

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 ≈ 81.6 cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3349495

Calculating x, length DF. Let a be the radius of the ascribed half circle. b = (a-6) units. c = (a-7) units. 7² = 6²+8²-2*6*8cosd 96cosd = 36+64-49 d = acos((36+64-49)/96) d = 57.9100487437° d is angle ACB. e = 180-d e = 122.089951256° e is angle ACE. Calculating a. a² = 8²+(a-6)²-2*8(a-6)cos122.089951256 a² = 64+a²-12a+36+8.5a-51 3.5a = 49 a = 14 units. Again, a is the radius of the half circle. Recall. c = (a-7) units. And a = 14 units. c = 14-7 c = 7...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3347305

Calculating the chord length. Let x be the radius of the half circle. a = (x-4) units. b = (x-9) units. c = (x-7) units. d = a+b d = (x-4)+(x-9) d = (2x-13) units. d is the length of the chord. e = ½(d) units. e = ½(2x-13) units. f = x-4-½(2x-13) f = ½(2x-8-2x+13) f = ½(5) units. It implies; 7² = g²+(½(2x-13))² g² = 7²-¼(4x²-52x+169) g² = ¼(196-4x²+52x-169) g² = ¼(52x+27-4x²) g = ½√(52x+27-4x²) units. Calculating x. (½(5))²+(½√(52x+27-4x²))² = (x-7)²...

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Mathematics Question and Solution

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