Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2104130

Let P be 2^(x) (P⁹/8192)-256P⁶ = 0 Let y be P³ (y³/8192)-256y² = 0 y³-2097152y² = 0 y = 2097152 P³ = y P³ = 2097152 P = 128 2^(x) = P 2^(x) = 128 2^(x) = 2^(7) x = 7

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2101410

Let AB be 4 units. Let BC be 3 units. Area ABCD is; 4*3 = 12 square units. Calculating Area CEF. tana = 3/2 a = atan(3/2)° a is angle AMD. b = atan(2/3)° b is angle DEM. c = (180-atan(3/2))° c is angle CME. sin(atan(2/3)) = d/2 d = 4√(13)/13 units. d is EM. e² = (4√(13)/13)²+2²-4*(4√(13)/3)sin(180-atan(3/2)) e = 10√(13)/13 units. e is side length of the inscribed regular triangle. Area CEF is; 0.5*(10√(13)/13)²*sin60 = 0.5*(100/13)*(√(3)/2) = 25√(3)/13 square units. Area Triangle CEF...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2100314

Let AB be 4 units. BC = 6 units. Let a be the side length of the inscribed square. Calculating a. b² = 4²-a² b = √(16-a²) It implies; a = √(16-a²) 6 = 4 Cross Multiply. 4a = 6√(16-a²) 2a = 3√(16-a²) 4a² = 9(16-a²) 4a² = 144-9a² 13a² = 144 a = 12√(13)/13 units. a = 3.32820117735 units. c² = 4²-(12/√(13))² c² = 16-(144/13) c = √(64/13) c = 8√(13)/13 units. It implies, area red is; 0.5*(8√(13)/13)(12√(13)/13) = 48/13 square units. sind = (8√(13)/13)/4 d = asin(2√(13)/13) e = (90-asin(2...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2098215

Sir Mike Ambrose is the author of the question. Radius of the ascribed circle is 13 cm. a = acos((2*13²-24²)/(2*13²)) a = 134.76027010392° b = ½(a) b = 67.38013505196° c = 40° d = b - c d = 27.38013505196° e = 90 - d e = 62.61986494804° Let the side of the inscribed blue square be f. Calculating f. (f/tan50)+f+(f/tan62.61986494804) = 24 f = 24/((1/tan50)+1+(1/tan62.6198644804)) f = 10.18238945915 cm. Area Blue is; f² = (10.18238945915)² = 103.68105509785 cm² g = ½(360 - 134.7602701...

Mathematics Question and Solution.

https://onlineedumath.com/update/mathematics-question-and-solution/2095204

Le the side of the regular hexagon be 1 unit. cosa = 0.5/1 a = 60° b = 60-36 b = 24° c = 108-24 c = 84° Therefore; The required angle, x is; ½(180-84) = ½(96) = 48°

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2094967

Sir Mike Ambrose is the author of the question. Let the side of the square be 1 unit. Area square is; 1² = 1 square unit. 1 = ½+¼-½(√(2))cosa ½(√(2))cosa = ¾-1 a = acos(-√(2)/4) a = 110.70481105464° b = 180-a b = 69.29518894536° c = 90-b c = 20.70481105464° (1/sin110.70481105464) = (1/2sind) d = asin(sin110.70481105464/2) d = 27.88556683609° Area S is; Area Semicircle with radius ½ unit - Area triangle with height ½ unit and base ½(sin(2*69.29518894536) units - 2(area sector with radi...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2094966

Sir Mike Ambrose is the author of the question. Let the length of the rectangle be 2 units. Length AB is: √(2) units. a² = 2+1-2√(2)cos75 a = √(4-√(3)) units. (a) Let Alpha be x. Calculating x. (1/sinx) = (√(4-√(3))/sin75) x = asin(sin75/√(4-√(3))) x = 39.89609063893° Area yellow is; Area triangle with height (2√(2)-√(6)) units and base 0.40352376128sin39.89609063893 units = 0.5*(2√(2)-√(6))*0.40352376128sin39.89609063893 = 0.04903810568 square units. Area Red i...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2093535

Let the side length of the regular decagon be 1 unit. a = (180*8)/10 a = 144° a is a interior angle of the regular decagon. b = 144-120 b = 24° c² = 2-2cos24 c = 0.41582338164 units. d = ½(180-24) d = 78° e = 360-120-90-78 e = 72° f = 144-78 f = 66° g = 180-66-72 g = 42° (0.41582338164/sin42) = (h/sin72) h = 0.59102293779 units. Area Orange is; 0.5*1*1sin24+0.5*0.59102293779*0.41582338164sin66 = 0.20336832154+0.11225699415 = 0.31562531569 square units. Calculating Purple Area. j =...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2092520

tan30 = 6/a a = 6√(3) cm. a = 10.39230484541 cm. sin30 = 6/b b = 12 cm. cos15 = c/12 c = (3√(6)+3√(2)) cm. c = 11.59110991547 cm. d = 11.59110991547²+10.39230484541²-2*11.59110991547*10.39230484541cos45 d = 8.48528137424 cm. (8.48528137424sin45) = (11.59110991547/sine) e = 75° f = √(100) f = 10 cm. g = 75-atan(3/4) g = 38.13010235416° cos38.13010235416 = h/10 h = 7.86610731855 cm. j² = 7.86610731855²+8²-2*7.86610731855*8cos75 j = 9.65925826289 cm. (9.65925826289/sin75) = (7.8661073185...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2092454

11-2 = (x²/4) x = √(36) x = 6. Calculating Ax, let it be a. (Area Under the curve at x = a and x = 6)(1/(6-a)) = (19/3) (30-(a³/12)-2a) = (114-19a)/3 360-a³-24a = 456-76a a³-52a+96 = 0 a = 2. Calculating Ay. Notice; Ax = 2 Ay = ¼(2²)+2 Ay = 3 Therefore; Shaded Area exactly is; Area Rectangle with length 11 units and width 4 units - (Area under the curve at x = 2 and x = 6) (11*4)-(76/3) = 44-(76/3) = ⅓(132-76) = ⅓(56) square units.

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