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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2109559

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Sir Mike Ambrose is the author of the question. Area Blue exactly in cm² decimal form is; Area trapezoid with two parallel side (7√(2)+14) cm and 15.3137084989 cm, and height 18.4852813742 cm. = ½((7√(2)+14)+15.3137084989)*18.4852813742 = 362.433549545 cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2108236

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Sir Mike Ambrose is the author of the question. Area Green is; Area triangle with height √(8(31-14√(3))) units and base √(178-72√(3))sin57.72115346403 units. = 0.5*√(8(31-14√(3)))*√(178-72√(3))sin57.72115346403 = 22.67949192422 square units. Area Red is; Area triangle with height 5√(2) units and base 6√(2) units + Area triangle with height ⅕(11√(29)) units and base ⅕(27sin(atan(5/2))) units. = ½*5√(2)*6√(2) + ½*⅕(11√(29))*⅕(27sin(atan(5/2))) = 30 + (297/10) = 597/10 square units. Therefor...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2108235

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Sir Mike Ambrose is the author of the question. Let the radius of the semicircle be 1 unit. Area Semicircle is; ½*1²*π 0.5π square units. Calculating AC = AB = BC sin67.5 = (AC)/1 AC = sin67.5 units. 1=a²+1-2acos82.5 a = 0.26105238444 units. b = AC - a b = 0.66282714807 unit. c = √(0.26105238444²(sin67.5)²-2*0.26105238444sin67.5*cos60) c= 0.82493683584 units. d = asin(0.26105238444sin60/0.82493683584) d = 15.90570135267° e = 60-d e = 44.09429864733° f = 0.650107 unit. g = 0.576911...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2106557

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tan30 = a/(2√(3)) a = 2 units. b = (2√(3)-2) units. tan30 = c/(2√(3)-2) c = ⅓(6-2√(3)) units. d = 2√(3)-⅓(6-2√(3)) d = ⅓(6√(3)-6+2√(3)) d = ⅓(8√(3)-6) units. It implies; Area Blue exactly in square units is; ½(2√(3))²*sin60-½(⅓(8√(3)-6))²*sin60 = 3√(3)-⅓(19√(3)-24) = ⅓(9√(3)-19√(3)+24) = ⅓(24-10√(3)) square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2106145

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Shaded/Area Blue is; 2(area sector with radius 4 unit and angle (180-2atan(½))° - area triangle with two side 4 unit respectively, and angle (180-2atan(½))°) + 2(area sector with radius 2 unit and angle (180-2atan(2))° - area triangle with two side 2 unit respectively, and angle (180-2atan(2))°) + 4(area sector with radius 2 unit and angle (2atan(2))° - area triangle with two side 2 unit respectively, and angle (2atan(2))°). = 2((180-2atan(½))×16π÷360) - ½(16sin(180-2atan(½)))) + 2((180-2ata...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2105685

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Sir Mike Ambrose is the author of the question. Let the square side be 2 units. Area Square is; 2² = 4 square units. Calculating Area Yellow. (2-a)²+1 = a²+4 4-4a+a²+1=a²+4 a = ¼ unit. b² = 1+(65/64)-2*⅛(√(65))cos(atan2+atan(3/2)) b = ⅛√(193) units. (b/sin(atan2+atan(3/2))) = ((⅛√(65))/sinc) c = asin(7√(193)/193)° c = 30.25643716353° d = acos(7√(193)/193)° d = 59.74356283647° e² = 4+(193/64)-(2*2√(193)/8)cos(acos(7√(193)/193)) e = (15/8) units. (15/8sin(acos(7/√(193)))) = (√(193)/8si...

Mathematics Question and Solution

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

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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

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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

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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

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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...
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