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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3394143

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Sir Mike Ambrose is the author of the question.Calculating Area Red : Area Green : Area Blue.Let AB be 2 units.Therefore CD = 1 unit.It implies;Area Blue is;Area triangle with height 0.72111025509 units and base sin(atan(3/2)) units.= 0.5*0.72111025509sin(atan(3/2))= 3/10 square units.Area Green is;Area trapezoid with two parallel side (3/2) units and 1 unit, and height ½ units - Area triangle with height (3/2) units and base ½ units.= ½*½((3/2)+1) - ½*½(3/2)= (5/8) - (3/8)= ¼ square units.Area...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3388285

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Calculating Red Area. a²+68² = 85² a² = 7225-4624 a = √(7225-4624) a= 51 units. Let b be the radius of the circle. Calculating b.  *68b+51b+85b* = 68*51 b = (68*51)/(68+51+85) b = 17 units. c = a-b c = 51-17 c = 34 units. tand = 68/51 d = atan(68/51)° d = 53.1301023542° It implies; Red Area is; ½(68*51)-½(34²sin(53.1301023542) = 1271.6 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3384116

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Calculating Area Triangle AED. Let x be CD. Figuring an equilateral triangle OCD considering the strategic given two equal angles, 60°. a = (x-8) units. a is DE. b = (x-10) units. b is OA. cos60 = c/8 c = 4 units. c is BC. d = (x-4) units. d is OB. Let AB = AE = y. y² = (x-10)²+(x-4)²-2(x-4)(x-10)cos60 y² = x²-20x+100+x²-8x+16-(x²-14x+40) y² = 2x²-28x+116-x²+14x-40 y² = x²-14x+76 y = √(x²-14x+76) units. Therefore, calculating x, length CD. √(x²-14x+...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3379579

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Calculating Blue Area Total. tana = 10/5 a = atan(2)° b = 180-a b = (180-atan(2))° (10/sin(180-atan(2))) = (5/sinc) c = 26.5650511771° d = 180-(180-atan(2))-26.5650511771 d = 36.8698976458° It implies; Area Blue (1) is; (36.8698976458π*10*10/360)-(0.5*10*5sin36.8698976458) = 32.1750554396-15 = 17.1750554396 cm² e = (½*10*5)-Area Blue (1). e = 25-17.1750554396 e = 7.8249445604 cm² It implies; Area Blue (2) is; 10²-(¼*10*10π)-e = 100-25π-7.8249445...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3372019

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Calculating Area T ÷ Area (R+S) to 2 d. p.  Let the side of the inscribed square be 2 units. Therefore; Area S is; Area triangle with two side 1.03528 units and 0.53589838486 unit, and angle 45° = 0.5*1.03528*0.53589838486sin45 = 0.1961531464 square units. Area R is; Area triangle with two side (2√(2)-2) units and 0.65961372961 units, and angle 72.367664609° = 0.5*(2√(2)-2)*0.65961372961sin72.367664609 = 0.26038499708 square units. Area T is; Area sector with radius 2√(2) units and...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3366743

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Calculating Shaded Area. a²+10² = 12² a = √(144-100) a = √(44) a = 2√(10) units. b = 10-a b = (10-2√(10)) units. b = 3.67544467966 units. cosc = 10/12 c = acos(⅚)° d = 90-45-c d = (45-acos(⅚))° tan(45-acos(⅚)) = e/10 e = 2.02410864032 units. f = 10-e f = 10-2.02410864032 f = 7.97589135968 units. Therefore, shaded area is; ½*d*f = 0.5*3.67544467966*7.97589135968 = 14.6574737317 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3353011

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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/3319726

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Calculating R, radius of the circle. (4√(2))² = 1+5²-2*5cosa 32 = 26-10cosa 16 = 13-5cosa cosa = (-3/5) a = 126.869897646° b = 360-2a b = 360-2*126.869897646 b = 106.260204708° c = ½(b) c = 53.130102354° It implies, R is; sin53.130102354 = (0.5*4√(2))/R R = 2√(2)/sin53.130102354 R = ½(5√(2)) units. R = 2.5√(2) units. R = 3.53553390594 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3280273

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Calculating Blue Area. a = (14-x) cm. Calculating x. 10² = x²+(14-x)² 100 = x²+196-28x+x² 2x²-28x+96 = 0 x²-14x+48 = 0 x²-6x-8x+48 = 0 x(x-6)-8(x-6) = 0 (x-6)(x-8) = 0 It implies; x ≠ 8 cm. x = 6 cm. Recall. a = (14-x) cm. And x = 6 cm. a = 14-6 a = 8 cm. b = 20-a b = 12 cm. c = 20-x c = 14 cm. Area Blue is; (½(12+14)*14)-(½*10*10) = ½(26*14)-½(100) = 182-50 = 132 cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3273110

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Calculating red area. tana = 10/5 a = atan(2)° b = 2a b = 2atan(2)° c = 180-b c = 180-2atan(2) c = 2atan(½)° Area red is; Area sector with radius 5 units and angle 2atan(2)°-Area triangle with height 5 units and base 5sin(2atan(2)) units+Area sector with radius 10 units and angle 2atan(½)°-Area triangle with height 10 units and base 10sin(2atan(½)) units.-2(area quarter circle with radius 5 units -area triangle with height and base 5 units each). = (2atan(2)π*5²/360)-(0....
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