Mathematics Question and Solution

https://onlineedumath.websites.co.in/update/mathematics-question-and-solution/1807684

a² = 10²+16²-2*10*16cos120 a = 2√(129) units. Where a is length AC. (3√(129)/sin120) = (16/sinb) b = 37.58908946897° c = 90-b c = 52.41091053103° d = 60-b d = 22.41091053103° e = 90-d e = 67.58908946897° f = 90-60 f = 30° cos37.58908946897 = g/10 g = 7.92405815693 units. i = 30+37.58908946897 i = 67.58908946897° tan67.58908946897 = j/7.92405815693 j = 19.2148198619 units. Where j is the radius of the arc. sin67.58908946897 = 19.2148198619/k k = 20.78460969082 units. l² = (2√(129)...

Mathematics Question and Solution

https://onlineedumath.websites.co.in/update/mathematics-question-and-solution/1806766

sin30 = a/12 a = 6 cm. Where a = AF. AF = EF = 6cm. tan30 = b/12 b = 12tan30 b = 4√(3) cm. Where b = AG. Notice; AG = EG = 4√(3) cm. c = AB-AG c = 12-4√(3) c = (12-4√(3)) cm. Where c = BG. d² = (4√(3))²-6² d = √(48-36) d = √(12) d = 2√(3) cm. Where d = FG. e = atan(6/(2√(3)) e = atan(3/√(3)) e = 60° Where e = angle EGF. Angle BGH = 180-60-60 Angle BGH = 60° It implies; cos60 = BG/f ½ = (12-4√(3))/f f = (24-8√(3)) cm. Where f = GH. Therefore, Length EH is; GH - EG = (24-8√(3)) - 4...

Mathematics Question and Solution

https://onlineedumath.websites.co.in/update/mathematics-question-and-solution/1806550

Let AC be 1 unit. Area smaller pentagon is; ½(5)*(1/(2tan(36))) = 1.72047740059 square units. a² = 1²+0.5²-cos108 a = 1.24860602048 units. Where a is CD. (1.24860602048/sin108) = (0.5/sinb) b = 22.38617755917° c = 108-22.38617755917 c = 85.61382244083° Calculating Area E. It is; 0.5*0.5*0.5*1.24860602048sin22.38617755917 = 0.05944103227 square units. (a) Area E ÷ Area Smaller Pentagon to 3 decimal places is; 0.05944103227 ÷ 1.72047740059 = 0.03454915028 ≈ 0.035 Calculating r,...

Mathematics Question and Solution

https://onlineedumath.websites.co.in/update/mathematics-question-and-solution/1806226

8 = 4 a = (8-a) Cross multiply. 64-8a = 4a 64 = 12a a = ⅓(16) cm. b = 8-a b = ⅓(8) cm. c = atan(⅔)° d = atan(3/2)° ⅔ = 8/e e = 12 cm ⅔ = f/8 f = ⅓(16) cm. g = 8-f g = ⅓(8) cm. Area Orange exactly in cm² is; Area square units side 8 cm - Area rectangle with length 4 cm and width ⅓(8) cm. = 8² - 4*⅓(8) = 64 - ⅓(32) = ⅓(192-32) = ⅓(160) cm²

Mathematics Question and Solution

https://onlineedumath.websites.co.in/update/mathematics-question-and-solution/1805745

The radius of the inscribed circle is 2 units. a = 2atan(⅓)° b = 2atan(⅕)° c = 180-a-b c = (180-2atan(⅓)-2atan(⅕))° sin(2atan(⅓)) = d/16 d = (48/5) units. cos(2atan(⅓)) = e/16 e = (64/5) units. f = (90-2atan(⅓)-2atan(⅕))° tan(90-2atan(⅓)-2atan(⅕)) = g/(48/5) g = (198/35) units. Therefore; Area Blue exactly in square units is; ½*(48/5)(198/35) = 4752/175 square units.

Mathematics Question and Solution

https://onlineedumath.websites.co.in/update/mathematics-question-and-solution/1805081

Let x² = p Calculating p. (4-p)^⅓+(p-1)^½ = 1 4-p = (1-(p-1)^½)³ 4-p = (p-2(p-1)^½)(1-(p-1)^½) 4-p = 3p-p(p-1)^½-2(p-1)^½+2p-2 (p+2)((p-1)^½) = 4p-6 p-1 = ((4p-6)/(p+2))² (p-1)(p²+4p+4) = 16p²-48p+36 p³+3p²-4 = 16p²-48p+36 Therefore, arriving at a polynomial equation. p³-13p²+48p-40 = 0 It implies; p = 5 p = 2(2+√(2)) p = 2(2-√(2)) Considering p = 5 And; x² = p Therefore; x² = 5 x = ±√(5)

Rainbow Clothing (Second Part)

https://onlineedumath.websites.co.in/update/rainbow-clothing-second-part/1804919

Short Story for Kids written by: Vanessa Weber. …One day, before finishing the school year, a Count came to the school to announce that there was going to be a ball in the palace, in honour of the new graduates and that they must attend without exception. The Girls in school went crazy. They started to call the best dressmakers to make the dresses of wealthy students before the ball. They wanted to be radiant because they all knew that the Count had a handsome son and that no girl in town had...

Mathematics Question and Solution

https://onlineedumath.websites.co.in/update/mathematics-question-and-solution/1803443

Let a be the side of the square. cos30 = b/8 b = 4√(3) cm. sin30 = c/8 c = 4 cm. a = b+12 a = (12+4√(3)) cm. Area Square is; a² = (12+4√(3))² = 358.27687752661 cm² d² = 12²+4²-2*4*12cos30 d = 8.76707255797 cm. (8.76707255797/sin30) = (12/sine) e = 180-43.18678543201 e = 136.81321456799° f = 360-e-180 f = 43.18678543201° g² = 8²+8.76707255797²+2*8*8.76707255797cos43.18678543201 g = 6.21165708246 cm. (6.21165708246/sin43.18678543201) = (8.76707255797/sinh) h = 75° i = 120-75 i = 45...

Best Friends

https://onlineedumath.websites.co.in/update/best-friends/1802129

Short Story for Kids written by: Catalina. Once upon a time, there were two friends called Vela and Lily, who were always together until one day, due to a study commission in class, Vela was sent to sit beside another girl who was called Poppy. They soon laughed together, and when Lily went to Vela´s house she was with Poppy, laughing and playing. Poppy didn't even noticed when Lily arrived. So Lily went home really sad, looked at the picture of them playing in the park, then went to bed and d...

Mathematics Question and Solution

https://onlineedumath.websites.co.in/update/mathematics-question-and-solution/1802109

Let the square side be 2 units. Area square is; 2² = 4 square units. Calculating Area A. a² = 2²+1²-2*2*1cos45 a = √(5-2√(2)) units. (√(5-2√(2))/sin45) = (2/sinb) b = asin(√(2)/(√(5-2√(2))))° c = 180-asin(√(2)/(√(5-2√(2)))) c = 106.3249499369° Area A is; Are sector with radius 2 units and angle 45° - Area triangle with height 2 units and base sin45° - Area sector with radius 1 unit and angle (asin(√(2)/(√(5-2√(2)))))° = (45π*4/360) - (½*2*sin45) - (asin(√(2)/√(5-2√(2)))π/360) = ½(π...

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Mathematics Question and Solution

Mathematics Question and Solution

Mathematics Question and Solution

Mathematics Question and Solution

Mathematics Question and Solution

Mathematics Question and Solution

Rainbow Clothing (Second Part)

Mathematics Question and Solution

Best Friends

Mathematics Question and Solution

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