Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/1809528

Blue area is; ½(2.5)²π - (180-2atan(3/4))π(2²)/360 + 0.5*2²sin(180-2atan(3/4)) - (180-2atan(4/3))π(1.5)²/360 + 0.5*1.5²sin(180-2atan(4/3)) + ½(4*3) - 2atan(4/3)π(1.5²)/360 + 0.5(1.5²)sin(2atan(4/3)) - 2atan(3/4)π(2²)/360 + 0.5(2²)sin(2atan(3/4)) = 9.81747704247-3.70918087201+1.92-1.44787749478+1.08+6-2.0864142405+1.08-2.57400443517+1.92 = 12 Area Blue = 12 square units.

Mathematics Question and Solution

https://onlineedumath.websites.co.in/update/mathematics-question-and-solution/1809129

Blue area is; 8(area quarter circle with radius 4 cm - area triangle with height and base 4 cm respectively - area quarter circle with radius 2 cm + area triangle with height and base 2 cm respectively) 8(¼(4²)π-½(4²)-¼(2²)π+½(2²)) = 8(4π-8-π+2) = 8(3π-6) = 24(π-2) cm²

Poor Kid, Rich Kid

https://onlineedumath.websites.co.in/update/poor-kid-rich-kid/1808812

Short story for kids. Charlie was an eight year old boy who was obedient, humble and dedicated. His father was a carpenter and his mother was a housewife and they barely had any money to eat because his father barely had any work in the village. Charlie went to school in the village every day. He was a very smart kid, always getting high results. He was top of his class even if he only studied a little. Michael was also eight years old. He was the son of a landowner that owned property at abou...

Mathematics Question and Solution

https://onlineedumath.websites.co.in/update/mathematics-question-and-solution/1808093

Let the side of the regular pentagon be 1 unit. Calculating Area Red. a² = 1²+1²-2*1*1cos108 a = 1.61803398875 units. b = 108-36-60 b = 12° (c/sin12) = (1.61803398875/sin96) c = 0.33826121272 unit. d = 1-c d = 0.66173878728 unit. e = 96-60 e = 36° tan36 = f/0.66173878728 f = 0.48078137139 unit. Area Red is; ½(df) = 0.5*0.48078137139*0.66173878728 = 0.15907584083 square units. Calculating Area Lilac. sin36 = 0.48078137139/g g = 0.81795412443 units. h = 1-f h = 0.51921862861 unit....

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)

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