Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3360637

Calculating r/R Let R = 2 units. tana = 1/2 a = atan(½)° b = 90-a b = atan(2)° tan(0.5atan(2)) = r/c ½(1+√(5))-1 = r/c ½(√(5)-1) = r/c c = 2r/(√(5)-1) c = ½(1+√(5))r units. d = 2-c d = ½(4-(1+√(5))r) units. e = (2+r) units. f = (2-r) units. Calculating r. (2+r)² = (2-r)²+(½(4-(1+√(5))r))² 4+4r+r² = 4-4r+r²+¼(16-8r(1+√(5))+2√(5)r²+6r²) 8r = ¼(6r²+2√(5)r²)+¼(16-8r(1+√(5)) 8r = ½(3r²+√(5)r²)+4-2r(1+√(5)) 16r = 3r²+√(5)r²+8+ -4r(1+√(5)) (3+√(5))r²...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3359796

Calculating r, radius of the inscribed circle. tana = 10/5 a = atan(2)° sin30 = r/b b = 2r units. c = (10-r) units. Calculating r. (10-r)² = 5²+(2r)²-10*2rcos(30+atan(2)) 100-20r+r² = 25+4r²+1.19830521758r 3r²+21.19830521758r-75 = 0 It implies; r ≠ -9.65534 units. r = 2.58924 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3358858

Calculating r, radius of the circle. a = 3+17+4 a = 24 units. a is the diameter of a half circle. b = ½(a) b = 12 units. b is the radius of the half circle. c = (12-r) units. d = ½(17) d = 8.5 units. e = 12-3-8.5 e = 12-11.5 e = 0.5 units. f²+8.5² = r² f = √(r²-72.25) units. Calculating r. (12-r)² = √(r²-72.25)²+0.5² 144-24r+r² = r²-72.25+0.25 144-24r = -72 24r = 144+72 24r = 216 4r = 36 r = 9 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3358036

Sir Mike Ambrose is the author of the question. Calculating Area Blue ÷ Area Red Exactly. Let the ascribed quarter circle radius be 4 units. Therefore; Area blue is; Area triangle with two side 1 unit and 3 units, and angle 2asin(1/3)° = ½*3sin(2asin(1/3)) = 0.94280904158 square units. Area red is; Area triangle with two side 1 unit and 3 units, and angle (180-2asin(1/3))° + Area triangle with two side 2 units and √(44/3) units, and angle 100.02498786° = ½*3sin(180...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3357429

Calculating Area Inscribed Blue Square. a² = 4²-2² a = √(12) a = 2√(3) units. b = 2a b = 4√(3) units. Let x be the side length of the inscribed blue square. x+c+c = 4 x+2c = 4 --- (1). d = ½(x+2c) units. 4² = (x+c)²+(½*x)² 16 = x²+2xc+c²+¼(x²) 64 = 5x²+8xc+4c² --- (2). At (1). x+2c = 4 x = (4-2c) --- (3). Calculating c. Substituting (3) in (2). 64 = 5(4-2c)²+8(4-2c)c+4c² 64 = 5(16-16c+4c²)+32c-16c²+4c² 64 = 80-80c+20c²+32c-16c²+4c² 64 = 80-48...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3357212

Calculating Area Green. Let r be the radius of the ascribed quarter circle. a²+1² = r² a² = r²-1 a = √(r²-1) cm. a is the diameter of the white inscribed circle. b = ½(a) b = ½√(r²-1) cm. b is the radius of the white inscribed circle. Therefore, area green is; Area ascribed quarter circle - Area inscribed white circle. ¼(r²)π-(½√(r²-1))²π = ¼(πr²)-¼(πr²)+¼(π) = ¼(π) cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3356333

Calculating Area S, Yellow Area. a = 20 units. a is the radius of the quarter circle. b = 2a b = 40 units. c²+20² = d² d = √(c²+400) units. e = 7+d e = (7+√(c²+400)) units. Calculating c. cosx = (7+√(c²+400))/40 --- (1). cosx = 20/√(c²+400) --- (2). Equating (1) and (2) to get c. (7+√(c²+400))/40 = 20/√(c²+400) Cross Multiply. 800 = 7√(c²+400)+c²+400 (400-c²)² = 49(c²+400) 160000-800c²+c⁴ = 49c²+19600 c⁴-849c²+140400 = 0 (c²-(849/2))² = -140400...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3355583

Calculating x. a² = 24²+x² a = √(x²+576) units. a is the diameter of the ascribed circle. b = ½(a) b = ½√(x²+576) units. b is the radius of the circle. c = (x-11) units. d = ½√(x²+576)-7+½√(x²+576) d = (√(x²+576)-7) units. Calculating x. 7*(√(x²+576)-7) = 11*(x-11) 7√(x²+576)-49 = 11x-121 7√(x²+576) = 11x-72 49(x²+576) = 121x²-1584x+5184 49x²+28224 = 121x²-1584x+5184 72x²-1584x-23040 = 0 9x²-198x-2880 = 0 x²-22x-320 = 0 (x-11)² = 320+(11)² (x-...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3354926

Calculating area yellow. 12 ~ a (12+6) ~ 6 Cross Multiply. 12*6 = 18a a = 4 units. Therefore, yellow area is; ½*12*6 - ½*4*6 - ½*6*3 = ½(72-24-18) = ½(72-42) = ½(30) = 15 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3354036

Sir Mike Ambrose is the author of the question. Calculating Area Green Total. Area green total exactly in decimal cm² is; Area triangle with two side (12-6√(3)) cm each and angle 60° + Area triangle with side 3.46410161514 cm and 2.5358983849 cm, and angle 60° + Area triangle with side 6 cm and 3.10582854123 cm, and angle 45° = 1.11920087684 + 3.80384757735 + 6.58845726812 = 11.5115057223 cm²

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Mathematics Question and Solution

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