Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2558853

Notice! Radius, a of the inscribed circle is 4 units. Radius, b of the inscribed semi circle is 7 units. 3²+4² = c² c = √(25) c = 5 units. d² = 5²+4² d = √(41) units. tane = 3/4 e = atan(3/4)° f = 90+e f = (90+atan(3/4))° g² = 2(4)²-2*4²cos(90+atan(3/4)) g = 7.155417528 units. h = ½(180-(90+atan(3/4))) h = 26.5650511771° j = 90-h j = 63.4349488229° k = 180-2j k = 53.1301023542° It implies; Length x is; tan53.1301023542 = 7/x x = 5¼ units. It i...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2558688

Shaded area will be; Area semi circle of radius √(2) cm - area quarter circle of radius 2 cm + area square of single side length √(2) cm. = ½(√(2))²π - ¼(2²)π + (√(2))² = π-π+2 = 2 cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2558651

Shaded area will be; Area quarter circle of radius 2 unit + 2(area quarter circle of radius √(2) unit - area triangle of height and base √(2) unit respectively). = ¼(4π) + 2(¼(2π) - ½(2)) = π + π - 2 = 2(π-1) square units. Or a² = 2(2)² a = √(8) a = 2√(2) units. b = ½(a) b = √(2) units Shaded Area is; Area semi circle with radius √(2) units - Area isosceles right-angled triangle with adjacent sides 2 units each + Area quarter circle with radius 2 units. (½*π*√(2)²)-...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2558608

Let the inscribed square side be a. b² = 2a² b = √(2)a cm. b is the diagonal of the inscribed square. c = 90+45 c = 135° It implies, calculating a, the inscribed square side length. 10² = 5²+(√(2)a)²-2*5*√(2)acos135 100 = 25+2a²+10a 2a²+10a-75 = 0 Resolving the above quadratic equation via completing the square approach to get a, the side length of the inscribed square. (a+(5/2))² = (75/2)+(5/2)² (a+(5/2))² = ¼(150+25) (a+(5/2))² = ¼(175) a = -(5/2)±√(¼(175)) a = -(5...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2558155

tana = 5/8 a = atan(5/8)° b = atan(8/5)° c = 180-45-a c = (135-atan(5/8))° d = (135-atan(8/5))° (e/sin(atan(8/5))) = (3/sin(135-atan(8/5))) e = 2.6108558075 units. (f/sin(atan(5/8))) = (6/sin(135-atan(5/8))) f = 3.2635697593 units. Area Green is; (0.5*8*5)-(0.5*2*2)-(0.5*2.6108558075*3sin45)-(0.5*3.2635697593*6sin45) = 20-2-2.7692307693-6.923076923 = 8.3076923077 square units. Or Area Green is; 0.5(3.2635697593+2.6108558075)*2√(2) = √(2)(5.8744255668) = 8.30...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2557749

a² = 24²+7² a = 25 units. a is DF. b²+20² = a² b² = 25²-20² b = 15 units. b is EF. tanc = 7/24 c = atan(7/24)° c is angle CED. tand = 15/20 d = atan(3/4)° d is EDF. e = 180-c-d e = (180-atan(7/24)-atan(3/4))° e = 126.8698976458° e is angle ADE. f = ½(180-e) f = 26.5650511771° f is angle DAE = angle AED. g = 20+24 g = 44 units. g is AC. Therefore the required length, length AB is; cos26.5650511771 = 44/h h = 22√(5) units. h = 49.193495505 units. h is...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2557552

√(x-2)-√(x+3) = 1 x-2=(1+√(x+3))² x-2=1+2√(x+3)+x+3 -6=2√(x+3) -3=√(x+3) 9=x+3 x=6. Checking accuracy. √(6-2)-√(6+3)=? √(4)-√(9)=? ±2-±3=? ±2+3=? +2+3≠1 Therefore; -2+3=1

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2557528

Let the single side length of the ascribed square be 2 unit. Therefore area of the ascribed square is; 4 square unit. Calculating shaded area (area yellow). It will be; Area square of single side length 2 unit - area circle of radius 1 unit + 8(area quarter of radius ½√(2) unit - area triangle of height and base ½√(2) unit respectively). = 4 - π + 8(¼(½√(2))²π - ½(½√(2))² = 4 - π + 8(⅛(π) - ¼) = 4 - π + π - 2 = 2 square unit. Therefore shaded fraction is; Area yellow (shaded area) ÷ Ar...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2556794

Calculating Area Red/Area Yellow. Let R, radius of the equal circles be 1 unit. Area Yellow is; 2(2(area sector with radius 1 unit and angle 60°) - area regular triangle with side length 1 unit) = 2(2(60π/360)-½*sin60) = 2(⅓(π)-¼(√(3))) = ⅔(π)-½√(3) = ⅙(4π-3√(3)) square units. = 1.2283696986 square units. Area Red is; Area circle with radius 1 unit - Area yellow. = π-⅙(4π-3√(3)) = ⅙(6π-4π+3√(3)) = ⅙(2π+3√(3)) square units. = 1.913222955 square units. Therefore,...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2556760

Notice! AC = 7+7 AC = 14 units. It implies; 14² = 2a² a² = ½(196) a = √(98) a = 7√(2) units. a is the side length of square ABCD. Therefore, shaded area yellow is; Area square with side length 7√(2) units - 2(area quarter circle with radius 7 units). = (7√(2)*7√(2))-2(¼*7*7π) For π = (22/7) = 98-½(22*7) = 98-77 = 21 square units.

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