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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2752561

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Calculating x, the length that form tangents of the two semi circles. x²+2²=6² x²=36-4 x²=32 x = √(32) cm. x = 4√(2) cm. Therefore; Area blue is; Area trapezium with two parallel length 2 cm and 4 cm, and height 4√(2) cm - Area triangle with two length 4 cm each and angle atan(2√(2)) - Area triangle with two length 2 cm each and angle (90+ atan(1/(2√(2))) = ½(2+4)*4√(2) - ½(4²)sin(atan(2√(2))) - ½(2²)sin(90+ atan(1/(2√(2)))) = 12√(2) - 7.54247233266 - 1.88561808316 = 7.54...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2752553

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Shaded area is; Area square with side 1542 units - Area equilateral triangle with side 1542 units - 2(area sector with radius 1542 units and angle 30°) = 1542² - ½(1542)²sin60 - 2(30÷360*1542²π) = 2377764 - 594441√(3) - 396294π = 103167.66684 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2752547

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Calculating R, radius of the bigger circle. R²=(R-1)²+(R-2)² R²-6R+5=0 Therefore; R ≠ 1 units. R = 5 units. Its diameter is 10 units. Calculating r, radius of the big circle. It will be; ½(2R-2) = ½(2*5-2) = ½(8) = 4 units. Therefore shaded area/area yellow is; Area circle with radius 5 units - Area circle with radius 4 units. = 5²π - 4²π = π(25-16) = 9π square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2752542

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Calculating AB, the diameter of the circle. Let it be x. Sin(atan(⅓)) = √(6²+2²)/x Sin(atan(⅓)) = √(40)/x x = √(40)/sin(atan(⅓)) x = 20 cm. x is AB. Therefore length AC is; AB - 2 AC = 20 - 2 AC = 18 cm. Or Let AC be x. 2 ~ 6 6 ~ x Cross Multiply. 2/6 = 6/x 2x = 36 x = 18 cm. AC = 18 cm.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2751959

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a = 180-100-50 a = 30° (20/sin100) = (b/sin30) b = 10.1542661189 cm  c = ½(180-100) c = 40° Let d be the radius of the circle. tan40 = d/e e = 1.1917535926d . f = (10.1542661189-1.1917535926d) units. g = 180-50 g = 130° sin(0.5*130) = d/h h = 1.103377919d cm. Calculating d. cos(0.5*130) = (10.1542661189-1.1917535926d)/1.103377919d 10.1542661189-1.1917535926d = 0.4663076582d 1.6580612508d = 10.1542661189 d = 10.1542661189/1.6580612508 d = 6.1241803427 cm....

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2750886

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Total red area is; 3(area square with side 5 units - area quarter circle with radius 5 units) + Area triangle with height 5 units and base 10 units - Area sector with radius 5 units and angle 2atan(½)° - Area triangle with two side 5 units each, and angle (180-2atan(½))°. = 3(25-¼(25π)+½(50)-(2atan½÷360*25π)-½(25)sin(180-2atan½) = 75-18.75π+25-11.591190225-10 = 19.5039475202 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2750870

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Sir Mike Ambrose is the author of the question. Let the side length of the square be x. Calculating x. 18²=x²+(x-6)² 324=x²+x²-12x+36 2x²-12x-288=0 x²-6x-144=0 (x-3)²=144+9 x = 3±√(153) x ≠ 3-3√(17) x = 3+3√(17) cm. Therefore; Area R to 1 d. p. in square cm is; Area trapezoid with two parallel length 6 cm and (3+3√(17)) cm, and height (3+3√(17)) cm - 2(area triangle with height 10.6846584374 cm and width 6 cm) - Area sector with radius 12 cm and angle 58.633022225. = ½...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2750863

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Please, move the above question left/right one time to review the solution of the question. Thank you.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2750851

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Calculating x. a = 4+1 a = 4 units. a is the radius of the quarter circle. b²+4² = 5² b = √(25-16) b = 3 units. tanc = 3/4 c = atan(3/4)° d = 90-c d = atan(4/3)° It implies; x² = 5²+5²-2*5*5cos(atan(4/3)) x = 4.472135955 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2750843

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Sir Mike Ambrose is the author of the question. Let the single side length of the inscribed regular pentagon be 2 units. Therefore; Area green is; Area rectangle with length 2 units and width 1.17557050458 units. = 2 * 1.17557050458 = 2.35114100916 square units. Area red is; Area regular pentagon with side length 2 units - Area triangle with two side 2 units each, and angle 108° - Area triangle with side 2 units and 0.7639320225 units, and angle 72° = ((10*2)/(4tan(180/...
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