Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2538182

Sir Mike Ambrose is the author of the question. Calculating Yellow Area. It is; Area triangle with height 4sin(atan(⅔)) units and base 8√(13)/9 units - Area triangle with height 1 unit and base ⅔ unit - Area triangle with height ¼ unit and base ⅔ unit = ½*4sin(atan(⅔))*(8√(13)/9) - ½*1*⅔ - ½*¼*⅔ = (32/9)-⅓-(1/12) = (113/36) square units. Area Orange is; Area triangle with height ⅓(10sin(atan(¾))) units and base (5√(13)/9) units. = ½*⅓(10sin(atan(3/2)))*(5√(13)/9) = (25/9) sq...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2536446

Equation of the curve is; y = ⅔(8x-x²) Calculating Area E. (Area under the curve at x = (3/2) and x = 4) - Area trapezium with parallel sides (13/2) units and (10⅔) units, and height (5/3) units. =(835/36) - ½*(5/2)*((13/2)+(32/3)) = (835/36) - (515/24) = (125/72) square units. Calculating Area F. ½(Area under the curve at x = 0 and x = 8) - Area triangle with height (32/3) units and base 4 units - Area triangle with height 6 units and base 8 units - (Area under the curve...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2530541

Notice! The ascribed polygon is a regular dodecagon (12 sides and 12 interior angles equal). It's since interior angle is; a = 180(12-2)/12 a = 1800/12 a = 150° The middle inscribed polygon is a regular octagon (8 sides and 8 interior angles equal). It's since interior angle is; b = ⅛*180(8-2) b = ⅛*(1080) b = 135° The completely inscribed polygon is a regular hexagon (6 sides and 6 interior angles equal). It's since interior angle is; c = ⅙*180(6-2) c = ⅙*(720) c = 120°...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2505441

55+2(90)+270+a = 180(5-2) a+505 = 540 540° is the sum of the interior angles of a pentagon. It implies; a = 540-505 a = 35° tan55 = b/4 b = 5.712592027 cm. c = b-4 c = 1.712592027 cm. tan55 = 8/d d = 5.6016603057 cm. e = d-4 e = 1.6016603057 cm. It implies, area ABCDE is; Area triangle with height 4 cm and base 5.712592027 cm + Area trapezoid with parallel sides 4 cm and 1.712592027 cm respectively and height 1.6016603057 cm. = ½*4*5.712592027+½*(4+1.712592027)*1...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2492054

Calculating equation of the curve. (y-12) = a(x-6)² At x = 0, y = 0 Calculating a. -12 = a*36 a = -⅓ It implies; y-12 = -⅓(x-6)² y = -⅓(x²-12x+36)+12 y = ⅓(-x²+12x-36+36) y = ⅓(12x-x²) Where y = ⅓(12x-x²) is the equation of the curve. Calculating x when y = (32/3). (32/3) = = ⅓(12x-x²) 32 = 12x-x² x²-12x+32 = 0 Calculating x via completing the square approach. (x-6)² = -32+36 x = 6±√(4) x ≠ 6-2 x = 6+2 x = 8 units. Calculating x when y = 0. 0 = ⅓(12x-x²) x² =...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2488540

Shaded region/area is; 2(sector area with radius 2cm and angle 60°) - (equilateral triangle area with sides 2cm each side) + (square area with sides 2cm each side) - (square area with sides 4cm each side - circle area with radius 2cm)/4 - (2(sector area with radius 2cm and angle 60°) - (equilateral triangle area with sides 2cm each side)). Therefore; 2(4π)/6 - (4sin60)/2 + (4) - (16 - 4π)/4 - (2(4π)/6 - (4sin60)/2) = (4π)/3 - √(3) + 4 - (4 - π) - ((4π)/3 - √(3)) = (4π)/3 - √(3) + 4...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2485183

Notice! The regular polygon has 12 sides (regular dodecagon). a = (180(12-2))/12 a = 1800/12 a = 150° a is the single interior angle of the regular dodecagon. b = ½(a) b = 75° c = 90-b c = 15° sin15 = 2/d d = 7.7274066103 cm. tan15 = e/d e = 7.7274066103tan15 e = 2.0705523608 cm. f = 2e f = 4.1411047216 cm. f is the side length of the regular dodecagon. cos15 = d/g g = 7.7274066103/cos15 g = 8 cm. It implies; Painted Area is; Area triangle with height...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2477130

Let x be the single interior angle of the regular polygon. a = 180-x-20 a = (160-x)° b = 180-x-30 b = (150-x)° c = 180(5-2) c = 540° d = 2(360-x)° It implies;. a+b+d+86 = c (160-x)+(150-x)+2(360-x)+86 = 540 396+720-4x = 540 1116-540 = 4x 4x = 576 x = 144° Again, x is the single interior angle of the regular polygon. Calculating n, number of sides of the regular polygon. Sum = 180(n-2) And Sum = xn, where x = 144° It implies; 144n = 180n-360 180n-144n = 360...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2470996

x² = (r+1)² - (r-1)² Therefore x = 2√(r) unit. y² = (r+1)² - (2√(r))² Therefore y = √(r²-2r+1) y = √(r-1)² y = (r-1) unit. z = (r+1) - y z = (r+1) - (r-1) Therefore z = 2 units. a = r+r Therefore a = 2r units. A sincere study and analysis of the composite circles deduced a right-angled triangle with two adjacent sides, 2 units and 2√(r) units respectively, and hypotenuse 2r units. Therefore; Calculating r, the radius of the three congruent circles. (2r)² = 2² + (2√(r))² 4r² = 4 + 4r 4r²...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2436205

(4+5+3)² = 2a² a² = 72 a = 6√(2) cm. a is the congruent adjacent sides of the right-angled triangle. b² = √(72)²+3²-2*√(72)*3cos45 b² = 81-36 b = √(45) b = 3√(5) cm. (3√(5)/sin45) = (3/sinc) c = 18.4349488229° d² = √(72)²+4²-2*√(72)*4cos45 d² = 88-48 d = √(40) d = 2√(10) cm. (2√(10)/sin45) = (4/sine) e = 26.5650511771° f = 90-c-e f = 90-18.4349488229-26.5650511771 f = 45° 2g² = 5² g² = 25/2 g = √(25/2) g = ½(5√(2)) cm. g = 3.5355339059 cm. It implies; Shaded Area is; Area quarter circl...

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