Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2497237

Let a be half AB. b = ½(3+7+2) b = 6 units. It implies; 6² = a²+c² c² = 36-a² c = √(36-a²) units. d = ½(7) d = 3.5 units. e = 4-3.5 e = 0.5 units. Therefore; c² = 0.5²+f² f² = 36-a²-0.25 f² = 35.75-a² f = √(35.75-a²) units. Calculating a, radius of the red half circle (half AB). a² = f²+3.5² a² = √(35.75-a²)²+3.5² 2a² = 35.75+12.25 2a² = 48 a² = 24 a = 2√(6) units. Again, a is the radius of the red half circle (half AB). It implies; AB = 2a AB =...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2496487

a² = 12²+5² a = √(144+25) a = 13 cm. a is AD. 12b+5b+13b = 12*5 30b = 60 b = 2 cm. b is the radius of the inscribed circle. tanc = 12/5 c = atan(12/5)° tan(0.5c) = 2/d ⅔ = 2/d d = 3 cm. d is AB. e = 12-2 e = 10 cm. Let CD = f f+3f = 13 4f = 13 f = ¼(13) cm. Again, f is CD. g = 3*¼(13) g = ¼(39) cm. g is AC. h = g-3 h = ¼(39-12) h = ¼(27) cm. h is BC. j = (180-2atan(12/5))° k² = 2(¼(39))²-2(¼(39))²cos(180-2atan(12/5)) k = ½(15) cm. Area green...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2495869

tana = 1/2 a = atan(1/2)° b = 180-2a b = (180-2atan(½))° Notice! Radius of the inscribed circle is 1 unit. Area yellow is; Area triangle with height 2 units and base 1 unit - Area square with side 1 unit + Area quarter circle with radius 1 unit - Area sector with radius 1 unit and angle (180-2atan(½))° + Area triangle with height 1 unit and base (180-2atan(½)) units. = (½*2*1)-(1*1)+(0.25π*1*1)-((180-2atan(½))π*1*1/360)+(0.5*1*1sin(180-2atan(½))) = 1-1+0.7853981634-1.107148...

Mathematics Question and Solution.

https://onlineedumath.com/update/mathematics-question-and-solution/2495838

Calculating the area of the inscribed square. a = ½(45) a = 22.5° b = ½(180-45) b = ½(135) b = 67.5° cos22.5 = 6/c c = 6.4943532018 units. Let d be the side length of the inscribed square. e² =2d² e = √(2)d unit. e = 1.4142135624d units. (√(2)d/sin45) = (f/sin67.5) f = 1.847759065d units. (g/sin45) = (d/sin67.5) g = 0.7653668647d units. d is; c = f+g 1.847759065d+0.7653668647d = 6.4943532018 2.6131259297d = 6.4943532018 d = 2.4852813743 units. Again, d i...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2493984

sin30 = a/6 a = 3 units. b = 6+2a b = 12 units. Let the side length of the inscribed regular pentagon be c. Calculating c. d² = 2c²-2c²cos108 108° is the single interior angle of the regular pentagon. d = 1.6180339887c units. e²+(0.5c)² = (1.6180339887c)² e = 1.5388417685c units. tan60 = 0.5c/f f = 0.2886751346c units. It implies; e+f = b 1.5388417685c+0.2886751346c = 12 1.8275169031c = 12 c = 6.5662867357 units. Again, c is the side length of the inscribed r...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2493882

Radius of the half circle is 5 units. 5² = 4²+a² a = 3 cm. tanb = 4/3 b = atan(4/3)° c = 2b c = 2atan(4/3)° 5² = 3²+d² d = √(25-9) d = 4 cm. tane = 3/4 e = atan(3/4)° f = 2e f = 2atan(3/4)° Shaded Area is; Area sector with radius 5 cm and angle 2atan(4/3)° - Area triangle with height 5 cm and base 5sin(2atan(4/3)) cm - Area sector with radius 5 cm and angle 2atan(3/4)° + Area triangle with height 5 cm and base 5sin(2atan(3/4)) cm. = (2atan(4/3)π*5*5/360)-(0.5...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2493854

a = 180-2(70) a = 40° a is angle ACB. b = 180-2a b = 180-80 b = 100° b is angle AOC. Let r be the radius of the circle. Calculating r. Observing Cosine Rule. 9² = 2r²-2r²cos100 81 = 2.3472963553r² r² = 81/2.3472963553 r = √(34.5077858686) r = 5.874332802 cm.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2493834

Calculating r, radius of the circle. a = (12-r) units. It implies; r² = 5²+(12-r)² r² = 25+144-24r+r² 24r = 169 r = (169/24) units. r = 7.0416666667 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2492951

Calculating length AB. Let a be the radius of the inscribed semi circle. b = 180-45 b = 135° c² = 12²+5²-2*5*12cos45 c = 9.1731775442 units. d = c+a d = (9.1731775442+a) units. e = 12+5 e = 17 units. Calculating a. 17² = a²+(9.1731775442+a)² 289 = a²+84.1471862574+18.3463550884a+a² 2a²+18.3463550884a-204.8528137426 = 0 Resolving the quadratic equation. a = 6.52481 units. f = 2a+c f = 2(6.52481)+9.1731775442 f = 22.2227975442 units f is CD = AB. AB = 22...

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 =...

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