Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3120902

Let the radius of the red circle be r. Calculating r. It will be; √(13²-5²)=√((9+r)²-(9-r)²)+√((4+r)²-(4-r)²) 12=√(36r)+√(16r) 12=10√(r) √(r)=1.2 r=1.44 units. Calculating angle PQR considering triangle PQR. It will be; Cos–¹((13²+5.44²-10.44²)/(2x13x5.44)) = 50.6923518839 Therefore length RX will be; √(4²+5.44²-2x4x5.44cos50.6923518839) = 4.24551165713 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3120587

Sir Mike Ambrose is the author of the question. Let the radius of the inscribed semi circle be 1 unit. Therefore; Shaded area ÷ Rectangle area in it's simplest decimal form will be; (0.25π-((180-2tan–¹(0.5))xπ÷360)+(0.5sin(180-2tan–¹(0.5)))) ÷ 2 = 0.0782494456 ÷ 2 = 0.0391247228 Or (1-(¼(4-π))-((180-2tan–¹(0.5))π÷360)+(0.5sin(180-2tan–¹)))÷2 = 0.0782494456 ÷ 2 = 0.0391247228

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3120582

Sir Mike Ambrose is the author of the question. Let the radius of one of the two equal circles be 1 unit. Total shaded area ÷ Rectangle area will be; (½(2x4)-π-(1-¼(4-π)-((180-2tan–¹(0.5))π÷360)+(0.5sin(180-2tan–¹(0.5)))))÷(2x4) = (4-π-(¼(π)-((180-2tan–¹(0.5))π÷360)+(0.5sin(180-2tan–¹(0.5)))))÷8 = (4-π-0.0782494456)÷8 = 0.78015790081÷8 = 0.0975197376

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3120539

Let x be the radius of the sector. b = (x-1) units. c = x+b c = x+(x-1) c = (2x-1) units. Therefore; 5*3 = (2x-1)*1 15 = 2x-1 2x = 16 x = 8 units. Again, a is the radius of the sector. Recall. b = (x-1) And x = 8 units. b = 8-1 b = 7 units. Calculating angle a. 8² = 7²+5²-2*7*5cosa 64 = 49+25-70cosa 70cosa = 74-64 cosa = 10/70 cosa = 1/7 Calculating sina. Notice. At cosa = 1/7 1 is adjacent. 7 is hypotenuse. Calculating opposite, let it be...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3120306

x ~ 7 7 ~ y Cross Multiply. y = 49/x units. Notice. 7 units is the radius of the green inscribed half circle. x = 5 units. x is the radius of the red inscribed half circle. Therefore; y = 49/5 units. y = 9.8 units. a = 7+5 a = 12 units. a is the width of the ascribed rectangle. b = 7+9.8 b = 16.8 units. b is the length of the ascribed rectangle. It implies; Area rectangle is; a*b = 12*16.8 = 201.6 square units. Let alpha be d. Calculating secd...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3120267

tana = 3/1.5 a = atan(2)° b = 3+1.5 b = 4.5 units. c = 3+1+x c = (4+x) units. Calculating x. It implies; tan(atan(2)) = c/b 2 = (4+x)/4.5 2 = (4+x)/(9/2) 2 = 2(4+x)/9 18 = 8+2x 10 = 2x x = 5 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3120259

Notice. Calculating the required angle, alpha. 4 units is the radius of the quarter circle. It implies; 3² = 4²+4²-2*4*4cosa 9 = 32-32cosa 32cosa = 32-9 a = acos(23/32) a = 44.0486256741° b = ½(180-a) b = 67.975687163° c = 90-b c = 22.024312837° d² = 4²+2²-2*4*2cos22.024312837 d = 2.273236245 units. It implies, the required angle, alpha is; Let it be f. (2.273236245/sin22.024312837) = (4/sine) e = 41.2886037977 f = 180-e f = 138.7113962023° Again, f...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3120233

Calculating area of the red inscribed circle. Let a be the radius of the blue ascribed circle. πa² =144π a² = 144 a = 12 cm. b = 2a b = 24 cm. b is the diameter of the blue ascribed circle. 2c² = 24² c² = 12*24 c = 12√(2) cm. c is the side length of the inscribed square. Let y be the radius of the red inscribed circle. d = 2y cm. d is the diameter of the red inscribed circle. 2e² = (2y)² e² = 2y² e = √(2)y cm. f = ½(e) f = ½√(2)y cm. g = 12√(2)-f g = ½(2...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3120228

a = ½(2+7) a = 4.5 units. a is the radius of the ascribed half circle. Let b be the radius of the inscribed circle. c = (4.5-2b) units. d = (4.5-b) units. e = 4.5-2-b e = (2.5-b) units. Calculating b. 4.5 ~ (4.5-b) (4.5-2b) ~ (2.5-b) Cross Multiply. 4.5(2.5-b) = (4.5-2b)(4.5-b) 11.25-4.5b = 20.25-4.5b-9b+2b² 2b²-9b+9 = 0 (b-¼(9))² = -(9/2)+(-9/4)² (b-¼(9))² = (81/16)-(9/2) (b-¼(9))² = (9/16) b = (9/4)±√(9/16) b = (9/4)±(3/4) Therefore; b ≠ 3 units....

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3120171

Let the side length of the regular heptagon be 1 unit. Calculating angle x. a = ⅐*180(7-2) a = ⅐(900)° a is the single interior angle of the regular heptagon. b = ½(360-2*⅐(900)) b = 180-⅐(900) b = ⅐(360)° c = ⅐(900)-90 c = ⅐(270)° sin(⅐(270)) = d/1 d = 0.62348980186 units. e = 1+2d e = 2.24697960372 units. f = ⅐(360)-⅐(270) f = ⅐(90)° Therefore, the required angle, x is; x = 180-g Calculating g. (2.24697960372/sing) = (1/sin(⅐(90))) g = 30° It imp...

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