Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3121510

Let the radius of the ascribed quarter circle be R. Let the radius of the inscribed circle be r. Therefore; 2²+(2r)²=R² 4+4r²=R² Therefore; R²-4r²=4 Multiplying through by ¼(π). It implies; ¼(πR²) - πr² = π Notice. ¼(πR²) = area of the ascribed quarter circle. πr² = area of the inscribed circle. Therefore area of the red shaded region in the given quarter circle is; π square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3121350

a = (10+x) units. a is the radius of the half circle. (10+10)² = 16²+b² b = √(400-256) b = √(144) b = 12 units. It implies; 12 ~ c 20 ~ 10 Cross Multiply. 20c = 120 c = 6 units. d = 21-6 d = 15 cm. e = 2d-21 e = 30-21 e = 9 units. Calculating x. x*(10+10+x) = 21*9 x²+20x = 189 x²+20x-189 = 0 x²+27x-7x-189 = 0 x(x+27)-7(x+27) = 0 (x+27)(x-7) = 0 Therefore; x = 7 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3121237

Let the radius of the circle be a. sinb = a/(a+a) b = 30° cos30 = c/2a c = √(3)a units. d = 2-c d = (2-√(3)a) units. sin30 = e/d e =½(2-√(3)a) units. cos30 = f/d ½√(3) = f/(2-√(3)a) f = ½(2√(3)-3a) units. g = a+a+a g = 3a units. h = f+g h = ½(2√(3)-3a)+3a h = ½(2√(3)+3a) units. h is the diameter of the half circle. j = ½h j = ¼(2√(3)+3a) units. j is the radius of the half circle. k = a+j k = a+¼(2√(3)+3a) k = ¼(2√(3)+7a) units. l = j-a l = ¼(2√(3)...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3121010

Sir Mike Ambrose is the author of the question. Area S exact, or to 3 d.p. will be; Area sector of radius 2√(7) units and angle (180 - 2sin–¹(4sin120÷(2√(7)))) + area triangle of two lengths 2 units and 4 units respectively and angle they form, 120° - area sector of radius 2√(7) units and angle 60° - area triangle of lengths 2√(7) units and 2 units, and angle they form, (180-(60+sin–¹(4sin120÷(2√(7)))) = (28πx(180 - 2sin–¹(4sin120÷(2√(7))))÷360) + (4sin120) - (28πx60÷360) - (2√(7)x(180...

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/3120654

Kindly move the question left/right one time to review the solution. Thank you nicely.

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...

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Mathematics Question and Solution

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Mathematics Question and Solution

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Mathematics Question and Solution

Mathematics Question and Solution

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