Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2449394

Let the square side be 1 unit. Let r be the radius of the semi circle. Calculating r. c² = 2(1)² c = √(2) units. c is the diagonal of the square. tand = 1/0.5 d = atan(2)° e = 180-d-45 e = (135-atan(2))° sin(135-atan(2)) = r/f f = r/sin(135-atan(2)) f = 1.0540925534r units. (0.5/sin(135-atan(2))) = (g/sin(atan(2))) g = 0.4714045208 units. It implies; r+f+g = c r+1.0540925534r+0.4714045208 = √(2) 2.0540925534r = √(2)-0.4714045208 2.0540925534r = 0.9428090416...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2447638

a = (1+x) units. a is the diameter of the semi circle. b = ½(a) b = ½(1+x) units. b is the radius of the semi circle. c = x units. c is the radius of the quarter circle. Notice! A-B = π A = B+π B = A-π It implies; Calculating x. It is; Area semi circle with radius ½(1+x) units - Area B + Area A - ½(area quarter circle with radius x units) = ½(area quarter circle with radius x units) ½(½(1+x))²π-B+A-½*¼(x²)π = ½*¼(x²)π ⅛(1+2x+x²)π-(A-π)+A-⅛(x²)π = ⅛(x²)π ⅛π+¼(x)π+π = ⅛(x...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2446965

Let a be 1 unit. (1/sin45) = (c/sin75) c = 1.3660254038 units. d = 75+45 d = 120° e = 60-15 e = 45° Calculating b. (b/sin15) = (1.3660254038/sin45) b = 0.5 units. Therefore; a/b is; 1÷0.5 = 1÷½ = 1*2 = 2

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2446155

a² = 3²+4² a = √(25) a = 5 units. 2b² = 5² b² = (25/2) b = √(25/2) b = ½(5√(2)) units. b is the radius of the semi circle. c = 90+45 c = 135° (½(5√(2))/sin135) = (3/sind) d = 36.8698976462° e = 180-135-36.8698976462 e = 8.1301023538° (f/sin8.1301023538) = (0.5*5√(2)/sin135) f = 0.7071067812 units. g² = 2r² g = √(2)r units. r is the radius of the inscribed circle. Calculating r. (0.5(5√(2))-r)² = (√(2)r)²+0.7071067812² 12.5-5√(2)r+r² = 2r²+0.5 r²+5√(2)r-12 = 0 Resolving the quadratic eq...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2445325

r = ½(7) units. r is the base radius of the cylinder. H = 6 units. H is height. h = 10-6 h = 4 units. h is height. Therefore, volume of the cylinder is; πr²H+½(πr²h) = π*(7/2)²*6+½*π*(7/2)²*4 = π((147/2)+(49/2)) = ½(196)π = 98π cubic units. = 307.8760800518 cubic units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2444750

Calculating R, radius of the circle. b = 360-240 b = 120° b is the angle that is subtended by the 9 units chord with the radius of the circle. R, radius of the circle is; Observing Cosine Rule. 9² = 2R²-2R²cos120 81 = 3R² R² = 27 R = √(27) R = 3√(3) units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2444722

Let the side length of the regular octagon be 1 unit. Notice! x, radius of the green inscribed circle is 1 unit. a = ⅛*180(8-2) a = ⅛(1080) a = 135° a is the single interior angle of the regular octagon. y² = 2-2cos135 y = √(√(2)+2) units. y = 1.847759065 units. y is the radius of the bigger circle ascribing the green circle. Therefore, the fraction of the bigger circle shaded is; Area green circle ÷ Area bigger circle πx² ÷ πy² = x²÷y² = 1²÷√(√(2)+2)² = 1÷(√(2)+2) = (√(2)-2)/(-2) = ½(2-...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2444075

a = 10 units. a is the radius of the circle. b = (20-2x) units. c = ½(b) c = ½(20-2x) c = (10-x) units. It implies; Calculating x. 10² = 2c² 100 = 2(10-x)² 100 = 200-40x+2x² 2x²-40x+100 = 0 x²-20x+50 = 0 Resolving the above quadratic equation via completing the square approach to get x. ( x-10)² = -50+(-10)² ( x-10)² = 50 x-10 = ±√(50) x = 10±5√(2) It implies; x ≠ 10+5√(2) x = 10-5√(2) units. x = 2.9289321881 units. The length, y of the side of the square is;...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2443798

Let the square side length be a. b² = 2a² b = √(2)a units. b is AC = BD, the diagonal of the square, ABCD. c = x units. d = (3-x) units. Calculating x, observing similar plane shape (right-angled) side length ratios. c - d 12 - 9 It implies; x - (3-x) 12 - 9 Cross Multiply. 9x = 12(3-x) 9x = 36-12x 21x = 36 x = (12/7) units. d = (3-x) And x = (12/7) units. d = 3-(12/7) d = ⅐(21-12) d = (9/7) units. Calculating a. It implies; b = √(9²+(9/7)²)+√(12²+(12/7)²) √(2)a = √(81+(81/49))+√(144+(1...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2443509

Notice! The composite figure (plane shape) is not drawn to scale. Let the side length of triangle ABC (equilateral triangle) be 1 unit. 1² = 2a²-2a²cos120 1 = 3a² a = √(1/3) a = ⅓√(3) units. a is the radius of the bigger circle. b = 2a b = ⅔√(3) units. b is the diameter of the bigger circle. Let c be the radius of the smaller circle. d = b-c d = (⅔√(3)-c) units. Therefore, calculating c. sin30 = c/d ½ = c/(⅔√(3)-c) 2c = ⅔√(3)-c 6c = 2√(3)-3c 9c = 2√(3) c = ⅑(2√(3)) units. c = 0.3849001...

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