Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2259284

Let BC be a (square side). tanb = 1/2 b = atan(½)° sinatan(½) = c/a c = 0.4472135955a d = 2c d = 0.894427191a d is CE. ((½)a)² = 2²+e² e² = (a²/4)-4 e = √(¼(a²-16)) e = ½√(a²-16) f = e+(a/2) f = ½√(a²-16)+(a/2) f = ½(√(a²-16)+a) f is CF. It implies; Observing Pythagoras Rule. d² = 2²+f² (0.894427191a)² = 4+(½(√(a²-16)+a))² 0.8a² = 4+¼((a²-16)+2a√(a²-16)+a²) 0.8a² = 4+¼(a²-16)+½(a√(a²-16))+¼(a²) 0.8a²-½(a²) = ½(a√(a²-16)) 1.6a²-a² = a√(a²-16) 0.6a² = a√(a²-16) 0.6a = √(a²-16) 0.36a² = a²-...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2259044

Calculating PQ. a = 8+2 a = 10 cm. a is the diameter, AC of the semi circle. b = ½(AC) b = ½(10) b = 5 cm. b is the radius of the semi circle. c = b-2 c = 5-2 c = 3 cm. 5² = 3²+d² d² = 25-9 d = √(16) d = 4 cm. d is the radius of the circle. 4² = 5²+5²-2*5*5cose 50cose = 50-16 cose = (34/50) e = acos(17/25)° f = 2e f = 2acos(17/25)° It implies; Length PQ is; (PQ)² = 5²+5²-2*5*5cos(2acos(17/25)) (PQ)² = 50-50cos(2acos(17/25)) (PQ)² = 53.76 PQ = √(53.76) PQ = 7.3321211119 cm. PQ = 7.33 cm...

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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2258577

Area S, exactly in square unit is; Area triangle with height 2 unit and base (2sin120) unit + Area triangle with height 2 unit and base 2√(2) unit - Area sector with radius 2 unit and angle (30+atan(√(2)))° = (½*2*2sin120) + (½*2*2√(2)) - (4π*(30+atan(√(2)))÷360) = √(3) + 2√(2) - (π(30+atan(√(2)))/90) square unit. = 4.56047793232 - 2.95783078745 = 1.60264714487 square units. ≈ 1.60 square units to 2 decimal places.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2258428

Notice. The green circles are congruent (their radius is equal). Let it be r. Calculating r. a = (1-r) units. b = (1+r) units. c = (1-r-r-r) = (1-3r) units. It implies; Observing Pythagoras Rule. b² = a²+c² (1+r)² = (1-r)²+(1-3r)² 1+2r+r² = 1-2r+r²+1-6r+9r² 4r = 1-6r+9r² 9r²-10r+1 = 0 Resolving the above quadratic equation observing factorization approach. 9r²-9r-r+1 = 0 9r(r-1)-1(r-1) = 0 (9r-1)(r-1) = 0 Therefore; r ≠ 1 unit. r = ⅑ units. It implies, radius of the green congruent cir...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2257715

Calculating Red Area. tana = 5/10 a = atan(½)° b = 2a b = 2atan(½)° tanc = 10/5 c = atan(2)° d = 2c d = 2atan(2)° It implies; Area Red is; Area sector with radius 5 units and angle 2atan(2)° - (2(area triangle with height 10 units and base 5 units)-area sector with radius 10 units and angle 2atan(½)°) - 2(Area quarter circle with radius 5 units-area triangle with height and base 5 units respectively) = (2atan(2)π*5*5/360) - (2(0.5*10*5)-(2atan(½)π*10*10/360)) - 2((¼*π*5*5)-½*5*5) = 27.6...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2257504

a² = 2*6² a² = 72 a = 6√(2) cm. a is diagonal of the square. Let r be the radius of the inscribed circle. It implies; b² = 2r² b = √(2)r cm. Therefore; 4+r+b = a 4+r+√(2)r = 6√(2) Calculating r. (1+√(2))r = 6√(2)-4 r = (6√(2)-4)/(1+√(2)) r = ((6√(2)-4)(1-√(2)))/(-1) r = (6√(2)-12-4+4√(2))/(-1) r = (10√(2)-16)/(-1) r = 2(8-5√(2)) cm. r = 1.8578643763 cm exactly in decimal.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2256984

Area Orange is; 87/10 square unit. Please, move the above question/figure left, one time to review the solution. Thank you.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2256354

Radius, r of one of the five congruent, inscribed circles is; 8r²+√(3)r-1=0 r = (√(35)-√(3))/16 m. Therefore; Total area of the five congruent, inscribed yellow circles is; 5πr² = 5π( (√(35)-√(3))/16)² = 5π(35-2√(105)+3)/256 = 5π(38-2√(105))/256 = 5π(19-√(105))/128 m² = 1.07416074883 m²

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Mathematics Question and Solution

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Mathematics Question and Solution

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Mathematics Question and Solution

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