Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2771070

Calculating angle x. Let BC be 2 units. a = 180-70-40 a = 70° a is angle ACB. cos70 = 1/b b = 2.9238044002 units. b is AB. c = 180-80-50 c = 50° c is angle ADC. d = ½(b) d = 1.4619022001 units. d is AY = DY. cos50 = e/2.9238044002 e = 1.8793852416 units e is CX = DX. f² = 1²+1.8793852416²-2*1*1.8793852416cos(70+50) f = 2.5320888863 units. f is MX. (2.5320888863/sin120) = (1/sing) g = 20° g is angle CXM. h² = 1.8793852416²+1.4619022001²-2*1.4619022001*...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2771049

Sir Mike Ambrose is the author of the question. Let the side length of the regular hexagon be 1 unit. Therefore; Area green is; Area regular hexagon with side 1 unit + Area regular pentagon with side 1 unit + Area square with side 1 unit + Area square with side ½√(3) units. = (6/4tan(180/6)) + (5/4tan(180/5)) + 1² + (½√(3))² = 2.59807621135 + 1.72047740059 + 1 + (3/4) = 6.06855361194 space units. Area red is; Area triangle with two side 1 unit and ½√(3) units, and angle 1...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2769787

Calculating radius of the quarter circle. Let a be the radius of the quarter circle. b = ½(DE) b = 2√(2) units. c²+(2√(2))² = a² c² = a²-8 c = √(a²-8) units. d = c-BE d = (√(a²-8)-5) units. e = c-CD e = (√(a²-8)-3) units. It implies; Calculating a. 2√(2) - (√(a²-8)-5) (√(a²-8)-3) - 2√(2) Cross Multiply. 8 = (√(a²-8)-3)(√(a²-8)-5) 8 = a²-8-8√(a²-8)+15 8√(a²-8) = a²-1 64(a²-8) = a⁴-2a²+1 64a²-512 = a⁴-2a²+1 a⁴-66a²+513 = 0 Resolving the above quadratic...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2769445

Calculating r. a = (2+r) units. b = (1+r) units. c = r+r c = 2r units. It implies; (2r)² = (1+r)²+(2+r)²-2(1+r)(2+r)cos60 4r² = 1+2r+r²+4+4r+r²-(2+3r+r²) 4r² = 2r²+6r+5-2-3r-r² 3r² = 3r+3 r²-r-1 = 0 (r-½)² = 1+(-½)² (r-½)² = (5/4) r = ½±√(5/4) r = ½±½√(5) It implies; r ≠ ½(1-√(5)) r = ½(1+√(5)) units (golden ratio). r = 1.6180339887 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2769438

Let x be 2 units. Therefore; Area square is; 8² = 64 square units. Calculating area rectangle. The length is; √(8²+6²) + 2cos(atan(4/3)) = 10+(6/5) = 56/5 units. The width is; 2sin(atan(4/3)) = 8/5 units. Area rectangle is; (56/5)*(8/5) = 448/25 square units. It implies; Area rectangle : Area square is; (448/25) : 64 = 448 : (25*64) = 56 : (25*8) = 14 : (25*2) = 7 : 25

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2769428

Area yellow is; Area triangle with two side (6√(65)/7) cm and 7.95918367347 cm, and angle acos(7/√(65))° = ½*(6√(65)/7)*7.95918367347sin(acos(7/√(65))) = 13.6443148688 cm² Area blue is; Area trapezium with two parallel side 5.34693877547 cm and 7.95918367347 cm, and height 4.57142857142 cm. =0.5*4.57142857142*(5.34693877547+7.95918367347) = 0.5*4.57142857142*13.3061224489 = 30.4139941689 cm² Therefore; Area Yellow ÷ Area Blue exactly in decimal is; 13.6443148688 ÷ 3...

Mathematics Question and Solution.

https://onlineedumath.com/update/mathematics-question-and-solution/2768639

a = ⅕*180(5-2) a = 108° a is the single interior angle of the regular pentagon. b = ⅙*180(6-2) b = 120° b is the single interior angle of the regular hexagon. c+90+(180-30)+2(108) = 180(5-2) c+90+150+216 = 540 c+456 = 540 c = 540-456 c = 84° d = a-c d = 108-84 d = 24° Therefore, the required angle, x is; x = b-d x = 120-24 x = 96°

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2768075

Sir Mike Ambrose is the author of the question. Area orange exactly in its decimal form is; Half area square with side 12 units - Area triangle with height 12 units and base 12tan15 units - Area triangle with two side 5.56921938165 units and 5.379452833 units, and angle 45° = ½(12²) - ½(12*12tan15) - ½(5.56921938165*5.379452833)sin45 = 72 - 19.292341855 - 10.5922308261 = 42.115427319 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2768035

Let a be the radius of the inscribed blue circle. b = (24-a) units. c = ½(24) c = 12 units. Therefore, Calculating a. a²+12² = (24-a)² a²+144 = 576-48a+a² 48a = 432 a = 9 units. Again, a is the radius of the inscribed blue circle. Area inscribed blue circle is; πa² = π(9²) = 81π square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2768026

Calculating shaded area (triangle BCE). Let a be the side length of the square. 5² = a²+3²-2*3*acosb 25 = a²+9-6acosb 16 = a²-6acosb --- (1). 8² = a²+3²-2*3*acos(90-b) 64 = a²+9-6a(cos90cosb+sin90sinb) 55 = a²-6asinb --- (2). Dividing (2) by (1). 55/16 = 1+tanb tanb = ((55/16)-1) b = atan(39/16) b = 67.6937949451° b is angle CBE. (8/sin67.6937949451) = (3/sinc) c = 20.3001576321° d = 180-b-c d = 92.0060474228° Therefore, shaded area (triangle BCE) is; ½*3*...

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