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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2390478

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Calculating Area Blue Plus Area Orange. Radius of the congruent four semi circles is 1 unit each. (a-1)²+1² = 2² a²-2a+2 = 4 a²-2a-2 = 0 Resolving the above quadratic equation via completing the square approach to get a. (a-1)² = 2+(-1)² a-1 = ±√(3) a = 1±√(3) It implies; a ≠ 1-√(3) a = 1+√(3) units. a = 2.7320508076 units. a is the side length of the square. Area Blue Plus Area Orange is; Area square with side (1+√(3)) units - 4(area semi circle with radius 1 unit) = (1+√(3))²-4(0.5π*1...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2390412

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Calculating x, side length of the regular pentagon. a = ⅕(180(5-2)) a = ⅕(180*3) a = 108°  a is the single interior angle of the regular pentagon. b = ½(180-108) b = 36° c = 108-36 c = 72° d = 45-36 d = 9° e = 180-72-9 e = 180-81 e = 99° f² = 2x²-2x²cos108 f² = 2x²+0.6180339887x² f² = 2.6180339887x² f = 1.6180339887x units. It implies; Observing Sine Rule. (1.6180339887x/sin99) = (1/sin9) 1.6180339887xsin9 = sin99 x = sin99/(1.6180339887sin9) x = 3.9021130327 units. Or (1/sin9) = (g/...

We are smart and clever!

https://onlineedumath.com/update/we-are-smart-and-clever/2389414

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Online Edumath Educators and Learners are Super Smart and Amazingly, Very Clever. Communicate us to mentor/teach/educate your child/children Mathematics online at affordable tuition, helping them become a lover of Mathematics, and also, a Mathematician. Call/WhatsApp: +2349076614992 or +2348152827445 Email: [email protected] [email protected] [email protected] Facebook Page: Online Edumath We are super smart and amazingly, very clever!

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2389376

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Let the radius of the red inscribed circle be r. Calculating r. 2a² = 6² a = √(18) a = 3√(2) units. 2b² = 8² b = √(32) b = 4√(2) units. c² = 6²+8² c = √(36+64) c = 10 units. 10² = 2d² d² = 50 d = √(50) d = 5√(2) units. d is the radius of the yellow ascribed semi circle. (5√(2))² = e²+(4√(2))² e² = 50-32 e = √(18) e = a =  3√(2) units. f = b-e f = 4√(2)-3√(2) f = √(2) units. f is length OD. g = d-r g = (5√(2)-r) units. h² = 2r² h = √(2)r units. It...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2389021

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Calculating yellow area. 2² = 2a²-2a²cos120 Where a = regular hexagon side length. 120° = single interior angle of the regular hexagon. It implies; 4 = 3a² a = (2/√(3)) units. a = 1.1547005384 units. Again, a is the side length of the regular hexagon. b = 4-2a b = 4-2(1.1547005384) b = 1.6905989232 units. Therefore; c² = 1.6905989232²+1.1547005384²-2*1.6905989232*1.1547005384cos60 c = 1.4964366227 units. c is the side length of one of the two equal lengths of the yellow area. (1.496436...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2388366

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Calculating r, radius of the quarter circle. a = (r-2) units. Therefore; r² = b²+(r-2)² r²-(r²-4r+4) = b² b² = 4r-4 b = √(4r-4) units. c = (r-4) units. Therefore; r² = d²+(r-4)² r²-(r²-8r+16) = d² d² = 8r-16 d = √(8r-16) units. e² = 2r² e = √(2)r units. It implies; e² = f²+2² (√(2)r)²-2² = f² f² = 2r²-4 f = √(2r²-4) units. Notice; b+d = f √(4r-4)+√(8r-16) = √(2r²-4) (4r-4)+2√((4r-4)(8r-16))+(8r-16) = 2r²-4 12r-16+2√((4r-4)(8r-16)) = 2r² 2√((4r-4)(8r-16)) = 2r²-12r+16 √((4r-4)(8r-16)) = r²-...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2387550

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Notice, the ascribed quadrilateral is regular (square). Calculating Area Blue. a² = 4²+8² a = √(16+64) a = √(80) a = 4√(5) units. b = ½(a) b = ½(4√(5)) b = 2√(5) units. tanc = 4/8  c = atan(½)° d = 90-c d = 90-atan(½) d = atan(2)° e² = (2√(5))²+8²-2*2√(5)*8cos(atan(2)) e² = 20+64-32 e² = 84-32 e² = 52 e = √(52) e = 2√(13) units. f = ½(e) f = ½(2√(13)) f = √(13) units. (2√(13)/sin(atan2)) = (8/sing) g = 82.8749836511° h = 180-g h = 180-82.8749836511 h =...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2387055

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Let the two equal lengths be 1 unit. a = 100-60-20 a = 100° (b/sin20) = (1/sin100) b = 0.3472963553 units. c = 360-120+100 c = 360+220 c = 140° It implies; d² = 1+0.3472963553²-2*0.3472963553cos140 d = 1.2855752193 units. Therefore, the required angle x, is; (1.2855752193/sin140) = (0.3472963553/sinx) x = 10°

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2386932

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Calculating Orange Area. Notice, radius of the three congruent circles is 2 units each. Orange Area is; Area semi circle with radius 2 units + Area equilateral triangle with side 2 units + 2(area semi circle with radius 2 units) - 3(area sector with radius 2 units and angle 60°) = ½(2²)π+½(2²sin60)+2(½(2²)π)-3(60π*2²/360) = 2π+√(3)+4π-2π = 4π+√(3) square units. Or Calculating Orange Area. Notice, radius of the three congruent circles is 2 units each. Orange Area is; Area equilateral t...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2386810

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Calculating angle x. Let the base of the quadrilateral be 1 unit. a = 180-64+86 a = 30° (1/sin86) = (b/sin64) b = 0.9009888098 units. (c/sin30) = (1/sin86) c = 0.501220949 units. d = 180-8-84 d = 180-92 d = 88°  (0.501220949/sin88) = (e/sin84) e = 0.4987790509 units. f² = 0.4987790509²+0.9009888098²-2*0.4987790509*0.9009888098cos94 f = 1.0598385285 units. (1.0598385285/sin94) = (0.9009888098/sing) g = 58° h = 180-8-58 h = 180-66 h = 114° It implies, the required angle x, is; x = 180-...
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