Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3226920

Calculating Area Blue Inscribed Circle. Let a be the radius of the blue inscribed circle. b = (a+5) cm. c = 12-a-5 c = (7-a) cm. d = (16-a-5) d = (11-a) cm. It implies; (a+5)² = (7-a)²+(11-a)² a²+10a+25 = 49-14a+a²+121-22a+a² a²+10a+25 = 170-36a+2a² a²-46a+145 = 0 (a-23)² = -145+(-23)² (a-23)² = 384 a = 23±√(384) a = 23±8√(6) It implies; a ≠ 23+8√(6) units. a = 23-8√(6) units. a = 3.40408205773 units. Area Blue Inscribed Circle is; πa² = π(23-8√(6))²...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3226397

Sir Mike Ambrose is the author of the question. Calculating Exactly Angle Alpha - Angle Beta. Let Alpha be x. Let Beta be y. (6+6√(2))² = 8²+10²-2*8*10cosa 36+72√(2)+72 = 164-160cosa 160cosa = 164-36-72-72√(2) 160cosa = 56-72√(2) 20cosa = 7-9√(2) cosa = (7-9√(2))/20 a = acos((7-9√(2))/20)° a = 106.642318459° 8² = 10²+(6+6√(2))²-2*10(6+6√(2))cosb 64 = 100+36+72√(2)+72-(120+120√(2))cosb (120+120√(2))cosb = 144+72√(2) cosb = (144+72√(2))/(120+120√(2)) cosb = ⅕(3√(2)) b...

Mathematics Question and Solution.

https://onlineedumath.com/update/mathematics-question-and-solution/3226027

Calculating Area Yellow. a = 22+½(24) a = 34 units. Considering a careful, smart analysis of the quarter circle and the inscribed irregular yellow pentagon area. Therefore, yellow area is; 2(area triangle with base ½(24) units and height 34 units) + Area rectangle with length 22 units and base ½(24) units. 2(½*½(24)*34)+(½(24)*22) = (12*34)+(12*22) = 12(34+22) = 12(56) = 672 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3226014

Calculating Area Red Inscribed Square. Let x be the side length of the red square. a = (5-x) cm. b = 5-½(x) b = ½(10-x) cm. Therefore; Calculating x. 5² = (5-x)²+(½(10-x))² 25 = 25-10x+x²+¼(100-20x+x²) 10x-x² = ¼(100-20x+x²) 40x-4x² = 100-20x+x² 5x²-60x+100 = 0 x²-12x+20 = 0 x²-10x-2x+20 = 0 x(x-10)-2(x-10) = 0 (x-10)(x-2) = 0 It implies; x ≠ 10 cm. x = 2 cm. Therefore, area red square is; x² = 2² = 4 cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3225253

Sir Mike Ambrose is the author of the question. Area red in its exact simplest decimal square units form is; Area triangle with height and base 1.24899959968 units and 1.20185042515 units + Area triangle with side ⅔ units and (26/15) units, and angle (75+atan(√(3)/7))° = ½(1.24899959968*1.20185042515) + ½(⅔*(26/15))sin(75+atan(√(3)/7)) = 0.75055534995+0.57767089074 = 1.32822624069 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3224810

Calculating Blue Shaded Area. tana = 10/6 a = atan(5/3)° b = 135-a b = (45+atan(3/5))° (6/sin(45+atan(3/5))) = (c/sin(atan(5/3))) c = 5.3033008589 units. Therefore, required blue area is; ½*6*5.3033008589sin45 = 11.25 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3224804

Calculating Area Triangle APD. Let CP be x. It implies; x ~ 4 9 ~ x Cross Multiply. x² = 36 x = 6 units. a² = 4²+6² a = √(16+36) a = √(52) a = 2√(13) units. a is BC, the width of the ascribed rectangle. b = 9²+6² b = √(81+36) b = √(117) b = 3√(13) units. b is CD, the length of the ascribed rectangle. ½*c*2√(13) = ½*4*6 √(13)c = 12 c = 12/√(13) c = (12√(13)/13) you units. d = b-c d = 3√(13)-(12√(13)/13) d = (39√(13)-12√(13))/13 d = (27√(13)/13) units....

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3224587

Sir Mike Ambrose is the author of the question. Calculating Green Area to 3 significant figures. Notice. 8 cm is the side length of the regular nonagon and also the regular bigger inscribed pentagon. a = ⅑*180(9-2) a = 140° a is the single interior angle of the regular nonagon. b = ⅕*180(5-2) b = 108° b is the single interior angle of the both inscribed regular pentagons. c = 108-½(180-108) c = 72° tan72 = d/(0.5x) d = 1.53884176859x cm. d is the height of the big...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3223465

Calculating x. Let r be the radius of the inscribed green circle. Let R be the radius of the ascribed quarter circle. (R-r)² = r²+5² --- (1). (R-r)²+5² = a² --- (2). a² = x²+r² --- (3). Substituting (3) in (2). (R-r)²+5² = x²+r² (R-r)² = x²+r²-5² --- (4). Substituting (4) in (1). x²+r²-5² = r²+5² x²-5² = 5² x² = 5²+5² x² = 25+25 x² = 50 x = √(50) x = 5√(2) units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3223450

Calculating radius of the semi circle. Radius, r of the semi circle is; Cos(2atan(1/(4+√(7))))=(5+√(7))/d Notice; d = 2r Therefore, d = (5+√(7))/Cos(2atan(1/(4+√(7)))) d = 8 units. And d = 2r 2r = 8 r (radius semi circle) is; 4 units.

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