Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3236878

Sir Mike Ambrose is the author of the question. Showing that brown area ÷ smaller octagon area = a/b. Let the side length of the smaller regular octagon be 1 units. a = ⅛*180(8-2) a = 135° a is the single interior angle of the regular octagons. 2b² = 1² b² = ½ b = ½√(2) units. c = 1+2b c = 1+2*½√(2) c = (1+√(2)) units. c is the height of the smaller regular octagon. Area smaller regular octagon is; (2(½(1+(1+√(2))))*½√(2))+(1*(1+√(2))) = (2+√(2))*½√(2)+(1+√(2)...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3235654

Sir Mike Ambrose is the author of the question. Calculating the exact hatched area. Let x be the radius of the inscribed circle. 2x² = a² a = √(2)x cm. b = x+a b = (x+√(2)x) cm. c = 16+b c = (16+x+√(2)x) cm. c is the diagonal of the ascribed square. Again. c² = 2(16)² c = 16√(2) cm. Therefore, calculating x. Equating the both c. (16+x+√(2)x) = 16√(2) (1+√(2))x = (16√(2)-16) x = (48-32√(2)) cm. x = 16(3-2√(2)) cm. x = 2.74516600406 cm. Again, x is the radi...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3235646

Calculating Shaded Area (Trapezoid). It implies; ½ ~ 1 ½√(3) ~ x. Where x is the base of the blue shaded trapezium. Cross multiply. ½(x) = ½(√(3)) Therefore x = √(3) units. Therefore area blue (area trapezium) is; ½*½(½√(3)+√(3)) = ¼*½(3√(3)) = ⅜√(3) square units. = 0.64951905284 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3235639

Calculating Length x. a = 180-45 a = 135° Length x is; x² = (½*5√(2))²+(½*7)²-(½*5√(2)*½*7*2cos135 x = √(½*25+¼*49-½*35√(2)cos135) x = √((50+49-70√(2)cos135)/4) x = ½√(99-70√(2)cos135) x = ½√(169) x = ½(13) x = 6.5 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3233059

Kindly move the question right/left one time to review the framework/analysis. Thank you nicely. Calculating area circle. Let the radius of the circle be r. r²=2²+(r-1)² r²=4+r²-2r+1 r = 2.5 units. Again, r is the radius of the circle. Therefore; Area circle is; π(2.5)² = 6.25π square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3233055

Calculating x, radius of the big inscribed green circle. Radius, r of the bigger inscribed red circle is; 2(1-r)²=(2r)² r²+2r-1=0 r = (√(2)-1) units. Therefore radius, x of the big inscribed green circle is; x+2(√(2)-1)=1 x = 1 - 2(√(2)-1) x = 1-2√(2)+2 x = (3-2√(2)) units. x = 0.17157287525 units.

Great Mathematician Paul Erdös

https://onlineedumath.com/update/great-mathematician-paul-erdos/3232501

Paul Erdös (1913-1996). Erdös lived a nomadic, possession-less life, moving from university to university, from colleague's spare room to conference hotel. He rarely published alone, preferring to collaborate – writing about 1,500 papers, with 511 collaborators, making him the second-most prolific mathematician after Euler. As a humorous tribute, an "Erdös number" is given to mathematicians according to their collaborative proximity to him: No 1 for those who have authored papers with him;...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3232174

Calculating Area Green. Let z be the width of the ascribed rectangle. Let y be the length of the ascribed rectangle. ½(az) = 22 a = 44/z cm. ½(by) = 48 b = 96/y cm. c = y-44/z c = (yz-44)/z cm. d = z-96/y d = (zy-96)/y cm. It implies; ½((yz-44)/z)((zy-96)/y) = 12 24zy = (yz-44)(zy-96) 24zy = (zy)²-140zy+4224 (zy)²-164zy+4224 = 0 Let zy = e. e²-164e+4224 = 0 Calculating e. (e-82)² = -4224+(-82)² (e-82)² = -4224+6724 (e-82)² = 2500 e = 82±√(25...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3232171

Sir Mike Ambrose is the author of the question. Calculating area red/area square. Let the single side length of the ascribed square be 2 units. Therefore; Area square is; 2*2 = 4 square units. Area Red is; (3/10) square units. It implies; Area Red ÷ Area Square is (3/10) ÷ 4 = 3/40

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3231294

Let Alpha be x. Calculating tanx. Angle ABD = Angle ACD = y. Let AB = AC = a. Let AD = b. b² = a²+10²-2a*10cosy b² = a²+100-20acosy --- (1). b² = a²+6²-2a*6cosy b² = a²+36-12acosy --- (2). cosy = a/10 --- (3). Equating (1) and (2). a²+100-20acosy = a²+36-12acosy 64 = 8acosy 8 = acosy cosy = 8/a --- (4). Substituting (3) in (4). 8/a = a/10 a² = 80 a = √(80) a = 4√(5) units. cosc = 4√(5)/10 c = acos(⅕(2√(5)))° Calculating alpha (x). 180 = 2acos...

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Mathematics Question and Solution

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Mathematics Question and Solution

Mathematics Question and Solution

Mathematics Question and Solution

Great Mathematician Paul Erdös

Mathematics Question and Solution

Mathematics Question and Solution

Mathematics Question and Solution

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