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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2595268

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Let the side length of the two congruent inscribed squares be 1 unit each. a² = 1+2² a = √(5) units. a is the radius of the half circle. tanb = (½)  b = atan(½)° (√(5)/sin(atan(½))) = (2/sinc) c = 23.5781784782° d = 180-c-atan(½) d = 129.8567703447° e = d-90 e = 39.8567703447° Area B (Area Orange Triangle) is; 0.5*√(5)sin39.8567703447 = 0.716515139 square units. f = 129.8567703447-atan(½) f = 103.2917191676° g = 0.5*√(5)²sin103.2917191676 g = 2.433030278 sq...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2595204

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Let alpha be a. Let AB be b. tana = 2/b --- (1). tana = b/(2+6)  tana = b/8 --- (2). Equating (1) and (2). 2/b = b/8 b² = 16 b = 4 units. Again, b is AB. Therefore, the required angle x (length AD) is; x² = 2²+4² x² = 20 x = √(20) x = 2√(5) units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2595176

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Let a be the radius of the circle. b = 2a units. b is the diameter of the circle. Observing similar plane shape (right-angled) side length ratios. 6 - 2a a - 10 Cross Multiply. 2a² = 60 a = √(30) units. Again, a is the radius of the circle. Area circle is; πa² = π√(30)² = 30π square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2595128

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Let BC be a. Let alpha be b. tanb = 24/a --- (1). tan(2b) = (24+26)/a tan(2b) = 50/a 2tanb/(1-tan²b) = 50/a --- (2). Substituting (1) in (2). 2(24/a)/(1-(24/a)²) = 50/a (48/a)/((a²-576)/a²) = 50/a 48a/(a²-576) = 50/a 24a/(a²-576) = 25/a 24a² = 25a²-(25*576) a² = (25*576) a = 5*24 a = 120 units. a is the required length, BC.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2595049

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Sir Mike Ambrose is the author of the question. Let the single side length of the square be 2 unit. Calculating area S. It is; Area trapezoid of two parallel side lengths 2 unit and (2-√(3)) unit and height 1 unit - area sector of radius 2 unit and angle 60° + area triangle of height √(3) unit and base 2 unit. Notice; √(2²-1²) = √(3) unit. Area S is; ½(4-√(3))-(4π)/6+½(2√(3)) = 2-½(√(3))-⅔(π)+√(3) = (12+3√(3)-4π)/6 square unit. Calculating area R. It is; Area squa...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2595040

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a = 180-30-33 a = 117° b+117+15+33+30+39 = 360 b = 360-180-54 b = 126° c+126+30+9+39+57 = 360 c = 99° d = 180-99-9 d = 180-108 d = 72° e = a-57 e = 117-57 e = 60° f = 180-60-33 f = 87° g = 180-f g = 93° (1/sin33)/(h/sin60) h = 1.5900905886 units. j = 180-15-93 j = 72° (1.5900905886/sin72) = (k/sin93) k = 1.6696288786 units. (1/sin30) = (l/sin57) l = 1.6773411359 units. m = h+l m = 1.5900905886+1.6773411359 m = 3.2674317245 units. (3.26743172...

We are smart and clever!

https://onlineedumath.com/update/we-are-smart-and-clever/2594819

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Please, communicate us for effective Mathematics coaching/teaching/mentoring and learning activities online at affordable tuition.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2593605

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Considering similar triangle (scalene) side length ratios.      n - 1 n+1 - n Cross multiply. Therefore; n²=n+1 n²-n-1=0 (n-½)²=1+¼ n =½±½(√(5)) Therefore; n ≠ ½(1-√(5)) n = ½(1+√(5)) unit.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2593364

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Let length AB be x. A careful analysis carried out on the given composite plane shape lead to the derivation of right-angled tiangle EQX with hypotenuse QX ⅓(4x) and the two adjacent side of the triangle, EQ ⅔(√(3))x and EX (x-1) respectively. Therefore applying Pythagoras rule to get x (length AB). (⅔(√(3))x)² + (x-1)² = (⅓(4x))² (12x²)/9 + x² - 2x + 1 = (16x²)/9 21x² - 18x + 9 = 16x² 5x² - 18x + 9 = 0 Resolving the above quadratic equation via factorization approach. (5x²-15x)...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2593252

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Calculating x (length OD). a = (x+4) units. a is the radius of the quarter circle (length OA = length OB). It implies; (x+4)² = 8²+x² x²+8x+16 = 64+x² 8x = 48 x = 6 units. Again, x is required length OD.
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