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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2689749

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Sir Mike Ambrose is the author of the question. Area purple exactly in decimal is; Area triangle with height 5cm and base 7.5cm - Area triangle with height 3cm and base 7.5cm - Area triangle with side 2cm and 1.89765856604cm, and angle at an(3/2)° - Area triangle with side 4.26973177358cm and 4.84664832643cm, and angle (at an(⅔)-atan(2/5))° = ½(5*(15/2)) - ½(3*(15/2)) - ½(2*1.89765856604)sin(atan(3/2)) - ½(4.26973177358*4.84664832643)sin(atan(⅔)-atan(2/5)) = 7.5 - 1.57894736843 - 2.13...

Mathematics teacher and she

https://onlineedumath.com/update/mathematics-teacher-and-she/2689196

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Sir Mike Ambrose is the author of the question. Notice; The single length of the square is equal the single side length of half the regular hexagon. Let it be 2 units. Therefore area square is; 2² = 4 square units. Area yellow is; Area square with length 2 units - area triangle with height 2 units and base ⅓(2√(3)) units - area triangle with height 2 units and base ⅔ units - area triangle with side (4/3) units and (4sin(atan⅓))/(3sin(120-atan⅓)) units and angle 60° = 4 -...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2687932

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a = 8+10 a = 18 units. a is GK. b² = 18²-9² b = √(243) b = 9√(3) units. b is DK. tanc = 9√(3)/9 c = atan(√(3)) c = 60° d² = 9²+8²-2*8*9cos60 d = √(73) units. d = 8.5440037453 units. d is BD. (8.5440037453/sin60) = (9/sine) e = 65.8175256444° e is angle DBG. It implies; sin65.8175256444 = 9√(3)/f f = 2√(73) units. f = 17.0880074906 units. f is the diameter of the circle. g = ½(f) g = √(73) units. g = 8.5440037453 units. g is the radius of the circle. T...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2687923

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Sir Mike Ambrose is the author of the question. Let the bigger regular pentagon side length be 1 unit. a = √(2-2cos180) a = 1.61803398875 units. b = sin36/sin108 b = 0.61803398875 units. c = √(2*0.61803398875²-2*0.61803398875²cos108) c = 1 unit. It implies; Area Blue is; Area triangle with height 1.61803398875 units and base sin72 units - Area triangle with height 1.61803398875 units and base 0.61803398875sin36. = ½*1.61803398875*sin72 - ½*1.61803398875*0.61803398875s...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2686853

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Let the two congruent lengths be a each. 21² = a²+b²+2abcos135 441 = a²+b²+√(2)ab --- (1) 14² = a²+b²-2abcos45 196 = a²+b²-√(2)ab --- (2) Adding (1) to (2). 637 = 2a²+2b²  b² = ½(637-2a²) --- (3). b = √(½(637-2a²)) --- (4). Substituting (3) and (4) in (1) to get a. 441 = a²+½(637-2a²)+√(2)a√(½(637-2a²)) 441 = a²+½(637-2a²)+a√(637-2a²) 882 = 2a²+637-2a²+2a√(637-2a²) 245 = 2a√(637-2a²) 245² = 4a²(637-2a²) 60025 = 2548a²-8a⁴ 8a⁴-2548a²+60025 = 0 It implies; a =...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2686335

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Area orange exactly in fraction is: Area triangle with height 5√(3) cm and base 5 cm. = ½(5√(3)*5) = ½(25√(3)) cm² = 21.6506350946 cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2686320

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a = ½(5) a = 2.5 units. a is the radius of the inscribed half circle. tanb = 2.5/5 b = atan(1/2)° tan(atan(0.5)) = r/c ½ = r/c c = 2r units. d = 5-c d = (5-2r) units. e = (2.5-r) units. f = (2.5+r) units. Calculating r. (2.5+r)² = (5-2r)²+(2.5-r)² 6.25+5r+r² = 25-20r+4r²+6.25-5r+r² 10r = 25-20r+4r² 4r²-30r+25 = 0 (r-¼(15))² = (-¼(25))+(-¼(15))² (r-¼(15))² = (225/16)-(25/4) (r-¼(15))² = (125/16) r = ¼(15)±¼(5√(5)) It implies; r = ¼(15-5√(5)) units. r =...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2684879

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y = (1+x²)^(-½) Differentiating via chain rule or function of a function rule. Let u = (1+x²) du/dx = 2x Therefore; y = u^(-½) dy/du = -½u^(-3/2) And; dy/dx = (dy/du)*(du/dx) dy/dx = -½u^(-3/2)*2x u = (1+x²) It implies; dy/dx = -½(1+x²)^(-3/2)*2x dy/dx = -x(1+x²)^(-3/2) dy/dx = -x(1/√(1+x²)³) dy/dx = -x/√(1+x²)³ Or  Using quotient rule. Let u = 1 du/dx = 0 Let v = √(1+x²) = (1+x²)^½ Calculating dv/dx via chain rule or function of a function rul...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2684776

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a = ½(5+35) a = 20 units. a is the radius of the ascribed semi circle. b = (20-c) units. d = a-5 d = 20-5 d = 15 units. Therefore; (20-c)² = c²+15² 400-40c+c² = c²+225 175 = 40c c = 35/8 c = 4.375 units. c is the radius of the inscribed pink circle. tane = 15/(4.375) e = atan(24/7)° f = 180-e f = (180-atan(24/7))° g = ½(180-atan(24/7))° sin(½(180-atan(24/7))) = h/4.375 h = 3.5 units. It implies, the required length, x is; x = 2h x = 2*3.5 x = 7 un...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2684412

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Sir Mike Ambrose is the author of the question. Let the big square area be 4 square units. Therefore the bigger square area will be; 16 square units. Area blue is; Area square with length 4 units - area triangle with height 2 units and base 1 unit - area triangle with height 4 units and base 3 units - area triangle with height (16/9) units and base ⅔ units - area triangle with height (16/9) units and base (4/3) units. = 16 - ½(2*1) - ½(4*3) - ½((16/9)*⅔) - ½((16/9)*(4/3)) = 16-...
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