Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3145973

Calculating r, radius of the half circle. Let the two equal lengths be a each. Therefore; r = 2a units. Calculating a. (2a)² = a²+9²-2a*9cosb 3a² = 81+18acosb cosb = (3a²-81)/(18a) cosb = (a²-27)/(6a) --- (1). cosb = 3/a --- (2). Equating (1) and (2). (a²-27)/(6a) = 3/a a²-27 = 18 a² = 45 a = √(45) a = 3√(5) units. Therefore r, radius of the half circle is ; Recall. r = 2a And a = 3√(5) units. r = 2(3√(5)) r = 6√(5) units. r = 13.416407865 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3145292

Calculating shaded area. tana = 5/10 a = atan(½)° Therefore; b = atan(2)° c = 90-2a c = 90-2atan(½) c = 36.8698976458° d = 180-2b d = 180-2atan(2) d = 53.1301023542° Shaded Area is; Area square with length 10 cm - 2(area triangle with height 10 cm and base 5 cm) - Area sector with radius 10 cm and angle 36.8698976458° - Area sector with radius 5 cm and angle 53.1301023542°. = 10²-2(½*10*5)-(36.8698976458π*10²/360)-(53.1301023542π*5²/360) = 100-50-32.1750554396-...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3145287

Calculating x. a = 2*120 a = 240° b = 360-a b = 120° c = ½(180-120) c = 30° d = 2*140 d = 280° e = 360-d e = 80° f = ½(180-80) f = 50° It implies; x = c+f x = 30+50 x = 80°

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3145283

Notice. r is the radius of the inscribed yellow half circle. r = ½(10) r = 5 units. Calculating R, radius of the ascribed circle. Calculating R. a = x+10+5 a = (x+15) units. b = ½(a) b = ½(x+15) units. b is the radius of the ascribed circle. c = a-2x c = 15+x-2x c = (15-x) units. d = ½(c) d = ½(15-x) units. Calculating x. b² = d²+5² (½(15+x))² = (½(15-x))²+5² ¼(225+30x+x²) = ¼(225-30x+x²)+25 60x = 100 6x = 10 x = (5/3) units. Recall. b = ½(15+x) And x = (5/3) units. b = ½(15+(5/3))...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3144604

Let AC = BD = DE = a. Calculating a. 14² = a²+(10+a)²-2a(10+a)cosb 96 = 2a²+20a-(20a+2a²)cosb --- (1). 14² = a²+10²+2a*10cosb 96 = a²+20acosb cosb = (96-a²)/(20a) --- (2). Substituting (2) in (1). 96 = 2a²+20a-(20a+2a²)(96-a²)/(20a) Therefore; a = 6 units. Recall. cosb = (96-a²)/(20a) at (2). And a = 6 units. cosb = (96-36)/120 b = acos (½) b = 60° Therefore; Area ABD is; ½*6*(10+6)sin60 = 24√(3) square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3144599

Calculating Purple Area. tanb = 2/1 b = atan(2)° tanc = ½ c = atan(½)° d = 180-b d = (180-atan(2))° e = 180-d-c e = 180-(180-atan(2))-atan(½) e = (atan(2)-atan(½))° It implies; (1/sin(atan(2)-atan(½))) = (f/sin(180-atan(2))) f = 1.490711985 units. Therefore area purple is; 2-2(0.5*1*1.490711985sin(atan(0.5)) = 2-(2/3) = 1⅓ square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3144596

Let 1 unit be the side length of the green square. Therefore; EN = ½ units. a = (1+2x) units. a is the diameter of the bigger circle. b = ½(a) b = ½(1+2x) units. b is the radius of the bigger circle. c = b-2x c = ½(1+2x)-2x c = ½(1-2x) units. It implies; (½(1+2x))² = (½)²+(½(1-2x))² ¼(1+4x+4x²) = ¼+¼(1-4x+4x²) 1+4x+4x² = 1+1-4x+4x² 8x = 1 x = ⅛ units. Recall. b = ½(1+2x) And x = ⅛ units. b = ½(1+2*⅛) b = ½(1+¼) b = ⅛(5) units. b = 0.625 units. Calcula...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3143806

R ~ (a+b) r ~ a Cross Multiply. aR = r(a+b) R/r = (a+b)/a R/r = 1+(b/a) And R/r = phi (golden ratio) Let phi be x. x-1 = b/a a/b = 1/(x-1) Where x (phi) is; x = ½(1+√(5)) a/b = 1/(½(1+√(5))-1) a/b = 1/(½(√(5)-1)) a/b = 2/(√(5)-1)

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3143803

Calculating Area A Divided By Area B (A/B). Let a be the two equal lengths. b = (3-a) units. c² = 4²+3² c = 5 units. Therefore; Calculating a. 5 ~ (3-a) 4 ~ a Cross Multiply. 5x = 12-4a 9a = 12 a = ⅓(4) units. Recall. b = 3-a And a = ⅓(4) units. b = 3-⅓(4) b = ⅓(5) units. d²+(4/3)² = (5/3)² d² = ⅑(25-16) d = √(9/9) d = 1 unit. Area B is; ½*d*a = ½*1*(4/3) = ⅔ square units. Area A is; ½*3*4-Area B = ½(3*4)-⅔ = 6-⅔ = ⅓(18-2) = ⅓(16) square units. Therefore; A/B is; ⅓(16)÷⅔ = (16/...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3143801

Let DC = 1 unit. a = 180-36+30 a = 114° a is angle BDC. (1/sin36) = (b/sin114) b = 1.55421636402 units. b is BC. c = 180-60-54 c = 180-114 c = 66° c is angle BAC. Therefore; (1.55421636402/sin66) = (d/sin(54)) d = 1.37638192047 units. d is AB. It implies; DC ÷ AB = 1÷1.37638192047 = 0.72654252801

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