Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3139965

Notice. The ascribed quadrilateral is a square. Let it's side length be x. a²+x² = 3² a = √(9-x²) units. 2 ~ 3 b ~ x Cross Multiply. b = ⅓(2x) units. It implies; Calculating x. x²-½(x*√(9-x²)) = ½(x+⅓(2x))*x 2x²-x√(9-x²) = ⅓(5x)*x 2x-√(9-x²) = ⅓(5x) x = 3√(9-x²) x² = 81-9x² 10x² = 81 x = ⅒(9√(10)) units. x = 2.84604989415 units. Again, x is the side length of the square. cosc = 2.84604989415/3 c = 18.434948823° sin18.434948823 = d/2 d = 0.63245553204 units. e = x-d e = 2.8...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3139219

Let OA be 1 unit. Area Triangle AOB is; ½*1*1 = ½ square units. Calculating Area Triangle ODG. a² =2(1)²-2(1)²cos30 a = √(2-√(3)) units. a = 0.51763809021 units. a is AC, the side length of the big square. b² = 2(0.51763809021)² b = 0.73205080758 units. b is AD, the diagonal of the big square. c² = 1²+0.73205080758²-2*0.73205080758cos120° c = 1.50597117916 units. c is OD. (1.50597117916/sin120) = (1/sind) d = 35.1039093611° d is angle ADO e = 180-35.1039093611-120 e = 24.8960906389° e...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3139214

Let a = 1 unit. It implies; 1 ~ b b ~ e Cross Multiply. e = b² f = (1-b²) units. cos60 = g/(1-b) g = ½(1-b) units. h = 2g+1 h = (2-b) units. It implies; Calculating b. (2-b)² = (1-b²)²+1²-2(1-b²)cos120 4-4b+b² = 1-2b²+b⁴+1+1-b² 1-4b+4b² = b⁴ b⁴+0b³-4b²+4b-1 = 0 It implies; b ≠ 1 unit. b ≠ -(1+√(2)) units. b = (√(2)-1) units. b = 0.41421356237 units. Recall. e = b² e = (√(2)-1)² e = (3-2√(2)) units e = 0.17157287525 units. It impl...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3139211

Calculating length RT. a = ½(10) a = 5 units. a is half the diagonal of the rectangle. b = 8+a b = 13 units. It implies; (RT)²+5² = 13² RT = √(169-25) RT = √(144) RT = 12 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3139208

Calculating x, length BE. a = 90-75 a = 15° a is angle CBE. sin15 = b/x b = (xsin15) units. b is CE. c = 5+b c = (5+(xsin15)) units. c is CD. cos15 = d/x d = (xcos15) units. d is BC. Notice. c = d (5+(xsin15)) = (xcos15) 5 = xcos15-xsin15 x(cos15-sin15) = 5 x = 5/(cos15-sin15) x = 5/(½√(2)) x = 5√(2) units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3138420

Let the length of the rectangle be a. Let the width of the rectangle be (6+b) units. ½(2a-4)(6+b)-70 = ½(6a)+½(a-4)b 12a+2ab-24-4b-140 = 6a+ab-4b 6a+ab = 164 Therefore; a(6+b) = 164 Notice. a is the length of the rectangle. (6+b) is the width of the rectangle. Therefore; Length*Width = a(6+b) = 164 It implies; Area Rectangle = 164 cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3138417

Let the side length of the square be x. a = (x-4) units. Calculating x. ½(x²) = ½*x(x-4)-10+30 x² = x(x-4)+40 x² = x²-4x+40 4x = 40 x = 10 units. Again, x is the side length of the square. Area Square is; x² = 10² = 100 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3138413

Calculating R, radius of the circle. 12a = 3*4 a = 1 unit. b = ½(3+4) b = 3.5 units. c = b-3 c = 0.5 units. d = 180-60 d = 120° e² = R²-3.5² e =√(R²-12.25) units. f² = 1²+0.5²-2*1*0.5cos120 f = ½√(7) units. f = 1.32287565553 units. (1.32287565553/sin120) = (1/sing) g = 40.8933946491° h = 90+g h = 130.8933946491° R is; R² = √(R²-12.25)²+1.32287565553²-2*1.32287565553*√(R²-12.25)cos130.8933946491 10.5 = 1.73205080756√(R²-12.25) (10.5)² = (1.732050807...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3137623

Calculating R, radius of the quarter circle. a = 3+4 a = 7 units. b² = 2(4)² b = 4√(2) units. c = R-b c = (R-4√(2)) units. d = 180-45 d = 135° R is; R² = 7²+(R-4√(2))²-2*7(R-4√(2))cos135 R² = 49+R²-8√(2)R+32+7√(2)(R-4√(2)) 8√(2)R = 81+7√(2)R-56 √(2)R = 25 R = ½(25√(2)) units. R = 17.6776695297 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3137622

Let BF be a. b² = 18²+a² b = √(324+a²) units. b is AB. c = (a+14) units. It implies; calculating a. (a+14) ~ √(324+a²) √(324+a²) ~ 18 Cross Multiply. 18(a+14) = 324+a² 18a+252 = 324+a² a²-18a+72 = 0 a²-12a-6a+72 = 0 a(a-12)-6(a-12) = 0 (a-12)(a-6) = 0 It implies; a ≠ 12 units. a = 6 units. Again, a is BF. Recall. b = √(324+a²) And a = 6 units. b = √(324+36) b = √(360) b = 6√(10) units Again, b is AB. Recall Again. c = (a+14) And a = 6 units. c = 6+14 c = 20 units Again, c is BH. I...

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