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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3074102

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Sir Mike Ambrose is the author of the question. Let CD = 2 units. Therefore; Calculating AB. AB = 1 + (2sin18*tan72 + 2sin36)tan54 AB = 1 + 3.07768353717tan54 AB = 1 + 4.23606797749 AB = 5.23606797749 units. It implies; Length AB ÷ Length CD to 2 decimal places is;  5.23606797749 ÷ 2 = 2.61803398874  ≈ 2.62

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3072681

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x² = (r+1)² - (r-1)² Therefore x = 2√(r) unit. y² = (r+1)² - (2√(r))² Therefore y = √(r²-2r+1) y = √(r-1)² y = (r-1) unit z = (r+1) - y z = (r+1) - (r-1) Therefore z = 2 units a = r+r Therefore a = 2r units A sincere study and analysis of the composite circles deduced a right-angled triangle with two adjacent sides, 2 units and 2√(r) units respectively, and hypotenuse 2r units. Therefore; Calculating r, the radius of the three congruent circles. (2r)² = 2² + (2√(r)...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3071591

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Area R is; Area sector with radius 8 cm and angle 20.16632290743° - Area triangle with height 8 cm and base (4.2sin 20.16632290743) cm = ( 20.16632290743 *64π÷360) - (½*8*4.2sin 20.16632290743) = 11.26299944816 - 5.79174146157  = 5.47125798659 cm² ≈ 5.47 cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3070480

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Area coloured is; Area sector with radius 3 units and angle 120° - Area triangle with height 3 units and base 3sin120 units + Area triangle with height 3 units and base 3sin60 = (120*9π÷360) - (½*9*½*√(3)) + (½*9*½√(3)) = 3π - ¼(9√(3)) + ¼(9√(3)) = 3π square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3069482

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Shaded area is; Area sector with radius 10 cm and angle 60° (100π*60)/360 = (100π)/6 = ⅓(50π) cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3068717

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Let the side length of the regular heptagon be 1 unit. a = ⅐(180*5) a = ⅐(900)° b = 0.5(360-2(900/7)) b = ⅐(360)° c = 2cos(360/7)+1 c = 2.24697960372 units. d² = 2-2cos(90/7) d = 1.8019377358 units. Where d is the radius of the arc. Area Orange is; 0.5*2.24697960372*1sin(360/7)+0.5*sin(900/7) = 1.26929543856 square units. Let e be alpha. Calculating e. e = 0.5((900/7)-(360/7)) e = ⅐(270)° (1.8019377358/sin(270/7)) = (2.24697960372/sinf) f = 128.96966294...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3067657

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18² = 14²+16²-2*14*16cosa 448cosa = 14²+16²-18² a = acos((14²+16²-18²)/448) a = 73.39845040098° (18/sin73.39845040098) = (14/sinb) b = 48.18968510422° c = 180-48.18968510422-73.39845040098 c = 58.4118644948° cotd = cota+cotb+cotc cotd = 1.80748828181  d = acot(1.80748828181) d = 28.95373454979° e = 58.4118644948-d e = 29.45812994501° f = 180-28.95373454979-73.39845040098 f = 77.64781504923° (14/sin77.64781504923) = (g/sin73.39845040098)  g = 13.73434221224 units....

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3066287

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8 = 4 a = (8-a) Cross multiply. 64-8a = 4a 64 = 12a a = ⅓(16) cm. b = 8-a b = ⅓(8) cm. c = atan(⅔)° d = atan(3/2)° ⅔ = 8/e e = 12 cm ⅔ = f/8 f = ⅓(16) cm. g = 8-f g = ⅓(8) cm. Area Orange exactly in cm² is; Area square units side 8 cm - Area rectangle with length 4 cm and width ⅓(8) cm. = 8² - 4*⅓(8) = 64 - ⅓(32) = ⅓(192-32) = ⅓(160) cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3064529

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Area coloured regions is; Half the area of the ascribed square. = ½(2*2) = 2 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3063189

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Sir Mike Ambrose is the author of the question. Let AC = 2 units. Therefore; AB = ⅖ unit. BC = (8/5) unit. It implies; Area Blue is; Area triangle with height ⅖ unit and base 2sin120 units + Area triangle with height 1 unit and base 0.4√(31)sin111.05172443535 units = (½*⅖*2sin120) + (½*1*0.4√(31)sin111.05172443535) = √(3)/5 + 1.03923048454   = 1.38564064606 square unit. Area Green is; Area triangle with height √(7) units and base 3√(21)/5 units = ½*√(7)...
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