Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2763914

Calculating Length AB. cosa = 5/6 a = acos(5/6)° b = 90-a b = (90-acos(5/6))° Therefore, the required length, AB is; cos(90-acos(5/6)) = 2/c Where c is AB. c = 2/cos(90-acos(5/6)) c = 3.6181361349 units. Therefore; AB = 3.6181361349 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2763226

a² = 24²+7² a = 25 units. b = 7+25 b = 32 units. c² = 24²+32² c = 40 units. d = ½(c) d = 20 units. d is the radius of the quarter circle. Therefore, the required length, ? is; Let it be e. e²+20² = 25² e = √(625-400) e = √(225) e = 15 units. Again, e is the required length.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2763213

a = ⅕*180(5-2) a = 108° a is the single interior angle of the ascribed regular pentagon. b = ½(180-108) b = 36° cos36 = (0.5*8)/c c = 4.94427191 units. d² = 2*4.94427191²-2*4.94427191²cos36 d = 3.05572809 units. e = 0.5d e = 1.527864045 units. cos(0.5*108) = 1.527864045/f f = 2.5993575699 units. f is the radius of the inscribed circle. Area inscribed circle is; πf² = π(2.5993575699²) = 21.2266727151 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2763209

Let the radius of the congruent circles be 1 unit. Therefore; Area blue is; 3(area sector with radius 1 unit and angle 60°) - 2(area equilateral triangle with radius 1 unit) = 3(60π/360) - 2(½(sin60)) = ½(π) - ½(√(3)) = ½(π-√(3)) square units. Using r units as radius. Shaded area will be; 3(60πr²/360) - 2(½(r²)sin60) = ½(πr²) - ½(√(3)r²) = ½(π-√(3))r² square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2763206

Calculating r, radius of the circle. r is; (17/2)²+(r-5)²=r² (289/4)+r²-10r+25=r² (289/4)+25=10r (389/4)=10r r = (389/40) mm. r = 9.725 mm.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2762591

Let the side length of the square be 2 units. tana = 2/1 c = atan(2)° d = 2a d = 2atan(2)° Calculating a. a² = 1²+1²-2*1*1cos(2atan(2)) a = 1.788854382 units. e = d-45 e = ((2atan(2))-45)° Calculating b. b² = 2-2cos((2atan(2))-90) b = 0.632455532 units. It implies; a÷b = 1.788854382÷0.632455532 = 2.8284271247

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2762397

Calculating length OB. a² = 6²+2² a = √(40) a = 2√(10) units. a is AC. tanb = 6/2 b = atan(3)° √(40)² = 2√(50)²-2√(50)²cosc 40 = 100-100cosc cosc = 6/10 c = acos(3/5)° c is angle AOC. d = ½(180-c) d = ½(180-acos(3/5)) d = 63.4349488229° d is angle OAC and angle OCA. e = b-d e = atan(3)-63.4349488229 e = 8.1301023542° e is angle OCB. Therefore, the required length, ? (OB) is; Let it be f. f² = √(50)²+2²-2*2√(50)cos8.1301023542 f = 5.0990195136 units. Ag...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2761578

Silver area is; 2(area rectangle with length 6 cm and width 3 cm - area quarter circle with radius 3 cm - area sector with radius 6 cm and angle 30° + area sector with radius 6 cm and angle 60° - area triangle with two length 6 cm each, and angle 60°). = 2((6*3)-¼(9π)-(30*36π÷360)+(60*36π÷360)-½(36sin60)) = 2(18-(9π/4)-3π+6π-9√(3)) = 2(18+(3π/4)-9√(3)) = (36+(3π/2)-18√(3)) cm² = 9.53547444414 cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2761575

Sir Mike Ambrose is the author of the question. Let the length of the two congruent rectangles be x. Let their width be y. Therefore area rectangle is; x * y = xy square units. Area blue is; Area rectangle with length x units and width y units unit - 2(area triangle with height y units and base (y²/x) units). = xy - 2*½(y³/x) = (x²y-y³)/x square units. Area blue ÷ Area rectangle is; (x²y-y³)/x ÷ xy = (x²y-y³)/x²y = 1 - (y/x)² Notice; Considering two similar...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2761562

Let the length of the two congruent rectangle be 1 unit. Let the width be x. Therefore; 1 ~ (1+x) x ~ 1 Cross Multiply. 1/x = (x+1)/1 x²+x-1 = 0 (x+½)²=1+¼ x = -½±½√(5) Therefore; x ≠ -½(1+√(5)) units. x = ½(√(5)-1) units. Let alpha be y. Therefore; Tany = (1+x)/1 Tany = (1+x) And x = ½(√(5)-1) unit. Tany = ½(√(5)-1)+1 Tany = ½√(5)-½+1 Tany = ½√(5)+½ Tany = ½(1+√(5)) Therefore; Tany = Tan alpha = Golden Ratio

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