Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2241064

tana = 12/8 a = atan(3/2)° b = 180-a b = (180-atan(3/2))° (10/sin(180-atan(3/2))) = (4/sinc) c = 19.4400348282° d = 180-b-c d = 180-19.4400348282-(180-atan(3/2)) d = 36.8698976458° e = 90-d e = 90-36.8698976458 e = 53.1301023542° It implies, Area S (shaded area green) is; Area trapezoid with height 12 units, and parallel sides 4 units and 12 units respectively - Area triangle with height 10 units and base 4sin36.8698976458 units - Area sector with radius 10 units and angle 53.1301023542°...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2224896

Notice; The side length of the regular hexagon is 2 units. a = ½(2) a = 1 unit. a is half the length of the regular hexagon. b = sin60 b = (√(3)/2) units. c = sin30 c = ½ units. d = 1+2(½) d = 2 units. Area Blue is; 2(area trapezoid with parellel sides 1 unit and 2 units, and height (√(3)/2) units) - 6(area sector with radius 1 unit and angle 60°) + 6(area equilateral triangle with side 1 unit). = 2(½*(2+1)(√(3)/2))-6(60π/360)+6(0.5sin60) = ½(3√(3))-π+½(3√(3)) = (3√(3)-π) square units....

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2209118

Area blue exactly in cm² decimal is; Area trapezoid with two parallel sides 12 unit and (12-16tan15) unit, and height 16 unit - Area triangle with height (12-16tan15) unit and base 4 unit - Area triangle with height and base 12 unit each - Area triangle with height 8√(2) unit and base (8-8tan15)sin45 unit. = ½*16(12+12-16tan15) - ½*4(12-16tan15) - ½(12²) - ½*8√(2)*(8-8tan15)sin45 = 157.702503369 - 15.4256258422 - 72 - 23.4256258422 = 46.8512516846 cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2187323

Sir Mike Ambrose is the author of the question. Area D exactly in cm² is; Area trapezoid with parallel sides 4 cm and 8 cm, and height 4 cm - Area triangle with height 4 cm and base 3 cm - Area sector with radius 4 cm and angle atan(4/3). = (½*4(4+8)) - (½*4*3) - (atan(4/3)*π*4²÷360) = 24 - 6 - (2πatan(4/3))/45 = 18 - (2πatan(4/3))/45 = (810 - (2πatan(4/3)))/45 cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2164280

Sir Mike Ambrose is the author of the question. Let Alpha be x. Calculating x; ½(180-atan2)-atan(0.5) x = ½(90-atan(0.5)) It implies; tan x exactly is; = tan(½(90-atan(0.5))) Calculating Area Orange. Notice, Area Orange is an isosceles triangle with one of the two congruent sides 1.01857603 units. It implies; Area Orange exactly in decimal is; Area triangle with height 1.01857603 units and base 1.01857603sin(atan2) units. = ½*1.01857603*1.01857603sin(atan2) = 0.46398282133 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2160284

Sir Mike Ambrose is the author of the question. Calculating k. 3k² = 108 k = 6 units. The equation of the curve is; y = 4x-⅓(x²) Area R is; Area under the curve at x=0 and x=(6-3√(2)). = 2(6-3√(2))²-(6-3√(2))²/9 = 6(8-5√(2)) square units. Area S is; Area rectangle with length 12 units and width 6 units - Area trapezoid with parallel sides 12 units and 9 units, and height 3 units - Area under the curve at x=3 and x=6. = (12*6) - ½*3(12+9) - 33 = 72 - ½(63) - 33 = 39 - ½(63) = ½(15) square un...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2153152

Sir Mike Ambrose is the author of the question. Let the side of the regular hexagon be 2 units. Therefore; Area Green is; Area regular equilateral triangle with side √(3) units. ½*√(3)*√(3)sin60 = ¼(3√(3)) square units. Area Blue is; Area trapezoid with parallel sides √(3) units and 2√(3) units, and height ½ unit - Area triangle with height ⅓√(3) units. ½*½(√(3)+2√(3)) - ½*1*⅓√(3) = ¼(3√(3))-√(3)/6 = 7√(3)/12 square units. Area Orange is; Area trapezoid with parallel sides 1 unit and ½ uni...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2149344

Sir Mike Ambrose is the author of the question. Let the side of the regular octagon be 1 unit. (a) Calculating alpha exactly. Let it be x. x = atan(1/(√(2)+1) x = 22.5° (b) Calculating Area Yellow ÷ Area Green exactly. Area yellow is; Area triangle with height √(2) units and base (2-√(2)) unit. = ½*√(2)*(2-√(2)) = (√(2)-1) square units. Area green is; Area trapezoid with parallel sides 1 unit and √(2) units, and height ½√(2) unit. = ½*½√(2)(√(2)+1) = ¼(2+√(2)) square units. It implies; A...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2130637

Sir Mike Ambrose is the author of the question. Let the side length of the inscribed equilateral triangle ABD be x. Calculating x. (12√(2))² = (½√(3)x)² + ((12√(2))-½(12√(2)-x))² It implies; x = 3(√(26-√(2)) cm. Therefore; Area Yellow exactly in cm² is; Area trapezoid with parallel sides (3√(26)-3√(2)) cm and (2√(26)-2√(2)) cm, and height ½(√(78)-√(6)) cm. = ½*½(√(78)-√(6))*((3√(26)-3√(2))+(2√(26)-2√(2))) = ¼(√(78)-√(6))(5√(26)-5√(2)) = 35√(3)-5√(39) = 5(7√(3)-√(39)) square...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2073877

Sir Mike Ambrose is the author of the question. P(2, (8/3)) Q(4, (32/15)) Gradient of the curve is; dy/dx = -4x/(x²-1)² For x = 2. dy/dx = -8/9 It implies; R(5, 0) Area S exactly in square units is; Area under the curve at x = 2 and x = 4 - Area trapezoid with parallel sides (8/3) units and (8/9) unit, and height 2 units. = 4 + ln(9/5) - ½*2((8/3)+(8/9)) = 4 + ln(9/5) - (32/9) = (4/9) + ln(9/5) = (4+9(ln(9/5)))/9 square units.

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