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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2730411

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a² = 4 a = 2 cm. a is the side length of the inscribed square. b² = 2a² b = √(2*2*2) b = 2√(2) cm. b is the radius of the ascribed semi circle. tanc = 2/(2√(2)) c = atan(1/√(2))° Therefore, the required length, PA is; cosc = (PA)/(2b) PA = 2bcosc PA = 2*2√(2)*cos(atan(1/√(2))) PA = 4.6188021535 cm.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2730400

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Since; AB = 2BC It implies; AB = (2/3)*12 AB = 8 cm. BC = (1/3)*12 BC = 4 cm. 12 cm is the side length of the ascribed square. tana = 12/8 a = atan(3/2)° b = 90-a b = atan(2/3)° 2/3 = c/4 c = (8/3) cm. d² = 4²+(8/3)² d = ⅓(4√(13)) cm. Calculating e, radius of the inscribed circle. (8/3)e+4e+(4√(13)/3)e = (8/3)*4 ⅓(20+4√(13))e = (32/3) e = 32/(20+4√(13)) e = 0.929632483 cm. Again, e is the radius of the inscribed circle. Therefore, shaded area exactl...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2730371

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Sir Mike Ambrose is the author of the question. Area blue is; Area triangle with side 8.81712800181 cm and 7.80776406404 cm, and angle 19.3341412463° = ½(8.81712800181*7.80776406404)sin19.3341412463 = 11.3960010284 ≈ 11.40 cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2728922

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Sir Mike Ambrose is the author of the question. Area purple exactly in square cm decimal form is; Area triangle with side 17.1220111351 cm and 15.6524758425 cm, and angle 75.963756532° - Area triangle with side 3.28886874952 cm and 2.857142857 cm, and angle 8.1301023539° + Area triangle with side 2.857142857 and 2.82842712466 cm, and angle 8.1301023539°  = ½(17.1220111351*15.6524758425)sin75.963756532 - ½(3.28886874952*2.857142857)sin8.1301023539 + ½(2.857142857*2.82842712466)sin8.1301...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2728916

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(16-x)²+x² = 12² 256-32x+x²+x² = 144 2x²-32x+112 = 0 x²-16x+56 = 0 (x-8)² = -56+(64) x = 8±√(8) x = (8-√(8)) cm. x = 5.1715728753 cm. y = 16-x y = 10.8284271247 cm. Area triangle red is; ½*x*y = 0.5*5.1715728753*10.8284271247 = 28 cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2728908

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Sir Mike Ambrose is the author of the question. Area Orange exactly in its simplest decimal cm square form is; Half area square with side 5√(5) cm - Half area square with side 4.472135955 cm - Area triangle with side 5√(5) cm and 7.9859570625 cm, and angle 36.869897646° = ½(5√(5))² - ½(4.472135955)² - ½(5√(5)*7.9859570625)sin36.869897646 = ½(125) - 10 - 26.7857142857 = 25.714285714 cm² = ⅐(180) cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2727569

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Let a be the radius of the quarter circle. b = x° c = (45-x)° It implies; sinx = 1/a --- (1). sin(45-x) = 2/a --- (2). At (1). a = 1/sinx --- (3). Substituting (3) in (2). sin(45-x) = 2/(1/sinx) sin(45-x) = 2sinx sin45cosx-cos45sinx = 2sinx ½√(2)(cosx-sinx) = 2sinx cosx-sinx = 2√(2)sinx cosx = 2√(2)sinx+sinx cosx = (2√(2)+1)sinx cosx/sinx = (2√(2)+1) sinx/cosx = 1/(2√(2)+1) tanx = (2√(2)-1)/7 x = atan((2√(2)-1)/7) x = 14.6388065952° Calculating a, radi...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2727339

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Let the single side length of the equilateral hexagon be 1 unit. Therefore; Area blue is; Area triangle with two sides 1 unit each, and angle 120° + Area triangle with base ½ units and height √(3) units. = ½(sin120) + ½(½*√(3)) = ¼√(3) + ¼√(3) = ½√(3) square units. = 0.5√(3) square units. Calculating area red. It is; Area irregular pentagon with sides ½ units, 1 unit, 1 unit, 1 unit and ½√(13) units - Area triangle with side 1 unit and ¼√(13) units, and angle (30-atan(...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2726967

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Let a be 1 unit. d = ⅙*180(6-2) d = 120° d is the single interior angle of the regular hexagon. cos60 = e/1 e = 0.5 units. f = a+2e f = 2 units. f is CF. g² = 0.5²+2²-2*0.5*2cos60 g = 1.8027756377 units. g is MF. (1.8027756377/sin60) = (0.5/sinh) h = 13.897886248° h is angle CFM. j = 60-h j = 46.102113752° j is angle EFN. k = ½(g) k = 0.9013878189 units. k is FN = MN. Calculating b. b² = 0.9013878189²+1²-2*0.9013878189*1cos46.102113752 b = 0.75 units....

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/2726826

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a = x+1+2 a = (x+3) units. a is BC. b = 4+2 b = 6 units. Calculating x. (2x)² = (x+3)²+6² 4x² = x²+6x+9+36 3x²-6x-45 = 0 x²-2x-15 = 0 x²-5x+3x-15 = 0 x(x-5)+3(x-5) = 0 (x-5)(x+3) = 0 It implies; x ≠ -3 x = 5 units.
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