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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3443686

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Sir Mike Ambrose is the author of the question.Area S, exactly in square units is;Area triangle with height 2 units and base (2sin120) units + Area triangle with height 2 units and base 2√(2) units - Area sector with radius 2 units and angle (30+atan(√(2)))°= (½*2*2sin120) + (½*2*2√(2)) - (4π*(30+atan(√(2)))÷360)= √(3) + 2√(2) - (π(30+atan(√(2)))/90) square units.= 4.56047793232 - 2.95783078745= 1.60264714487 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3442714

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Calculating b/a.Let x be the side length of the square.Therefore;a+b = x c² = 15²+8²c² = 225+64c = √(289)c = 17 units.d²+x² = 17²d = √(289-x²) units.e = x-de = (x-√(289-x²)) units.b²+x² = 15²b = √(225-x²) units.Recall.a+b = xAnd b = √(225-x²) units.a = (x-√(225-x²)) units.cosy = x/15 --- (2).cosy = (x-√(225-x²))/8 --- (3).Equating (2) and (3).x/15 = (x-√(225-x²))/88x = 15(x-√(225-x²))8x = 15x-15√(225-x²)15√(225-x²) = 7x225(225-x²) = 49x²50625-225x² = 49x²50625 = 274x²x² = 50625/274x = √(184.762...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3441948

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Sir Mike Ambrose is the author of the question.Calculating Area Orange.yB = 6Area OABC = 161/5 square units.Let xB be a.Calculating g, gradient of length AB.(y2-y1)/(x2-x1) = gg = (6-4)/(a-0)g = 2/aTherefore, h, gradient at the perpendicular is;h = -1/gh = -1/(2/a)h = -a/2Let xC be b.It implies;(6-0)/(a-b) = hCalculating b.6/(a-b) = -a/212 = -a²+abb = (a²+12)/a units.Again, b is xC = OC.c = xC-xBc = ((a²+12)/a)-ac = 12/a units.Calculating a, observing trapezoid area formula and triangle area fo...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3440998

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Calculating x, length AD.Let AB = AC = a.cosb = x/32 --- (1).a² = 32²+x²-2*32*xcosba² = 1024+x²-64xcosb --- (2).a² = 23²+x²+2*23*xcosba² = 529+x²+46xcosb --- (3).Equating (2) and (3).1024+x²-64xcosb = 529+x²+46xcosb1024-64xcosb = 529+46xcosb495 = 110xcosbcosb = 495/(110x) --- (4).Therefore, x, length AD is;Equating (1) and (4).x/32 = 495/(110x)110x² = 32*495x² = (32*495)/110x² = 144x = 12 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3440095

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Calculating r, radius of the half circle.a = 2r units.a is the diameter of the half circle.b = ½(2r-4)b = (r-2) units.c²+(r-2)² = (4√(3))²c²+r²-4r+4 = 48c² = 44+4r-r²c = √(44+4r-r²) units.d = (r-4) units.e = b-de = (r-2)-(r-4)e = 2 units.It implies, radius of the circle, r is;r² = 2²+√(44+4r-r²)²r² = 4+44+4r-r²2r²-4r-48 = 0r²-2r-24 = 0r²-6r+4r-24 = 0r(r-6)+4(r-6) = 0(r-6)(r+4) = 0It implies;r ≠ -4 r = 6 units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3439142

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Calculating the required red rectangle area.a = √(4) = 2 units.b = √(16) = 4 units.c = √(9) = 3 units.d = a+bd = 2+4d = 6 units.e = b-ae = 4-2e = 2 units.f² = 6²+2²f = √(40)f = 2√(10) units.f is the length of the red rectangle.g² = 3²+3²g² = 18g = √(18)g = 3√(2) units.g is the diagonal of the 9 square units, square.h = 90-45-atan(2/6)h = (45-atan(⅓))°cos(45-atan(⅓)) = j/(3√(2))j = 3√(2)cos(45-atan(⅓))j = 3.7947331922 units.j is the width of the red rectangle.Therefore, area red rectangle is;f *...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3438244

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Sir Mike Ambrose is the author of the question.Area blue exactly is square units decimal form is;½(Area triangle with height (2√(2)+2√(2+√(3))) units and base 12.9282032303sin75 units - Area triangle with height 2 units and base (2sin150) units - Area trapezoid with two parallel side (2√(2)+2√(2+√(3))) units and (2√(2+√(3))) units, and height √(2) units)=½((0.5*(2√(2)+2√(2+√(3)))*12.9282032303sin75) - (0.5*2*2sin150) - (0.5*√(2)((2√(2)+2√(2+√(3)))+(2√(2+√(3)))))= ½(41.7846096909 - 1 - 7.4641016...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3437473

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Calculating Blue Area, Square.Let x be the side length of the blue square.a = (x+2) units.a is the diameter of the circle.b = ½(a)b = ½(x+2) units.b is the radius of the circle.c = ½(x-2) units.d = ½(x) units.Calculating x², area of the blue square.(½(x+2))² = (½(x))²+(½(x-2))²¼(x²+4x+4) = ¼(x²)+¼(x²-4x+4)x²+4x+4 = x²+x²-4x+44x = x²-4xx² = 8xx = 8 units.Therefore, x², area blue square is;8*8= 64 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3436640

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Calculating R, radius of the circle.Let theta be x.x+x+x = 360x = 120°a² = 6²+5²-2*5*6cos120a² = 61+30a = √(91) units.(√(91)/sin120) = (6/sinb)b = 33.0044915989°c² = 5²+15²-2*5*15cos120c² = 250+75c = √(325)c = 5√(13) units.(5√(13)/sin120) = (15/sind)d = 46.102113752°e = b+de = 33.0044915989+46.102113752e = 79.1066053509°f² = 6²+15²-2*6*15cos120f² = 261+90f = √(351)f = 3√(39) units.g = ½(f)g = 1.5√(39) units.Therefore, R, radius of the circle is;sin79.1066053509 = (1.5√(39))/RR = (1.5√(39))/sin7...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3435572

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Calculating Alpha, let it be x.Let the equal lengths be 1 unit each.a = 180-30-40a= 110°(1/sin30) = (b/sin40)b = 2sin40b = 1.28557521937 units.c² = 1.28557521937²+1²-2*1.28557521937*1cos30c = 0.65270364466 units.Calculating x, Alpha.(0.65270364466/sin30) = (1/sinx)sinx = sin30/0.65270364466x = asin(0.5/0.65270364466)x = 50°Again, x is Alpha.
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