Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3476500

Calculating x, chord of the circle..a² = 1 square units.a = 1 unit.a is the side length of the 3 inscribed equal squares.b = 1+½(1)+yb = (1.5+y) units.c = 1+1c = 2 units.d² = 2²+0.5²d² = 4+0.25d = √(4.25) units.d is r, the radius of the circle.e² = (1.5+y)²+1²e² = 3.25+3y+y²e = √(3.25+3y+y²) units.e is also r, radius of the circle.Calculating y.Equating d and e.√(4.25)² = √(3.25+3y+y²)4.25 = 3.25+3y+y²y²+3y-1 = 0(y+(3/2))² = 1+(3/2)²(y+(3/2))² = (13/4)y = -(3/2)±√(13/4)y = -(3/2)±√(13/4)It impl...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3475634

Sir Mike Ambrose is the author of the question.AB exactly is;= 16tan(3acos(8/9)) - 2√(17)= 2(8tan(3acos(8/9))-√(17)) cm.= 102.760478669 cm.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3474697

Sir Mike Ambrose is the author of the question. Equation of the curve is;y = ¼(x²)+4Shaded area exactly in square units is;Area triangle with height 8 units and base 4 units - Area sector with radius 4√(5) units and angle (2atan(0.5))° + Area triangle with height 4√(5) units and base 4√(5)sin(2atan(0.5)) units = (½*4*16) - ((2atan(0.5))*π*(4√(5))²÷360) + (½*4√(5)*4√(5)sin(2atan(0.5)))= 16 - (4πatan(0.5))/9 + 32= 48 - (4πatan(0.5))/9= 4(108-πatan0.5)/9 square units.= 10.9081912799 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3473757

Sir Mike Ambrose is the author of the question.Calculating Area Orange.Area orange exactly in square units is;Area triangle with height ⅓(10√(2)) units and base 5sin45 units - Area triangle with height (8/3) units and base 2√(2)sin45 units - Area triangle with height ⅔√(10) units and ⅓(7sin(atan(2)-45)) units.= (½*⅓(10√(2))*½(5√(2))) - (½*(8/3)*(2√(2)/√(2)) - (½*⅔√(10)*⅓(7sin(atan(2)-45)))= ⅓(25) - ⅓(8) - (7/9)= ⅓(17) - 7/9= (51-7)/9= 44/9 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3472894

Sir Mike Ambrose is the author of the question.Let the side of the regular pentagon be 1 unit.a = 360-2(108)-90a = 54°tan72 = b/0.5b = 1.53884176859 units.tan54 = 1.53884176859/cc = 1.11803398875 units.d = c-0.5d = 0.61803398875 units.(e/tan36)+(e/tan27) = dWhere e is the radius of the inscribed circle.e = 0.61803398875/((1/tan36)+(1/tan27))e = 0.18509595408 units.f = 180-72-54f = 54°Therefore;g = d = 0.61803398875 units.Shaded Area Red is;Area triangle with height 0.61803398875 units and base...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3471934

Sir Mike Ambrose is the author of the question.Let the side of the square be 2 units.Therefore;a = 3√(5)/5 units.b = 2√(5)/5 units.c = √(5)/5 units.d = 2√(5)/5 unitsIt implies;a² = b² + c² + d² is;(3√(5)/5)² = (2√(5)/5)² + (√(5)/5)² + (2√(5)/5)²9/5 = 4/5 + 1/5 + 4/59/5 = 9/5.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3471120

Sir Mike Ambrose is the author of the question.Area yellow in square units to 2 decimal places is;Area triangle with height (tan70+tan(450/7)) units and base (tan70+tan54)sin80 units.= ½(tan70+tan(450/7))(tan70+tan54)sin80= 9.79563286034 square units.≈ 9.80 square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3470087

Sir Mike Ambrose is the author of the question.At x = 0, y = 2.At y = 16, x = 1.Gradient of the curve at x = 1 or at the tangent is;dy/dx = 3In2*2^(3x+1)For x = 1dy/dx = 48In2Therefore coordinate Q is (x¹, 0).Calculating x¹.(0-16)/(x¹-1) = 48In2x¹= (3In2-1)/3In2It implies;Area Red exactly as a single fraction in its simplest form is;Area trapezoid with parallel sides 2 units and 16 units, and height 1 unit - Area triangle with height 16 units and base (1-((3In2-1)/3In2)) units.= (½*1(2+16)) - (...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3469047

Calculating Area Pink.a*b = 4*(4+1)ab = 20a = 20/b units.c = a+bc = (20/b)+bc = (b²+20)/b units.c is the diameter of the ascribed pink circle.d = ½(c)d = (b²+20)/(2b) units.d is the radius of the pink circle.e = b-de = b-((b²+20)/(2b))e = (2b²-b²-20)/(2b)e = (b²-20)/(2b) units.f = ½(4+4+1)-4f = 4.5-4f = 0.5 units.g = ½(4)g = 2 units.cosh = 2/b --- (1).cosh = 0.5/((b²-20)/(2b))cosh = b/(b²-20) --- (2).Calculating b.Equating (1) and (2).2/b = b/(b²-20)Cross Multiply.2b²-40 = b²b² = 40b = √(40)b =...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3468430

Calculating Area Red.a = 1+(161/9)+(10/9)a= 1+(171/9)a = 1+19a = 20 units.a is the diameter of the ascribed circle.b = ½(a)b = 10 units.b is the radius of the ascribed circle.Let x be the radius of the inscribed circle.c = (10-x) units.d = 10-1d = 9 units.It implies;(10-x)² = x²+9²-2*9*xcosy100-20x+x² = x²+81-18xcosy81xcosy = 20x-19cosy = (20x-19)/(18x) --- (1).cosy = (161/9)/(2x) --- (2).Calculating x.Equating (1) and (2).(20x-19)/(18x) = (161/9)/(2x)2(20x-19) = (161/9)*1840x-38 = 32240x = 360...

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