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Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3480837

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Sir Mike Ambrose is the author of the question.Calculating Exactly, Golden Area ÷ Large Square Area.Let the side of the large square be 2 units.Therefore;Area large square is;2²= 4 square units.Area gold is;Area triangle with height 2 units and base ⅔ units - Area triangle with height 1 unit and base ½(√(2))sin135 units.= (½*⅔*2) - (½*1*½(√(2))sin135)= ⅔ - ¼= 5/12 square units.Therefore;Area Gold ÷ Area Large Square Exactly is;(5/12)÷4= 5/48

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3480462

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Calculating Area Green.Let theta be x.a = 90-39a = 51°x+x+27 = 512x = 51-272x = 24x = 12°b+x+39 = 180b = 180-39-xAnd x = 12°b = 180-39-12b = 129°Let c be the hypotenuse of the ascribed right-angled triangle.Therefore;c/sin129 = d/sin12d = (csin12)/(sin129)d = 0.26753235702c units.Calculating c.½*c*0.26753235702c*sin39 = 260.08418178377c² = 26c² = 308.85541783c = 17.5742828539 units.Again, c is the hypotenuse of right-angled triangle.sin39 = e/ce = csin39e = 17.5742828539sin39e = 11.0598545581 u...

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3480099

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Calculating The Red Inscribed Semi Circle Area.Let x be the area of the inscribed half circle.a² = 2x²a = √(2)x units.Calculating x.1² = x²+(√(2)x)²1 = x²+2x²1 = 3x²x = 1/√(3) units.Again, x is the radius of the red inscribed half circle.Area red inscribed half circle is;½*πx²= ½*π(1/√(3))²= ⅙(π) square units.

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3479279

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Total coloured area is;2(area triangle with height 6.69991708075 cm and base √(65)sin(atan(10)-atan(7/4)) cm= 2*½*6.69991708075*√(65)sin(atan(10)-atan(7/4))= 6.69991708075*3.28362272769= 22 cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3478376

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Sir Mike Ambrose is the author of the question.Radius, r of the inscribed circle is;r = (3-√(3)) cmTherefore;Area purple exactly in square cm is;Area trapezium with parallel sides (3-√(3)) cm and 4 cm, and height 3+√(3) cm - 2(area triangle with height (3-√(3)) cm and base (3√(3)-3) cm).= ½*(3+√(3))(4+3-√(3)) - 2(½*(3-√(3))*(3√(3)-3))= (9+2√(3)) - (12√(3)-18)= (27-10√(3)) cm²

Mathematics Question and Solution

https://onlineedumath.com/update/mathematics-question-and-solution/3477389

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Sir Mike Ambrose is the author of the question. P(2, (16√(5)/5))Gradient of the curve at the tangent is;= 24/5√(5)Therefore;Gradient of the curve at the normal is;= -5√(5)/24It implies;Coordinate Q is;Q(4, (167√(5)/60))Therefore area R as a single fraction in square units is;(Area under the curve at x = 2 and x = 4) - (Area trapezium with parallel sides 167√(5)/60 units and 16√(5)/5 units, and height 2 units).= (24-⅓(8√(5))) - ½*2((167√(5)/60 )+(16√(5)/5))= 24 - ⅓(8√(5)) - (359√(5)/60)= (1440-5...

Mathematics Question and Solution

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

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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

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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

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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

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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.

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