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Find the surface area of a hand held fan (modeled with negligible depth) with radius 8 cm and a 60 degree angle at the centre

60 degrees = π/3 radians A = 1/2r 2 θr = 8θ = π/3 1/2 x 8 2 x π/3 = 33.5103216... cm 2 33.5103216... x 2 = 67.0 cm 2 to 3 s.f.
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How do I differentiate (x^2 + 3x + 3)/(x+3)

In order to differentiate this fraction, you will need to use the quotient rule, which if you don't remember is: y = u/v then dy/dx = (v du/dx − u dv/dx)/ v^2) First you need to identify your initial variabl...
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Solve the equation sin2x = tanx for 0° ≤ x ≤ 360°

sin2x = tanx Take everything to left hand side, so LHS equals 0 sin2x - tanx = 0 Recall double angle formula : sin2x = 2sinxcosx, also notice that tanx can be written as sinx/cosx giving us: 2sinxcosx - sinx...
SM
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A curve has equation y = 3x^3 - 7x + 10. Point A(-1, 14) lies on this curve. Find the equation of the tangent to the curve at the point A.

Firstly, we define a tangent as a straight line touching a curve at 1 point only.We can describe a straight line using this linear relation:y - y 1 = m.(x - x 1 )We know a point on this line A(-1, 14) = (x 1...
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A curve has equation y = (x-1)e^(-3x). The curve has a stationary point M. Show that the x-coordinate of M is 4/3.

(In the following answer, y' denotes dy/dx , i.e. the derivative of y with respect to x , where y is a function of x ) y = (x-1)e -3x = uv , where u = x-1 and v = e -3x . We have that u' = 1 and using the Ch...
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