Math Is Fun Forum

Hey guys,

Needed some help on 2 proof questions:

1) Prove that the centre of mass of a uniform wire in the form of a semi-circle of radius r is at a distance 2r/pie (sorry don't know how to insert symbol) from the centre.

2) Prove that the centre of mass of a uniform semi-circular laminar of radius r is at a distance 4r/3pie from the centre.

I hope you guys can help. Thanks

kind regards,

dadon

1) Find the equation of the line through the origin which is parallel to the line 4x - 27 - 5 = 0

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2) The equation of a curve is y = (x-3)(x+4). Find the gradient of the curve:
a) at the point the curve crosses the y-axis
b) at each of the points where the curve crosses the x-axis

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3) Find the coordinates of the point(s) on the curve y=3x^3 - x + 8 at which the gradient is
a) 8
b) 0

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4) The equation of a curve s=4t^2 +5t. Find the gradient of the normal at each of the points where the curve crosses the t-axis.

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5) If the gradient of a curve is y=2x^2 -3x -2. Find
a) the gradient at the point where x=0
b) the co-ordinates of the point where y=0
c) the gradient at each of the points found in b)

I have done part a) of the question which need checking & need help on part b)

a) Find the centre and radius of the following circle:

2x^2 + 2y^2 + -4x + 10y = 8

radius = 3.3 centre = (1, -2.5) << this is what i got

b) Find the equation of the tangent to the circle when the circle intersects the x-axis in the positive quadrant.