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attached is a word document including my question an answer as I wanted to include diagrams. the question is a M2 question

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C4 June 2014 Q4: Water is flowing into a vase. When the depth of water is h cm, the volume of water V cm^3 is given by V=4πh(h+4). Water flows into the vase at a constant rate of 80π cm^3/s. Find the rate of change of the depth of water in cm/s, when h=6.

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A cubic polynomial has the form p(z)=z^3+bz^2+cz+d, z is Complex and b, c, d are Real. Given that a solution of p(z)=0 is z1=3-2i and that p(-2)=0, find the values of b, c and d.

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If y=5x+4x^3, find dy/dx.

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The finite region S is bounded by the y-axis, the x-axis, the line with equation x = ln4 and the curve with equation y = ex + 2e–x , (x is greater than/equal to 0). The region S is rotated through 2pi radians about the x-axis. Use integration to find the

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