Optimizing Wetted Area in a Rotating Disk Evaporator

momu
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A circular disk of radius r is used in an evaporator and is rotated in a vertical plane. It is to be partially submerged in the liquid so as to maximize the exposed wetted area of the disk. show that the center of the disk should be positioned at height r/sqrt(1+pi^2)

ok i absolutely know how to do this question but I'm having a tough time deriving the equation for the submerged portion.. if i can get help on that i would be greatful thanks.
 
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Nevermind haha
 
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Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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