Calculus Problem: Boat propeller/matrix/derivatives

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Here's the problem, attached to the post. I've tried using matrices to solve it but I'm not sure if the answers I am getting are correct. The professor hinted that the answers should be whole numbers, but I keep getting decimals. Any help??

I've uploaded a scan of my work, scan02 is where I plugged in for the X's and found the derivatives. I then put them into a matrix.

Thanks,
ITF
 

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ITF said:
Here's the problem, attached to the post. I've tried using matrices to solve it but I'm not sure if the answers I am getting are correct. The professor hinted that the answers should be whole numbers, but I keep getting decimals. Any help??

I've uploaded a scan of my work, scan02 is where I plugged in for the X's and found the derivatives. I then put them into a matrix.

Thanks,
ITF

Sorry, I have to reply in order to attach my matrix working. The limit is three files. Anyhoo, :smile: my work isn't exactly the "prettiest" but at least I hope it's clean enough for a Helper to show me where I went wrong. It also shows the answers I got for each variable, (A, B, C, D,..etc.)

Thanks again!
ITF
 

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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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