Algebra: distance from a fixed point

AI Thread Summary
The discussion centers on a mathematical problem involving the distance from a fixed point, where the initial calculation leads to the expression +(2a-b)-(3a+2b), resulting in -a-3b. Participants express confusion over the book's answer of a+b, suggesting it may be a typo. The consensus is that the correct interpretation should yield a distance of 2a+b miles north. Clarification on the book's content is sought, indicating potential errors in the material. Overall, the conversation highlights the importance of verifying mathematical solutions against reliable sources.
drooble122
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Homework Statement
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Basic algebra
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The first image is the question and the second is the answer.
My thinking is let's say North is positive, and South is negative. Fixed point O is the starting point. Then the question becomes +(2a-b)-(3a+2b). The answer should be -a-3b. I cannot fathom why the book gives the answer as a+b. Any help would be appreciated. Thank you.
 
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I'd say you were correct. What book are you using?
 
It's probably a typo and they meant to say 2a+b miles north.
 
Office_Shredder said:
It's probably a typo and they meant to say 2a+b miles north.
Exactly.
 
I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
Essentially I just have this problem that I'm stuck on, on a sheet about complex numbers: Show that, for ##|r|<1,## $$1+r\cos(x)+r^2\cos(2x)+r^3\cos(3x)...=\frac{1-r\cos(x)}{1-2r\cos(x)+r^2}$$ My first thought was to express it as a geometric series, where the real part of the sum of the series would be the series you see above: $$1+re^{ix}+r^2e^{2ix}+r^3e^{3ix}...$$ The sum of this series is just: $$\frac{(re^{ix})^n-1}{re^{ix} - 1}$$ I'm having some trouble trying to figure out what to...
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