Incorrect Homework Statement: Identifying an Error in a Given Problem

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AI Thread Summary
The discussion centers around an incorrect homework statement regarding the value of pi. Participants clarify that while pi is often approximated as 3.14, it is actually an irrational number and cannot be expressed as a simple decimal. The distinction between approximation and exact value is emphasized, highlighting that pi is transcendental and has infinite, non-repeating digits. The conversation also references external resources for further understanding of pi. Accurate comprehension of pi is crucial for solving related mathematical problems correctly.
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Homework Statement



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Homework Equations





The Attempt at a Solution


The one that I check marked is incorrect, am I missing something?
 
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-EquinoX- said:
The one that I check marked is incorrect, am I missing something?
You might like to reconsider that statement about pi, Equi.
 
hmm.. isn't pi = 3.14?
 
-EquinoX- said:
hmm.. isn't pi = 3.14?

Pi is an irrational number, 3.14 is very much rational. What do you think?
 
-EquinoX- said:
hmm.. isn't pi = 3.14?

Pi is approximately 3.14 (to two decimal places), not equal to.
 
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
Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks

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