Greatest Integer Function help

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The discussion revolves around a homework problem involving a plumber's pricing structure, which includes an initial fee of $80 and an additional charge of $25 per hour. The user initially proposed an incorrect equation, y=28[(x+1)]+80, and expressed confusion about the greatest integer function's relevance to the problem. Other participants pointed out the mistake in using "28" and suggested replacing it with the correct values to formulate the equation accurately. The conversation highlights the need for clarity in applying the greatest integer function to the pricing scenario. Ultimately, the user is seeking assistance to correctly solve the problem.
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Greatest Integer Function.. help!

Homework Statement


Well this is the problem a plomer charges 80 bucks ones he arrives at your home and charges and extra 25 per hour.. Give the equation,,
Kind of i don't get it is for extra credit but still i don't like it when i don't know how to do it

2. The attempt at a solution
i put these but i think is wrong..
y=28[(x+1)]+80
But if i put 1hour.. plus 1 gives 2 hours so he would be chargin 2 hours just for working one..
Nice deal! hahaha But still i don't think this is it
 
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Welcome to PF!

Hi Kino! Welcome to PF! :smile:
Kino said:
… a plomer charges 80 bucks ones he arrives at your home and charges and extra 25 per hour..

y=28[(x+1)]+80

Well, basically it's right (except for the "28" of course :wink:) …

you just need to replace (x+1) by something else …

then you can check that it's right in exactly the same way that you checked that (x+1) was wrong. :smile:

(btw, what did this have to do with "greatest integer"? :confused:)
 


I meant the parentesis are the integers signs but i didnt now how to put them...
But today i may get the answer so i'll publish it
 
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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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