Cylinder problem:restriction on the height if the radious

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The discussion revolves around determining the relationship between the radius and height of a cylindrical frame made from 6m of wire. The initial expression for the radius in terms of height is r = 3 - 2h / 3π. A restriction is needed for the height when the radius must be at least 10, which is clarified to be in centimeters, equating to 0.1m. Participants note a potential error in the inequality direction during calculations. The conversation emphasizes the importance of unit consistency and correct mathematical operations in solving the problem.
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A cylindrical frame consisting of three circles and four vertical supports is built from 6m of wire, as shown. The frame is then covered with paper to form a closed cylinder.
1. Determine an expression for the radius r in terms of the height h.
2. determine the restriction on the height if the radious of the cylendar must be atleast 10.
I got the first one;
1.r=3-2h/3pi
But I did not get the second one
2.
10 > 3- 2h/3pi

3pi(10)> 3- 2h

30pi-3 > -2h

(30pi - 3)/-2 < h

Can someone help me? Thanks
 
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A good question would be 10 what? m? Miles? pounds?

Recall that the length of the wire is given in meters, so if you try to make a 10m diameter circle you will have troubles.
 
^ sorry, 10cm
 
You need to use 10cm=0.1m, as you used 6m initially. Also, I think your < is the wrong way round.
 
^ thank you
 
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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