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May 27th, 2013, 01:17 PM  #1 
Newbie Joined: May 2013 Posts: 14 Thanks: 0  arithmetic progression
I have attached the questions...[attachment=0:2ker6nlf]576.png[/attachment:2ker6nlf]please someone help me out.

May 27th, 2013, 02:12 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,472 Thanks: 2039 
The eighth hole would have a diameter of 18.8mm, so the ninth hole would have a diameter of 21.2mm, which is greater than the width of the plate. This is possible only if the holes are not all circular. Without knowing the shape of the holes, one can't find their area, so the question about area can't be answered.

May 27th, 2013, 03:49 PM  #3 
Senior Member Joined: Sep 2012 From: British Columbia, Canada Posts: 764 Thanks: 53  Re: arithmetic progression
It says "diameter" of the holes, so they're probably circular. I think this is actually a trick question. Like skipjack said, the size of each hole after the 8th is larger than the width of the plate, so it is impossible to have an even larger hole "drilled" into it. 
May 27th, 2013, 07:52 PM  #4 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,316 Thanks: 1023  Re: arithmetic progression
WHAT is the topic of what' this is about, William: arithmetic series? Tangent circles? Circle areas? Fitting circles in a rectangle? If it's arithmetic series, then sum of the 8 diameters = (number of terms) * (1st term + last term)/2 =8(2 + 18.8)/2 = 83.2 So if the holes (circles) are made consecutively, then evidently impossible. Did your teacher make that up? If so, then he/she should be shot at sunrise :wink: 
May 28th, 2013, 01:01 AM  #5 
Newbie Joined: May 2013 Posts: 14 Thanks: 0  Re: arithmetic progression
^^ It's arithmetic series. Why a sum is greater than the plate itself? Could be the holes on plates are in series? *just guessing* 
May 28th, 2013, 06:16 AM  #6  
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 408  Re: arithmetic progression Hello, will.i.am1! Where did this problem come from? As skipjack pointed out, the problem is quite impossible. Quote:
Quote:
[color=beige] . [/color][color=blue]What?[/color] Perhaps they meant the 8th hole . . . Then we have: [color=beige]. . . . . . . . . . . [/color] 50\,\times\,20)\,\,869.6 \;=\;130.4\text{ mm}^2" />  
May 28th, 2013, 08:15 AM  #7 
Global Moderator Joined: Dec 2006 Posts: 20,472 Thanks: 2039 
If the holes are circular and don't overlap, there isn't enough room for the first eight holes (as there's only just about enough room for the sixth, seventh and eighth). There is room for the first seven holes.

May 28th, 2013, 11:24 AM  #8 
Newbie Joined: May 2013 Posts: 14 Thanks: 0  Re: arithmetic progression
[attachment=0:303xb3ai]circ.png[/attachment:303xb3ai]

May 28th, 2013, 05:58 PM  #9 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,316 Thanks: 1023  Re: arithmetic progression
Huh?! Why not then make one 18.8 hole and be finished May I suggest you (somehow) post your question properly. Is this from your teacher? 
May 29th, 2013, 01:06 AM  #10 
Newbie Joined: May 2013 Posts: 14 Thanks: 0  Re: arithmetic progression
What you meant by post your question properly? Yes, this question is given me by teacher. 

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