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April 12th, 2018, 11:40 PM  #1 
Member Joined: Apr 2018 From: On Earth Posts: 34 Thanks: 0  Please help with Paper Question!
I do not really know how I should go about doing question number 4c, which I have highlighted in yellow. If i knew how to do 4C I am pretty sure that I would be able to do the next questions, but I am stuck on this, please help!
Last edited by Student2018; April 12th, 2018 at 11:53 PM. 
April 12th, 2018, 11:46 PM  #2 
Senior Member Joined: Oct 2009 Posts: 405 Thanks: 140 
I can't read anything on the attachment

April 12th, 2018, 11:57 PM  #3 
Member Joined: Apr 2018 From: On Earth Posts: 34 Thanks: 0  This should be better
This should be better

April 16th, 2018, 06:59 AM  #4 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,185 Thanks: 871 
I don't see a "4" so I assume that the (a), (b), (c), etc. on the page are all problem 4. Basically you start with a paper size "$\displaystyle A_0$", of area 1 square meter and make smaller sheets by cutting the previous sheet in half. So $\displaystyle A_1$ has area 1/2(1)= 1/2 square meter, $\displaystyle A_2$ has area have of that (1/2)(1/2)= 1/4, $\displaystyle A_3$ has area half of that, (1/2)(1/4)= 1/8, etc. Since we are just multiplying by 2 in the denominator we have powers of 2 in the denominator: $\displaystyle A_n$ has area $\displaystyle frac{1}{2^n}$. That was question (a) and you were able to do that, right? For the next question we are told that the dimensions of $\displaystyle A_4$ are x meters long and y meters wide. $\displaystyle A_3$ is formed by putting two of those together, length wise. So $\displaystyle A_3$ has length x m still but width 2y m. That is (b) and, since you are not asking about (b), you were able to do that, correct? Now (c) asks us to use both (a), that $\displaystyle A_n$ area $\displaystyle \frac{1}{2^n}$ square meters, and (b). that while [math]A_4[math] has length x m and width y m, $\displaystyle A_3$ has length x m and width 2ym to determine x and y separately. I'm not sure we really use the results of (a) and (b)! I would simply note that original sheet $\displaystyle A_0$ had both length and width 1. Since we keep the same length, cutting only lengthwise each time, halving the width, the length of $\displaystyle A_n$ is x= 1 while the width is $\displaystyle \frac{1}{2^n}$ m. 
April 16th, 2018, 07:23 AM  #5 
Global Moderator Joined: Dec 2006 Posts: 19,045 Thanks: 1618 
They're all question 4, as can be seen in this pdf file.


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