suli92 Posted June 25, 2011 Report Share Posted June 25, 2011 what did you do to find the numerator? there are some methods, and the easiest one is the graphical method. if you see the pattern and seriously think about it you'll find a way. sorry if my clues are very vague. don't want to give too much guidance as I'm actually not allowed to. Thank you for helping me, I still haven't found the formula for the denominator, I'll keep trying and see if i can get anything. The first draft is tommorow so i have no idea wat to do. At least now i can focus on a specific part and try to find some sort of pattern. Thanks again Reply Link to post Share on other sites More sharing options...
dessskris Posted June 25, 2011 Report Share Posted June 25, 2011 it's due tomorrow?????argh. fine. the easiest method would be graphing the data of n and the denominator for each value of r. then find the best regression. it's a simple model. after that, generalise it for all values of r. Reply Link to post Share on other sites More sharing options...
Jacob Arnould Posted July 11, 2011 Report Share Posted July 11, 2011 (edited) Hi guys, I am having trouble finding the GS (yes I have read the ENTIRE thread). What I've done so far: - I have noticed the pattern with both the numerator and the denominator - I have found a GS for the numerators - I have plotted En(1), En(2), En(3), En(4 and En(5) against n - I now have five quadratic equations - I have noticed a pattern in the five equations: 'a' stays constant, 'b' is -1 each time, and c is r^2 Now my problem is trying to "generalize" my five equations into ONE general statement in terms of r and n. P.S what does "generalize" mean? THANKS! Edited July 11, 2011 by Jacob Arnould Reply Link to post Share on other sites More sharing options...
dessskris Posted July 11, 2011 Report Share Posted July 11, 2011 good job! generalise basically means.....generalise. lol. it's like when you have many equations for various values of r. but you only found for some values of r, not for every number. but doing it for every number will drive you nuts therefore you are asked to give some examples and then generalise it, make them to be in terms of r. a random example: when r=1, y=x+2 when r=2, y=2x+4 when r=3, y=3x+8 when r=4, y=4x+16 now you have to "generalise" it. can you see the pattern? the general equation, or the general statement for all values of r is y=rx+2r. I hope this makes sense. do you know what to do now? you are almost done good luck with this IA! 3 Reply Link to post Share on other sites More sharing options...
Indre Posted August 17, 2011 Report Share Posted August 17, 2011 Hello everybody, I have just one question about the limitations of the GS: is one of the limitations the relation between n and r? I mean, can that be that n cannot exceed r? I'd really appreciate your help! Reply Link to post Share on other sites More sharing options...
dessskris Posted August 17, 2011 Report Share Posted August 17, 2011 Hello everybody, I have just one question about the limitations of the GS: is one of the limitations the relation between n and r? I mean, can that be that n cannot exceed r? I'd really appreciate your help! not really... it's not a limitation lol it's just something you somehow noticed. the limitation in this task is very simple! don't think too hard. it's just like what n can be and what r can be. should you need more hints please ask again. Reply Link to post Share on other sites More sharing options...
Indre Posted August 17, 2011 Report Share Posted August 17, 2011 Yeah, okay, all these n and r are natural and not equal to zero. That's what I've already written, and it's obvious. But if, for example, we take n=10, and r=12, there is no such element in the row, for the row n=10 has only 11 elements! o.O Am I wrong? And yeah, sorry, r cannot exceed n, not vice versa. Reply Link to post Share on other sites More sharing options...
dessskris Posted August 17, 2011 Report Share Posted August 17, 2011 Yeah, okay, all these n and r are natural and not equal to zero. That's what I've already written, and it's obvious. But if, for example, we take n=10, and r=12, there is no such element in the row, for the row n=10 has only 11 elements! o.O Am I wrong? And yeah, sorry, r cannot exceed n, not vice versa. ahhh right, sorry, I didn't really take the time to think about this. lol okay, yep you are right. that would be a good thing to mention in the portfolio yes. Reply Link to post Share on other sites More sharing options...
Indre Posted August 17, 2011 Report Share Posted August 17, 2011 Yayy, thank you! Now I can finish my IA. Reply Link to post Share on other sites More sharing options...
AdnaH Posted August 20, 2011 Report Share Posted August 20, 2011 Can anyone tell me how should I use the technology here???Im kinda confused because it doesn't seem to be very easy to justify this kind of theory by calculator or any program. What is it supposed to be used here?Moreover, I arrived at my general statements, I think so, but stillformula for denominator cannot be applied for all elements, because it depends on rwhat should I do?Thanks Reply Link to post Share on other sites More sharing options...
dessskris Posted August 20, 2011 Report Share Posted August 20, 2011 Can anyone tell me how should I use the technology here??? Im kinda confused because it doesn't seem to be very easy to justify this kind of theory by calculator or any program. What is it supposed to be used here? when validating your general statement you can plot a graph using technology. Moreover, I arrived at my general statements, I think so, but still formula for denominator cannot be applied for all elements, because it depends on rwhat should I do? Thanks of course haha it depends on r and n should you have any question just ask again. Reply Link to post Share on other sites More sharing options...
Ensar Posted August 21, 2011 Report Share Posted August 21, 2011 Hello everyone I have only one question: Does GS differ for the middle numbers in rows due to different denominators? I mean, only if you use an example of E5(2)= 15/9, you can come to your GS but in my case, I have two GSs one for fractions in the middle and one for other fractions. Help would be truthfully appreciated! Reply Link to post Share on other sites More sharing options...
dessskris Posted August 21, 2011 Report Share Posted August 21, 2011 Hello everyone I have only one question: Does GS differ for the middle numbers in rows due to different denominators? I mean, only if you use an example of E5(2)= 15/9, you can come to your GS but in my case, I have two GSs one for fractions in the middle and one for other fractions. Help would be truthfully appreciated! no, you will get only ONE general statement for all the fractions. are those general statements very different btw? if yes maybe you made a mistake! Reply Link to post Share on other sites More sharing options...
Ensar Posted August 21, 2011 Report Share Posted August 21, 2011 No, they are not. However, I can clearly see the pattern and I can conclude which limitations might exist for the GS, but I cannot seem to find a right GS for all denominators It is really easy to find for numerator. But, am I on the right path? Should I use this example and make fractional GS? Btw, thanks for answer Reply Link to post Share on other sites More sharing options...
dessskris Posted August 22, 2011 Report Share Posted August 22, 2011 No, they are not. However, I can clearly see the pattern and I can conclude which limitations might exist for the GS, but I cannot seem to find a right GS for all denominators It is really easy to find for numerator. But, am I on the right path? Should I use this example and make fractional GS? Btw, thanks for answer what do you mean use this example? it's called general statement. you get it by generalising... I think you should work on the numerator alone and THEN work on the denominator alone, don't work out the general statement for the whole fraction at the same time because it's gonna confuse you. even when you work on the denominator, it would be confusing already. so, if it help, draw a new triangle consisting the denominator only. then observe and analyse them. in case you didn't read, please read the first at least two or three pages of this thread and you will know how to get the general statement. I wrote it not just to help one or two people, but for everyone. no problem. if there's any more question don't be afraid to ask. Reply Link to post Share on other sites More sharing options...
Akayuki + Lucifel Posted August 28, 2011 Report Share Posted August 28, 2011 Augh, I reeeaaallllyy frustrated at the moment. I read the whole thread 3 times finally understood where the GS for the numerator comes from and I am stuck with the denominator. I do have the GS for that as well but I want to know how to get there... Basically what I don't understand is Remember that 1 is the 1st term in each row, and in this term r=0. When r=1 (the 2nd term from the left), get a table of the denominators and the n (n starts from 2). Then you find the GS for the denominator in terms of n. When r=2 (the 3rd term from the left), get a table of the denominators and the n (n starts from 3). Then you find the GS for the denominator in terms of n. When r=3 (the 4th term from the left), get a table of the denominators and the n (n starts from 4). Then you find the GS for the denominator in terms of n. Do the same thing for when r=4 and when r=5. You've got all the general statements in terms of n. Now your goal is to make them to be ONE general statement in terms of r and n. Hint: The general statement is in quadratic form (denominator=an²+bn+c) Tabulate r and the general statements. I am sure you will see some kind of pattern in the values of a, b and c. Find them with a similar method as before, Get a table of a and r. Then you find the GS for a in terms of r. Get a table of b and r. Then you find the GS for b in terms of r. Get a table of c and r. Then you find the GS for c in terms of r. So you've got a, b and c. Put them in the general statement involving n. You will get the GS for the denominator in terms of n and r. This task is fairly easy, though it seems complicated in the beginning. Good luck to all of you!! Previously it was stated that r= 1, 2, 3, etc. should be plotted against n. When it comes to r=4 it starts with n=5? Does that mean that the first terms in the LIST should take a value of 0? Also I am struggling to form any GSs for the r=x from these tables... I really appreciate the help you have given so far Reply Link to post Share on other sites More sharing options...
dessskris Posted August 28, 2011 Report Share Posted August 28, 2011 the first terms don't have to start at 0. if it starts from n=5 then when you plot its graph, your graph starts from n=5 and the plot area between 0 and 5 should be blank. Reply Link to post Share on other sites More sharing options...
IB is killing me Posted September 3, 2011 Report Share Posted September 3, 2011 Hi everyone, I am given the portfolio assignment and thankfully it isn't that hard. But, I have trouble explaining it. By looking at the numbers, I've noticed that the numerator increases by 1 than the previous number. What I meant is, in the 3rd row the numerator is 6 and it increases by four and becomes 10 in the next one. Then, 10 increases by five and becomes 15 in the 5th row. However, it seems to me that my explanation is sort of awkward. So I decided to ask you guys how you would explain it. I am attaching the portfolio method. Thanks in advance for your help! =) I've had this assignment too. For the general statement of the numerator and row number relationship I got a(n)=n(n+1) / 2 . I put it in the graphing calculator under STAT, and calculated the quad. regression. Hi. Could you go more into details about the quad. regrssion and etc.? Reply Link to post Share on other sites More sharing options...
ukbavaria Posted September 4, 2011 Report Share Posted September 4, 2011 What about the 1s... how do they fit in? Reply Link to post Share on other sites More sharing options...
dessskris Posted September 4, 2011 Report Share Posted September 4, 2011 they do fit in indeed. if you noticed the patterns. Reply Link to post Share on other sites More sharing options...
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