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Calling All Mathmatical Geniuses

1 by ghhyrd
Elite SG Admiral
Please, calling all geniuses, I have probably not come to the right place, but I need desperate help.

I have completely forgotten everything on this subject, so could someone with a big heart and a big brain (or even if this is easy, I have just had a complete mental wipeout) please find out one equation, that can be applied to

5 to get 7, 9 to get 26, 13 to get 57, and 17 to get 100.

Please show the method.

1 equation that works for

5-7

9-26

13-57

17-100

Thanks!
'Memory and imagination are but one thing, which for diverse considerations, have diverse names'
¦- F R E D E N T H U S I A S T -¦

2 by ghhyrd
Elite SG Admiral
Any takers? Tonight? Please?
'Memory and imagination are but one thing, which for diverse considerations, have diverse names'
¦- F R E D E N T H U S I A S T -¦

7 by Wanderer
SG Patroller
First make an assumption that it is 2nd order polynomial (educated guess). Then form the equations..
1) 25A + 5B + C = 7
2) 81A + 9B + C = 26
3) 169A + 13B + C = 57
4) 289A + 17B + C = 100

Use these as simultaneous equations.. First calculate B using 1) and 2) (really simple elimination, just get rid of C) and you should come up with something like B = (19 -56A)/4

Then substitute the B in the 3) and 4) with this and calculate A (again the same simple elimination of C) which should be 3/8. Then use the earlier B = ... to get B ( -1/2 ) and finally calculate the C using any of the original functions ( 1/8 ).

So you end up with f(x) = 3/8 x^2 - 1/2 x + 1/8

Or thats how i would do it.

8 by ghhyrd
Elite SG Admiral
Wanderer wrote:First make an assumption that it is 2nd order polynomial (educated guess). Then form the equations..
1) 25A + 5B + C = 7
2) 81A + 9B + C = 26
3) 169A + 13B + C = 57
4) 289A + 17B + C = 100

Use these as simultaneous equations.. First calculate B using 1) and 2) (really simple elimination, just get rid of C) and you should come up with something like B = (19 -56A)/4

Then substitute the B in the 3) and 4) with this and calculate A (again the same simple elimination of C) which should be 3/8. Then use the earlier B = ... to get B ( -1/2 ) and finally calculate the C using any of the original functions ( 1/8 ).

So you end up with f(x) = 3/8 x^2 - 1/2 x + 1/8

Or thats how i would do it.
Umm. I will give that a try, but did you actually test it?
Where did f(x) come from,
and
Does x^2 mean X squared?


By the way, this question is simple but hard. It just needs one formula or equation such as 7=5^2-2 or even 7=5+2, but one equation that works for all of them, turning
5 into 7
9 into 26
13 into 57
17 into 100
'Memory and imagination are but one thing, which for diverse considerations, have diverse names'
¦- F R E D E N T H U S I A S T -¦

11 by Wanderer
SG Patroller
Dunno... i have never really been educated about proper terms in math in English (only in Finnish) so i just tossed in a term i quickly dug from the internet (wiki 'translation')..



Also for the note.. that is just a single example of vast (actually infinite) number of equations that get the correct result. Higher order polynomials, trigonometrical, exponential, combinations of these, etc.

13 by ghhyrd
Elite SG Admiral
BlackHole wrote:
simultaneous equations
Curiousity here, is that another term for "system of equations" or does it mean something else?
Maybe

Simultaneous equations are where you will have two equations
e.g 2X + 15Y = 21
and 3Y + 21X = 23

X = ?
Y = ?
Wanderer wrote:x^2 is x squared

Test it yourself if you like.

With f(x) i just marked the thing as function
Yeah, I realised it all like 1 second after I posted it. I don't think it was right, I was always off by .25 using this. So I just put it into brackets and added + 1/20*5) in the end.
'Memory and imagination are but one thing, which for diverse considerations, have diverse names'
¦- F R E D E N T H U S I A S T -¦

14 by Wanderer
SG Patroller
Off by 0.25? I do not seem to agree...

f)x) = 3/8 * x^2 - 4/8 * x + 1/8

f(5) = 3/8 * 25 - 4/8 * 5 + 1/8
f(5) = (75 - 20 + 1) / 8
f(5) = 56/8 = 7

f(17) = 3/8 * 289 - 4/8 * 17 + 1/8
f(17) = (867 - 68 +1) / 8
f(17) = 800/8 = 100

f(9) = 208/8 = 26
f(13) = 456/8 = 57

15 by ghhyrd
Elite SG Admiral
Very strange, I tried it via calculator and it was very specific that it was off by .25, but It coudld be possible that I misinterpreted a certain part;

You put F(x)= 3/8X^2 - 1/2X+1/8
But is it meant to be;
F(x)= 3/8X^2 - 1/2(X + 1/8)
It was kinda unclear so I put it like this;
F(x)= (3/8x^2) - (((1/2x)+1/8)+1/20*5)

Which may be in some way a deviation from your original form, but still works so I will not complain ;)
'Memory and imagination are but one thing, which for diverse considerations, have diverse names'
¦- F R E D E N T H U S I A S T -¦
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