We know C=F, -40. What is |K|=|F|?

sonhouse
Posers and Puzzles 30 Jul '12 10:34
1. sonhouse
Fast and Curious
30 Jul '12 10:34
I got close just doing the formula, (((K-273.15)*1.8)-32)=F
How do you come up with a formula where the absolute value of K=F?
2. SwissGambit
Caninus Interruptus
30 Jul '12 14:241 edit
Originally posted by sonhouse
I got close just doing the formula, (((K-273.15)*1.8)-32)=F
How do you come up with a formula where the absolute value of K=F?
Take the usual formula for K to F:
(K-273.15)*1.8+32=F
We want to find the point at which the temp value is the same for both scales, so substitute:
(c-273.15)*1.8+32=c
Solve for c:
1.8c-491.67+32=c
-459.67=-0.8c
574.5875=c
3. sonhouse
Fast and Curious
30 Jul '12 15:41
Originally posted by SwissGambit
Take the usual formula for K to F:
(K-273.15)*1.8+32=F
We want to find the point at which the temp value is the same for both scales, so substitute:
(c-273.15)*1.8+32=c
Solve for c:
1.8c-491.67+32=c
-459.67=-0.8c
[b]574.5875
=c
[/b]
I am talking about the absolute value of K Vs absolute value of F, not C.

It is ~164, that is 164 degrees K = ~-164 degrees F, just wanted to see if there was an exact solution and how you derive a formula that would give that exact solution.
4. SwissGambit
Caninus Interruptus
30 Jul '12 17:044 edits
Originally posted by sonhouse
I am talking about the absolute value of K Vs absolute value of F, not C.

It is ~164, that is 164 degrees K = ~-164 degrees F, just wanted to see if there was an exact solution and how you derive a formula that would give that exact solution.
Ahh, now I know what you want. I didn't understand exactly what you were asking for in the opening post.

The variable "c" was not meant to be Celsius, but a generic variable. Sorry about the confusion. I will use "x" this time. ðŸ™‚

The steps are the same as before. Just start with -x on the right side this time:
(x-273.15)*1.8+32=-x
1.8x -491.67+32=-x
-459.67=-2.8x
x=164.1678571

Edit: But if you speak in terms of absolute value, then both of my answers are solutions. ðŸ™‚
5. sonhouse
Fast and Curious
30 Jul '12 17:351 edit
Originally posted by SwissGambit
Ahh, now I know what you want. I didn't understand exactly what you were asking for in the opening post.

The variable "c" was not meant to be Celsius, but a generic variable. Sorry about the confusion. I will use "x" this time. ðŸ™‚

The steps are the same as before. Just start with -x on the right side this time:[quote](x-273.15)*1.8+32=-x
1.8x ...[text shortened]... t if you speak in terms of absolute value, then both of my answers are solutions. ðŸ™‚
I used the windows PC calculator and got this:

164.1678571 428571 428571 428571.....

I separated the digits by the 1's to show the repeating series.

I wonder if there is a way, perhaps another number base, that would make that an exact solution, somewhat akin to the difference between calling it 4.333333333....Vs
4 1/3 (exact solution)

So in base 10, there is no exact solution just an infinite series.
6. SwissGambit
Caninus Interruptus
30 Jul '12 22:011 edit
Originally posted by sonhouse
I used the windows PC calculator and got this:

164.1678571 428571 428571 428571.....

I separated the digits by the 1's to show the repeating series.

I wonder if there is a way, perhaps another number base, that would make that an exact solution, somewhat akin to the difference between calling it 4.333333333....Vs
4 1/3 (exact solution)

So in base 10, there is no exact solution just an infinite series.
If there is a repeating decimal, it can be expressed as a fraction. You don't need another number base [not sure why that would help anyway ðŸ˜›].

45967/280 does the trick in this case.
7. sonhouse
Fast and Curious
31 Jul '12 01:162 edits
Originally posted by SwissGambit
If there is a repeating decimal, it can be expressed as a fraction. You don't need another number base [not sure why that would help anyway ðŸ˜›].

45967/280 does the trick in this case.
Well my calculator says 45967/280 covers the 164.1678571 part exactly but it misses out on the actual repeaters, the 428571's that repeat forever.

How did you suss out that fraction anyway? You have fraction sniffing software?
8. SwissGambit
Caninus Interruptus
31 Jul '12 01:461 edit
Originally posted by sonhouse
Well my calculator says 45967/280 covers the 164.1678571 part exactly but it misses out on the actual repeaters, the 428571's that repeat forever.

How did you suss out that fraction anyway? You have fraction sniffing software?
My windows calc program gives

164.1678571 428571 428571 428571 4286

I am not sure why you are not seeing the repeating digits. You should.

I used an old algebra trick to get the fraction. Software didn't come into play until it was time to reduce the fraction. ðŸ™‚

N = 164.1678571 428571 428571

create another equation by multiplying both sides by some power of 10, such that the repeating digits line up with the first equation:

1000000N = 164167857.1428571 428571

Now subtract the first equation from the second:

999999N = 164167692.975

get rid of the decimals:

999999000N = 164167692975

solve for N and you have your fraction:

164167692975/999999000

now all that remains is to reduce it.

45967/280
9. sonhouse
Fast and Curious
31 Jul '12 11:04
Originally posted by SwissGambit
My windows calc program gives

164.1678571 428571 428571 428571 4286

I am not sure why you are not seeing the repeating digits. You should.

I used an old algebra trick to get the fraction. Software didn't come into play until it was time to reduce the fraction. ðŸ™‚

N = 164.1678571 428571 428571

create another equation by multiplying both sid ...[text shortened]... your fraction:

164167692975/999999000

now all that remains is to reduce it.

45967/280
but with that method don't you need to include all the infinite number of repeats? That would seem to me to need an infinite number of zeros in the first part, 1000000000000000000000000000..........N to get the whole thing.
10. SwissGambit
Caninus Interruptus
31 Jul '12 13:462 edits
Originally posted by sonhouse
but with that method don't you need to include all the infinite number of repeats? That would seem to me to need an infinite number of zeros in the first part, 1000000000000000000000000000..........N to get the whole thing.
I did include the infinite repeats. They were there when I subtracted one equation from the other, but they were lined up, and thus disappeared due to the subtraction. It's a pretty sweet trick.

Here's a simpler example to illustrate.

Make up some number with repeating digits:

14.512 757575757575...

Created 2nd equation and subtract the first:

100N = 1451.2 757575757575....
-(N = 14.512 757575757575....)
-------------------------
99N = 1436.763 (the repeating 75's died in the subtraction!)
99000N=1436763
N=1436763/99000
N=478921/33000 (unlucky - this couldn't be reduced much, but there it is. Plug it into a calculator and you should get all the repeating digits).
11. sonhouse
Fast and Curious
31 Jul '12 13:56
Originally posted by SwissGambit
I did include the infinite repeats. They were there when I subtracted one equation from the other, but they were lined up, and thus disappeared due to the subtraction. It's a pretty sweet trick.

Here's a simpler example to illustrate.

Make up some number with repeating digits:

14.512 757575757575...

Created 2nd equation and subtract th ...[text shortened]... ch, but there it is. Plug it into a calculator and you should get all the repeating digits).
So the answer would be the same no matter how many repeating digits were included? It would also be the same if you only used the first set of digits and ignored the rest?
12. SwissGambit
Caninus Interruptus
31 Jul '12 14:15
Originally posted by sonhouse
So the answer would be the same no matter how many repeating digits were included? It would also be the same if you only used the first set of digits and ignored the rest?
You always include all repeating digits. You just write down enough to make sure they are lined up for the subtraction.
13. sonhouse
Fast and Curious
31 Jul '12 16:37
Originally posted by SwissGambit
You always include all repeating digits. You just write down enough to make sure they are lined up for the subtraction.
I'm still stuck on the part where you can't write down an infinite series...
14. SwissGambit
Caninus Interruptus
01 Aug '12 00:14
Originally posted by sonhouse
I'm still stuck on the part where you can't write down an infinite series...
But why would you need to?
15. sonhouse
Fast and Curious
01 Aug '12 01:15
Originally posted by SwissGambit
But why would you need to?
I thought I said that then I thought you said you included the infinite series which is why I'm confused.