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2006-08-19 17:59:40 · 9 answers · asked by Ninik 3 in Science & Mathematics ➔ Mathematics
-40 C = -40 F
2006-08-19 18:04:48 · answer #1 · answered by Lee J 4 · 1⤊ 0⤋
-40 C = -40 F
How and why ?
The reason that they are equivalent at -40 is simply due to the linear relationship between the two scales with respect to the different sizes of their degree units and their different zero points. Due to these combined factors, the scales just happen to mathematically coincide at -40.
Because of this equivalence at -40 degrees, you can use the following formulas to interconvert between them.
F = ((C+40) × 9/5) - 40
C = ((F+40) × 5/9) - 40
where:
F = Fahrenheit
C = Celsius
Other conversion formulas exist, but these formulas are based on their equivalence at -40 degrees, making the equations symmetrical with the only difference being the 9/5 or 5/9 ratios.
The fraction 9/5 results because of the ratio between the differences between the freezing and boiling points on the two scales.
Celsius:
Freezing = 0
Boiling = 100
Difference = (100 - 0) = 100 degrees
Fahrenheit:
Freezing = 32
Boiling = 212
Difference = (212 - 32) = 180 degrees
(Fahrenheit Diff / Celsius Diff) = 180/100 = 18/10 = 9/5
This ratio physically means that a difference of 9 degrees Fahrenheit is exactly equal to a difference of 5 degrees Celsius because Celsius degrees are bigger than Fahrenheit degrees, hence the ratios 9/5 and 5/9 as seen in the various conversion formulas.
2006-08-19 19:31:25 · answer #2 · answered by Jay T 3 · 3⤊ 0⤋
I can answer your first question: the Fahrenheit and Celsius coincide at the temperature of -40. Try it, convert each temperature to the opposite and you'll still get -40. Now for the "how and why?", I don't know.
2006-08-19 18:19:26 · answer #3 · answered by fictitiousness ;-) 2 · 0⤊ 0⤋
It's actually extremely simple and requires just a little bit of algebra.
One of the formulae we use is
F = 1.8 C + 32 (where 1.8 = 9/5)
Just replace F with C so that we want to calculate the temperature at which
the F temperature equals the C temperature:
C = 1.8 C + 32
Doing the algebra we get
-.8 C = 32
or, finally, C = -40
2006-08-19 18:05:30 · answer #4 · answered by juanm8149 1 · 1⤊ 0⤋
They could never coincide. The temperature is always the same for either scale, only the numbers are different.
2006-08-19 18:05:19 · answer #5 · answered by niceguy 2 · 0⤊ 2⤋
-40
2015-02-15 06:31:11 · answer #6 · answered by oscar 1 · 0⤊ 0⤋
they are equal at -40
2006-08-19 18:14:25 · answer #7 · answered by magneto077 2 · 0⤊ 0⤋
Never.
Edit: OK, I'll defer to the answer above.
2006-08-19 18:04:52 · answer #8 · answered by normobrian 6 · 0⤊ 1⤋
-40
let x = fahrenheit
y= celsius
1)x=(9y/5)+32
2)x=y since you want them equal
substitute x in(2) in x in (1)
x=(9y/5)+32 becomes
y=9y/5+32
y-32=9y/5
5y-160=9y
-4y=160
y=-40
=) please help( i ned 10pts)
2006-08-19 18:21:35 · answer #9 · answered by !_! 2 · 2⤊ 0⤋