.Let me get this. 2 systems
A --------- B
14 --------- 36
133 ------- 87
c -------- k
At which temperature are both temperatures equal
say this happens at temperature t, which is equal in both systems (this obviously should fall within 36 and 87 k)
then
(t - 14) / (133-14) = (t - 36)(87 -36)
68t = 4284-714
t = 3570/68 = 52.5 which is the answer.
2006-07-26 00:14:06
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answer #1
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answered by blind_chameleon 5
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Temperature systems always have a linear relationship to each other, so let's come up with the equation that relates the two.
We'll treat it just like we're finding the equation of a line, except instead of using (x,y) as coordinate pairs, we'll use (A,B). We need a line that goes through two points: (14,36) and (133,87).
The slope of the line will be:
m = (87-36)/(133-14)
= 51/119
= 3/7
So, if we wanted to write the equation in slope-intercept form, so far it would look like this: B = (3/7)A + b. We just need to find b, so we plug in one of the points:
87 = (3/7)133 + b
Simplifying:
87 = 57 + b
30 = b
So our equation is B = (3/7)A + 30. As a test, we can plug in the coordinates for either point, and we find they both work.
Now, we want to find the point where the two temperature scales are equal -- in other words, A = B. So we substitute A for B, giving us:
A = (3/7)A + 30
Solving:
7A = 3A + 210 (multiply both sides by 7)
4A = 210 (subtract 3A from both sides)
A = 210/4 = 52.5 (divide both sides by 4)
So the two temperature scales read the same at 52.5 degrees.
Hope that helped!
2006-07-26 03:37:44
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answer #2
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answered by Jay H 5
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Try rephrasing your question. At the moment I haven't the foggiest what you're on about.
2006-07-26 00:01:28
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answer #3
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answered by tgypoi 5
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