Kendra F. answered • 06/29/17
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So if we write this out, let's say Monday's high temp is "m" and Tuesday's high temp is "t" in degrees Fahrenheit.
The difference between Mondays high temperature and 0 degrees Fahrenheit is x
m - 0 = x
m = x
The difference between Tuesday's high temperature and 0 degrees Farenheight is greater than x.
t - 0 > x
t > x
m = x
t > m
Linda claims, "If I knew whether Tuesday's high temperature was above or below 0 degrees Fahrenheit I could figure out which days high temperature was colder..
Linda is not correct, it doesn't matter whether Tuesday was above or below 0ºF, the high temp on Tuesday is always greater than Monday. t > m
Kendra F.
Yes, if you're dealing with absolute temperatures where the difference between the high temp and 0ºF is always positive, you would need to know whether Tuesdays temp was +/- .
|-7| - 0 = x
then x = 7
|t| - 0 > 7
|t| > 7
then: t > 7 or t < -7
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07/01/17
Jina L.
can you explain that a little bit more please
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08/30/17
Jina L.
can you explain the part on why she would be correct a little bit more please
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08/30/17
Kendra F.
Sure. The person who posted the question specified later in the comment thread that the difference in temperature was an absolute difference, meaning it is always positive. This is an important piece of information that changes the solution. If you sketch out a number line like so;
Absolute temperature difference |T| > |M| puts Monday and Tuesday here. (reflected across zero)
<--------T-----M------0----M-----T------->
If the difference is absolute (always+) the temperatures are reflected over zero because |T| > |M|. If Tuesday is negative, it's on the far left of the number line, so Monday is warmer. If Tuesday is positive, it's on the far right of the number line and will be warmer.
Now, if the the difference in temperature is not absolute with T > M ; Tuesday would always be to the right of Monday and thus always be warmer. The number lines would look like this; with T always to the +right of Monday.
Scenarios for difference in Temperature. T > M
<-----M----T-----0--------------->
<-----M----------0-----T--------->
<-----------------0---M----T----->
I hoped this helps to explain it better.
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08/30/17
Tina U.
hi, do you mind answering the question again for me in the point of view saying she's correct. Thank You !
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09/03/17
Kendra F.
Sure, If Tina is correct in needing to know whether Tuesday was above (+temp) or below zero (-temp) then the difference in temperatures are absolute values. Let's say the high temp on Monday is "m" and the high temp on Tuesday is "t".
The difference between Mondays high temperature and 0 degrees Fahrenheit is x.
|m - 0| = x
The difference between Tuesday's high temperature and 0 degrees Fahrenheit is greater than x.
|t - 0| > x
The absolute value essentially removes the +/- sign of the temperature making the information necessary in determining which day was warmer later on.
Example: Monday's high temperature could be -2ºF or 2ºF and the difference between Mondays high temp and 0ºF would be a 2º difference in temperature irrespective of whether it was above or below zero.
Then we have Monday and Tuesdays high temp as ;
|m - 0| = x
|m| = x
The absolute value of Mondays high temp equals
x
|t - 0| > x
|t| > x
The absolute value of Tuesdays high temp is greater than x
Replace x with |m| since they're equal.
|t| > |m|
The absolute value brackets remove any +/- signs on the temperatures, therefore making the information necessary later on.
Examples of values that work for: |t| > |m|
t = -8ºF and m = +4ºF ; |-8| > |4|
t = -8ºF and m = -4ºF ; |-8| > |-4|
t = +8ºF and m = +4ºF ; |8| > |4|
t = +8ºF and m = -4ºF ; |8| > |-4|
Plotted on a number line around 0ºF.
<---- t ------ m ------ 0 ------ m ------ t ----->
So, if the difference between the days temperature and zero is always given as a +, absolute value then it would be necessary to know whether Tuesday was above or below zero.
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09/04/17
Stella L.
lets say |-7|>|x|. The absolute value would be 7, however, we would be plotting the actual value on the number line. In this case wouldn't Linda be correct?
06/30/17