Which expression is equivalent to 36 + 81?
2 answers:
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With the given table, this isn't possible without resorting to an approximation of an approximation.
The interval![[0,8]](https://tex.z-dn.net/?f=%5B0%2C8%5D)
can be partitioned as ![[0,2]\cup[2,4]\cup[4,6]\cup[6,8]](https://tex.z-dn.net/?f=%5B0%2C2%5D%5Ccup%5B2%2C4%5D%5Ccup%5B4%2C6%5D%5Ccup%5B6%2C8%5D)
, with the respective midpoints of 
. So the average temperature is given exactly by the definite integral
which is approximated by
where the coefficient
comes from the fact that each subinterval has length 2, and so 
.
However, you don't know the values of
at these points. At best you can approximate them, perhaps by interpolating (you have the details needed to do it, at any rate).
Are you sure you're not supposed to find the average temperature over the entire set of observation times, i.e. over
?
The interval
which is approximated by
where the coefficient
However, you don't know the values of
Are you sure you're not supposed to find the average temperature over the entire set of observation times, i.e. over