Instantaneous power calculation between equal time increments.

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Homework Statement



If given cumulative (Adding up every increment to the next) KWh values at an interval of 5 mins each. is it possible to determine instantaneous power from it?

Homework Equations


P=IV
P(t) = VI cos(ωt) cos(ωt −θ )

The Attempt at a Solution



Well, because the question is more about stating a method than actually calculating something. I have thought about it. I think the instantaneous power should just be the difference of Power at time1 and Power at time 2, in this case. Now, of course, if i actually had a circuit, i could go around doing analysis and coming up with Voltage in terms of time and Current in terms of time. That way i can easily come up with a function of instantaneous power with a variable of time in it.
But what this stats is more like, if you are given a value of power for every 5 minutes then what the instantaneous power should be using only the data given? I can't think of much except for taking the value of power at time 2 and subtracting it from value of power at time 1. And that should give me the power that was recorded between those 2 instances.
 
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No, it is not possible to find an instantaneous power. The best you can do is the average over 5 minutes because that is all the information you have.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...

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