Two ways you can evaluate 15(90-3)
2 answers:
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Answer:
a)
The combined resistance of a circuit consisting of two resistors in parallel is given by:
where
R is the combined resistance
are the two resistors
We can re-write the expression as follows:
Or
In order to see if the function is increasing in r1, we calculate the derivative with respect to r1: if the derivative if > 0, then the function is increasing.
The derivative of R with respect to r1 is:
We notice that the derivative is a fraction of two squared terms: therefore, both factors are positive, so the derivative is always positive, and this means that R is an increasing function of r1.
b)
To solve this part, we use again the expression for R written in part a:
We start by noticing that there is a limit on the allowed values for r1: in fact, r1 must be strictly positive,
So the interval of allowed values for r1 is
From part a), we also said that the function is increasing versus r1 over the whole domain. This means that if we consider a certain interval
a ≤ r1 ≤ b
The maximum of the function (R) will occur at the maximum value of r1 in this interval: so, at
For 175 : 250 divide them both by 25 to get 
< 
25 goes into 175 > 7 times > 25 into 250 is 10 times! >
For the second one 16 : 40 just divide the top and bottom by 8 since 8 is a common factor of both which will give us
.
8 goes into 16, 2 times and 40, 5 times.
25 goes into 175 > 7 times > 25 into 250 is 10 times! >
For the second one 16 : 40 just divide the top and bottom by 8 since 8 is a common factor of both which will give us
8 goes into 16, 2 times and 40, 5 times.