Is 4/3 and 8/6 a proportion
2 answers:
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Given:
The inequality is:
To find:
The y-intercept, slope and type of line (solid or dotted).
Solution:
The slope intercept form of a line is:
...(i)
Where, m is the slope and b is the y-intercept.
We have,
The relation equation is:
...(ii)
On comparing (i) and (ii), we get
It means the slope is 5 and the y-intercept is 3.
The sign of the inequality in the given inequality is ">". It means the boundary line is not included in the solution set. So, the boundary line is a dotted line.
Therefore, the slope is 5, the y-intercept is 3 and the line is a dotted line.
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