Mia removes the plug from a trough to drain the water. The volume, in gallons, in the trough after it has been unplugged can be
1 answer:
Answer:
The correct option is D) (5x − 2)(2x − 3).
Step-by-step explanation:
Consider the provided expression.
Where x is time in minutes.
We need to find the appropriate form of the expression that would reveal the time in minutes when the trough is empty.
When the trough is empty the whole expression becomes equal to 0.
Substitute the whole expression equal to 0 and solve for x that will gives us the required expression.
Now consider the provided option.
By comparison the required expression is D) (5x − 2)(2x − 3).
Hence, the correct option is D) (5x − 2)(2x − 3).
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Answer:13.86km
Step-by-step explanation: see attachment
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