The monthly output at the Olek Carpet Mill is Q(x) = 15,000 + 2x2 units, (40 ≤ x ≤ 60) where x is the number of workers employed at the mill. If there are currently 50 workers, find the instantaneous rate of change of monthly output with respect to the number of workers. That is, find Q'(50). Q'(50) =

Step-by-step explanation:

We have been given that the monthly output at the Olek Carpet Mill is units, where x is the number of workers employed at the mill. We are asked to find instantaneous rate of change of monthly output with respect to the number of workers.

Let us find derivative of our given function.  

To find instantaneous rate of change at , we will substitute in our derivative function as:

Therefore, the instantaneous rate of change is 200 with respect to the number of workers.

d

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.