Whats 0.2 divide by 0.4 work and answer
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The question is an illustration of composite functions.
- Functions c(n) and h(n) are
and
- The composite function c(n(h)) is
- The value of c(n(100)) is
- The interpretation is: <em>"the cost of working for 100 hours is $130000"</em>
The given parameters are:
- $5000 in fixed costs plus an additional $250
- 5 systems in one hour of production
<u>(a) Functions c(n) and n(h)</u>
Let the number of system be n, and h be the number of hours
So, the cost function (c(n)) is:
This gives
The function for number of systems is:
<u>(b) Function c(n(h))</u>
In (a), we have:
Substitute n(h) for n in
Substitute
<u>(c) Find c(n(100))</u>
c(n(100)) means that h = 100.
So, we have:
<u>(d) Interpret (c)</u>
In (c), we have:
It means that:
The cost of working for 100 hours is $130000
Read more about composite functions at:
We're going to "cut" the repeating part here in a few steps. First, we're going to put the number in a variable:
Next, to get rid of the negative, we can multiply either side by -1 to get
Now, we won't actually use this -x directly; instead, we want to create two new values, one by multiplying either side by 10:
and the other by multiplying either side by 1000:
Next, we can get rid of the repeated part of the number by subtracting -10x from -1000x:
And finally, we can divide either side of the equation by -990 to find that