How many inches of lumber are remaining?
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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:
Answer:
Given expression:
Separate the variables:
Reduce the first fraction:
Therefore:
Check the picture below.
so is really just a cylinder with a cone on the side, notice, since the diameter of the base is 4, the radius is half that then.
so we just simply get the volume of the cylinder, and the cone, and sum them up
so is really just a cylinder with a cone on the side, notice, since the diameter of the base is 4, the radius is half that then.
so we just simply get the volume of the cylinder, and the cone, and sum them up