A company has two packaging machines in a unit, each with a different daily capacity. The capacity of machine 1 is defined by the function f (m) = (m + 4) 2 + 100, and the capacity of machine 2 is defined by the function g (m) = (m + 12) 2 - 50, where m is the number of minutes the packaging machine operates. Create the function C (m) that represents the combined capacity of the two machines.

Question

Geovanni Rosario

Mathematics

30 July, 19:21

A company has two packaging machines in a unit, each with a different daily capacity. The capacity of machine 1 is defined by the function f (m) = (m + 4) 2 + 100, and the capacity of machine 2 is defined by the function g (m) = (m + 12) 2 - 50, where m is the number of minutes the packaging machine operates. Create the function C (m) that represents the combined capacity of the two machines.

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Brylee Blair · Answer 1

I assume that there is an operato ^ missing in each function and that the right functions are:

f (m) = (m+40) ^2 + 10 and

g (m) = (m+12) ^2 - 50

C (m) = f (m) + g (m)

To perform that sum you need to expand the two square parentheses, this way:

f (m) = (m+40) ^2 + 10 = m^2 + 80m + 1600 + 10 = m^2 + 80m + 1610

g (m) = (m+12) ^2 - 50 = m^2 + 24m + 144 - 50 = m^2 + 24m + 94

Now you can add f (m) + g (m) = 2m^2 + 104m + 1704

Answer: c (m) = 2m^2 + 104m + 1704