Answer:
he expression is undefined where the denominator equals
0
, the argument of an even indexed radical is less than
0
, or the argument of a logarithm is less than or equal to
0
.
The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.
Step-by-step explanation:
The maximum messages are 224
The formula of the altitude of an equilateral triangle with side x:

We have:

Substitute:
X+y<=20 is false, because it tries to correlate the amount of hats and scarfs with the time, without considering the time to knit each object
x<=5 is correct, he can at most make 5 hats for more he is missing yarn
y<=8 is correct, same reasoning but with scarfs
5x+8y<=20 is false, it compares the yarn requirements with the total time
12x+6y<=20 is correct, a corrected version of the first constraint which uses the worktime of each object essentially meaning "the time worked on all objects has to be less than the 20 hour time total"
so
x<=5
y<=8
12x+6y<=20
are correct