The function uses W as the variable but the options show only x's as the variable, so I'm asumming W in the answer
Answer:
0 < W < 50
Correct option: A
Step-by-step explanation:
Domain of functions
Some functions have restricted values of the independent variable x. It can be due to mathematical restrictions, like dividing by 0 or taking the square root of a negative number, of it can be due to practical conditions of the situation being modeled.
In this case, the area of a rectangle is given by the quadratic function.
[tex]A=50W - W^2[/tex]
Since the area of a rectangle cannot be negative (and should be positive, though it could be zero), the practical domain of A is determined when
[tex]50W - W^2\geq 0[/tex]
Taking common factor W
[tex]W(50 - W)\geq 0[/tex]
Since W must be positive W>0
[tex]50 - W\geq 0[/tex]
Or equivalently
[tex]50 \geq W[/tex]
[tex]W \leq 50[/tex]
The total interval is
[tex]0 < W<50[/tex]
Correct option: A
Please note: The real restriction should be
[tex]0 < W\leq 50[/tex]
if we allowed the area to be positive, but I'm providing the most possible correct available option
