Answer:
A. (0, 5)
Step-by-step explanation:
Physically speaking, the volume of the box and the side of the square cutout are positive value. So that the following inequations must be satisfied:
[tex]h > 0[/tex] (1)
[tex]16-2\cdot h >0[/tex] (2)
[tex]10-2\cdot h > 0[/tex] (3)
From (1), (2), (3) we find that:
(1):
[tex]h > 0[/tex]
(2):
[tex]16 > 2\cdot h[/tex]
[tex]8 > h[/tex]
[tex]h < 8[/tex]
(3):
[tex]10 > 2\cdot h[/tex]
[tex]5 > h[/tex]
[tex]h < 5[/tex]
We see that equation above is the multiplication of a first grade monomial and two first grade binomials, which means that:
[tex]h > 0 \,\land\,h < 5\,\land\,h< 8[/tex]
[tex]0< h < 5[/tex]
In other words, the reasonable domain for this situation is A.
