Answer:
1. volume = 40[tex]w^{2}[/tex](20 - w)
2. Domain of V (w) : (0, 20)
Step-by-step explanation:
1. Given that: l = 4w, h + G = 200 feet.
where: l is the length of the base, h is the height, G is the girth or perimeter of the rectangle, and w the width.
Girth = Perimeter = 2 (l + w)
= 2(4w + w)
= 10w
⇒ h + G = h + 10w = 200
h = 200 - 10w ............. 1
The volume of the box can be determined by;
volume = length × width × height
= l × w × h
= 4w × w × (200 - 10w)
= 40[tex]w^{2}[/tex](20 - w)
The volume of the box = 40[tex]w^{2}[/tex](20 - w)
2. From the equation of the volume, 4w > 0, w > 0 and 20 - w > 0 (w> 20)
To have the box, w should not be equal to 0 or 20.
Domain of V (w) : (0, 20)
