Answer:
Explanation:
a) The volume of a rectangular boxlike bag is given by the formula V = lwh, where l is the length, w is the width, and h is the height. In this case, we know that the length is three times the width, or l = 3x. The height is not given, but we can express it in terms of x and the other dimensions. Since the total dimensions of the bag must not exceed 44 inches, we have:
l + w + h ≤ 44
Substituting l = 3x and rearranging, we get:
h ≤ 44 - l - w
h ≤ 44 - 3x - x
h ≤ 44 - 4x
Therefore, the volume of the bag is:
V = lwh = (3x)(x)(44 - 4x) = 132x^2 - 12x^3
b) To graph the function y = V(x), we can plot points for different values of x and connect them with a smooth curve. Here is a possible set of points:
x V(x)
0 0
5 3300
8 5376
10 6600
12 7128
15 6750
20 4800
We can plot these points and connect them with a smooth curve to obtain the graph of y = V(x). The graph should have a maximum point, which represents the maximum volume that the bag can have while still meeting the airline's requirements. This maximum volume occurs at x = 11/3 inches, and its value is V(11/3) = 8000/27 cubic inches.