An open box is made from a square piece of cardboard 30 inches on a side by cutting identical squares and turning up the sides. A) express the volume of the box as V, as a function of the length of the side of the square cut from each corner, x. B) Find and interpert V(3), V(4), V(5),V(6),V(7). What is happening to the volume of the box as th elength of the side of the square cut from each corner increases? C) Find the domain of V

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MathPhys MathPhys · Answer 1 · 2020-02-03T17:16:07+01:00

Step-by-step explanation:

A)

The length of the box is 30 − 2x inches.

The width of the box is 30 − 2x inches.

The height of the box is x inches.

So the volume is:

V = x (30 − 2x)²

B)

V(3) = 3 (30 − 6)² = 1728

V(4) = 4 (30 − 8)² = 1936

V(5) = 5 (30 − 10)² = 2000

V(6) = 6 (30 − 12)² = 1944

V(7) = 7 (30 − 14)² = 1792

As x increases, the volume of the box increases to a maximum and then decreases.

C)

The ends of the domain occur when V = 0.

0 = x (30 − 2x)²

x = 0 or 15

So the domain is (0, 15).