Question

A box is formed by cutting squares from the corners of a rectangular piece of cardboard. The volume of the box is found by the equation V(h)=h(16-2h)(10-2h) where his a side of the square cutout. Which is the reasonable domain for this situation?
a. (0,5)
b. (0,10)
c. (0,8)
d. (0,infinity)

Answer 1

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:

$h > 0$ (1)

$16-2\cdot h >0$ (2)

$10-2\cdot h > 0$ (3)

From (1), (2), (3) we find that:

(1):

$h > 0$

(2):

$16 > 2\cdot h$

$8 > h$

$h < 8$

(3):

$10 > 2\cdot h$

$5 > h$

$h < 5$

We see that equation above is the multiplication of a first grade monomial and two first grade binomials, which means that:

$h > 0 \,\land\,h < 5\,\land\,h< 8$

$0< h < 5$

In other words, the reasonable domain for this situation is A.