Mai wants to make an open top box by cutting out corners of a square piece of cardboard and folding up the sides. the cardboard is 10 cm by 10 cm. the volume v(x) in cubic cm of the open top box is a function of the side length x in cm of the square cutouts

The volume of a shape is the amount of space in it;

The volume as a function of side length (x) is:

From the question, we have the dimension of the cardboard to be;

When side length (x) is removed from the cardboard, the dimension of the box becomes:

So, the volume of the box is:

Substitute known values

Expand

Expand

Rewrite as:

Express as a function

Hence, the required function is:

Read more about volume functions at:

link

The domain for x is all real numbers greater than zero and less than 5 com

Step-by-step explanation:

The question is

What is the volume of the open top box as a function of the side length x in cm of the square cutouts?

see the attached figure to better understand the problem

Let

x -----> the side length in cm of the square cutouts

we know that

The volume of the open top box is

we have

substitute

Find the domain for x

we know that

so

The domain is the interval (0,5)

The domain is all real numbers greater than zero and less than 5 cm

therefore

The volume of the open top box as a function of the side length x in cm of the square cutouts is

to find the unit price, we must figure out the cost of one item (in this case one dish towel).   to do this, we divide the total price ($7.92) by the number of items bought (for this problem it is 8, because there are eight dish towels in one pack).  

$7.92/8 = $0.99

therefore, the unit price, or the price of one dish towel, is $0.99.

hope this !

(-1,-0.5)

step-by-step explanation: