a cardboard box which has a volume of 60 cubic inches and has the dimensions of (x-1) (x-6) (x-2) what is the lenght, width and height of the box

To find the length, width, and height of the box, we need to solve the equation involving the dimensions.

The given equation is:

(x - 1)(x - 6)(x - 2) = 60 cubic inches

Expand the equation:

(x^2 - 7x + 6)(x - 2) = 60
x^3 - 9x^2 + 20x - 12 = 60
x^3 - 9x^2 + 20x - 72 = 0

To solve this equation, we can use factoring or a numerical method such as using a graphing calculator or approximation methods. Factoring might be difficult for this cubic equation, so let's use a numerical method.

Using a graphing calculator or any numerical method, we find that one of the roots (solutions) of the equation is x = 6.

Therefore, (x - 1) = (6 - 1) = 5
(x - 6) = (6 - 6) = 0
(x - 2) = (6 - 2) = 4

So, the length, width, and height of the box are 5 inches, 0 inches, and 4 inches, respectively.

To find the length, width, and height of the cardboard box, we need to solve for the value of x in the given dimensions.

The given dimensions are (x-1), (x-6), and (x-2), which represent the length, width, and height of the box, respectively.

We know that the volume of a box is calculated by multiplying its length, width, and height. In this case, it is given that the volume is 60 cubic inches. So, we can create the following equation:

(volume) = (length) * (width) * (height)
60 = (x-1)(x-6)(x-2)

To find the value of x, we can simplify the equation and solve it. Here's the step-by-step process:

1. Expand the equation:
60 = (x^2 - 7x + 6)(x - 2)

2. Distribute (x - 2) to (x^2 - 7x + 6):
60 = x^3 - 7x^2 + 6x - 2x^2 + 14x - 12

3. Combine like terms:
60 = x^3 - 9x^2 + 20x - 12

4. Rearrange the equation to standard form:
x^3 - 9x^2 + 20x - 72 = 0

At this point, you can either solve the cubic equation for x using advanced mathematical methods or use an online cubic equation solver. Once you have the value of x, you can substitute it back into the original dimensions (x-1), (x-6), and (x-2) to find the length, width, and height of the box.

60=(x-1)(x-6)(x-2)

60=(x^2-7x+6)(x-2)
60=(x^3-2x^2-7x^2+14x+6x-12)

x^3-9x^2+20x-72=0

Hmmmm. Ok, graph this equation, find where it crosses the x axis, I see x=7.59
which makes lwh then 6.59;1.59;5.59

check 6.59*1.59*5.59=