Question

PLEASE HELP! I been stuck on this assignment for over 2 weeks. My teacher gave me a simple explanation when I asked for help, but I still didn't understand it. I asked for more help and now they aren't responding anymore. I'm desperate. Nobody else I have asked understands it either. Here is the question:
Thomas wants to make a box with no lid out of a cardboard sheet to hold a marble collection. He plans to cut out four congruent squares from all corners of the sheet and then fold up the sides to make the box.


Thomas buys a cardboard sheet that is 8 by 12 inches. Let x be the side length of each cutout. Create an equation for the volume of the box, find the zeroes, and sketch the graph of the function.

What is the size of the cutout he needs to make so that he can fit the most marbles in the box?

If Thomas wants a volume of 12 cubic inches, what size does the cutout need to be? What would be the dimensions of this box?


This has to do with polynomials by factoring.


Please EXPLAIN IT so that I UNDERSTAND it. Don't just give me the answer. THANK YOU so much in advance. :)

Answer 1

Answer:

Question 1: x = 0,6,4

Step-by-step explanation:

#1. If we let x be the side of the cut-out square, the formula for the volume of the box is

$\text{Volume} = (12 - 2x)(8 - 2x)(x).$

Expanding gives us

$\text{Volume} = 4x^3 - 40x^2 + 96x.$

To find the zeros, we need to set the equation to 0, and the values of x that would result to zero would be:

$x = 0, 6, 4$

Answer 2

As how it is told 'he' wanted to make a box with no lid for his marble connection, 'he' wants to cut out four "Identical" squares from all of the corners of the sheet (which I'm assuming is that there is four corners) and by doing so he then wants to fold all the sides...

So he buys one that is 8 by 12 inches, so you can draw a box that is (8, 12) put an 'x' at all four corners and 'cut' it the corners out.

Here's the formula that you can use... Which could be either one I guess..

-Cube = a 3

-- a is the side length

-Rectangular prism = a * b * c

-- a, b, c are the length, width, and height

The volume of a cube is side times side times side. Since each side of a square is the same, it can simply be the length of one side cubed. If a square has one side of 4 inches, the volume would be 4 inches times 4 inches times 4 inches, or 64 cubic inches.

Once you found a function I think you should use the quadratic equation, which is- y=x2-20x+96

And you could use that equation to graph it out... But if they want it to be the volume of 12 cubic inches then er-... Yeah that's were i'm stumped at... My apologies..