Hey guys just want to make sure I do a video on this question. I know you may have struggled with word ### problem

s in the past so I want to make sure I get you started with this question so if you would please make sure you start reading the question and what you are doing here should, we have a box with an open lid. It's really nice that you actually get a sketch of this whole situation, telling you that you're starting with a piece of cardboard that's 14" x 12". The very first step I would recommend if you didn't have the sketch I would say go ahead and sketch what they tell you to do, in this case we already have a sketch so let's go ahead and add these labels from our info 14 inches by 12 inches I would definitely use the longer side to represent that 14 inch and please excuse my awfulness on straight lines but this one represents that between that line and the end of the others line for my cardboard, the length is 14 inches, the other side or my short side between here and here, the length is 12 inches.

The ### problem

states that you would cut a piece of square out of each piece of this cardboard so you can fold it into an opening Top box, just like the image shown here, the dimensions of our box will be a height of X, where X represents the length of this little piece of square that we're going to cut out of each corner, we also have length and width So for this box, let's go back to an unfolded box and let's see what the measurements are for the length and width for the length , which we started with a length of 14 inches, and then we cut out two small squares with dimensions X, since we are cutting these two exes, then the length we can mark here on the inside is 14 minus 2x.

We can do the same with the width. The width is the initial 12 minus the 2x lengths we're going to cut out. The width will be 12 minus 2x Now that we have this complete sketch, let's go ahead and read exactly what they're asking us to do. We want to find out how long this square is or what the value of x is. If we know that the volume of the box is 144 #### cubic

inches, it might be helpful to check how We find that the volume of the box is the value equal to length times width times height.

Okay, so in this case we're going to write this in function notation, so we have f of X. The function of X is length times width times height. Let's replace each of these values with their equivalence the length of my box this edge over here is equal to this edge over here so we have 14 minus 2x the width of the box is equal to this edge we have 12 minus 2x and then the height of the box is equal to that Length of the square you are looking for. It's equal to X. I'm looking for the value of x when the volume is equal to 244.

That means I'm going to solve the equation of 144. This is the value of My function 144 is equal to 14 minus 2x times 12 minus 2x times X I will not be To work out the full solution here in the video, this is enough to make you realize that you will have a #### cubic

function, and to be able to solve this function you have to multiply everything by you would get 144 on one side and then set to equal zero hopefully the ### problem

works fine with the grouping and if not then you can always graph this function and observe, what your real solutions are, you will also be able to find the complete solution in the worked out ### problem

in degree Good luck to you

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