Therefore, when x is approximately 1. I started with 4.From our first spreadsheet and from our work with Algebra Expresser, we know that the other value lies somewhere between 4. But you said you were looking for a formula that would cover any case. Expanded Investigations Modification to the Problem Statement: Given a rectangular sheet of cardboard 15 in by 25 in. In units, what are the dimensions of the box? So if you can divide all of the terms by 9, it won't change the equation. Because of this previous knowledge, I started with the x-value 1. Find width and length of open box given the volume A rectangular piece of metal is 30 in longer than it is wide. Let me just rewrite it. Note that we picked specific values for L and W. It'll simplify things.
So you have x plus 9 times x minus 5 is equal to 0. If we'd like to know the values of x where the slope is horizontal - that is, where the curve reaches a maximum or minimum - we can set the derivative equal to zero and solve for x.Subtract, you get 0. You need calculus to solve it but I am only 13 so I need some help. That's, literally, the volume of the box. We get the following spreadsheet when we start with 0 and increment by 1 until we reach 8. Well , 4 plus 0 plus 5 is 9, so that is divisible by 9. Let's just figure out what divided by 9 is. Choose the correct graph. I used the following spreadsheet to find a more exact answer. Using calculus and the concept of the derivative can accpmplish the same thing. There is no x value that will satisfy these equations. Volume of an Open Box This video will demonstrate how to calculate the maximum volume of an open box when congruent squares are removed from a rectangular sheet of cardboard. In fact, this is the same point you'd find by completing the graph. The smaller the red area is the flatter the box. In the above diagram, the yellow portion of the box is the bottom and the blue portions are the sides. It is not 15 by 25 , but it does have the 3 to 5 ratio that our original box has.
The size of the red area also tells you the height of the box. Let's just figure out what divided by 9 is. And that seems pretty reasonable for our reality.
So you can solve the problem by completing the graph, without using calculus.