Elena is making an open top box by cutting squares out of the corners of a piece of paper that is 5 in wide and 7 in long and then folding up the sides. If the side lengths of her... Elena is making an open top box by cutting squares out of the corners of a piece of paper that is 5 in wide and 7 in long and then folding up the sides. If the side lengths of her square cutouts are ____inches then the volume of the box is given by V(x)=x (5-2x) (7-2x)
Understand the Problem
The problem describes a scenario where squares are cut from the corners of a rectangular piece of paper to form an open-top box. The volume of the box is given as a function of x, where x represents the side length of the cut-out squares. The task is simply the introduction of the problem, and defining the equation of the volume.
Answer
$x$ is the side length of the cut-out squares, and $V$ is the volume of the box as a function of $x$.
Answer for screen readers
$x$ represents the side length of the squares cut from each corner of the rectangular piece of paper, and $V$ is the volume of the open-top box as a function of $x$.
Steps to Solve
Here, there are only definitions to reiterate, so no calculation steps are involved.
- Define $x$
$x$ represents the side length of the squares cut from each corner of the rectangular piece of paper.
- Define the volume $V$
The volume $V$ of the open-top box is given as a function of $x$.
$x$ represents the side length of the squares cut from each corner of the rectangular piece of paper, and $V$ is the volume of the open-top box as a function of $x$.
More Information
Understanding how the dimensions of the box relate to $x$ is crucial for setting up the volume equation. If the original dimensions of the paper are known, the dimensions of the box can be expressed in terms of $x$.
Tips
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