Question
Math Equation Response Question
Curtis is making a box out of a square piece of cardboard. He cuts out squares from each corner of the cardboard and then folds the cardboard into a box without a lid.
Curtis writes the volume of the box as (50-2x)(50-2x)(x)in cubed. Identify the parts of the volume that represent the area of the base of the box.
This field supports both keypad and keyboard input. Use the keyboard to access and interact with the on-screen math keypad, which accepts LaTeX markup. Use the down arrow key to open the keypad and navigate its buttons. Use the escape key to close the keypad and return to the input field.
Curtis is making a box out of a square piece of cardboard. He cuts out squares from each corner of the cardboard and then folds the cardboard into a box without a lid.
Curtis writes the volume of the box as (50-2x)(50-2x)(x)in cubed. Identify the parts of the volume that represent the area of the base of the box.
This field supports both keypad and keyboard input. Use the keyboard to access and interact with the on-screen math keypad, which accepts LaTeX markup. Use the down arrow key to open the keypad and navigate its buttons. Use the escape key to close the keypad and return to the input field.
Answers
GPT-4o mini
In the expression for the volume of the box, \( V = (50 - 2x)(50 - 2x)(x) \), the parts that represent the area of the base of the box can be identified as follows:
The area of the base of the box is determined by the dimensions of the base, which are given by the two factors \( (50 - 2x) \) and \( (50 - 2x) \).
Thus, the area of the base \( A \) can be expressed as:
\[
A = (50 - 2x)(50 - 2x) = (50 - 2x)^2
\]
So, the part of the volume equation that represents the area of the base is \( (50 - 2x)(50 - 2x) \), or equivalently \( (50 - 2x)^2 \).
The area of the base of the box is determined by the dimensions of the base, which are given by the two factors \( (50 - 2x) \) and \( (50 - 2x) \).
Thus, the area of the base \( A \) can be expressed as:
\[
A = (50 - 2x)(50 - 2x) = (50 - 2x)^2
\]
So, the part of the volume equation that represents the area of the base is \( (50 - 2x)(50 - 2x) \), or equivalently \( (50 - 2x)^2 \).