a company making rectangular fish tanks is restricting the sum of their total dimensions to 52 inches.for one group of designs.the length and width will be the same.which of the following functions represents the volume in terms of the width?
To determine the volume of a rectangular fish tank, you need to multiply its length, width, and height. In this case, since the length and width are the same, let's call them both "x".
Given that the sum of the length, width, and height should be restricted to 52 inches, we can set up an equation:
2x + x = 52.
This equation accounts for the length, width, and height (which is just another x since it's a square tank).
Simplifying the equation, we get:
3x = 52.
To isolate x, we divide both sides of the equation by 3:
x = 52/3.
Now that we have the value of x, we can express the volume in terms of the width. As mentioned, both the width and length are equal to x, so:
Volume = x * x * x = x^3.
Substituting the value of x, we have:
Volume = (52/3)^3.
Therefore, the function representing the volume in terms of the width is:
Volume = (52/3)^3.