Question

I need help finding this information for a box. I've gotten up to step 5, but past that, I'm very lost.
V=125 in^3, length=5 in, width=5 in, height=5 in
It took the formula V=lwh, and changed it into looking for length(l=v/wh). Then it told me to change l to x, and the whatever difference height is from width, so it becomes x=v/(x+0). After that is where I need help, please
Simplify the equation and write it in standard form.

Find the solutions to this equation algebraically using the Fundamental Theorem of Algebra, the Rational Root Theorem, Descartes' Rule of Signs, and the Factor Theo

Answer 1

Can u please post the actual question please @HannahChristine , BTW your pic looks cute and funny!

Answer 2

Thanks.
It's fairly long, because it's an activity, but my box is 5x5x5.
Option 2 - Rectangular Box

You will need the following materials to find the volume of a rectangular box:

A rectangular box such as a cereal or shoe box
Ruler or tape measure
Graphing technology (e.g., graphing calculator or GeoGebra)

Procedure:

Measure and record the length, width and height of the rectangular box you have chosen in inches. Round to the nearest whole number.

Apply the formula of a rectangular box (V = lwh) to find the volume of the object.

Now suppose you knew the volume of this object and the relation of the length to the width and height, but did not know the length. Rewriting the equation with one variable would result in a polynomial equation that you could solve to find the length.

Rewrite the formula using the variable x for the length. Substitute the value of the volume found in step 2 for V and express the width and height of the object in terms of x plus or minus a constant. For example, if the height measurement is 4 inches longer than the length, then the expression for the height will be (x + 4).

Simplify the equation and write it in standard form.

Find the solutions to this equation algebraically using the Fundamental Theorem of Algebra, the Rational Root Theorem, Descartes' Rule of Signs, and the Factor Theorem.

(Hint: If the numbers are large, graph the function first using GeoGebra to help you find one of the zeros. Use that zero to find the depressed equation which can be solved by factoring or the quadratic formula.)

Substitute 0 for the function notation and, using graphing technology, graph the function.

Answer the following questions
What does the Fundamental Theorem of Algebra indicate with respect to this equation?
What are the possible rational solutions of your equation?
How many possible positive, negative and complex solutions are there in your equation?
Graph the function. What type of function has been graphed (linear, quadratic, cubic, or quartic)? Provide your reasoning and describe the end behavior of the graph.
How do the solutions of the equation compare to the length of the rectangular object, and the x-intercept of the graph? Provide both the solutions and measurement.

Send to your instructor a lab report with the following information:
Title(1 point)
Materials Used (1 point)
Procedure(1 point)
Data (20 points)
Include:
A description of the rectangular box chosen (1 point)
The length, width, height and volume of the object (3 points)
The equation for the volume of the object written in terms of x (2 point)
The graph of the function (2 point)
The solutions of the equation including the algebraic work used to find the solutions (6 points)
Answers to the five questions (6 points)
Conclusion(2 points)
What did you think of the project?
What did you learn?
Do you have any questions or concerns?

Answer 3

Now, as the problem stated l = x,
and we are assuming that the height is longer than length and width is shorter than length ( it does not matter how you take it )
then h = x+a :: a is constant
and w = x-b :: b is constant

Answer 4

Now i think you can proceed further!