Question

A graphing calculator is recommended. An open box is to be constructed from a piece of cardboard 20 cm by 40 cm by cutting squares of side length x from each corner and folding up the sides, as shown in the figure. length width x x (a) Express the volume V of the box as a function of x. V(x) = 4x^3 - 120x^2 + 800x (b) What is the domain of V? (Use the fact that length and volume must be positive. Enter your answer using interval notation.) (-inf, 10)

          A graphing calculator is recommended.

An open box is to be constructed from a piece of cardboard 20 cm by 40 cm by cutting squares of side length x from each corner and folding up the sides, as shown in the figure.

length
width
x
x

(a) Express the volume V of the box as a function of x.
V(x) = 4x^3 - 120x^2 + 800x

(b) What is the domain of V? (Use the fact that length and volume must be positive. Enter your answer using interval notation.)
(-inf, 10)

A graphing calculator is recommended.

An open box is to be constructed from a piece of cardboard 20 cm by 40 cm by cutting squares of side length x from each corner and folding up the sides, as shown in the figure.

length
width
x
x

(a) Express the volume V of the box as a function of x.
V(x) = 4x^3 - 120x^2 + 800x

(b) What is the domain of V? (Use the fact that length and volume must be positive. Enter your answer using interval notation.)
(-inf, 10)

Added by Glenn W.

Precalculus with Limits

Ron Larson 2nd Edition

Instant Answer

Solved by Expert Khushbu Rani

08/27/2023

Step 1

To do this, we need to find the dimensions of the box in terms of x. From the diagram, we can see that the length of the box is 20 - x and the width is 40 - x. The height of the box is x. Therefore, the volume of the box is V(x) = (20 - x)(40 - x)(x) = x(800 - Show more…

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Graphing calculator is recommended. An open box is to be constructed from a piece of cardboard 20 cm by 40 cm by cutting squares of side length x from each corner and folding up the sides, as shown in the figure. Express the volume V of the box as a function of x. (b) What is the domain of V? (Use the fact that length and volume must be positive. Enter your answer using interval notation.)