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An open box is to be made from a square piece of cardboard, 22 inches on a side, by cutting equal squares with sides of length x from the corners and turning up the sides (see figure below). If the volume of the box is represented by v (x) = x(22 - 2x), %3D determine the domain of V(x).

An open box is to be made from a square piece of cardboard, 22 inches on a side, by cutting equal squares with sides of length x from the corners and turning up the sides (see figure below). If the volume of the box is represented by v (x) = x(22 - 2x), %3D determine the domain of V(x).

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Find the domain of V(x)

**Problem Statement:** An open box is to be made from a square piece of cardboard, 22 inches on a side, by cutting equal squares with sides of length \( x \) from the corners and turning up the sides (see figure below). If the volume of the box is represented by \( V(x) = x(22 - 2x)^2 \), determine the domain of \( V(x) \). **Figures Explanation:** 1. **Diagram of the Cardboard:** - The figure shows a square piece of cardboard with side length of 22 inches. - Four smaller squares, each with side length \( x \), are cut out from each of the corners. - The remaining shape forms a smaller square with folded edges acting as sides of the open box. 2. **3D Box Diagram:** - This is an illustration of the resulting open box when the sides are folded upwards. - The height of the box is \( x \), and the length and width of the base are both \( (22 - 2x) \). **Choice of Domain:** Select one: a. \( D = \{x \mid x > 0\} \) b. \( D = \{x \mid 0 < x < 22\} \) c. \( D = \{x \mid 44 < x < 88\} \) d. \( D = \{x \mid 11 < x < 22\} \) e. \( D = \{x \mid 0 < x < 11\} \)
Transcribed Image Text:**Problem Statement:** An open box is to be made from a square piece of cardboard, 22 inches on a side, by cutting equal squares with sides of length \( x \) from the corners and turning up the sides (see figure below). If the volume of the box is represented by \( V(x) = x(22 - 2x)^2 \), determine the domain of \( V(x) \). **Figures Explanation:** 1. **Diagram of the Cardboard:** - The figure shows a square piece of cardboard with side length of 22 inches. - Four smaller squares, each with side length \( x \), are cut out from each of the corners. - The remaining shape forms a smaller square with folded edges acting as sides of the open box. 2. **3D Box Diagram:** - This is an illustration of the resulting open box when the sides are folded upwards. - The height of the box is \( x \), and the length and width of the base are both \( (22 - 2x) \). **Choice of Domain:** Select one: a. \( D = \{x \mid x > 0\} \) b. \( D = \{x \mid 0 < x < 22\} \) c. \( D = \{x \mid 44 < x < 88\} \) d. \( D = \{x \mid 11 < x < 22\} \) e. \( D = \{x \mid 0 < x < 11\} \)
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