Suppose the dimensions of the cardboard in Example 4.33 are Nx10 in. by (N+1)x10 in., where N is the fourth non-zero digit of your student ID number. For example, if my student ID number is 13002506, then the fourth non-zero digit is 5 (ignore all zeros), and the dimensions of my cardboard are 50 in. by 60 in. Please let me know if you are unsure how to determine the dimensions of the cardboard material for you problem. (a) Let x be the side length of each square and write the volume of the open-top box as a
Suppose the dimensions of the cardboard in Example 4.33 are Nx10 in. by (N+1)x10 in., where N is the fourth non-zero digit of your student ID number. For example, if my student ID number is 13002506, then the fourth non-zero digit is 5 (ignore all zeros), and the dimensions of my cardboard are 50 in. by 60 in. Please let me know if you are unsure how to determine the dimensions of the cardboard material for you problem. (a) Let x be the side length of each square and write the volume of the open-top box as a
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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N = 1
Transcribed Image Text:### Example 4.33: Cardboard Dimensions and Open-Top Box Volume
Suppose the dimensions of the cardboard in Example 4.33 are **Nx10 inches** by **(N+1)x10 inches**, where **N** is the fourth non-zero digit of your student ID number.
#### Example:
If your student ID number is 13002506, then the fourth non-zero digit is 5 (ignore all zeros), and the dimensions of your cardboard are **50 inches by 60 inches**. Please let me know if you are unsure how to determine the dimensions of the cardboard material for your problem.
#### Problems:
1. **Let \( x \) be the side length of each square and write the volume of the open-top box as a function of \( x \).**
2. **Determine the domain of consideration for \( x \), as well as**
3. **the dimensions of the box with maximum volume.**
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