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What is the restricted domain of this problem? (That is, what x values "make sense"?) Number Number What is the restricted range of this problem? (That is, what V values "make sense"?)

What is the restricted domain of this problem? (That is, what x values "make sense"?) Number Number What is the restricted range of this problem? (That is, what V values "make sense"?)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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I only need the restricted range and the questions under it I just posted the first picture as a refrence 

**Transcription: Volume Calculation of a Box** **Problem Statement:** 1. **Volume Function Equation:** - What is the equation that represents the Volume of the box as a function of the cut size of the box? \( V(x) = \) (Input field with math operation buttons: \( a^b, \frac{a}{b}, \sqrt{a}, |a|, \pi, \sin(a) \)) 2. **Domain Restriction:** - What is the restricted domain of this problem? (That is, what x values "make sense"?) \( \text{Number} \leq x \leq \text{Number} \) 3. **Range Restriction:** - What is the restricted range of this problem? (That is, what V values "make sense"?) \( \text{Number} \leq V(x) \leq \text{Number} \) (round to 2 decimal places) 4. **Optimization Questions:** - To maximize the volume of the newly created box, how much should be cut from each corner? \( x = \text{Number} \) inches - What is the maximum volume the box can hold? \( V = \text{Number} \, \text{in}^3 \) 5. **Largest Possible Cut Size:** - What is the largest cut size you can cut out of the paper and still create a box with volume 130 \( \text{in}^3 \)? \( x = \text{Number} \) (Note: Each "Number" represents an interactive input field where specific values are to be input by the student solving the problem.)
Transcribed Image Text:**Transcription: Volume Calculation of a Box** **Problem Statement:** 1. **Volume Function Equation:** - What is the equation that represents the Volume of the box as a function of the cut size of the box? \( V(x) = \) (Input field with math operation buttons: \( a^b, \frac{a}{b}, \sqrt{a}, |a|, \pi, \sin(a) \)) 2. **Domain Restriction:** - What is the restricted domain of this problem? (That is, what x values "make sense"?) \( \text{Number} \leq x \leq \text{Number} \) 3. **Range Restriction:** - What is the restricted range of this problem? (That is, what V values "make sense"?) \( \text{Number} \leq V(x) \leq \text{Number} \) (round to 2 decimal places) 4. **Optimization Questions:** - To maximize the volume of the newly created box, how much should be cut from each corner? \( x = \text{Number} \) inches - What is the maximum volume the box can hold? \( V = \text{Number} \, \text{in}^3 \) 5. **Largest Possible Cut Size:** - What is the largest cut size you can cut out of the paper and still create a box with volume 130 \( \text{in}^3 \)? \( x = \text{Number} \) (Note: Each "Number" represents an interactive input field where specific values are to be input by the student solving the problem.)
We are constructing a box from a piece of paper. The paper is a piece of "ledger-sized paper" which measures 11"×17". We will remove a square of size "x" inches from each corner and turn up the edges. A piece of ledger paper is the same size as taping the long sides of two pieces of standard 8.5×11 paper together. **Diagram Explanation:** - The diagram shows a rectangular piece of paper measuring 11 inches by 17 inches. - Dotted lines indicate squares of size "x" inches being cut out from each corner of the rectangle. - Once these squares are removed, the edges are turned up to form a box. Once we remove the squares of size "x" inches from each corner and turn up the edges, we create a box: Label the dimensions of the newly created box using the variable "x". **Calculations:** - **Height (h)**: Provided space to calculate based on the variable "x". - **Width (w)**: Provided space to calculate based on the variable "x". Each calculation section includes mathematical input fields, allowing for calculations using basic arithmetic operations and functions such as exponents, square roots, and trigonometric functions.
Transcribed Image Text:We are constructing a box from a piece of paper. The paper is a piece of "ledger-sized paper" which measures 11"×17". We will remove a square of size "x" inches from each corner and turn up the edges. A piece of ledger paper is the same size as taping the long sides of two pieces of standard 8.5×11 paper together. **Diagram Explanation:** - The diagram shows a rectangular piece of paper measuring 11 inches by 17 inches. - Dotted lines indicate squares of size "x" inches being cut out from each corner of the rectangle. - Once these squares are removed, the edges are turned up to form a box. Once we remove the squares of size "x" inches from each corner and turn up the edges, we create a box: Label the dimensions of the newly created box using the variable "x". **Calculations:** - **Height (h)**: Provided space to calculate based on the variable "x". - **Width (w)**: Provided space to calculate based on the variable "x". Each calculation section includes mathematical input fields, allowing for calculations using basic arithmetic operations and functions such as exponents, square roots, and trigonometric functions.
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