Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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![**Using Symbols to Represent Mathematical Phrases**
In this exercise, we will learn how to translate a verbal phrase into a symbolic mathematical expression using the variable \( x \).
**Problem Statement:**
Convert the following phrase into symbols:
"The sum of 146 and the product of a number raised to the third power and 14."
**Solution:**
To express the given phrase in symbols, follow these steps:
1. Identify the parts of the phrase:
- "The sum of 146..."
- "...and the product of a number raised to the third power and 14."
2. Let \( x \) represent the number in the expression.
3. Break down the phrase into mathematical symbols:
- "A number raised to the third power" becomes \( x^3 \).
- "The product of a number raised to the third power and 14" becomes \( 14x^3 \).
- "The sum of 146 and the product..." becomes \( 146 + 14x^3 \).
Thus, the phrase is symbolically written as:
\[ 146 + 14x^3 \]
**Note:**
Ensure each step correctly translates the verbal description into mathematical operations. Use parentheses where necessary to maintain the correct order of operations.
Make sure to check your inputs and calculations for accuracy.
**Interactive Components:**
- Entered the expression into the input field panel provided on the website.
- Confirmed the accurate formulation using the "Check" button.
**Interface Controls:**
- "Save For Later" option to save progress.
- "Submit Answer" to finalize and check the solution with provided tools.
This approach facilitates understanding complex word problems by systematically converting them into mathematical expressions.](https://content.bartleby.com/qna-images/question/93d6464e-f155-4940-8921-7114e2ab97cc/c4625c0f-f4e4-4779-824f-bc44008077b9/x6eef2c_processed.jpeg)
Transcribed Image Text:**Using Symbols to Represent Mathematical Phrases**
In this exercise, we will learn how to translate a verbal phrase into a symbolic mathematical expression using the variable \( x \).
**Problem Statement:**
Convert the following phrase into symbols:
"The sum of 146 and the product of a number raised to the third power and 14."
**Solution:**
To express the given phrase in symbols, follow these steps:
1. Identify the parts of the phrase:
- "The sum of 146..."
- "...and the product of a number raised to the third power and 14."
2. Let \( x \) represent the number in the expression.
3. Break down the phrase into mathematical symbols:
- "A number raised to the third power" becomes \( x^3 \).
- "The product of a number raised to the third power and 14" becomes \( 14x^3 \).
- "The sum of 146 and the product..." becomes \( 146 + 14x^3 \).
Thus, the phrase is symbolically written as:
\[ 146 + 14x^3 \]
**Note:**
Ensure each step correctly translates the verbal description into mathematical operations. Use parentheses where necessary to maintain the correct order of operations.
Make sure to check your inputs and calculations for accuracy.
**Interactive Components:**
- Entered the expression into the input field panel provided on the website.
- Confirmed the accurate formulation using the "Check" button.
**Interface Controls:**
- "Save For Later" option to save progress.
- "Submit Answer" to finalize and check the solution with provided tools.
This approach facilitates understanding complex word problems by systematically converting them into mathematical expressions.
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