### Linear Approximation and Error Calculation #### Problem Statement 1. **Linear Approximation Calculation:** Use the Linear Approximation to estimate the value and compare it with the value given by a calculator. \( \sqrt{(4.92)(3.04)(4.04)} \) Use decimal notation and give your answer to four decimal places. **Student's Answer:** \[ \sqrt{(4.92)(3.04)(4.04)} \approx 7.7738 \] This is marked as **Incorrect**. 2. **Percentage Error Calculation:** Calculate the percentage error obtained by using the approximation. Percentage error is the ratio of the absolute value of the error to the actual value of the expression, expressed as a percentage. Use decimal notation and give your answer to three decimal places. **Student's Answer:** \[ \text{Percentage error: } 0.3496\% \] This is marked as **Incorrect**. #### Explanation 1. **Linear Approximation:** - First, break down the original expression \( \sqrt{(4.92)(3.04)(4.04)} \). - Utilize a calculator to find the exact value. Compare this exact value with the approximated value. - Linear Approximation might involve truncating or simplification steps. Ensure detailed calculation steps for better understanding. 2. **Percentage Error Calculation:** - Determine the exact value of \( \sqrt{(4.92)(3.04)(4.04)} \) using a calculator. - Calculate the absolute error: \( | \text{Exact value} - \text{Approximated value} | \). - Calculate the percentage error: \[ \text{Percentage Error} = \left(\frac{\text{Absolute Error}}{\text{Exact Value}}\right) \times 100% \] Verify calculations up to three decimal places as required. #### Diagram/Graph Explanation There are no diagrams or graphs in this text. However, if there were, an explanation would include titles, labels, units, and how to interpret any data points or trends shown. End of transcription.
### Linear Approximation and Error Calculation #### Problem Statement 1. **Linear Approximation Calculation:** Use the Linear Approximation to estimate the value and compare it with the value given by a calculator. \( \sqrt{(4.92)(3.04)(4.04)} \) Use decimal notation and give your answer to four decimal places. **Student's Answer:** \[ \sqrt{(4.92)(3.04)(4.04)} \approx 7.7738 \] This is marked as **Incorrect**. 2. **Percentage Error Calculation:** Calculate the percentage error obtained by using the approximation. Percentage error is the ratio of the absolute value of the error to the actual value of the expression, expressed as a percentage. Use decimal notation and give your answer to three decimal places. **Student's Answer:** \[ \text{Percentage error: } 0.3496\% \] This is marked as **Incorrect**. #### Explanation 1. **Linear Approximation:** - First, break down the original expression \( \sqrt{(4.92)(3.04)(4.04)} \). - Utilize a calculator to find the exact value. Compare this exact value with the approximated value. - Linear Approximation might involve truncating or simplification steps. Ensure detailed calculation steps for better understanding. 2. **Percentage Error Calculation:** - Determine the exact value of \( \sqrt{(4.92)(3.04)(4.04)} \) using a calculator. - Calculate the absolute error: \( | \text{Exact value} - \text{Approximated value} | \). - Calculate the percentage error: \[ \text{Percentage Error} = \left(\frac{\text{Absolute Error}}{\text{Exact Value}}\right) \times 100% \] Verify calculations up to three decimal places as required. #### Diagram/Graph Explanation There are no diagrams or graphs in this text. However, if there were, an explanation would include titles, labels, units, and how to interpret any data points or trends shown. End of transcription.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 35RE
Related questions
Question
![### Linear Approximation and Error Calculation
#### Problem Statement
1. **Linear Approximation Calculation:**
Use the Linear Approximation to estimate the value and compare it with the value given by a calculator.
\( \sqrt{(4.92)(3.04)(4.04)} \)
Use decimal notation and give your answer to four decimal places.
**Student's Answer:**
\[
\sqrt{(4.92)(3.04)(4.04)} \approx 7.7738
\]
This is marked as **Incorrect**.
2. **Percentage Error Calculation:**
Calculate the percentage error obtained by using the approximation. Percentage error is the ratio of the absolute value of the error to the actual value of the expression, expressed as a percentage.
Use decimal notation and give your answer to three decimal places.
**Student's Answer:**
\[
\text{Percentage error: } 0.3496\%
\]
This is marked as **Incorrect**.
#### Explanation
1. **Linear Approximation:**
- First, break down the original expression \( \sqrt{(4.92)(3.04)(4.04)} \).
- Utilize a calculator to find the exact value. Compare this exact value with the approximated value.
- Linear Approximation might involve truncating or simplification steps. Ensure detailed calculation steps for better understanding.
2. **Percentage Error Calculation:**
- Determine the exact value of \( \sqrt{(4.92)(3.04)(4.04)} \) using a calculator.
- Calculate the absolute error: \( | \text{Exact value} - \text{Approximated value} | \).
- Calculate the percentage error:
\[
\text{Percentage Error} = \left(\frac{\text{Absolute Error}}{\text{Exact Value}}\right) \times 100%
\]
Verify calculations up to three decimal places as required.
#### Diagram/Graph Explanation
There are no diagrams or graphs in this text. However, if there were, an explanation would include titles, labels, units, and how to interpret any data points or trends shown.
End of transcription.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faccc7427-2c55-44a5-b68e-19581b7568be%2F0af8477d-dbaf-4205-ac9b-16462517eeef%2Ffdoz44_processed.png&w=3840&q=75)
Transcribed Image Text:### Linear Approximation and Error Calculation
#### Problem Statement
1. **Linear Approximation Calculation:**
Use the Linear Approximation to estimate the value and compare it with the value given by a calculator.
\( \sqrt{(4.92)(3.04)(4.04)} \)
Use decimal notation and give your answer to four decimal places.
**Student's Answer:**
\[
\sqrt{(4.92)(3.04)(4.04)} \approx 7.7738
\]
This is marked as **Incorrect**.
2. **Percentage Error Calculation:**
Calculate the percentage error obtained by using the approximation. Percentage error is the ratio of the absolute value of the error to the actual value of the expression, expressed as a percentage.
Use decimal notation and give your answer to three decimal places.
**Student's Answer:**
\[
\text{Percentage error: } 0.3496\%
\]
This is marked as **Incorrect**.
#### Explanation
1. **Linear Approximation:**
- First, break down the original expression \( \sqrt{(4.92)(3.04)(4.04)} \).
- Utilize a calculator to find the exact value. Compare this exact value with the approximated value.
- Linear Approximation might involve truncating or simplification steps. Ensure detailed calculation steps for better understanding.
2. **Percentage Error Calculation:**
- Determine the exact value of \( \sqrt{(4.92)(3.04)(4.04)} \) using a calculator.
- Calculate the absolute error: \( | \text{Exact value} - \text{Approximated value} | \).
- Calculate the percentage error:
\[
\text{Percentage Error} = \left(\frac{\text{Absolute Error}}{\text{Exact Value}}\right) \times 100%
\]
Verify calculations up to three decimal places as required.
#### Diagram/Graph Explanation
There are no diagrams or graphs in this text. However, if there were, an explanation would include titles, labels, units, and how to interpret any data points or trends shown.
End of transcription.
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