Use the contour map to calculate the average rate of change from A to B and from A to C if a = -11. -6 -4 B 6 from A to B: 4 y A 2 4 6 Ca c=0 X (Use decimal notation. Give your answers to two decimal places.)
Use the contour map to calculate the average rate of change from A to B and from A to C if a = -11. -6 -4 B 6 from A to B: 4 y A 2 4 6 Ca c=0 X (Use decimal notation. Give your answers to two decimal places.)
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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![**Using Contour Maps to Calculate Average Rate of Change**
In this exercise, we'll use a contour map to calculate the average rate of change from points \( A \) to \( B \) and from points \( A \) to \( C \), given that \( a = -11 \). Please use decimal notation and present your answers to two decimal places.
**Contour Map Explanation:**
The contour map provided shows several curves, each corresponding to a specific value of a function at different points. Key points \( A \), \( B \), and \( C \) are indicated on the map, with contours labeled for different values of the function, including \( a = 0, 2, 4, 6, 8 \).
**Instructions:**
1. Identify the coordinates of points \( A \), \( B \), and \( C \) on the contour map.
2. Calculate the difference in function values between \( A \) and \( B \) and between \( A \) and \( C \).
3. Compute the change in the slope by finding the horizontal distance between these points.
4. Use the formula for the average rate of change:
\[
\text{Average Rate of Change} = \frac{\Delta f}{\Delta x}
\]
where \( \Delta f \) is the change in function value and \( \Delta x \) is the change in x-coordinate.
**Graph/Diagram Explanation:**
- The vertical axis represents the \( y \)-coordinate.
- The horizontal axis represents the \( x \)-coordinate.
- Contour lines are labeled with constant function values.
- Points \( A \), \( B \), and \( C \) are marked within specific contours.
**Calculations:**
- From \( A \) to \( B \):
\[
\boxed{\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_}
\]
- From \( A \) to \( C \):
\[
\boxed{\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_}
\]
Ensure your calculations match the coordinates and contour labels precisely from the map, and present your answers to two decimal places for accuracy.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F465caa6c-d81b-4842-ae73-3b358c19bf60%2F02813a7b-37bf-4aa2-b5fa-61791e7d64ba%2Fpnvlagd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Using Contour Maps to Calculate Average Rate of Change**
In this exercise, we'll use a contour map to calculate the average rate of change from points \( A \) to \( B \) and from points \( A \) to \( C \), given that \( a = -11 \). Please use decimal notation and present your answers to two decimal places.
**Contour Map Explanation:**
The contour map provided shows several curves, each corresponding to a specific value of a function at different points. Key points \( A \), \( B \), and \( C \) are indicated on the map, with contours labeled for different values of the function, including \( a = 0, 2, 4, 6, 8 \).
**Instructions:**
1. Identify the coordinates of points \( A \), \( B \), and \( C \) on the contour map.
2. Calculate the difference in function values between \( A \) and \( B \) and between \( A \) and \( C \).
3. Compute the change in the slope by finding the horizontal distance between these points.
4. Use the formula for the average rate of change:
\[
\text{Average Rate of Change} = \frac{\Delta f}{\Delta x}
\]
where \( \Delta f \) is the change in function value and \( \Delta x \) is the change in x-coordinate.
**Graph/Diagram Explanation:**
- The vertical axis represents the \( y \)-coordinate.
- The horizontal axis represents the \( x \)-coordinate.
- Contour lines are labeled with constant function values.
- Points \( A \), \( B \), and \( C \) are marked within specific contours.
**Calculations:**
- From \( A \) to \( B \):
\[
\boxed{\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_}
\]
- From \( A \) to \( C \):
\[
\boxed{\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_}
\]
Ensure your calculations match the coordinates and contour labels precisely from the map, and present your answers to two decimal places for accuracy.
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