9. Using the contour map, answer the questions that follow. (a) Estimate fe and fy at point B. (b) Estimate fa and fy at point C. (c) What is the sign of fx at point B? (d) What is the sign of fy at point B? 2 0- -2 -4 -20 B -10 70 50 30 /// 10 0. 10 C -30 -10 1° -4 -2 0 4 2 Rogawski et al., Calculus: Early Transcendentals, 4e, © 2019 W. H. Freeman and Company -30 -50 -70 111 -X
9. Using the contour map, answer the questions that follow. (a) Estimate fe and fy at point B. (b) Estimate fa and fy at point C. (c) What is the sign of fx at point B? (d) What is the sign of fy at point B? 2 0- -2 -4 -20 B -10 70 50 30 /// 10 0. 10 C -30 -10 1° -4 -2 0 4 2 Rogawski et al., Calculus: Early Transcendentals, 4e, © 2019 W. H. Freeman and Company -30 -50 -70 111 -X
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
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Hi I am really struggling with this problem I don't even know how to start this problem can you please help me I am desperate because I don't know how to do this problem can you please help me.
can you do this step by step and can you label the parts as well please I really need help
![**Contour Map Analysis**
Below is a contour map from Rogawski et al., *Calculus: Early Transcendentals, 4e*, © 2019 W. H. Freeman and Company. Using this contour map, we will address the following questions:
![Contour Map]()
(a) Estimate \( f_x \) and \( f_y \) at point \( B \).
(b) Estimate \( f_x \) and \( f_y \) at point \( C \).
(c) What is the sign of \( f_x \) at point \( B \)?
(d) What is the sign of \( f_y \) at point \( B \)?
### Detailed Explanation of the Contour Map:
- **Axes:** The \( x \)-axis ranges from \(-4\) to \(4\) and the \( y \)-axis from \(-4\) to \(4\).
- **Contour Lines:** The map features contour lines labeled with values indicating different elevations (or potential function values): \( -70, -50, -30, -10, 0, 10, 30, 50, \) and \( 70 \).
- **Points of Interest:**
- **\( A \):** Located at \((4, -2)\)
- **\( B \):** Approximately at \((-2, 2)\)
- **\( C \):** Approximately at \((2, 2)\)
### Questions and Solutions
1. **Estimate \( f_x \) and \( f_y \) at point \( B \):**
- \( f_x \) represents the rate of change of the function \( f \) in the \( x \)-direction. By observing the contour lines passing through or near point \( B \), we estimate \( f_x \) by the spacing between contours in the \( x \)-direction.
- \( f_y \) represents the rate of change of \( f \) in the \( y \)-direction which can be similarly estimated by the spacing between the contours in the \( y \)-direction.
2. **Estimate \( f_x \) and \( f_y \) at point \( C \):**
- Similar to point \( B \), we analyze the contour lines around point \( C \):
- For \( f_x \), observe the changes in contour spacing horizontally through \( C \).
- For \( f_y](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F465caa6c-d81b-4842-ae73-3b358c19bf60%2Fe7a85a65-b60f-49c7-b241-7c9e5fd4edfa%2Fued23a9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Contour Map Analysis**
Below is a contour map from Rogawski et al., *Calculus: Early Transcendentals, 4e*, © 2019 W. H. Freeman and Company. Using this contour map, we will address the following questions:
![Contour Map]()
(a) Estimate \( f_x \) and \( f_y \) at point \( B \).
(b) Estimate \( f_x \) and \( f_y \) at point \( C \).
(c) What is the sign of \( f_x \) at point \( B \)?
(d) What is the sign of \( f_y \) at point \( B \)?
### Detailed Explanation of the Contour Map:
- **Axes:** The \( x \)-axis ranges from \(-4\) to \(4\) and the \( y \)-axis from \(-4\) to \(4\).
- **Contour Lines:** The map features contour lines labeled with values indicating different elevations (or potential function values): \( -70, -50, -30, -10, 0, 10, 30, 50, \) and \( 70 \).
- **Points of Interest:**
- **\( A \):** Located at \((4, -2)\)
- **\( B \):** Approximately at \((-2, 2)\)
- **\( C \):** Approximately at \((2, 2)\)
### Questions and Solutions
1. **Estimate \( f_x \) and \( f_y \) at point \( B \):**
- \( f_x \) represents the rate of change of the function \( f \) in the \( x \)-direction. By observing the contour lines passing through or near point \( B \), we estimate \( f_x \) by the spacing between contours in the \( x \)-direction.
- \( f_y \) represents the rate of change of \( f \) in the \( y \)-direction which can be similarly estimated by the spacing between the contours in the \( y \)-direction.
2. **Estimate \( f_x \) and \( f_y \) at point \( C \):**
- Similar to point \( B \), we analyze the contour lines around point \( C \):
- For \( f_x \), observe the changes in contour spacing horizontally through \( C \).
- For \( f_y
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