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(c) 60 70 M 30 14 6 10 | | 3 5 7 2 20 바 30 6 3 60 20 10 | 5 70 14 7

(c) 60 70 M 30 14 6 10 | | 3 5 7 2 20 바 30 6 3 60 20 10 | 5 70 14 7

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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Consider the partial order with domain {3, 5, 6, 7, 10, 14, 20, 30, 60, 70} and with x ≤ y if
x evenly divides y. Select the correct Hasse diagram for the partial order. 

### Line Graphs Depiction The image contains two line graphs labeled (c) and (d) respectively. Both graphs present a series of vertical and zigzagged lines, each numbered at key segments of the lines. Below is a detailed description and transcription of both graphs: #### Graph (c): 1. **Lines and Segments**: - A zigzag line starts from the bottom with segments marked as follows: - From the left bottom, a line segment of 3 units going upwards. - Continues with a segment of 6 units. - An angled segment connects the previous one, rising to a 30-unit mark. - Proceeding further, another angled segment reaches a point marked at 60 units and finally at 70 units. 2. **Vertical Numbers**: - On the left vertical side in numerical order from top to bottom: 30, 6, 3. - On the middle vertical side: 60, 20, 10, 5. - On the right vertical side: 70, 14, 7. #### Graph (d): 1. **Lines and Segments**: - This graph also features a zigzag pattern but differs slightly from Graph (c): - Starts from the bottom with 3 units going upwards. - Follows with a 6-unit vertical line. - An angled segment reaches the mark of 30 units. - Another angled line surpasses the 60-unit and 70-unit mark. 2. **Vertical Numbers**: - On the left vertical side in numerical order from top to bottom: 30, 6, 3. - On the middle vertical side: 60, 20, 10, 5. - On the right vertical side: 70, 14, 7. ### Analysis: Both graphs illustrate numerical relationships and developmental structures often used in mathematical or scientific visual data representation. These types of graphs can help in depicting progressive numerical changes, likely suitable for educational purposes such as teaching students how to read and interpret data through graphical representation. The consistent numerical annotations provide clear markers for understanding shifts and transitions in the values displayed on both graphs.
Transcribed Image Text:### Line Graphs Depiction The image contains two line graphs labeled (c) and (d) respectively. Both graphs present a series of vertical and zigzagged lines, each numbered at key segments of the lines. Below is a detailed description and transcription of both graphs: #### Graph (c): 1. **Lines and Segments**: - A zigzag line starts from the bottom with segments marked as follows: - From the left bottom, a line segment of 3 units going upwards. - Continues with a segment of 6 units. - An angled segment connects the previous one, rising to a 30-unit mark. - Proceeding further, another angled segment reaches a point marked at 60 units and finally at 70 units. 2. **Vertical Numbers**: - On the left vertical side in numerical order from top to bottom: 30, 6, 3. - On the middle vertical side: 60, 20, 10, 5. - On the right vertical side: 70, 14, 7. #### Graph (d): 1. **Lines and Segments**: - This graph also features a zigzag pattern but differs slightly from Graph (c): - Starts from the bottom with 3 units going upwards. - Follows with a 6-unit vertical line. - An angled segment reaches the mark of 30 units. - Another angled line surpasses the 60-unit and 70-unit mark. 2. **Vertical Numbers**: - On the left vertical side in numerical order from top to bottom: 30, 6, 3. - On the middle vertical side: 60, 20, 10, 5. - On the right vertical side: 70, 14, 7. ### Analysis: Both graphs illustrate numerical relationships and developmental structures often used in mathematical or scientific visual data representation. These types of graphs can help in depicting progressive numerical changes, likely suitable for educational purposes such as teaching students how to read and interpret data through graphical representation. The consistent numerical annotations provide clear markers for understanding shifts and transitions in the values displayed on both graphs.
### Understanding Tension in Members of a Truss Here we have two figures (a) and (b) representing the tension distribution in the members of a simple truss. The diagrams use red lines to illustrate the forces acting on each section, along with labeled numerical values for clarity. #### Figure (a) - **Vertical Columns**: - From left to right: - First column: 30 (top), 6 (middle), and 3 (bottom) - Second column: 60 (top), 20 (middle), 10 (bottom), and 5 (bottom) - Third column: 70 (top) and 14 (bottom), 7 (bottom) - **Description**: - The red lines indicate sections of members with varying internal forces. - There is a distribution where the forces start high at the top, with a progressive drop as it descends in the first and second columns. - The forces in the third column (7 and 14) are at the bottom. #### Figure (b) - **Vertical Columns**: - From left to right: - First column: 30 (top), 6 (middle), and 3 (bottom) - Second column: 60 (top), 20 (middle), and 10 (bottom), 5 (bottom) - Third column: 70 (top) and 14 (bottom), seven (bottom) - **Description**: - Similar to figure (a), the red lines indicate the force distribution in each member with slight variations in connections between the columns. - The force transitions show the dropping force trend from top to bottom, implying a functional similarity between the two configurations. ### Key Points 1. Both diagrams are pixel representations of the truss members' internal forces. 2. The numerical values likely indicate the magnitude of forces in each member. 3. They illustrate the importance of the structural design and ensuring that forces are balanced for stability and integrity. ### Purpose Understanding these diagrams helps in: - **Structural Analysis** by providing a visual representation of how forces are distributed within a structure. - **Design Optimization** where an engineer can redesign weak members for enhanced performance. - **Safety Assurance** by assessing the force distribution and ensuring no member exceeds permissible limits which might lead to failure. Analyzing such diagrams is crucial for structural engineers and architects who need to ensure that
Transcribed Image Text:### Understanding Tension in Members of a Truss Here we have two figures (a) and (b) representing the tension distribution in the members of a simple truss. The diagrams use red lines to illustrate the forces acting on each section, along with labeled numerical values for clarity. #### Figure (a) - **Vertical Columns**: - From left to right: - First column: 30 (top), 6 (middle), and 3 (bottom) - Second column: 60 (top), 20 (middle), 10 (bottom), and 5 (bottom) - Third column: 70 (top) and 14 (bottom), 7 (bottom) - **Description**: - The red lines indicate sections of members with varying internal forces. - There is a distribution where the forces start high at the top, with a progressive drop as it descends in the first and second columns. - The forces in the third column (7 and 14) are at the bottom. #### Figure (b) - **Vertical Columns**: - From left to right: - First column: 30 (top), 6 (middle), and 3 (bottom) - Second column: 60 (top), 20 (middle), and 10 (bottom), 5 (bottom) - Third column: 70 (top) and 14 (bottom), seven (bottom) - **Description**: - Similar to figure (a), the red lines indicate the force distribution in each member with slight variations in connections between the columns. - The force transitions show the dropping force trend from top to bottom, implying a functional similarity between the two configurations. ### Key Points 1. Both diagrams are pixel representations of the truss members' internal forces. 2. The numerical values likely indicate the magnitude of forces in each member. 3. They illustrate the importance of the structural design and ensuring that forces are balanced for stability and integrity. ### Purpose Understanding these diagrams helps in: - **Structural Analysis** by providing a visual representation of how forces are distributed within a structure. - **Design Optimization** where an engineer can redesign weak members for enhanced performance. - **Safety Assurance** by assessing the force distribution and ensuring no member exceeds permissible limits which might lead to failure. Analyzing such diagrams is crucial for structural engineers and architects who need to ensure that
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