300 T(w) = 530 - w Here is the graph of y = T(w): 10 2. 100 200 300 400 500 600 w (headwind speed) What does T(110) mean in this situation? At what value of w does the graph have a vertical asymptote? Explain how you know and what the asymptote means in this situation. (Answer all parts of this question in the box below.) T (travel time)
300 T(w) = 530 - w Here is the graph of y = T(w): 10 2. 100 200 300 400 500 600 w (headwind speed) What does T(110) mean in this situation? At what value of w does the graph have a vertical asymptote? Explain how you know and what the asymptote means in this situation. (Answer all parts of this question in the box below.) T (travel time)
Algebra and Trigonometry (6th Edition)
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![### Understanding Travel Time and Headwind Speed
**Equation:** \( T(w) = \frac{300}{530 - w} \)
Here is the graph of \( y = T(w) \):
[Graph Explanation]
- The graph represents the relationship between travel time (\( T \), in hours) and headwind speed (\( w \), in miles per hour).
- The x-axis represents the headwind speed \( w \) ranging from 0 to 600 mph.
- The y-axis represents the travel time \( T \), with values ranging from 0 to 10 hours.
**Key Observations:**
- As headwind speed (\( w \)) increases, the travel time (\( T \)) also increases.
- The graph shows a vertical asymptote, meaning that as \( w \) approaches a certain value, \( T \) tends to infinity.
**Questions for Understanding:**
1. **What does \( T(110) \) mean in this situation?**
- Answer this by calculating \( T(110) \) using the given equation.
2. **At what value of \( w \) does the graph have a vertical asymptote? Explain how you know and what the asymptote means in this situation.**
- Determine the value of \( w \) where the denominator of the equation \( 530 - w \) approaches zero.
- Discuss the implications of an infinite travel time within the context of increasing headwind speed.
---
**Answer Box:**
Provide explanations for the following questions using appropriate mathematical calculations and reasoning:
1. \( T(110) \) calculation.
2. Explanation of the vertical asymptote and its significance in this context.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4e202941-0b4f-4d55-bf31-4c67329224e7%2F389e922d-36eb-41b2-b9c4-a455438ffa7c%2Faysf3n_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding Travel Time and Headwind Speed
**Equation:** \( T(w) = \frac{300}{530 - w} \)
Here is the graph of \( y = T(w) \):
[Graph Explanation]
- The graph represents the relationship between travel time (\( T \), in hours) and headwind speed (\( w \), in miles per hour).
- The x-axis represents the headwind speed \( w \) ranging from 0 to 600 mph.
- The y-axis represents the travel time \( T \), with values ranging from 0 to 10 hours.
**Key Observations:**
- As headwind speed (\( w \)) increases, the travel time (\( T \)) also increases.
- The graph shows a vertical asymptote, meaning that as \( w \) approaches a certain value, \( T \) tends to infinity.
**Questions for Understanding:**
1. **What does \( T(110) \) mean in this situation?**
- Answer this by calculating \( T(110) \) using the given equation.
2. **At what value of \( w \) does the graph have a vertical asymptote? Explain how you know and what the asymptote means in this situation.**
- Determine the value of \( w \) where the denominator of the equation \( 530 - w \) approaches zero.
- Discuss the implications of an infinite travel time within the context of increasing headwind speed.
---
**Answer Box:**
Provide explanations for the following questions using appropriate mathematical calculations and reasoning:
1. \( T(110) \) calculation.
2. Explanation of the vertical asymptote and its significance in this context.
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