Math 111 Focus Set 6 Name: Answer the following questions. Your work will be assessed on completeness, correctness, and presentation. Please refer to the Focus Set Guidelines for additional information on presentation of your work (pencil, solutions on separate paper, legible handwriting, organized solution, proper labeling, etc.) The following is used for all problems 1-6 below: A scientist adds 60 ml of pure water and 15 ml of acid to a beaker, creating a 20% acid solution. 1. Explain/show how this 20% value is calculated. 2. Explain/show how adding an additional 45 ml of pure water will give you a 12.5% acid solution. 3. Model the scenario above, where the concentration of acid is a function of the amount of water added. Hint: This should a rational function. 4. Discuss practical aspects of your function and what they mean in this context: a. Domain b. Range c. When is your function Increasing, decreasing, constant? d. Vertical and horizontal asymptotes 5. How many ml of water must be added to obtain a _% solution? (you pick a percentage, but your solution should include algebra) 6. Discuss the inverse of your function a. Find and name your inverse function using reasonable notation. b. What are the practical domain and range of your inverse function? c. Discuss how your inverse can be used. In other words, what would be the purpose of using your inverse function? Give an example using your inverse and explain it using the context.
Math 111 Focus Set 6 Name: Answer the following questions. Your work will be assessed on completeness, correctness, and presentation. Please refer to the Focus Set Guidelines for additional information on presentation of your work (pencil, solutions on separate paper, legible handwriting, organized solution, proper labeling, etc.) The following is used for all problems 1-6 below: A scientist adds 60 ml of pure water and 15 ml of acid to a beaker, creating a 20% acid solution. 1. Explain/show how this 20% value is calculated. 2. Explain/show how adding an additional 45 ml of pure water will give you a 12.5% acid solution. 3. Model the scenario above, where the concentration of acid is a function of the amount of water added. Hint: This should a rational function. 4. Discuss practical aspects of your function and what they mean in this context: a. Domain b. Range c. When is your function Increasing, decreasing, constant? d. Vertical and horizontal asymptotes 5. How many ml of water must be added to obtain a _% solution? (you pick a percentage, but your solution should include algebra) 6. Discuss the inverse of your function a. Find and name your inverse function using reasonable notation. b. What are the practical domain and range of your inverse function? c. Discuss how your inverse can be used. In other words, what would be the purpose of using your inverse function? Give an example using your inverse and explain it using the context.
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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Transcribed Image Text:Math 111
Focus Set 6
Name:
Answer the following questions. Your work will be assessed on completeness, correctness, and
presentation. Please refer to the Focus Set Guidelines for additional information on presentation
of your work (pencil, solutions on separate paper, legible handwriting, organized solution, proper
labeling, etc.)
The following is used for all problems 1-6 below: A scientist adds 60 mL of pure water and 15
ml of acid to a beaker, creating a 20% acid solution.
1. Explain/show how this 20% value is calculated.
2. Explain/show how adding an additional 45 mL of pure water will give you a 12.5% acid
solution.
3. Model the scenario above, where the concentration of acid is a function of the amount of
water added. Hint: This should a rational function.
4. Discuss practical aspects of your function and what they mean in this context:
a. Domain
b. Range
c. When is your function Increasing, decreasing, constant?
d. Vertical and horizontal asymptotes
5. How many ml of water must be added to obtain a
percentage, but your solution should include algebra)
6. Discuss the inverse of your function
_% solution? (you pick a
a. Find and name your inverse function using reasonable notation.
b. What are the practical domain and range of your inverse function?
c. Discuss how your inverse can be used. In other words, what would be the
purpose of using your inverse function? Give an example using your inverse and
explain it using the context.
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