Please see attached file for the complete details of the problems.
WEEK 3 HOMEWORK
1. Why do you factor a quadratic equation before you solve? Give an example.
2. When solving a rational equation, why it is OK to remove the denominator by multiplying both sides by the LCD and why can you not do the same operation when simplifying a rational expression? Give an example.
3. What square root property is essential to solve any radical equation involving square root? Give an example.
4. What are extraneous solutions of an equation? Why do they sometimes occur in the process of solving rational or radical equations? Provide examples to support your answer. Give an example.
5. What are the different types of equations you have learned to solve? Give an example.
6. Why are there usually two solutions in quadratic equations? Give an example.
7. Choose an example of a rational equation from the textbook and present a step-by-step solution.
8. Under what situation would one or more solutions of a rational equation be unacceptable? Give an example.
6.2 Perform the indicated operation
# 76 Perform the indicated operation
6.5 Simplify each complex fraction
6.5 #64. Commuting students. At a well-known university, of the
undergraduate students commute, and of the graduate
students commute. One-tenth of the undergraduate students
drive more than 40 miles daily, and of the graduate
students drive more than 40 miles daily. If there are twice
as many undergraduate students as there are graduate
students, then what fraction of the commuters drive more than 40 miles daily?
Note: On the next question,just answer #68)
68. Telephoto lens. Use the formula from Exercise 67 to find
the image distance i for an object that is 2,000,000 mm from a 250-mm telephoto lense.
(67. Lens equation. The focal length f for a camera lens is
related to the object distance o and the image distance i by
62. Bear population. To estimate the size of the bear
population on the Keweenaw Peninsula, conservationists
captured, tagged, and released 50 bears. One year later, a
random sample of 100 bears included only 2 tagged bears.
What is the conservationist's estimate of the size of the bear population?
50. The golden ratio. The ancient Greeks thought that the
most pleasing shape for a rectangle was one for which the
ratio of the length to the width was approximately 8 to 5,
the golden ratio. If the length of a rectangular painting is
2 ft longer than its width, then for what dimensions would
the length and width have the golden ratio?
30. Rise and run. If the rise is
and the run is 5, then what is
the ratio of the rise to the run?
3. Missing proceeds. Ruth and Betty sell apples at a farmers
market. Ruth's apples sell at 2 for $1 while Betty's slightly
smaller apples sell at 3 for $1. When Betty leaves to pick
up her kids they each have 30 apples and Ruth takes
charge of both businesses. To simplify things, Ruth puts all
60 of the apples together and sells them at 5 for $2. When
Betty returns, all of the apples have been sold, but they
begin arguing over how to divide up the proceeds. What
is the problem? Explain what went wrong.
This posting contains the solution to every problem in the posting.