Inverse Variation Read 7.1 Examples 1-4

Transcription

1 CC Algebra II HW #52 Name Period Row Date Inverse Variation Read 7.1 Eamples 1-4 Section Vocabulary Eplain how direct variation equations and inverse variation equations are different. Tell whether and y show direct variation, inverse variation, or neither. (See Eample 1.) 3. y = 2 y 5. = 8 7. y = + 4 In Eercises 11 14, tell whether and y show direct variation, inverse variation, or neither. (See Eample 2.)

2 The variables and y vary inversely. Use the given values to write an equation relating and y. Then find y when = 3. (See Eample 3.) 19. = 3 4, y = = 12, y = Modeling With Mathematics The number y of songs that can be stored on an MP3 player varies inversely with the average size of a song. A certain MP3 player can store 2500 songs when the average size of a song is 4 megabytes (MB). (See Eample 4.) a. Make a table showing the number of songs that will fit on the MP3 player when the average size of a song is 2 MB, 2.5 MB, 3 MB, and 5 MB. b. What happens to the number of songs as the average song size increases?

3 CC Algebra II HW #53 Name Period Row Date Simplifying and Multiplying Rational Epressions Read 7.3 Eamples 1-4 Section Which One Doesn t Belong? Which rational epression does not belong with the other three? Eplain your reasoning. In Eercises 3 10, simplify the epression, if possible. (See Eample 1.) In Eercises 11 20, find the product. (See Eamples 2, 3, and 4.) 3 4y y y ( ) 2 49

4 21. Error Analysis Describe and correct the error in simplifying the rational epression. 23. Using Structure Which rational epression is in simplified form? (A) (B) (C) (D) Modeling With Mathematics Write a model in terms of for the total area of the base of the building.

5 CC Algebra II HW #54 Name Period Row Date Dividing Rational Epressions Read 7.3 Eamples 5-7 Section 7.3 In Eercises 27 34, find the quotient. (See Eamples 5 and 6.) 32 3 y 27. y y ( ) Problem Solving Manufacturers often package products in a way that uses the least amount of material. One measure of the efficiency of a package is the ratio of its surface area to its volume. The smaller the ratio, the more efficient the packaging. a. Write an epression for the efficiency ratio S V of a cylindrical package. Hint: The formula for the surface area of a cylinder is S 2πr 2 2 = + 2πrh and the volume is V = πr h. b. Find the efficiency ratio for each cylindrical can listed in the table. c. Rank the three cans in part (b) according to efficiency. Eplain.

6 37. Modeling With Mathematics The total amount I (in millions of dollars) of healthcare ependitures and the residential population P (in millions) in the United States can be modeled by 171,000t +1,361,000 I = and P = 2.96t t where t is the number of years since Find a model M for the annual healthcare ependitures per resident. Estimate the annual healthcare ependitures per resident in (See Eample 7.) 44. Critical Thinking Find the epression for the question mark that makes the following statement true ? = Using Structure Perform the indicated operations (6 + 9) Maintaining Mathematical Proficiency Write the prime factorization of the number. If the number is prime, then write prime. (Skills Review Handbook)

7 CC Algebra II HW #55 Name Period Row Date Adding and Subtracting Rational Epressions With Like Denominators Read 7.4 Eamples 1, 2 Section 7.4 In Eercises 3 8, find the sum or difference. (See Eample 1.) Etra problems not in the tetbook: A. B In Eercises 9 16, find the least common multiple of the epressions. (See Eample 2.) 9. 3, 3( 2) , , 8

8 For Eercises 31 and 33, rewrite the function g in the form g() = a h + k. Graph the function. Describe the graph of g as a transformation of the graph of f () = a. (See Eample 5.) 31. g() = g() = Making an Argument Your friend claims that the least common multiple of two numbers is always greater than each of the numbers. Is your friend correct? Justify your answer.

9 CC Algebra II HW #56 Name Period Row Date Adding and Subtracting Rational Epressions With Unlike Denominators Read 7.4 Eamples 3-4 Section Writing Eplain how adding and subtracting rational epressions is similar to adding and subtracting numerical fractions. Error Analysis Describe and correct the error in finding the sum. 17. In Eercises 19 26, find the sum or difference. (See Eamples 3 and 4.)

10 Tell whether the statement is always, sometimes, or never true. Eplain. 27. The LCD of two rational epressions is the product of the denominators. 47. Problem Solving You plan a trip that involves a 40-mile bus ride and a train ride. The entire trip is 140 miles. The time (in hours) the bus travels is y 1 = 40, where is the average speed (in miles per hour) of the bus. The time (in hours) the train travels is y 2 = 100. Write and simplify a model that shows the total time y of the trip *54. Challenge* Mathematical Connections Find an epression for the surface area of the bo.

11 CC Algebra II HW #57 Name Period Row Date Comple Fractions Read 7.4 Eample 6 Section Complete the Sentence A fraction that contains a fraction in its numerator or denominator is called a(n). In Eercises 39 44, simplify the comple fraction. (See Eample 6.)

12 *51. Challenge* Rewriting a Formula You borrow P dollars to buy a car and agree to repay the loan over t years at a monthly interest rate of i (epressed as a decimal). Your monthly payment M is given by either formula below. Pi M = i 12t or M = Pi(1+i)12t (1+i) 12t 1 a. Show that the formulas are equivalent by simplifying the first formula. b. Find your monthly payment when you borrow $15,500 at a monthly interest rate of 0.5% and repay the loan over 4 years.

13 CC Algebra II HW #58 Name Period Row Date Solving Rational Equations (Part I) Read 7.5 Eamples 1, 2, 3a Section Writing When can you solve a rational equation by cross multiplying? Eplain Writing A student solves the equation 3 = and obtains the solutions 3 and 4. 3 Are either of these etraneous solutions? Eplain. In Eercises 3 10, solve the equation by cross multiplying. Check your solution(s). (See Eample 1.) = = = = 3 2

14 11. Using Equations So far in your volleyball practice, you have put into play 37 of the 44 serves you have attempted. Solve the equation = 37+ to find the number of consecutive serves you need to put into play in order to raise 44 + your serve percentage to 90%. 13. Modeling With Mathematics Brass is an alloy composed of 55% copper and 45% zinc by weight. You have 25 ounces of copper. How many ounces of zinc do you need to make brass? (See Eample 2.)

15 CC Algebra II HW #59 Name Period Row Date Solving Rational Equations (Part II) Read 7.5 Eamples 3b, 4 Section 7.5 Using Structure Identify the least common denominator of the equation = = 1 2 In Eercises 19 30, solve the equation by using the LCD. Check your solution(s). (See Eamples 3 and 4.) = = = = = = 2 + 3

16 31. Error Analysis Describe and correct the error in the first step of solving the equation. 33. Problem Solving You can paint a room in 8 hours. Working together, you and your friend can paint the room in just 5 hours. a. Let t be the time (in hours) your friend would take to paint the room when working alone. Complete the table. (Hint: (Work done) = (Work rate) (Time)) b. Eplain what the sum of the epressions represents in the last column. Write and solve an equation to find how long your friend would take to paint the room when working alone. Maintaining Mathematical Proficiency Evaluate the function for the given value of. (Section 4.1) 61. f () = , = 2