Lesson Practice B 5.1 For use with the lesson “Model ... - Schoolwires

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Lesson

5.1

Date ¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª

Practice B

For use with the lesson ¡°Model Inverse and Joint Variation¡±

Tell whether x and y show direct variation, inverse variation, or neither.

3

3. x 5 ??}?

y

x

2. y 5 ??}?

3

1. y 5 2x 1 3

1

4. ??}??xy 5 2

2

Lesson 5.1

The variables x and y vary inversely. Use the given values to write an

equation relating x and y. Then find y when x 5 0.5.

5. x 5 4, y 5 6

5

6. x 5 2, y 5 ??}?

2

8. x 5 23, y 5 2

3

4

9. x 5 ??}?, y 5 }

??2 ?

3

1

7. x 5 48, y 5 ??}?

12

1

1

10. x 5 ??}?, y 5 }

??3 ?

2

Determine whether x and y show direct variation, inverse variation,

or neither.

11.

x

1

2

3

4

y

1

4

9

16

12.

x

2

5

8

15

y

60

24

15

8

13.

x

1

4

7

10

y

7.5

30

52.5

75

14. x 5 3, y 5 5, z 5 30

1

15. x 5 6, y 5 ??}?, z 5 24

2

3

16. x 5 ??}?, y 5 18, z 5 9

2

In Exercises 17¨C20, use the following information.

Simple Interest The simple interest I (in dollars) for a savings account is jointly

proportional to the product of the time t (in years) and the principal P (in dollars).

After fifteen months, the interest on a principal of $2500 is $78.13.

17. Find the constant of variation k.

18. Write an equation that relates I, t, and P.

19. What will the interest I be after ten years?

20. What does the constant of variation k represent?

In Exercises 21¨C23, use the following information.

Boyle¡¯s Law Boyle¡¯s Law states that for a constant temperature, the pressure p of a

gas varies inversely with its volume V. A sample of oxygen gas has a volume of

50.25 cubic milliliters at a pressure of 20.6 atmospheres.

21. Find the constant of variation k.

22. Write an equation that relates p and V.

23. Find the volume of the oxygen gas if the pressure changes to 15.2 atmospheres.

5-6

Algebra 2

Chapter Resource Book

Copyright ? Houghton Mifflin Harcourt Publishing Company. All rights reserved.

The variable z varies jointly with x and y. Use the given values to write an

equation relating x, y, and z. Then find z when x 5 4 and y 5 7.

Answers for Chapter 5

Lesson 5.1 Model Inverse and

Joint Variation

43725

14. 10 yr 15. 43,725 16. d 5 }

?? p ?

Teaching Guide

19. 4.541 kilocalories

1. Divide distance by speed traveled; 4 h;

about 4 h 44 min 2. Sample answer: speed

Study Guide

Practice Level A

1. direct variation 2. neither 3. inverse

variation 4. inverse variation

6

15 15

212

5. y 5 }

??x ?; 3 6. y 5 }

?? x ?; }

??2 ? 7. y 5 }

?? x ?; 26

16

3 3

6

8. y 5 }

?? x ?; 8 9. y 5 }

??x ?; ??}2 ? 10. y 5 }

??x ?; 3

11. direct variation 12. neither 13. inverse

variation 14. neither 15. direct variation

16. inverse variation 17. z 5 4xy; 40

1

18. z 5 2xy; 20 19. z 5 }

??2 ??xy; 5 20. 0.04

21. I 5 0.04tP 22. $240 23. The interest rate

17. 7950 units 18. 0.22; H 5 0.22mT

15

1. inverse 2. neither 3. direct 4. y 5 }

?? x ?; 5

12

2 2

5. y 5 }

?? x ?; 4 6. y 5 }

??x ?; ??}3 ? 7. about 231 8. 36

Problem Solving Workshop:

Using Alternative Methods

1. about 347 2. about 93 mm2

Challenge Practice

1. False. y will decrease because y and x are

inversely related.

a

2. True. If y 5 }

?? 2 ?and x is replaced with 2x, you

x

a

a

?? 2?.

have y 5 ??}2 ?5 }

(2x)

4x

3. True. If y varies directly with x, then y 5 ax,

1

of the savings account.

so x 5 ??}a??y. So, x varies directly with y.

Practice Level B

4. False. z will decrease when y > 0 and z will

increase when y < 0. 5. w varies jointly with x

and y, and inversely with the square root of z.

1. neither 2. direct variation 3. inverse

variation 4. inverse variation

5

24

4

5. y 5 }

?? x ?; 48 6. y 5 }

??x ?; 10 7. y 5 }

??x ?; 8

26

2

1 1

8. y 5 }

?? x ?; 212 9. y 5 }

??x ?; 4 10. y 5 }

??6x?; }

??3 ?

}

1 w?? z??

x 5 ??}?p ??}??; x varies jointly with w and the

a

y

square root of z, and inversely with y.

1

}

w?? z??

y 5 ??}a ?p ??}

??; y varies jointly with w and the

x

11. neither 12. inverse variation 13. direct

variation 14. z 5 2xy; 56 15. z 5 8xy; 224

square root of z, and inversely with x.

28

1

16. z 5 }

??3??xy; }

??3 ? 17. 0.025 18. I 5 0.025tP

z 5 a2 p }

?? 2 ??; z varies jointly with the squares of

19. $625 20. The interest rate of the savings

account 21. 1035.15

x and y, and inversely with the square of w.

1035.15

22. V 5 }

?? p ? 23. 68.1 mL3

Practice Level C

1. direct variation 2. neither 3. inverse

variation 4. inverse variation

8.64

15

5. y 5 }

?? x ?; 34.56 6. y 5 }

?? x ?; 60

5

7. y 5 }

??8x?; 2.5 8. direct variation 9. neither

answers

decreases; time traveled increases; time will

increase as speed decreases

Copyright ? Houghton Mifflin Harcourt Publishing Company. All rights reserved.

Rational Functions

x 2y 2

w

6. t varies directly with u, and inversely with the

1

square of v and with w. u 5 ??}a ?p tv 2w; u varies

jointly

with t, with the square of v, and with w.

}

}

???u? ?

?? }?; v varies directly with the

v5?

? ?a? ?p }

???tw? ?

square root of ?u?, and inversely with the square

u

tv

10. inverse variation 11. z 5 18xy; 540

roots of ?t? and ?w?. w 5 a p }

?? 2 ?; w varies

15

25

125

12. z 5 }

??2 ??xy; 225 13. z 5 }

??84 ??xy; }

??14 ?

directly with u, and inversely with t and the square

of v.

Algebra 2

Chapter Resource Book

A1

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