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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