8-5 Variation Functions
6. Suppose d varies directly as f , and d varies inversely as g. Find g when d = 6 and f = –7, if g = 12 when d = 9 and f
= 3.
ANSWER: –42
24. Suppose x varies directly as y, and x varies inversely as z. Find z when x = 10 and y = –7, if z = 20 when x = 6 and y
= 14.
ANSWER: –6
Determine whether each relation shows direct or inverse variation, or neither.
30. Suppose a varies directly as b, and a varies inversely as c. Find b when a = 7 and c = –8, if b = 15 when c = 2 and
a = 4.
ANSWER: –105
State whether each equation represents a direct, joint, inverse, or combined variation. Then name the
constant of variation.
34. a = 3bc
ANSWER: joint; 3
38. 9n = pr
ANSWER: combined; 9
40. a = 27b
ANSWER: direct; 27
42. –10 = gh
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ANSWER: inverse; –10
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ANSWER: direct; 27 Functions
8-5 Variation
42. –10 = gh
ANSWER: inverse; –10
44. CCSS PRECISION The volume of a gas v varies inversely as the pressure p and directly as the temperature t.
a. Write an equation to represent the volume of a gas in terms of pressure and temperature. Is your equation a
direct, joint, inverse, or combined variation?
b. A certain gas has a volume of 8 liters, a temperature of 275 Kelvin, and a pressure of 1.25 atmospheres. If the
gas is compressed to a volume of 6 liters and is heated to 300 Kelvin, what will the new pressure be?
c. If the volume stays the same, but the pressure drops by half, then what must have happened to the temperature?
ANSWER: a.
; combined
b. approximately 1.82 atmospheres or
c. It dropped by half.
46. MUSIC The maximum number of songs that a digital audio player can hold depends on the lengths and the quality of
the songs that are recorded. A song will take up more space on the player if it is recorded at a higher quality, like
from a CD, than at a lower quality, like from the Internet.
a. If a certain player has 5400 megabytes of storage space, write a function that represents the number of songs the
player can hold as a function of the average size of the songs.
b. Is your function a direct, joint, inverse, or combined variation?
c. Suppose the average file size for a high-quality song is 8 megabytes and the average size for a low-quality song is
5 megabytes. Determine how many more songs the player can hold if they are low quality than if they are high
quality.
ANSWER: a.
b. inverse
c. 405
48. CCSS CRITIQUE Jamil and Savannah are setting up a proportion to begin solving the combined variation in which
inversely as y. Who has set up the correct proportion? Explain your reasoning. Page 2
z varies
directly
as xbyand
z varies
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b. inverse
c. 405
8-5 Variation
Functions
48. CCSS CRITIQUE Jamil and Savannah are setting up a proportion to begin solving the combined variation in which
z varies directly as x and z varies inversely as y. Who has set up the correct proportion? Explain your reasoning.
ANSWER: Jamil; Savannah multiplied when she should have divided and divided when she should have multiplied.
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