8-5 Variation Functions
If x varies directly as y, find x when y = 8.
7. x = 6 when y = 32
SOLUTION: Use a proportion that relates the values.
9. x = 14 when y = –2
SOLUTION: Use a proportion that relates the values.
11. MOON Astronaut Neil Armstrong, the first man on the Moon, weighed 360 pounds on Earth with all his equipment
on, but weighed only 60 pounds on the Moon. Write an equation that relates weight on the Moon m with weight on
Earth w.
SOLUTION: The equation that relates weight on the Moon m with weight on Earth w is:
If a varies jointly as b and c, find a when b = 4 and c = –3.
13. a = –60 when b = –5 and c = 4
SOLUTION: Use a proportion that relates the values.
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8-5 Variation Functions
If a varies jointly as b and c, find a when b = 4 and c = –3.
13. a = –60 when b = –5 and c = 4
SOLUTION: Use a proportion that relates the values.
15. a = 24 when b = 8 and c = 12
SOLUTION: Use a proportion that relates the values.
If f varies inversely as g, find f when g = –6.
17. f = 15 when g = 9
SOLUTION: Use a proportion that relates the values.
19. f = –12 when g = 19
SOLUTION: Use a proportion that relates the values.
SERVICE
21. COMMUNITY
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Every year students at West High School collect canned goods for a local food pantry.
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They plan to distribute flyers to homes in the community asking for donations. Last year, 12 students were able to
distribute 1000 flyers in four hours.
8-5 Variation Functions
21. COMMUNITY SERVICE Every year students at West High School collect canned goods for a local food pantry.
They plan to distribute flyers to homes in the community asking for donations. Last year, 12 students were able to
distribute 1000 flyers in four hours.
a. Write an equation that relates the number of students s to the amount of time t it takes to distribute 1000 flyers.
b. How long would it take 15 students to hand out the same number of flyers this year?
SOLUTION: a. The number of students s varies directly as the number of flyers distributed and inversely as the amount of time t.
Therefore,
b. Substitute t = 15 in the expression.
23. Suppose a varies directly as b, and a varies inversely as c. Find b when a = 5 and c = –4, if b = 12 when c = 3 and
a = 8.
SOLUTION: Use a proportion that relates the values.
Determine whether each relation shows direct or inverse variation, or neither.
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8-5 Variation Functions
Determine whether each relation shows direct or inverse variation, or neither.
25. SOLUTION: Since
, the relation shows direct variation.
27. SOLUTION: Since neither
is constant, the relation is neither direct nor inverse.
29. If x varies inversely as y and x = 16 when y = 5, find x when y = 20.
SOLUTION: Use a proportion that relates the values.
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Since neither
is constant, the relation is neither direct nor inverse.
8-5 Variation Functions
29. If x varies inversely as y and x = 16 when y = 5, find x when y = 20.
SOLUTION: Use a proportion that relates the values.
31. Suppose x varies directly as y, and x varies inversely as z. Find z when x = 8 and y = –6, if z = 26 when x = 8 and y
= 13.
SOLUTION: Use a proportion that relates the values.
State whether each equation represents a direct, joint, inverse, or combined variation. Then name the
constant of variation.
33. fg = –2
SOLUTION: Inverse variation;
Constant of variation = –2
35. SOLUTION: . Combined variation; Constant of variation = 10.
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SOLUTION: 8-5 Variation. Combined
Functionsvariation; Constant of variation = 10.
37. SOLUTION: . Direct variation;
Constant of variation = 4.
39. –2y = z
SOLUTION: Direct variation; Constant of variation = –2.
41. SOLUTION: Inverse variation; Constant of variation = 7.
43. m = 20cd
SOLUTION: Joint variation Constant of variation = 20
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