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• direct variation
• constant of variation
• joint variation
• inverse variation
• combined variation
Direct Variation
If y varies directly as x and y = –15 when x = 5, find y when x = 3.
Use a proportion that relates the values.
Cross multiply.
y1 = –15, x1 = 5, and x2 = 3
Direct Variation
Direct Variation
–45 = 5y2 Simplify.
–9 = y2 Divide each side by 5.
Answer: When x = 3, the value of y is –9.
A. A
B. B
C. C
D. D A B C D
0% 0%0%0%
If y varies directly as x and y = 12 when x = –3, find y when x = 7.
A. –28
B.
C.
D.
Joint Variation
Suppose y varies jointly as x and z. Find y when x = 10 and z = 5, if y = 12 when x = 3 and z = 8.
Use a proportion that relates the values.
Joint variation
y1 = 12, x1 = 3, z1 = 8,x2 = 10, and z2 = 5
Cross multiply.
Joint Variation
600 = 24y2 Simplify.
Answer: When x = 10 and z = 5, y = 25.
25 = y2 Divide each side by 24.
A. A
B. B
C. C
D. D A B C D
0% 0%0%0%
Suppose y varies jointly as x and z. Find y when x = 3 and z = 2, if y = 11 when x = 5 and z = 22.
A.
B.
C.
D.
Inverse Variation
If r varies inversely as t and r = –6 when t = 2, find r when t = –7.
Inverse Variation
r1 = –6, t1 = 2, and t2 = –7
Cross multiply.
Inverse Variation
Simplify.
Divide each side by –7.
Answer: When t = –7, r is .
A. A
B. B
C. C
D. D A B C D
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If a varies inversely as b and a = 3 when b = 8, find a when b = 6.
A.
B. 4
C. 16
D. 144
Combined Variation
Suppose f varies directly as g, and f varies inversely as h. Find g when f = 6 and h = –5, if g = 18 when h = 3 and f = 5.
First, set up a correct proportion for the information given.
g varies directly as f, so ggoes in the numerator. hvaries inversely as f, so hgoes in the denominator.
Solve for k.
Combined Variation
f1 = 5, h1 = 3, g1 = 18, f2 = 6, and h2 = –5
Set the two proportions equal to each other.
Cross multiply.
Simplify.
Divide each side by 15.
Answer: When f = 6 and h = –5, the value of g is –36.
A. A
B. B
C. C
D. D A B C D
0% 0%0%0%
A. –30
B. 30
C. 36
D. 40
Suppose f varies directly as g, and f varies inversely as h. Find g when f = 6 and h = –16, if g = 10 when h = 4 and f = –6.
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