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Roman55 [17]
3 years ago
13

If r varies directly as p and inversely as q2, and r = 27 when p =3 and q = 2, find r when p = 2 and q= 3

Mathematics
1 answer:
WITCHER [35]3 years ago
8 0

Answer:

k = 36 and r = 8

Step-by-step explanation:

Given that r varies directly as p and inversely as q² then the equation relating them is

r = \frac{kp}{q^2} ← k is the constant of variation

To find k use the condition r = 27 when p  3 and q = 2, thus

27 = \frac{3k}{4} ( multiply both sides by 4 )

108 = 3k ( divide both sides by 3 )

k = 36

r = \frac{36p}{q^2} ← equation of variation

When p = 2 and q = 3, then

r = \frac{36(2)}{3^2} = \frac{72}{9} = 8

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