Question

When p = 12, t = 2, and s = 1/6, r = 18. If r varies directly with p and inversely with the product of s and t, what is the constant of variation?

A: 1/8

B: 1/2

C: 4 1/2

D: 18

Answer 1

r = kp/st
18 = 12k/(1/6 x 2)
18 = 12k/(1/3)
18 = 36k
k = 18/36 = 1/2

Answer 2

The constant of variation if r varies directly with p and inversely with the product of s and t is 1/2

Direct and inverse variation

This are variations that shows that relationship between two variables

If r varies directly with p and inversely with the product of s and t, thisis expressed as:

r = kp/st

Given that  p = 12, t = 2, and s = 1/6

18 = k * 12/2(1/6)

18 = k * 12(3)

18 = 36k

k = 1/2

Hence the constant of variation if r varies directly with p and inversely with the product of s and t is 1/2

Learn more on variation here: https://brainly.com/question/6499629

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