Write an equation to model each relationship.

36. m varies directly as n. when m=18, n=12

m =

37. s varies jointly as t and v. when s=8, t=4/5, v=2

s =

38. c varies inversely as d. when c=1/4, d=12

c =

. much appreciated.

36.  m = (3/2)n

37.  s = 5tv

38.  c = 3/d

Step-by-step explanation:

Each of the variations in these problems has its own associated equation. You only need to make use of the given values to find the constant of variation (k) and fill in the equation.

36. The constant for direct variation is the ratio of the given values:

  k = m/n = 18/12 = 3/2

Then the equation for the direct variation is ...

  m = (3/2)n

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37. The constant for the joint variation is the expression ...

  k = s/(tv) = 8/((4/5)·2) = 8/(8/5) = 8·5/8 = 5

Then the equation for the joint variation is ...

  s = 5tv

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38. The constant for the inverse variation is the product of the given values:

  k = cd = (1/4)(12) = 3

Then the equation for the inverse variation is ...

  c = 3/d