Question

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 =

please help. much appreciated.
​

Answer 1

36. m = (3/2)n

37. s = 5tv

38. c = 3/d

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.

• direct variation: y = kx; k = y/x
• joint variation: z = kxy; k = z/(xy)
• inverse variation: y = k/x; k = xy

_____

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

___

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

___

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