Question

If t varies inversely as a and t= 2 when a = -4, what is t when a = 1/3?

1. -2 2/3
2. -24
3. - 1/6
4. -2/3

Answer 1

t = - 24

Explanation:

Given t varies inversely as a then the equation relating them is

t =
`(k)/(a)` ← k is the constant of variation

To find k use the condition t = 2 when a = - 4

2 =
`(k)/(-4)` ( multiply both sides by - 4 )

- 8 = k

t =
`(-8)/(a)` ← equation of variation

When a =
`(1)/(3)` , then

t =
`(-8)/((1)/(3) )` = - 24