Answer:
t = - 24
Step-by-step explanation:
Given t varies inversely as a then the equation relating them is
t = [tex]\frac{k}{a}[/tex] ← k is the constant of variation
To find k use the condition t = 2 when a = - 4
2 = [tex]\frac{k}{-4}[/tex] ( multiply both sides by - 4 )
- 8 = k
t = [tex]\frac{-8}{a}[/tex] ← equation of variation
When a = [tex]\frac{1}{3}[/tex] , then
t = [tex]\frac{-8}{\frac{1}{3} }[/tex] = - 24
