Answer:
y = [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
Given that y varies inversely with x then the equation relating them is
y = [tex]\frac{k}{x}[/tex] ← k is the constant of variation
To find k use the condition y = [tex]\frac{1}{3}[/tex] when x = [tex]\frac{1}{2}[/tex] , thus
[tex]\frac{1}{3}[/tex] = [tex]\frac{k}{\frac{1}{2} }[/tex] = 2k ( divide both sides by 2 )
k = [tex]\frac{1}{6}[/tex]
y = [tex]\frac{1}{6x}[/tex] ← equation of variation
When x = [tex]\frac{1}{4}[/tex] , then
y = [tex]\frac{1}{6(\frac{1}{4}) }[/tex] = [tex]\frac{1}{\frac{3}{2} }[/tex] = [tex]\frac{2}{3}[/tex]
