Answer:
y = 360
Step-by-step explanation:
Given y is inversely proportional to x² then the equation relating them is
y = [tex]\frac{k}{x^2}[/tex] ← k is the constant of proportion
To find k use the condition y = 10 when x = 3 , then
10 = [tex]\frac{k}{3^2}[/tex] = [tex]\frac{k}{9}[/tex] ( multiply both sides by 9 )
90 = k
y = [tex]\frac{90}{x^2}[/tex] ← equation of proportion
When x = [tex]\frac{1}{2}[/tex] , then
y = [tex]\frac{90}{(\frac{1}{2})^2 }[/tex] = [tex]\frac{90}{\frac{1}{4} }[/tex] = 90 × 4 = 360
