Answer:
d
Step-by-step explanation:
Given y is directly proportional to x² then the equation relating them is
y = kx² ← k is the constant of proportion
To find k use the condition y = [tex]\frac{1}{8}[/tex] when x = [tex]\frac{1}{2}[/tex], then
[tex]\frac{1}{8}[/tex] = k([tex]\frac{1}{2}[/tex] )² = [tex]\frac{1}{4}[/tex] k ( multiply both sides by 8 )
1 = 2k ( divide both sides by 2 )
k = [tex]\frac{1}{2}[/tex]
y = [tex]\frac{1}{2}[/tex] x² ← equation of proportion
When y = [tex]\frac{9}{2}[/tex] , then
[tex]\frac{9}{2}[/tex] = [tex]\frac{1}{2}[/tex] x² ( multiply both sides by 2 )
9 = x² ( take the square root of both sides )
x = ± [tex]\sqrt{9}[/tex] = ± 3
with positive value x = 3 → d
