Answer:
x = 3[tex]\sqrt{3}[/tex]
Step-by-step explanation:
Given y varies directly as x², then the equation relating them is
y = kx² ← k is the constant of variation
To find k use the condition y = 27 when x = 3 , then
27 = k × 3² = 9k ( divide both sides by 9 )
3 = k
y = 3x² ← equation of variation
When y = 81, then
81 = 3x² ( divide both sides by 3 )
27 = x² ( take the square root of both sides )
x = [tex]\sqrt{27}[/tex] = [tex]\sqrt{9(3)}[/tex] = 3[tex]\sqrt{3}[/tex]
