Answer:
x = - 10.5
Step-by-step explanation:
Given that 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 = 8 when x = 3.5 , then
8 = [tex]\frac{k}{3.5^2}[/tex] ( multiply both sides by 3.5²
8 × 3.5² = k , that is
k = 98
y = [tex]\frac{98}{x^2}[/tex] ← equation of proportion
When y = [tex]\frac{8}{9}[/tex] , then
[tex]\frac{8}{9}[/tex] = [tex]\frac{98}{x^2}[/tex] ( cross- multiply )
8x² = 882 ( divide both sides by 8 )
x² = 110.25 ( take the square root of both sides )
x = ± [tex]\sqrt{110.25}[/tex] = ± 10.5
Thus x = - 10.5 ← is the negative value of x
