Respuesta :
Answer:
x = 2[tex]\sqrt{10}[/tex]
Step-by-step explanation:
Given that y varies inversely as the square of x then the equation relating them is
y = [tex]\frac{k}{x^2}[/tex] ← k is the constant of variation
To find k use the condition y = 2 when x = 4
k = yx² = 2 × 4² = 2 × 16 = 32
y = [tex]\frac{32}{x^2}[/tex] ← equation of variation
When y = [tex]\frac{4}{5}[/tex], then
[tex]\frac{4}{5}[/tex] = [tex]\frac{32}{x^2}[/tex] ( cross- multiply )
4x² = 160 ( divide both sides by 4 )
x² = 40 ( take the square root of both sides )
x = [tex]\sqrt{40}[/tex] = [tex]\sqrt{4(10)}[/tex] = 2[tex]\sqrt{10}[/tex]
