Answer:
x = 2√2
Step-by-step explanation:
If is inversely proportional to x², then:
[tex]y \propto \dfrac{1}{x^2} \implies y=\dfrac{k}{x^2} \quad \textsf{(for some constant k)}[/tex]
Given:
Substitute the given values into the found equation and solve for k:
[tex]\implies 2=\dfrac{k}{4^2}[/tex]
[tex]\implies 2=\dfrac{k}{16}[/tex]
[tex]\implies k=32[/tex]
Therefore:
[tex]y=\dfrac{32}{x^2}[/tex]
To find the value of x when y = 4, substitute y = 4 into the found equation and solve for x:
[tex]\implies 4=\dfrac{32}{x^2}[/tex]
[tex]\implies x^2=\dfrac{32}{4}[/tex]
[tex]\implies x^2=8[/tex]
[tex]\implies x=\sqrt{8}[/tex]
[tex]\implies x=\sqrt{4 \cdot 2}[/tex]
[tex]\implies x=\sqrt{4} \sqrt{2}[/tex]
[tex]\implies x=2\sqrt{2}[/tex]
