Answer:
x = 2
Step-by-step explanation:
Given that x varies inversely with y then the equation relating them is
x = [tex]\frac{k}{y}[/tex] ← k is the constant of variation
To find k use the condition x = 4 when y = 8
k = xy = 4 × 8 = 32, hence
x = [tex]\frac{32}{y}[/tex] ← equation of variation
When y = 16, then
x = [tex]\frac{32}{16}[/tex] = 2
Answer: 2 (third option)
Step-by-step explanation:
The equation of inverse variation where the variable "x" varies inversely as the variable "y", has the form:
[tex]x=\frac{k}{y}[/tex]
Where "k" is the constant of variation.
As you know that [tex]x=4[/tex] when [tex]y=8[/tex], then you can substitute values and solve for the constant of variation "k":
[tex]4=\frac{k}{8}\\\\k=4*8\\k=32[/tex]
Substitute "k" and [tex]y=16[/tex] into [tex]x=\frac{k}{y}[/tex] to find x when [tex]y=16[/tex]:
[tex]x=\frac{32}{16}\\\\x=2[/tex]
