We have been given that the inverse variation [tex]y=\frac{3\times 10^8}{x}[/tex] shows the relationship between wavelength in meters, x, and frequency, y. We are asked to find the wavelength for radio waves with frequency [tex]3\times 10^9[/tex].
To find the required wavelength, we substitute [tex]y=3\times 10^9[/tex] in our given equation and solve for x as:
[tex]3\times 10^9=\frac{3\times 10^8}{x}[/tex]
[tex]x=\frac{3\times 10^8}{3\times 10^9}[/tex]
We can see that both numerator and denominator has 3, so we can cancel it out.
[tex]x=\frac{1\times 10^8}{1\times 10^9}[/tex]
Using quotient rule of exponents [tex]\frac{a^m}{a^n}=a^{m-n}[/tex], we will get:
[tex]x=1\times 10^{8-9}[/tex]
[tex]x=1\times 10^{-1}[/tex]
Therefore, the wavelength for radio waves would be [tex]1\times 10^{-1}[/tex] meters and option B is the correct choice.
