the inverse variation equation shows the relationship between wavelength in meters, x, and frequency, y: $y…

the inverse variation equation shows the relationship between wavelength in meters, x, and frequency, y: $y = \\frac{3\\times10^{8}}{x}$. what is the wavelength for radio waves with frequency $3\\times10^{9}$?\n$1\\times10^{-1}$ m\n$3\\times10^{-1}$ m\n$3\\times10^{17}$ m\n$9\\times10^{17}$ m

the inverse variation equation shows the relationship between wavelength in meters, x, and frequency, y: $y = \\frac{3\\times10^{8}}{x}$. what is the wavelength for radio waves with frequency $3\\times10^{9}$?\n$1\\times10^{-1}$ m\n$3\\times10^{-1}$ m\n$3\\times10^{17}$ m\n$9\\times10^{17}$ m

Answer

Explanation:

Step1: Substitute the given frequency into the equation

Given $y = \frac{3\times10^{8}}{x}$ and $y = 3\times10^{9}$. Substitute $y$ into the equation: $3\times10^{9}=\frac{3\times10^{8}}{x}$.

Step2: Solve for $x$

Cross - multiply to get $3\times10^{9}x=3\times10^{8}$. Then $x=\frac{3\times10^{8}}{3\times10^{9}}$. Using the rule of exponents $\frac{a^{m}}{a^{n}}=a^{m - n}$, we have $x = 10^{8-9}=10^{-1}$. And $\frac{3}{3}=1$, so $x = 1\times10^{-1}$ m.

Answer:

$1\times10^{-1}$ m