%Radio Quiz

\rbqquest{Let $x(t)$ be the temperature of my house in degrees Celsius with $t$ in hours. Suppose it satisfies the ODE:
\[\frac{dx}{dt}+kx=kq_e(t).\]

\begin{enumerate}
\item What are the units on $k$?
\item What are the units on $q_e$?
\end{enumerate}}

\rbqchoice{
\begin{enumerate}
\item Units on $k$:
\begin{enumerate}[a)]
\item $\frac{\text{degrees}}{\text{hour}}$
\item degees Celsius
\item $\frac{1}{\text{hour}}$
\item $k$ is dimensionless
\end{enumerate}
\smallskip
\item Units on $q_e$:
\smallskip
\begin{enumerate}[a)]
\item $\frac{\text{degrees}}{\text{hour}}$
\item degrees Celsius
\item $\frac{1}{\text{hour}}$
\item $q_e$ is dimensionless
\end{enumerate}
\end{enumerate}
}

\rbqans{
\begin{enumerate}
\item The units on $k$ are $\frac{1}{\text{hour}}$. Since $x$ is in
  degrees Centigrade and $t$ has units in hours, $\frac{dx}{dt}$ has units $\frac{\text{degrees}}{\text{hour}}$. Thus $kx$ has units $\frac{\text{degrees}}{\text{hour}}$, which implies $k$ has units $\frac{1}{\text{hour}}$.

\item The units on $q_e$ are degrees Celsius.  From the equation we
  see that $q_e$ has the same units as $x$.
\end{enumerate}}
