1 rev = 2π rad, so 3 rev = 6π rad.

• Max electrons in a shell: \(2n^2\)
• Max electrons in a subshell: \(4\ell + 2\)
• Number of orbitals in a subshell: \(2\ell + 1\)

The telex system represented an important intermediate stage between the telegraph and modern digital data communication. According to the textbook:

• Telex machines first appeared as an evolution of telegraph technology, using telephone-like rotary dialing to connect teleprinters (teletypes)
• By 1935, message routing was the last barrier to full automation of the system
• The first wide-coverage telex network was implemented in Germany in the 1930s, used primarily for government communication
• Technical specifications: 45.5 bits per second; up to 25 telex channels could share a single long-distance telephone channel
• This made telex the least expensive method of reliable long-distance communication at the time

Telex eventually became a global business standard for transmitting documents internationally, particularly important for news agencies (like Reuters) and international trade, before being superseded by fax and then email in the late 20th century.

From the functional equation $f(xy)=f(x)f(y)$ with $f(0)\neq 0$, putting $x=y=0$ gives $f(0)=f(0)^2 \Rightarrow f(0)=1$. Putting $y=0$: $f(0)=f(x)f(0) \Rightarrow f(x)=1$ for all $x$.

So $\frac{dy}{dx}=1$, giving $y=x+C$. With $y(0)=1$: $C=1$, so $y=x+1$.

$y(1/4)+y(3/4)=(1/4+1)+(3/4+1)=5/4+7/4=12/4=\mathbf{3}$