For the parabola $y^2=4\sqrt{5}x$: tangent in slope form is $y=mx+\frac{\sqrt{5}}{m}$.

For the circle $x^2+y^2=5/2$ (radius $\sqrt{5/2}$): distance from origin to tangent $= \frac{|\sqrt{5}/m|}{\sqrt{1+m^2}}=\sqrt{5/2}$

$\frac{5/m^2}{1+m^2}=\frac{5}{2}\Rightarrow\frac{1}{m^2(1+m^2)}=\frac{1}{2}\Rightarrow m^2+m^4=2\Rightarrow m^4+m^2-2=0$

Hmm: $m^4+m^2-2=(m^2+2)(m^2-1)=0$, so $m=\pm1$. Statement II gives $m^4-3m^2+2=0=(m^2-1)(m^2-2)=0$, so $m=\pm1,\pm\sqrt{2}$ — this is different. But $m=\pm1$ works for both. At $m=1$: tangent is $y=x+\sqrt{5}$ ✓. Statement I is true; Statement II is false (wrong equation).

Tracking displacement:

• North 4 km: position (0, 4)
• East 3 km: position (3, 4)
• South 4 km: position (3, 0)

The North and South movements cancel each other (both 4 km). The person ends up 3 km East of the start.

Shortest distance = \(\sqrt{3^2 + 0^2} = \mathbf{3}\ \text{km}\

The textbook discusses noise in the Shannon-Weaver model context and identifies three categories:

1. Physical (Mechanical/Engineering) Noise: Unexplained variation or random error in the communication channel. Examples: a loud motorbike during conversation, smudges on a printed page, “snow” on a TV set, mist on a car windscreen, a crackling microphone. Shannon was primarily concerned with this type.
2. Semantic Noise: Arises from differences in meaning — when sender and receiver do not share the same knowledge, cultural background, experience, attitudes, beliefs, or linguistic skills. This is “the very essence of the study of human communication.”
3. Psychological Noise: The textbook mentions “psychological interference with encoding and decoding” — arising from emotional states, biases, prejudices, or mental conditions that distort how messages are encoded or decoded.

Channel overload — when the channel capacity is exceeded — is also mentioned as a source of distortion distinct from noise per se.

W = Fd cosθ; max when θ=0° (cos0=1).

• B < Be: Be (2s², full subshell) has higher IE₁ than B (2p¹, easier to remove)
• O < N: N (2p³, half-filled, extra stable) has higher IE₁ than O (2p⁴, one paired electron easier to remove)