Initial intensity $I$. After A, $I_A = I/2$. Since $I_B$ is also $I/2$, axes of A and B are parallel ($\theta_{AB} = 0$).

Insert C at angle $\phi$ to A. Then angle between C and B is also $\phi$.

Final intensity $I' = I_A \cos^2 \phi \cos^2 \phi = \frac{I}{2} \cos^4 \phi$.

Given $\frac{I}{2} \cos^4 \phi = \frac{I}{8} \implies \cos^4 \phi = \frac{1}{4} \implies \cos^2 \phi = \frac{1}{2}$.

Thus, $\cos \phi = \frac{1}{\sqrt{2}} \implies \phi = 45^\circ$.

In the PRECEDE-PROCEED Model (Green & Kreuter), the phases are:

1. Social assessment
2. Epidemiological assessment
3. Educational and ecological assessment — This phase identifies:

• Predisposing factors: knowledge, attitudes, beliefs, values
• Enabling factors: skills, resources, barriers
• Reinforcing factors: rewards, feedback, social support

This model is widely used in community health nursing to plan and evaluate health education programmes — essential knowledge for Head Nurse and Charge Nurse positions.

The textbook is specific about Life magazine (begun 1936) and Look magazine (begun 1937) as the large-circulation picture magazines that “provided an outlet and a vast audience for documentary work.” The Great Depression of the 1930s provided the subject matter: the Farm Security Administration (FSA) under Roy Stryker commissioned photographers including Walker Evans, Arthur Rothstein, Russell Lee, and Dorothea Lange to document Depression-era America. World War II further developed photojournalism — photographers including Margaret Bourke-White, Robert Capa, W. Eugene Smith, and Edward Steichen documented the global conflict. The development of the 35mm “candid” camera by Oskar Barnack (Leica, first marketed 1925) made documentary photographers “infinitely more mobile and less conspicuous.” Colour film for transparencies was introduced in 1935; the Polaroid Land camera in 1947.

Let $u=\cot^{-1}x$. Solve $u^2-7u+10>0$, i.e., $(u-2)(u-5)>0$.

This gives $u<2$ or $u>5$.

Since $\cot^{-1}x$ is a decreasing function with range $(0,\pi)$:

• $u<2 \Rightarrow \cot^{-1}x<2 \Rightarrow x>\cot2$ (decreasing function reverses inequality)
• $u>5 \Rightarrow \cot^{-1}x>5 \Rightarrow x<\cot5$

Solution: $x\in(-\infty,\cot5)\cup(\cot2,\infty)$