Preliminary treatment of sewage is the initial phase of wastewater management, focusing on removing coarse materials and debris to safeguard subsequent biological or chemical processing equipment. This initial step enhances the effectiveness and prevents potential damage to further treatment stages. The key stages involved in preliminary sewage treatment include:
1. Screening:
(i) Removes large solid objects such as plastics, rags, leaves, and paper using metal screens or bar racks.
(ii) Essential for preventing blockages and protecting equipment further down the treatment line.
2. Grit Removal:
(i) Separates out heavy inorganic materials like sand, gravel, and pebbles in a grit chamber.
(ii) Aids in preventing wear and tear on mechanical equipment such as pumps and pipes.
3. Skimming:
(i) Removes floating substances such as fats, oils, and lighter debris in skimming tanks.
(ii) Crucial for keeping pipelines clear of obstructions.
4. Pre-Sedimentation:
(i) Allows large suspended solids to settle in sedimentation tanks.
(ii) Lessens the burden of organic material on secondary treatment processes.
The slope of the tangent to the curve \( x = \sin\theta \) and \( y = \cos 2\theta \) at \( \theta = \frac{\pi}{6} \) is ___________.
Solve the following L.P.P. by graphical method:
Maximize:
\[ z = 10x + 25y. \] Subject to: \[ 0 \leq x \leq 3, \quad 0 \leq y \leq 3, \quad x + y \leq 5. \]