Observe the graph and select the correct option:
The species-area relationship follows the equation: \[ S = C A^Z \] where:
- \( S \) is species richness,
- \( A \) is the area,
- \( C \) and \( Z \) are constants.
This equation, proposed by Alexander von Humboldt, suggests that species richness increases with area but not linearly.
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: \[ 0 \leq x \leq 3, \quad 0 \leq y \leq 3, \quad x + y \leq 5. \]