Mutualism is a type of ecological interaction in which two different species benefit from each other. Mutualism is a form of symbiotic relationship where both organisms involved derive mutual benefit. It is an important ecological interaction that promotes survival and reproduction.
Types of Mutualism:
1. Obligate Mutualism: The relationship is essential for the survival of both species.
2. Facultative Mutualism: Both species benefit, but they can survive independently.
Examples of Mutualism:
Lichen: A mutualistic association between fungi and algae/cyanobacteria.
Pollination: Bees collect nectar from flowers (food source) while aiding in pollination.
Mycorrhizae: Fungi and plant roots exchange nutrients and water.
Nitrogen Fixation: Rhizobium bacteria live in leguminous plant roots, fixing nitrogen for the plant while receiving carbohydrates.
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: \[ 0 \leq x \leq 3, \quad 0 \leq y \leq 3, \quad x + y \leq 5. \]