Explain the basic emotions given by Paul Ekman.
Points:
(i) Happiness
(ii) Sadness
(iii) Anger
(iv) Fear
Paul Ekman identified six basic emotions that are universally recognized across different cultures.
Four of these emotions are:
Happiness: A positive emotional state associated with pleasure and life satisfaction, contributing to well-being and fostering social connections. Sadness: A response to loss or disappointment, aiding in grief processing and encouraging support-seeking behavior.
Anger: A reaction to perceived threats or injustices. While it can drive action, uncontrolled anger may lead to conflict.
Fear: A survival instinct that activates the fight-or-flight response in threatening situations, helping to avoid danger. These emotions are fundamental to human behavior, communication, and survival.
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: \[ 0 \leq x \leq 3, \quad 0 \leq y \leq 3, \quad x + y \leq 5. \]