The following equation needs to be numerically solved using the Newton $$-$$ Raphson method $${x^3} + 4x - 9 = 0.\,\,$$ The iterative equation for this purpose is ($$k$$ indicates the iteration level)

The presence of hardness in excess of permissible limit causes

The alkalinity and the hardness of a water sample are 250 mg/L and 350 mg/L as $$CaCo_3$$, respectively. The water has

The plan of a map was photo copied to a reduced size such that a line originally 100mm, measures 90mm. The original scale of the plan was 1:1000. The revised scale is