In Newton-Raphson iterative method, the initial guess value $$\left( {{x_{ini}}} \right)$$ is considered as zero while finding the roots of the equation: $$\,f\left( x \right) = - 2 + 6x - 4{x^2} + 0.5{x^3}.\,\,\,$$ The correction, $$\Delta x,$$ to be added to $${{x_{ini}}}$$ in the first iteration is __________.

For step-size, $$\Delta x = 0.4,$$ the value of following integral using Simpson's $$1/3$$ rule is ______

A groundwater sample was found to contain 500 mg/L total dissolved solids (TDS). TDS (in %) present in the sample is ________.

A triangular gate with a base width of 2 m and a height of 1.5 m lies in a vertical plane. The top vertex of the gate is 1.5 m below the surface of a tank which contains oil of specific gravity 0.8. Considering the density of water and acceleration due to gravity to be 1000 $$kg/m^3$$ and 9.81 $$m/s^2$$, respectively, the hydrostatic force (in kN) exerted by the oil on the gate is __________.