Simpson's rule for integration gives exact result when $$f(x)$$ is a polynomial function of degree less than or equal to ________.

The cylinder shown below rolls without slipping. In which direction does the friction force act? Towards which of the following points is the acceleration of the point of contact A on the cylinder directed?

A velocity field is given as $$$\overrightarrow V = 3{x^2}y\widehat i - 6xyz\widehat k$$$
Where $$x,y,z$$ are in $$m$$ and $$V$$ $$m/s.$$ Determine if

(i) It represents an incompressible flow
(ii) The flow is irrotational
(iii) The flow is steady .

Shown below are three cylindrical gates which restrain water in $$2$$-$$D$$ channel. Which gate experiences the maximum vertical component, the minimum vertical component and the maximum horizontal component of the hydrostatic force?