Given
$$y = \int\limits_1^{{x^2}} {\cos t\,\,\,dt,} $$ $${\,\,\,}$$ then $${{dy} \over {dx}} = \_\_\_\_\_.$$

Two plates with symmetrical $$V$$ joint penetration of $$V$$ angle $$60deg$$ are to be arc welded in a single pass. The power $$P(kW)$$-arc length $$L$$ $$(mm)$$ characteristic is given by $$P=4+0.8L-0.1$$$${L^2}$$. Assuming that the top surface of the weld is flat & flush with the plate top surface, & the energy losses are $$20\% $$, the density of filler material is $$8gm/cc$$ and the energy required to melt $$1$$ $$gm$$ is $$1400$$ joules. The plate dimensions are $$1000mm$$ length & $$5mm$$ thickness. The maximum welding speed is .......................

The consumption of an oxy-acetylene flame for cutting of steel contains more oxygen

When the depth of cut is increased, the specific cutting energy