Consider F and C below. F(x, y, z) = yzexzi + exzj + xyexzk, C: r(t) = (t2 + 3)i + (t2 − 1)j + (t2 − 2t)k, 0 ≤ t ≤ 2 (a) Find a function f such that F = ∇f. f(x, y, z) = (b) Use part (a) to evaluate C F · dr along the given curve C.

The force on a cutting tool are 2600n vertically downward and 2100 horizontal. determine the resultant force acting on the tool and the angle at which it acts.

Apipe with an outside diameter of 15 cm is exposed to an ambient air and surrounding temperature of -20°c. the pipe has an outer surface temperature of 65°c and an emissivity of 0.85. if the rate of heat loss from the pipe surface is 0.95 kw per meter of length, the external convective heat transfer coefficient (h) is: (a) 12.5 w/m"k (b) 18.6 w/mk (c) 23.7 w/mk (d) 27.9 w/mk (e) 33.5 w/mk

Wiy doeres rere okhn a pump whon working betwon the same pressure range?