Suppose that, at a specific point p, the directional derivatives of the function f (x, y ) are known in two nonparallel directions given by the unit vectors u and v. in particular, suppose that d f d s = a in the u direction and d f d s = b in the v direction. is it possible to find the gradient of f at the point p? if so, show how to do it. if not, explain why not.

If this plastic cup is heated to its melting point, what will eventually happen to all the particles in the plastic? a. the particles will begin to move enough that they slide past each other. b. bonds will form and the liquid will become a solid. c. the spaces between the particles will get smaller. d. the particles will change state and become a crystalline solid.

The car hoist allows the car to be driven onto the platform, after which the rear wheels are raised. if the loading from both rear wheels is 1380 lb, determine the force in the hydraulic cylinder ab. neglect the weight of the platform itself. member bcd is a right-angle bell crank pinned to the ramp at c. the force is positive if in tension, negative if in compression.

Who was the first scientist to measure speed as distance over time?