Suppose that over a certain region of space the electrical potential v is given by the following equation.

v(x, y, z) = 2x2 − 3xy + xyz

(a) find the rate of change of the potential at p(2, 2, 5) in the direction of the vector

v = i + j − k.

(b) in which direction does v change most rapidly at p?

(c) what is the maximum rate of change at p?

Zed is making a centerpiece for his dining room table by putting sand in a cube-shaped vase. the vase is 0.25 meters in length, width, and height. he bought 25 kg of sand. assume the density of dry sand is 1,602 kgm3. what is the volume of the sand that zed purchased? the volume of the sand is approximately m3. enter your answer as the number that correctly fills in the blank in the previous sentence. if necessary, round your answer to six decimal places, like so: 42.536475