Na certain region, the electric potential due to a charge distribution is given by the equation v(x, y,z)=3(x^2)(y^2) +y(z^3) - 2x(z^3), where x, y, and z are measured in meters and v is in volts. calculate the magnitude of the electric field vector at the position (x, y,z)=(1.0,1.0,1.0).

The electric field is the negative of the gradient of the electric potential:

At the point (1.0, 1.0, 1.0), the electric field has magnitude

a) one student is chosen from classroom a, then a student is chosen from classroom b.  

step-by-step explanation:

independent events are ones in which the probability of one event does not affect the probability of the second event.

one student is chosen from classroom a; this does not affect the chances of choosing a student from classroom b.   this makes these independent events.

when one card is chosen from a standard deck and then set aside before a second card is chosen, the probability of the second card being chosen changes.   this makes them dependent events.

when one student is chosen from classroom a and then a second student is chosen from classroom a, the probability of choosing the second student changes.   this makes them dependent events.

when a letter is chosen from the alphabet and then a second letter is chosen, the probability of choosing the second letter changes.   this makes them dependent events.

1) 2/5

2) zero=0/1

3) zero=0/2

4) -4/5

5) undefined=3/0