A torus is formed when a circle of radius2 centered at [3, 0] is revolved about the yaxis. Use the shell method to write an integral for the volumeof the torus.

y² + (x - 3)² = 4 is the equation.

Step-by-step explanation:

The equation of the said circle is

y² + (x - 3)² = 4

y = √[4 - (x - 3)²]

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.