Find the values of t so that the tangent line to the given curve is contains the given point? given r(t)=2ti+t^2j-t^2k at point (0,-4,4)

t = -2,2

Step-by-step explanation:

The curve equation,

Let at t=a tangent to the curve.

Equation of tangent:  

L(k) = r(a) + k r'(a)

Put t=a

Equation of tangent:

Tangent passing through (0,-4,4)

Therefore,

2a + 2k = 0   ⇒  k = -a

At t = -2,2  tangent line to the curve passing through (0,-4,4)

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.

you would have to sell 24 bracelets.

step-by-step explanation:

84/3.5 = 24