Determine whether the statement is true or false. if it is true, explain why. if it is false, explain why or give a counterexample. the functions r1(t) = 3cos(t)i + 3 sin(t)j + (3cos(t) + 3sin(t)) k and r2(t) = ti, (9-t^2)j, t+(9-t^2) are different parametrizations of the same curve

FALSE

Step-by-step explanation:

No, they are not

Counter-example:

Take t = 4  

If r1 and r2 were the same curve, there should exist some value for which

Taking the absolute value on both sides

since the function cos(x) takes values between -1 and 1.

But 4 is greater than 3, and we have a contradiction.

So, r1 and r2 are not the same curve.

$15 each

step-by-step explanation:

$45/3 children= $15 each

what is the question?

step-by-step explanation: