#ATTENDANCE QUIZ for Lecture 5 of Math251(Dr. Z.)
#EMAIL  RIGHT AFTER YOU WATCHED THE VIDEO
#BUT NO LATER THAN  Sept. 21, 2020, 8:00PM (Rutgers time)
#THIS .txt FILE (EDITED WITH YOUR ANSWERS)
#TO:
#DrZcalc3@gmail.com
#Subject: aq5
#with an ATTACHMENT CALLED:
#aq5FirstLast.txt
#(e.g. aq4DoronZeilberger.txt)



#THE ATTENEDANCE QUESTIONS AND ANSWERS IN LECTURE 5

#LIST ALL THE ATTENDANCE QUESTIONS FOLLOWED BY THEIR ANSWERS

Attendance question1
Let a:=7th digit of your RUID
Let b:=9th digit of your RUID
Find the curvature of the curve
r(t)=<t^a, t^b, t^(2*a)> at the point <2^a, 2^b,4^a>
RUID:203002353

Ans:
a=3 b=3
step1:
r(t)=<t^3,t^3,t^6>=<2^3,2^3,4^3>
t^3=8,t^3=8,t^6=64
sol.t=2
step2:
t=2
r(t)'=<3t^2,3t^2,6t^5>=<12,12,192>
r(t)''=<6t,6t,30t^4>=<12,12,480>
step3:
r'(t)Xr''(t)=(3t^2*30t^4-6t*6t^5)i-(3t^2*30t^4-6t*6t^5)j+(3t^2*6t-6t*3t^2)k=(54t^6)i-(54t^6)j
r'(2)Xr''(2)=<12,12,192>X<12,12,480>=3456i-3456j
Ir'(2) X r''(2)I=4887.5
Ir'(2)I^3=7160993.79
step4:
kappa(2)=Ir'(2)Xr''(2)I / Ir'(2)I^3=4887.5/7160993.79=6.825*10^(-4)
The curvature at the designated point is the number 6.825*10^(-4).

Attendance question2
who is your favorite rock band?

Ans:
I think I don't have it.