#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)
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#Subject: aq5
#with an ATTACHMENT CALLED:
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#(e.g. aq4DoronZeilberger.txt)



#THE ATTENEDANCE QUESTIONS AND ANSWERS IN LECTURE 5

#LIST ALL THE ATTENDANCE QUESTIONS FOLLOWED BY THEIR ANSWERS

#ATTENDANCE QUIZ QUESTION 1: Let a be the 7th digit of your RUID. Let b be the 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:192005137
#a=1
#b=7
#r(t)=<t,t^7,t^2> at point (2,128,4)
#t=2,t^7=128,t^2=4 so t=2
#r'(t)=<1,7t^6,2t>
#r''(t)=<0,42t^5,2>
#r'(1)=<1,7,2> and r''(1)=<0,42,2>
#r'(1) x r''(1) = <-70,-2,42>
#|<-70,-2,42>|=2*sqrt(1667)
#(|r'(1)|)^3=(3*sqrt(6))^3=162*sqrt(6)
#Ans: [2*sqrt(1667)]/[162*sqrt(6)] = sqrt(1667)/[81*sqrt(6)]

#ATTENDANCE QUIZ ANSWER 1: The curvature of r(t)=<t,t^7,t^2> at point (2,128,4) is sqrt(1667)/[81*sqrt(6)].

#ATTENDANCE QUIZ QUESTION 2: Who is your favorite rock band?

#ATTENDANCE QUIZ ANSWER 2: Personally, I don't listen to rock that often but if I had to choose, I would say The Beatles are my favorite rock band.