#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 QUESTION 1:
#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^2a> at the point <2^a, 2^b, 4^a>

#SOLUTION:
#a=2, b=5
#P=<4, 32, 16>
#r(t)=<t^2, t^5, t^4>
#solve t in r(t) at P
#t=2
#r'(t)=<2t, 5t^4, 4t^3> 
#r'(2)=<4, 80, 32>
#r"(t)=<2, 20t^3, 12t^2>
#r"(2)=<2, 160, 48>
#r'(2)×r"(2)=<-4736, -128, 624>
|r'(2)×r"(2)|=16*sqrt(89201)
|r'(2)|=4*sqrt(465)
kappa(2)=(16*sqrt(89201))/(4*sqrt(465))^3=sqrt(89201)/465

#ATTENDANCE QUESTION 2:
#WHO IS YOUR FAVORITE ROCK BAND?

#SOLUTION:
#The Beatles.