#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

1. Question: 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).

Answer: 
r(t)=<t^4,t^3,t^8>
r'(t)=<4t^3,3t^2,8t^7>
r"(t)=<12t^2,6t,56t^6>
r'xr"t=(120t^8)i-(128t^9)j-(23t^4)k
|r'xr"t|=((120t^8)^2+(128t^9)^2+(23t^4)^2)^1/2
|r'(t)|=(16t^6+9t^4+64t^14)^1/2
P=(16,64,256)
k(t)=|r'xr"t|/(|r'(t)|)^3
k(t)=(((120(16)^8)^2+(128(64)^9)^2+(23(256)^4)^2)^1/2)/(16(16)^6+9(64)^4+64(256)^14)^3/2

2. Question: Who is your favorite rock band? 
Answer: Nirvana