#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. aq5DoronZeilberger.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 (3)
#Let b:=9th digit of your RUID (7)
#Find the curvature of the curve
#r(t)= <t^a, t^b, t^(2*a)> at the point (2^a, 2^b, 4^a)

#ANSWER TO QUESTION 1:
#r(t)= <t^3, t^7, t^6> at the point (8, 128, 64)
#t^3 = 8, t^7 = 128, t^6 = 64
#t = 2
#kappa(t) = |r'(t) x r"(t)| / (|r'(t)|^3)
#r'(t) = <3*t^2, 7*t^6, 5*t^5>
#r'(2) = <3*2^2, 7*2^6, 5*2^5>
#	= <12, 448, 160>
#r"(t) = <6*t, 42*t^5, 25*t^4>
#r"(2) = <6*2, 42*2^5, 25*2^4>
#	= <12, 1344, 400>
#kappa(2) = |<12, 448, 160> x <12, 1344, 400> | 
#	/ (|<12, 448, 160>|^3)
#kappa(2) = |<448*400 - 1344*160, 12*160 - 12*400, 12*1344 - 12*448>|
#	/ (|<12, 448, 160>|^3)
#kappa(2) = |<-35840, -2880, 10752>| / (|<12, 448, 160>|^3)
#kappa(2) = sqrt(35840^2 + 2880^2 + 10752^2) 
#	/ (sqrt(12^2 + 448^2 + 160^2)^3
#curvature = sqrt(1408405504) / sqrt(226448)^3
#	= 64*sqrt(343849) / (4*sqrt(14153))^3
#	= sqrt(343849) / (sqrt(14153)^3)



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

#ANSWER TO QUESTION 2:
#The Beatles. Of course.