#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


# Question 1: let a:=7th digit of your RUID, b:=9th digit of your RUID
# Find the curvature of the curve r(t) = <t^a, t^b, t^(2a)> at point <2^a, 2^b, 4^a>

# for me: a=2, b=5
# find curvature of r(t) = <t^2, t^5, t^4> at point <4,32,16>

# Find t:
# t^2=4, t^5=32, t^4=16
# t=2

# r'(t) = <2t, 5t^4, 4t^3>
# r''(t) = <2, 20t^3, 12t^2>

# r'(2) = <4,80,32>
# r''(2) = <2,160,48>

# |r'(2) x r''(t)| = |<-1280,-128,480>| = sqrt(1885184)
# |r'(2)|^3 = sqrt(7440)^3

# kappa(2) = sqrt(1885184)/sqrt(7440)^3 ~= 0.00213952551109


# Question 2: Who is your favorite rock band?

# Queen