#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: aq4
#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) Find the curvature of the curve r(t) = <t^a, t^b, t^(2*a)> at the point <2^a, 2^b, 4^a>
a = 7th digit of your RUID  = 4
b = 9th digit of your RUID = 7

    Answer: find t first 
    <t^4, t^7, t^(8)> at the point <2^4, 2^7, 4^4>, t = 2
    Now, find r'(t) = <4t^3,7t^6,8t^77>
    r''(t) = <12t^2,42t^5,56t^6>
    |r'(t)|^3  = t^9(64t^8+49t^6+16)^1.5
    r't x r''(t) = <56t^12,−128t^9,84t^8> 
    ||cross product|| =4t^8 * sqrt(196t^8+1024t^2+441)

    Dividing magnitude of cross product and |r'(t)|^3 at t = 2: 
    Curvature is sqrt(66804573) / 47706912

2) Who is your favorite rock band?

    Answer: Linkin Park