#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:
#a = 7th RUID digit
#b = 9th RUID digit

#RUID is 192001812

#find curvature of the curve:
#r(t) = <t^a, t^b, t^(2*a)> at point <2^a, 2^b, 4^a>

#answer to AQ 1:
#a = 8
#b = 2

#r(t) = <t^8, t^2, t^(2*8)> at point <2^8, 2^2, 4^8>

#r(t) = <t^8, t^2, t^(16)> at point <256, 4, 65536>

#x(t) = 256 --> t = 2

#r'(t) = <8t^7 i , 2t j , 16t^15 k> 
#r''(t) = <56t^6 i , 2 j , 240t^14 k> 

#r'(2) = <1024 i, 4 j, 524288 k>
#r''(2) = <3584 i, 2 j, 3932160 k>

#|r'(t) x r''(t)| = <4*3932160 - 524288*2, 1024*3932160 - 524288*3584, 1024*2 - 4*3584>
#|r'(t) x r''(t)| = <14680064, 2147483648, -12288>
#|r'(t) x r''(t)| = sqrt(14680064^2 + 2147483648^2 + -12288^2)
#|r'(t) x r''(t)| = 2147533823.44899

#|r'(t)|^3 = sqrt(1024^2 + 4^2 + 524288^2)
#|r'(t)|^3 = 524289.000014305^3

#k = (|r'(t) x r''(t)|) / (|r'(t)|^3)
#k = 2147533823.44899/144116012722946000


#k = 0.0000000149014240879498


#Attendance question 2
#who is your favorite rock band?

#answer to AQ 2:
#green day!