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

#ANSWER TO QUESTION 1:

RUID: 192005757
a = 7, b = 7

r(t) = <t^7, t^7, t^14>
P = (128, 128, 16384)

<t^7, t^7, t^14> = <128, 128, 16384>

t^7 = 128, t^7 = 128, t^14 = 16384

t = 2

r'(t) = <7t^6, 7t^6, 14t^13>
r''(t) = <42t^5, 42t^5, 182t^12>

Plug in t = 2
r'(2) = <7(2)^6, 7(2)^6, 14(2)^13> = <448, 448, 114688>
r''(2) = <42(2)^5, 42(2)^5, 182(2)^12> = <1344, 1344, 745472>

Formula = |r'(t) x r''(t)| / |r'(t)|^3

|r'(t) x r''(t)| = 

|   i    j     k     |   |  448  112688 | * i - |  448  112688 | * j + |  448  448  | * k
|  448  448  112688  | = | 1344  745472 |       | 1344  745472 |       | 1344 1344  |
| 1344 1344  745472  | 

= 334082900*i - 334082900*j 


|334082900*i - 334082900*j| = sqrt(334082900^2 + 334082900^2) = 334082900*sqrt(2)

|r'(2)| = sqrt(448^2 + 448^2 + 114688^2) = 1344*sqrt(7282)

|r'(2)|^3 = 17678624882688*sqrt(7282)

|r'(t) x r''(t)| / |r'(t)|^3 = 334082900*sqrt(2) / 17678624882688*sqrt(7282)

k(t) = 83520725*sqrt(3641) / 16091968299466752


#QUESTION 1: What is your favorite rock band

#ANSWER TO QUESTION 1: I don't really listen to rock, but I really like the Beatles.