# Attendance Quiz
# Attendance question #1: Let a = 7th digit of your RUID, let b = 9th digit. Find the curvature of the curve
# r(t) = <t^7, t^2, t^14> at the point <2^7, 2^2, 4^7>

# Solution to attendance Question 1:

# 4^7 = 2^2^7 = 2^14
# t^7 = 2^7, t^2 = 2^2, t^14 = 2^14
# t = 2

# r'(t) = <7t^6, 2t, 14t^13>
# r''(t) = <42t^5, 2, 182t^12>
# r'(1) = <7(1)^6, 2(1), 14(1)^13> = <7, 2, 14>
# r''(1) = <42(1)^5, 2, 182(1)^12> = <42, 2, 182>
# r'(1) x r''(1) = <336, -686, -70>
# |r'(1)| = sqrt(249) = 15.7797
# |r'(1)|^3 = 15.7797^3 = 3929.1284
# |r'(1) x r''(1)| = sqrt(112896 + 470596 + 4900) = sqrt(588392) = 767.0671
# |r'(1) x r''(1)| / |r'(1)|^3 = 767.0671 / 3929.1284 = 0.1952
# The curvature of the curve r(t) = <t^7, t^2, t^14> at the point <2^7, 2^2, 4^7> is 0.1952

# Attendance question #2: Who is your favorite rock band?

# I actually do not listen to much rock music but if I were to choose any I would choose The Beatles.