Problem 9. The vector function r(t) = (cost + tsin t)i + (sin t − t cost)j + 1 2 √ 3t 2k determines a curve C in space. (a) Find the unit tangent vector T(t) and the principal normal vector N. (b) Find the curvature, κ of C. (c) Determine the tangential and normal components of acceleration; express the acceleration vector, a(t) in terms of T and N.

the central idea is that:

individuals should refuse to cooperate with institutions they believe unjust.

thoreau felt  that governments were more often agents of corruption than justice, even democracies, and that just because the majority feels a certain way does not make it just or correct in absolute terms. he uses the fact that slavery exists in our democracy to support this idea.

he goes on to say that, as a result, people should live true to their own internal laws regarding right and wrong, as a product of reflection and a moral life, rather than following every law that society imposes. 

step-by-step explanation:

b

step-by-step explanation:

well what did you do it matters what you did : )

step-by-step explanation: