Let C be a smooth curve with parametrization r(t). We know from class that at time t its acceleration vector has the form

a(t) = aT(t)T(t) + aN(t)N(t),
where aT(t) and aN(t) are the tangential and normal components of the acceleration. Use this fact to show that, for each t, the vector r0(t)×r00(t) is parallel to B(t).

Using the given fact to show that, for each t, the vector r'(t)×r"(t) is parallel to B(t), below is proof.

B(t) = λ [r'(t) * r"(t)]   where, λ = 1 / [ aₙ(t) ||r'(t)|| ]

Step-by-step explanation:

a(t) = aT(t)T(t) + aN(t)N(t), where aT(t) and aN(t) are the tangential and normal components of the acceleration.

In the attached workings, the above fact is used to show that for every 't', the vector r'(t)×r"(t) is parallel to B(t).

step-by-step explanation:

milk=16 large

soda=280 kids

juice box=82 regular

63 soda +63 regular

124 large total

answer is the third choice:

3x^5+4x^4+x^3+2x^2-10x-7=0

step-by-step explanation: