Answer:
D. The mean will shift to the left.
Because if they sell lower priced cars it will bring the average price down causing the mean to move to the left
Assuming the fish pond is round, what you're given is the circumference.
So you know that 2<span>πr = 27.
We want to solve for the diameter, or d = 2r. We should isolate that.
2r = 27/</span><span>π
2r = 8.59 yards, or ~9 yards.</span>
Answer:
Therefore r'(t) =-k sin t i + k cos t j and |r'(t)| = k so T(t) = r'(t)/|r'(t)| = -sin t i + cos t j and T'(t) = -cos t i- sin t j . This gives |T'(t)| = 1, so using this equation, we have κ(t) = |T'(t)|/|r'(t)| = 1/k.
Step-by-step explanation:
We are already given the definition of curvature and the parametrization needed to find the curvature of the circle. In genecral the curvature κ is equal to κ(t)=|T'(t)|/|r'(t)| where r(t) is a parametrization of the curve and T(t) is the normalized tangent vector respect to the parametrization, that is, T(t)=r'(t)/|r'(t)|.
Now, using the derivatives of sines and cosines, and the definition of norm, we obtain that:
r(t) = k cos t i + k sin t j ⇒ r'(t)=-k sin t i + k cos t j ⇒|r'(t)|²=sin²t+cos²t=1
T(t) = r'(t)/|r'(t)|=-sin t i +cos t j ⇒ T'(t)= -cos t i - sin t j ⇒|T'(t)|²=cos²t+sin²t=1
