Question

16. Find aN at time t=1 for the plane curve r(t)= 8t^2i + 5tj. Round your answer to three decimal places. Please use good handwriting, thank you!

Answer #1

Consider the parameterized motion given by
r(t)=3t^2i-2t^2j+(6-t^3)k.
Where is the object at time t=1? What is the velocity at t=1?
What is the speed at t=1?
How far does the object move from 0≤t≤1? Round your
answer to 2 decimal places.
* r, i, j, and k should all have vector arrows above them

Let C be the plane curve determined by the function
r(t)=(3-t^2)i+(2t)j where -2<=t<=2.
-Find T(t), T'(t), the magnitude of T'(t), and
N(t).
Please show work, Thank you!

Give your answer to two decimal places
1) Find the curvature of the curve r(t)=〈 5+ 5cos t , −5 ,−5sin
t 〉 at the point t=11/12π
2) Find the curvature of the curve r(t)= 〈4+3t,5−5t,4+5t〉 the
point t=5.

1) Find the curvature of the curve r(t)= 〈2cos(5t),2sin(5t),t〉
at the point t=0
Give your answer to two decimal places
2) Find the tangential and normal components of the acceleration
vector for the curve r(t)=〈 t,5t^2,−5t^5〉 at the point t=2
a(2)=? →T + →N

Find T, N, and κ for the plane curve r(t) = (7t+2) i + (5 - t^7)
j

1.
(1 point) For the curve given by
r(t)=〈−7t,−4t,1+7t2〉r(t)=〈−7t,−4t,1+7t2〉,
Find the derivative
r′(t)=〈r′(t)=〈, , , 〉
Find the second derivative
r″(t)=〈r″(t)=〈
Find the curvature at t=1t=1
κ(1)=κ(1)=
2.
(1 point) Find the distance from the point (-1, -5, 3) to the
plane −4x+4y+0z=−3.

1) Find the curvature of the curve r(t)= 〈4+3t,5−5t,4+5t〉 the
point t=5.
2) Find a plane through the points (2,-3,8), (-3,-3,-6),
(-6,3,-7)

Find the arc length of the curve on the given interval. (Round
your answer to three decimal places.)
Parametric Equations
Interval
x = 6t + 5, y = 7 − 5t
−1 ≤ t ≤ 3

18. Find aT at time t=2 for the space curve r(t)= (9t-1)i + t^2
j -8tk

Let a = 2i -3k; b= i+j-k
1) Find a x b.
2) Find the vector projection of a and b.
3) Find the equation of the plane passing through a with normal
b.
4) Find the equation of the line passing through the points a and
b.
Please help and show your steps. Thank you in
advance.

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