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bannedccnt
27.10.2019 •
Mathematics
Consider the vector function given below.
r(t)=(3t^2, sin(t)-tcos(t), cos(t)+tsin( t> 0
do the following
(a) find the unit tangent and unit normal vectors t(t) and n(t)
t(t) = < , , >
n(t) = < , , >
(b) find the curvature
k(t) =
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Ответ:
T' = dr/dt = <6t, tsin(t), tcos(t)>
The unit vector T = T'/|T'| = <6t, tsin(t), tcos(t)>/sqrt(36t^2 + t^tsin(t)^2 +t^2cos(t^2))
T = <6t, tsin(t), tcos(t)>/(t*sqrt(37)) = <6, sin(t), cos(t)>/sqrt(37)
Now the normal unit vector N is perpendicular to r/|r| and T. It is the second derivative of r/|r| with repsect to time
N' = d^2r/dt^2 = <6, sin(t) + tcos(t), cos(t) - tsin(t)>
N= N'/|N'| = <6, sin(t) + tcos(t), cos(t) - tsin(t)>/sqrt(36 + sin^2t +2tsin(t)cos(t)+t^2cos^2t + cos^2(t) -2tcos(t) sin(t) +t^2sin^2t)
N = <6, sin(t) + tcos(t), cos(t) - tsin(t)>/sqrt(37 +t^2)
Ответ:
3) is wrong, you should have answered 16. 4) is also wrong it's 24
5) is 14. 7) is 11
Step-by-step explanation: