Length of curves Use a scalar line integral to find the length of the following curves. 31. r ( t ) = 〈 20 sin t 4 , 20 cos t 4 , t 2 〉 , for 0 ≤ t ≤ 2
Length of curves Use a scalar line integral to find the length of the following curves. 31. r ( t ) = 〈 20 sin t 4 , 20 cos t 4 , t 2 〉 , for 0 ≤ t ≤ 2
Solution Summary: The author calculates the length of the curve r(t)=langle 20mathrmsint
The curves F1(t) = ( − 3t, t5, t²) and r₂(t) = (sin(2t), sin( - 4t), t - ) intersect at the origin.
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Find the acute angle of intersection (in radians) on the domain 0 << to at least two decimal
places.
2'
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Describe the motion of a particle with position (x, y) as t varies in the given interval. (For each answer, enter an ordered pair of the form x, y.)
x = 4 + sin(t), y = 6 + 3 cos(t), π/2 ≤ t ≤ 2π
The motion of the particle takes place on an ellipse centered at (x, y) =
› = ( [
(x, y) =
As t goes from 1/2 to 2π, the particle starts at the point (x, y) =
and moves clockwise three-fourths of the way around the ellipse to
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