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Mathematics
Mathematics
Problem
The curve defined by
r
(
t
)
=
⟨
e
k
t
cos
t
,
e
k
t
sin
t
⟩
\mathbf r(t)=\langle e^{kt}\cos t,\,e^{kt}\sin t\rangle
r
(
t
)
=
⟨
e
k
t
cos
t
,
e
k
t
sin
t
⟩
for
0
≤
t
≤
2
π
0\le t\le2\pi
0
≤
t
≤
2
π
has length
10
π
10\pi
10
π
. Which of the following values of
k
k
k
satisfies this condition? a)
0.554
0.554
0.554
b)
0.405
0.405
0.405
c)
0.420
0.420
0.420
d)
0.300
0.300
0.300
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