The curve defined by for has length

MATHEMATICS · Single correct · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions

Problem

The curve defined by

\mathbf r(t)=\langle e^{kt}\cos t,\,e^{kt}\sin t\rangle

for

0\le t\le2\pi

has length

10\pi

. Which of the following values of

k

satisfies this condition? (a)

0.554

(b)

0.405

(c)

0.420

(d)

0.300