The helix is traced for

MATHEMATICS · Subjective · AP · Calculus BC · Applications of Integration · Applications of Integration

Problem

The helix r(t)=⟨5cos⁡t, 5sin⁡t, ct⟩\mathbf r(t)=\langle 5\cos t,\,5\sin t,\,ct\rangle is traced for 0≤t≤2π0\le t\le 2\pi, where cc is a positive constant. Determine the value of cc such that the length of the helix over this interval is 40π40\pi.

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