Consider following parametric equations for a curve. x = e-St cos(5t), y = e-St sin(5t), z = e-5t Determine the value of t that corresponds to the point (1, 0, 1). t = 0 Write a vector equation r(t) for the given curve. r(t) = Find r'(t). r'(t) = <-5e-5sin (5t) - 5 cos (5t)e -5t x = e Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point cos(5t), y e-5t sin(5t), z = est, (1, 0, 1) -5t E (x(t), y(t), z(t)) = -5*cos(5t) — 5 sin (5t)e-5t, - 5e-5t> -

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