Find the exact length of the curve. x=et+e−t, y=5−2t, 0≤t≤2 For a curve given by parametric equations x=f(t) and y=g(t), arc length is given by

The length of a curve C parameterized by a vector function r(t) = x(t) i + y(t) j over an interval a ≤ t ≤ b is

In this case, we have

x(t) = exp(t ) + exp(-t )   ==>   dx/dt = exp(t ) - exp(-t )

y(t) = 5 - 2t   ==>   dy/dt = -2

and [a, b] = [0, 2]. The length of the curve is then

the answer is 0.5 mpm

step-by-step explanation:

the line goes half way through the square each time (which is 0.5 or half of course) so that would mean its 0.5 mpm.