two particles start at the origin and move along the x axis. for 0 <= t <= 10, their respective position functions are given by x1 = cos(t) and x2 = (e^-3t) + 1. for how many values of t do the particles have the same velocity?

Find the equations for the velocities of both particles. $$ v_1=x_1^{\prime}=\frac{\differentialD}{\differentialD t}\left(\cos\left(t\right)\right), $$ $$ v_1=-\sin\left(t\right) $$ $$ v_2=x_2^{\prime}=\frac{\differentialD}{\differentialD t}\left(\exponentialE^{-3t}+1\right)=-3\left(\exponentialE^{-3t}\right)+0, $$ $$ v_2=-3\exponentialE^{-3t} $$ Now, let v1 = v2. $$ v_1=v_2, $$ $$ -\sin\left(t\right)=-3\exponentialE^{-3t}, $$ $$ \sin\left(t\right)=3\exponentialE^{-3t}, $$ $$ \sin\left(t\right)-3\exponentialE^{-3t}=0 $$ Then, find the values of t, from 0 to 10, as separated by commas. $$ t=0.5712,3.1414,6.2832,9.4248 $$