Given =(+(+(t)=etcos(3t)i+etsin(3t)j+3etk find the derivative ′′(t) and norm of the derivative. ′=r′(t)= ‖′‖=‖r′(t)‖= then find the unit tangent vector (t) and the principal unit normal vector (t)

Carmen and matt are conducting different chemistry experiments in school. in both experiments, each student starts with an initial amount of water in a flask. they combine two chemicals which react to produce more water. carmen's experiment starts with 30 milliliters of water in a flask, and the water increases in volume by 8.5 milliliters per second. matt's experiment starts with 10 milliliters of water and increases in volume by 28% each second.