Aperturbation in the temperature of a stream leaving a chemical reactor follows a decaying sinusoidal variation, according to the following mathematical equation,
t(t)=5e^(-at ).sin⁡(wt)
where a and w are constant.
then show that the temperature t (t) is maximum at time “t”. also verify that t= 1/w.〖tan〗^(-1) (w/a)
determine the maximum temperature value at t= 1/w.〖tan〗^(-1) (w/a).

When a charged balloon sticks to a wall, the downward gravitational force is balanced by an upward static friction force. the normal force is provided by the electrical attraction between the charged balloon and the equal but oppositely charged polarization induced in the wall's molecules. if the mass of a balloon is 1.2 g, its coefficient of static friction with the wall is 0.71, and the average distance between the opposite charges is 0.80 mm, what minimum amount of charge must be placed on the balloon in order for it to stick to the wall? express your answer to two significant figures and include appropriate units.