Consider the spiral given by c(t) = (e2t cos(2t), e2t sin(2t)). Show that the angle between c and c' is constant. c'(t) = Let θ be the angle between c and c'. Using the dot product rule we have the following. c(t) · c'(t) = c(t) · c'(t) cos(θ) 2e4t = cos(θ)

The management of a supermarket wants to adopt a new promotional policy of giving a free gift to every customer who spends more than a certain amount per visit at this supermarket. the expectation of the management is that after this promotional policy is advertised, the expenditures for all customers at this supermarket will be normally distributed with a mean of $95 and a standard deviation of $20. if the management wants to give free gifts to at most 10% of the customers, what should the amount be above which a customer would receive a free gift?