Consider a vibrating string of length L = π that satisfies the wave equation 4∂2u = ∂2u, 00. ∂x2 ∂t2
Assume that the ends of the string are fixed, and that the string is set in motion with no initial velocity from the initial position
u(x, 0) = 12 sin 2x − 16 sin 5x + 24 sin 6x. Find the displacement u(x, t) of the string.

60 2(x + 2) in the diagram, gef and hef are congruent. what is the value of x?

If value of cos330° is √3/2 then find tan165°.

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?