1. (4 puntos cada uno) resuelva cada uno de los siguientes odes o problemas de valor ini- cial lineales homogeneos, hallando la solución general o particular. provea todos los pasos en cada problema realizado. (a) 41" + 4y' + y = 3re* (b) sin)

If f(x)= sqrt4x+9+2, which inequality can be used to find the domain of f(x)?

An octagonal prism has jow many lateral faces?

Afriend of mine is giving a dinner party. his current wine supply includes 10 bottles of zinfandel, 8 of merlot, and 11 of cabernet (he only drinks red wine), all from different wineries. (a) if he wants to serve 3 bottles of zinfandel and serving order is important, how many ways are there to do this? ways (b) if 6 bottles of wine are to be randomly selected from the 29 for serving, how many ways are there to do this? ways (c) if 6 bottles are randomly selected, how many ways are there to obtain two bottles of each variety? ways (d) if 6 bottles are randomly selected, what is the probability that this results in two bottles of each variety being chosen? (round your answer to three decimal places.) (e) if 6 bottles are randomly selected, what is the probability that all of them are the same variety? (round your answer to three decimal places.)