(a) conmpute the wronskian of the fanctions u and use it to explain why these two cannot be a pair of solutions on the entire real line of an equation egation y" +pny' +qny = o (hint: think about abel's theoen) (b) assune that gi and ge are solutions of the equation y" +pit)g+ y- 0 showtht ciyi+ca is a solution of the eqation fo any values of the constants ci. c

What is the expression in factored form? 225x^2 - 144 a. 9(5x+4)^2 b. 9(5x-4)^2 c. 9(4x+5)(4x-5) d. 9(5x+4)(5x-4)

What is the expression in factored form? 3x^2 + 18x + 24 a. 3(x+2)(x+4) b. 3(x-2)(x+4) c. 3(x-2)(x-4) d. 3(x+2)(x-4)

Carla was trying to decide what to do saturday evening. she has $100 available to spend for the evening. she has narrowed her choices down to these events: braves game, a concert of an artist she likes, or the georgia aquarium. admission to the braves game is $25, hot dogs cost $10, sodas cost $5. the concert costs $25 for admission, $20 for a souvernir t-shirt, and $10 for a soda. the georgia aquarium has the show of a lifetime with an all you can eat and drink that costs $100. carla does not want to take any driving chances, so in addition to the cost of the aquarium, she will also need to pay for her uber/lyft, which is $15 each way. which option should carla choose if she wants to spend the least? based on that choice, what then is carla's oppotunity cost? fully explain your answer in at least one paragraph.