Which of the following functions are solutions of the differential equation y'' + y = sin(x)?a) y= sinx
b) y= cosx
c) y=1/2sinx
d) -1/2xcosx

Find the balance at the end of 4 years if 1000 is deposited at the rate of

The perimeter of a stage is 116 feet. it is 17 feet wide. how long is it?

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.