As Norman drives into his garage at night, a tiny stone becomes wedged between the treads in one of his tires. As he drives to work the next morning in his Toyota Corolla , as his tires make 10 rotations every second, the distance of the stone from the pavement, in inches, varies sinusoidally with the time he spends traveling. Assume that his wheel has a radius of 12 inches and that at t  0 seconds, the stone is at the bottom of the tire. Determine the equation that most closely models the distance of the stone, in inches, from the pavement, h(t), as a function of time, in seconds, t.

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.