Ethan is observing an amusement park ride where the riders go around in a counterclockwise circular motion. The carts take 2 seconds to complete a full rotation. The center of the ride is 24 feet above the ground as shown in the diagram, and the cart Ethan is observing is labeled X. Explain why a sinusoidal function could be used to model the height of cart X, above the ground, as a function of time?

In a coastal town, the humidity, measured in grams of water per kilogram of air, increases by 43% for every 1 degree celsius increase in temperature. a scientist observes that the humidity on monday morning is 5.75 grams per kilogram. he wants to know how much the temperature must increase for the humidity to reach at least 49.17 grams per kilogram. let t represent the increase in temperature, in degrees celsius, from monday morning's observation. write an inequality to represent the situation, and use it to determine the desired temperature increase.