A 20-meter ladder is sliding down a vertical wall so the distance between the top of the ladder and the ground is decreasing at 8 meters per minute. At a certain instant, the top of the ladder is 12 meters from the ground.
What is the rate of change of the distance between the bottom of the ladder and the wall at that instant (in meters per minute)?

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.