The two ends of a uniform rod of length L are insulated. There is a constant source of thermal energy Q0≠0, and the temperature is initially u(x, 0) = f(x). (a) Show mathematically that there does not exist any equilibrium temperature distribution. Briefly explain physically. (b) Calculate the total thermal energy in the entire rod.

Suppose that a customer is purchasing a car. he conducts an experiment in which he puts 10 gallons of gas in the car and drives it until it runs out of gas. he conducts this experiment 15 times on each car and records the number of miles driven. full data set car 1 238238 216216 205205 212212 240240 274274 297297 252252 260260 247247 257257 243243 296296 243243 290290 car 2 245245 204204 215215 209209 251251 165165 221221 295295 172172 287287 268268 305305 320320 260260 297297 describe each data set, that is determine the shape, center, and spread. sample mean for car 1 x overbar equalsx=216216 mi / 10 gal (type an integer or decimal rounded to one decimal place as needed.) sample mean for car 2 x overbar equalsx=209209 mi / 10 gal (type an integer or decimal rounded to one decimal place as needed.)