Let an aluminum rod of length 20 cm be initially at the uniform temperature of 25°C. Suppose that at time t=0, the end x=0 is cooled to 0°C while the end x=20 is heated to 60°C, and both are thereafter maintained at those temperatures. Required:
a. Find the temperature distribution in the rod at any time t.
b. Plot the initial temperature distribution, the final (steady state) temperature distribution, and the temperature distributions at two representative intermediate times on the same set of axes.
c. Plot u versus t for x=5, 10, and 15.
d. Determine how much time must elapse before the temperature at x=5 cm comes(and remains) within 1% of its steady state value.

It appears that people who are mildly obese are less active than leaner people. one study looked at the average number of minutes per day that people spend standing or walking. among mildly obese people, the mean number of minutes of daily activity (standing or walking) is approximately normally distributed with mean 376 minutes and standard deviation 64 minutes. the mean number of minutes of daily activity for lean people is approximately normally distributed with mean 528 minutes and standard deviation 107 minutes. a researcher records the minutes of activity for an srs of 7 mildly obese people and an srs of 7 lean people. use z-scores rounded to two decimal places to answer the following: what is the probability (image for it appears that people who are mildly obese are less active than leaner people. one study looked at the averag0.0001) that the mean number of minutes of daily activity of the 6 mildly obese people exceeds 420 minutes? what is the probability (image for it appears that people who are mildly obese are less active than leaner people. one study looked at the averag0.0001) that the mean number of minutes of daily activity of the 6 lean people exceeds 420 minutes?