(a) The temperature of a 22 m long metal bar is 14°C at one end and 33°C at the other end. Assuming that the temperature increases linearly from the cooler end to the hotter end, what is the average temperature of the bar? Tave = 23.5 °C (b) Explain why there must be a point on the bar where the temperature is the same as the average, and find it. [Let x be the distance along the bar from zero.] x = 9.5 m along the bar.

a. Write the equation of the line tangent to the curve where y=0 b. Using the same point in part a, write the equation of the normal line.

You will be graded on your written work as well as your answer. You and Austin start at the same place when a dinosaur attacks! At t = 0 hours, you run North at 3 miles/hour while Austin runs West at 9 miles/hour. At the bottom you will answer, "how fast is the distance between us changing at t = 0.5 hours?" In your written work: a) Draw a picture and clearly label the variables. b) What relationship should you use to help you? (some equation from geometry, using your picture and your variables.) Write the relationship using the variables from your picture. c) Use implicit differentiation to take the derivative of your relationship. You do not need to solve or simplify. d) How fast is the distance between us changing at t 0.5 hours? miles/hour

What is the slope of the line