I don't understand how to complete this problem: Find the minimum diameter of an 17.3 m long tungsten wire that will stretch no more than 9.43 mm when a load of 361 kg is hung on the lower end.

You'll need to use the Young's modulus of tungsten. It can describe the force exerted by an object under strain:

F = Y x A x deltaL / Lo

I don't know if your prof wants you to take into account the weight of the tungsten wire as well as the load, though.