1. The problem statement, all variables and given/known data I had a rather tough multivariable calculus final, and the class was creamed by it. Apparently the professor thinks a 40% average is okay. But here is a portion of the problems. Please help me solve 'em. I'm not exactly sure if I'm taking the right path in these, but I did work on them to try and solve it. F. show that G. xyz=a3 encloses a tetrahedron with any of its tangent planes. Show that the area of the tetrahedron is constant. In my work, I sometimes just considered a3 to be any constant "c" for simplicity's sake. 2. Relevant equations (Look..... there's a ton of relevant equations..) 3. The attempt at a solution Here is my attempt at a solution. F. http://postimg.org/image/fif8ixl53/ I'm actually pretty happy with this solution, seeing as I may have gotten it somewhere. But as for really figuring it out entirely I couldn't. I was just stuck at y/x and I can't really see how the equation works out. http://postimg.org/image/xudxf024b/ There's my attempt at the end. I'm really not sure if this was mathematically allowed. G. http://postimg.org/image/o2myzhgw9/ Here's my attempt at this...... I really dunno what to do. It feels really simple, but at the time I tried I just couldn't do it. I know you can represent the area of a tet by multiplying xy(.5) and then z(.5) which gives the area but I ended up not being able to do that. I think. I couldn't figure out how to write the equations. You can see those equations in the bottom left- they're boxed. I don't know if those are right. I'm not sure if the denominator is interchangable with the other remaining variable. I tried to draw level curves with one variable fixed at 1 in those 3 graphs, but I'm not sure if those were "right". Etc etc............... Thanks.