A detailed report of findings on the altitudes which can be reached by super pressure balloons and how various factors and considerations affect this. Superpressure balloons are deployed and researched by various organisations including NASA, to solve technical limitations such as cell tower coverage as well as advancing fields of research. Balloons are used in planetary exploration, and weather prediction to teaching primary school physics. The versatile yet simple aerostat has been a valuable tool in many areas of engineering and their altitude ceiling is of great scientific interest. To solve the problem without the ability to physically reproduce the scenario, required mathematical models to be created as a means of simulating the effects of real world physics. A degree great enough to output an accurate and hence useful result without becoming too complex to be computable is the fine balance attempted to be created by this paper.
This problem is an applied optimization problem. The problem is to minimize
the area of the triangle formed by a tangent line to the function y = 1⁄9 x2.
The triangle is defined by the origin, the x-intercept of the tangent line, and the
y-intercept of the tangent line. Only triangles formed in the first quadrant are
LaTeX is the best way to write mathematics. It completely pisses all over Word. However, it does take some time to get used to so might not be worth your while if you won't write too much. The way I use it is to first download and install a latex editor and then get writing, but I would recommend that you use this website instead since you can get going a lot quicker. The upshot of the whole business is that you type in here and then a pdf is generated with all the equations looking ace. I'll give you some examples.