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Problem 1 - Modelling with functions and equations

This is a hand-in written by **Group 60** (FIRE) for the weekly **module #1** in the mathematical modelling course (**DAT026**) at Chalmers University of Technology.

Group 60 consists of:

**Mazdak Farrokhzad**901011-0279

twingoow@gmail.com

Program: IT

Time spent: 24 hours 23 minutes

**Niclas Alexandersson**920203-0111

nicale@student.chalmers.se

Program: IT

Time spent: 19 hours 22 minutes

**We hereby declare that we have both actively participated in solving every exercise, and all solutions are entirely our own work.**

A number of mathematical equations are listed below. Their justification (why they are true or reasonable), how well they model reality and a categorization of them are done for each equation.

The equation describes the relationship between the catheti (\(a, b\)) and the hypotenuse (\(c\)) for a right angled triangle. It can easily be proved by considering a square with a smaller rotated square in it - which results in there being 4 right angled triangles as well it.

It has been a well known relationship for a few thousand years. And it is very easy to prove mathematically.

The solution is exact.

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