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what are the importance of nonlinear equation in practical life?

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A lot of things depending on what you are interested in.  Parabola are really useful for lighting.  The silver part of a flashlight is shaped like a three dimensional parabola because of some of the properties of parabola.  Similarly ellipsoidal lenses are also used in specifically stage lighting.

Parabola are also really useful for predicting the trajectory of a moving object.  If you are interested in sports, the arc of a basketball or a tennis ball or anything that you throw into the air will be a parabolic shape.  If you have a good idea of what parabola look like, and how they work, you could better predict where your shots will go when you project a ball through the air.

If you are interested in teaching, most of the time the scores of your kids will fall into a pattern that is known as the "normal" curve which has a really complicated equation to it which isn't even a polynomial (if you are unaware of what a polynomial, just know that the equation is hard to express or interpret even for calculus).  Regardless, advanced mathematics has allowed us to understand how it works, and understanding that curve can help us know how to grade kid's tests if your test is hard enough that nobody gets over 80% of the questions.

If you are interested in music, all sound comes in waves which is a non-linear equation so it helps to know how those waves interact with each other when recording music, or when at a live event and setting up the speakers.

If you are interested in tailoring in any form whether professionally or if you enjoy cos-playing for conventions, knowing how to make a pattern, or how a flat surface needs to contort to cover a 3d body.  That is a really complicated concept and getting good at predicting what lines you need to draw for a pattern is essentially getting good at topological, nonlinear equations.

Anyway, nonlinear equations are great.  They help predict a lot of things in our daily lives.  And they don't need to involve numbers to be a nonlinear equation.  Sometimes you have to deal with the numbers, but often you are just dealing with the shape of the graph, and when that's the case it helps to know what properties those shapes have.  Sometimes that's a geometric thing, but often it's an algebraic thing.

Hope that helps!