Today we were introduced to polynomial combinations. We were given examples of adding, subtracting, and multiplying two polynomials, but we weren't given any real-world examples of division. Can anyone provide an example of a real-world situation in which you would divide two different polynomials? I have a much easier time understanding and applying concepts if I can see examples of them in practice.
Need help coming up with a real-world scenario.
- Thread starter drew.l
- Start date
Dr.Peterson
Elite Member
- Joined
- Nov 12, 2017
- Messages
- 16,090
What sort of examples were given for the other operations? I'd like to see what you (or they) consider "real world".
Most math is not directly related to the real world, but is used in solving general problems that might in turn be applied in the real world. The details of the math may be well hidden; and, in addition, the applications of a technique may be within some math you aren't ready for yet. One example would be in determining the asymptote of a rational function (that is, how it behaves for very large input), which might be useful in determining the long-range effect of some climate model. That might be very real-world, but you're not going to be sitting there as a climatologist dividing two polynomials!
But we could fake a "real-world" application by supposing that some two quantities are polynomial functions of time, and finding their ratio as a function of time.
If you are familiar with the concept of elasticity in economics, ratios of polynomials will arise whenever polynomials are good approximations to the underlying economic functions.
[MATH]q = 520 - 0.5p - 0.004p^3 \implies \epsilon = \left | \ \dfrac{0.012p^3+ 0.5p}{520 - 0.5p - 0.004p^3} \ \right |.[/MATH]
[MATH]q = 520 - 0.5p - 0.004p^3 \implies \epsilon = \left | \ \dfrac{0.012p^3+ 0.5p}{520 - 0.5p - 0.004p^3} \ \right |.[/MATH]