# B What are some real world example of these equations?

1. Sep 26, 2017

### Apple_Mango

I am in Algebra one. I am curious to know the real world applications in some of the equations I'm learning. I asked my math teacher and he didn't know any answers.

I am interested in using slope formula and linear inequalities in real life. How will I be using this in physics? I would like someone to give me a problem to solve for myself.

2. Sep 26, 2017

### Staff: Mentor

The easiest, and most frequent examples which involve linearity and inequalities are problems in operations research. Imagine you have a small airline with, say six airplanes. Now invent a schedule for flights with turn around time, staff them with crews and consider, that there are many boundaries like allowed take-off and landing times on a globe with many different time zones, maximal serving periods for pilots and cabin, inspection intervals for the equipment and what ever you want to consider. These all are boundary conditions which can be expressed by linear inequalities and your goal is a maximum time in air for the airplanes with minimal staff.

Last edited: Sep 26, 2017
3. Sep 26, 2017

### Staff: Mentor

One example would be recording the motion of an object such as a car going at some unknown speed in a straight line.

Plot its distance from the origin at each second and then determine its speed.

We do a similar experiment in physics lab with an Atwood machine where we record a vibrating pen indicator from 1 meter high. The pen will trace out a sine curve that gets more stretched as it moves faster. We then make measurements from crest to crest and knowing the rate of oscillation of the pen we can determine the speed at each moment and from that the acceleration at each moment (which should be g).

4. Sep 26, 2017

### jbriggs444

It's been about 40 years ago that I was tasked with a real world [mostly] linear optimization problem for pig feeding. The swine needed certain minimums of various nutrients which could be provided by various feed types. The feed types had prices per pound and various nutrient values per pound. The goal was to select a feed mix that minimized total cost per pig per day. Except for the one non-linear constraint, it was a perfect fit for linear programming (simplex method).

If only the Internet had been around back then, I'd have been able to find it online rather than re-inventing the wheel. https://www.jstor.org/stable/25556356?seq=1#page_scan_tab_contents

5. Sep 26, 2017

### Staff: Mentor

There are lots of even simpler examples than the operations research example that @fresh_42 gave. For a mass of m = 10 kg, sketch a graph of the equation F = ma for various accelerations. Here the slope of this line is the mass involved.

Another physics-related example is F = kx, where k is the spring constant for some spring, x is the displacement from the relaxed position of the spring, and F is the force to stretch the spring x units. Sketch a graph of the equation F = kx, with k = 10 (in appropriate units). If it takes a force of 20 N to stretch the spring 1 cm, how much force will it take to stretch the spring 3 cm?

6. Sep 26, 2017

### symbolipoint

I'm not sure what to tell you for linear INEQUALITIES; but use of linear equations will occur everywhere for almost everything. Fuel efficiency is one of just so many examples for slope. This is DISTANCE per VOLUME OF FUEL.

7. Sep 27, 2017

### Asymptotic

Although it may not be explicitly stated, the slope formula is employed in the scaling of analog signals.
One of many examples is shown in the Analog Devices article,

8. Sep 30, 2017

### Apple_Mango

The article above is too complex for me to understand. I'll just try reading an Algebra 1 physics book on my own once I completed Algebra one. Thanks for the response.

9. Sep 30, 2017

### symbolipoint

Keep studying physical sciences, any applied technology or engineering, and pay attention to "applied" problem exercises in your book. You will find MANY examples for introductory level algebra. Just too many and you ask for a list; often too hard to do.

Another example: Concentration Adjustment for a Mixture or Blend. Often needs equation in ONE variable; depending on situation, maybe two variables...