The phenomenon was again noted in by the physicist Frank Benford who tested it on data from 20 different domains and was credited for it. His data set included the surface areas of rivers, the sizes of US populations, physical constantsmolecular weightsentries from a mathematical handbook, numbers contained in an issue of Reader's Digestthe street addresses of the first persons listed in American Men of Science and death rates.
Solution a Draw a graph showing the results. Ok, first of all we need to draw a graph.
Now which axis is going to represent each variable? Well, the length of the spring depends on how much weight we put on the spring. In general, the dependent variable is plotted as the range, which are y values on the graph.
So on our graph the length of the spring will be plotted as y values. So our graph will look like this: Notice how a straight line fits quite nicely through all the data points. Now on to part b: Well, we can use our graph to work this out quite quickly.
What we need to do is find the point on the line which corresponds to a length of 11 cm. We can do this by tracing a horizontal line from 11 cm on the length axis across to the right until it intersects our plotted line. Then, to find the weight, we just trace a vertical line from this point down to the weight axis: So the weight we find on the weight axis is 4 kg.
This is the answer to part b. This is the same sort of question as part bexcept this time we start at 7 kilograms on the weight axis, trace upwards and the sideways across to the length axis, like this: You have to make as good an estimate as possible.
Simple — it equals zero. The intercept on the length axis seems to be around the 5 cm mark, so the length of the spring with no weight on it is 5 cm. This is the trickiest bit of the question. We have to come up with an equation which describes the line in the graph. How are we gonna do this?
Odds are that our equation is going to look something like these. So ours will look something like: If we put these values into the general form of our equation, we can work out what B is: But we still need to work out what A is.
We solved what B was by picking a particular point on the graph and putting the values of that point into the equation. How about we pick another point and do the same again to try and work out what A is?
We can put these values into our equation, as well as the value of B which we now know, like this: Now the great thing about having an equation is we can check that our answers are consistent with each other. We can do this by using it to check our answers to parts b and c. If I want the spring to stretch to 11 cm long, how much weight should I put on?Modeling Real Life Situations with Graphs of Functions in Patterns and Functions.
For example, if you can determine the pattern in the following table then you can use the pattern operation(s) to write the equation. · graph - . Straight line graphs can be used to describe how a lot of things behave in real life.
For instance, something as simple as buying vegetables from a shop – usually the price is given in dollars per kilogram bought. The graph of . What are real life applications of graphs? Update Cancel. Answer Wiki. 7 Answers. Sneha Dubey, Of course, Facebook Graph Search is a real-life example of application of graph algorithms.
You can read more about it here: Introducing Graph Search | Facebook. k Views · View Upvoters. Benford's law, also called Newcomb-Benford's law, law of anomalous numbers, and first-digit law, is an observation about the frequency distribution of leading digits in many real-life sets of numerical plombier-nemours.com law states that in many naturally occurring collections of numbers, the leading significant digit is likely to be small.
For example, in sets that obey the law, the number 1 appears as. Introduction to Graph Theory from University of California San Diego, National Research University Higher School of Economics. We invite you to a fascinating journey into Graph Theory — an area which connects the elegance of painting and the.
Find an example online of a graph used in real-life (include the link that goes directly to the webpage with the graph). Describe at least one mathematical feature of the graph (e.g.
shape, slope, coordinates, axes, quadrants, etc.) and how the feature/graph can help us to analyze the real-life situation.