Skip to main content

What are some real life examples of direct variation?

A direct variation model can be written in the form y=kx where k is said to be the constant of proportionality. Y is said to vary directly with x, or y is proportional to x. If x increases so does y, and if x decreases y does so also.


(1) The formula d=rt where d is a distance, r a rate, and t the time represents a direct variation model. As written, for a constant speed (r as the rate), d the distance varies directly with t time. (e.g. if you drive at a constant speed, say 60mph, the distance increases the longer you drive by a constant 60 miles every hour driven.)


Rewritten as d=tr we see that distance can vary directly with the speed for a fixed (constant) time. Thus is we drive for exactly one hour, we will cover more distance if the speed is increased.


(2) If you are paid an hourly wage, your gross income varies directly with the number of hours you work (excluding overtime, holiday pay, etc...) If I make $10 per hour, then my gross pay is G=10t where t is the number of hours I worked.


(3) The formula f=ma where f is the force, m the mass of an object, and a is the acceleration shows that the force varies directly with the acceleration. (Throw something harder and the impact is greater.)


(4) In chemistry we have PV=nRT, the ideal gas law. P is the pressure exerted, V is the volume, n is the amount of gas, R is a constant, and T is the temperature. From the formula we see that the pressure varies directly with the amount of gas, and is also proportional to the temperature. (We say that the pressure varies jointly with the amount of gas and the temperature.) Also, the volume varies jointly with the amount of gas and the temperature.


(5) In business we have R=C*CC where R is the retail price, C is the cost, and CC is the cost complement.


(6) `F=(Gm_1m_2)/r^2 ` is Newton's gravitational Law. The force of attraction varies jointly with the masses of the objects. (G is the gravitational constant.)

Comments

Post a Comment

Popular posts from this blog

Is there a word/phrase for "unperformant"?

As a software engineer, I need to sometimes describe a piece of code as something that lacks performance or was not written with performance in mind. Example: This kind of coding style leads to unmaintainable and unperformant code. Based on my Google searches, this isn't a real word. What is the correct way to describe this? EDIT My usage of "performance" here is in regard to speed and efficiency. For example, the better the performance of code the faster the application runs. My question and example target the negative definition, which is in reference to preventing inefficient coding practices. Answer This kind of coding style leads to unmaintainable and unperformant code. In my opinion, reads more easily as: This coding style leads to unmaintainable and poorly performing code. The key to well-written documentation and reports lies in ease of understanding. Adding poorly understood words such as performant decreases that ease. In addressing the use of such a poorly ...
Post a Comment
Read more

Is 'efficate' a word in English?

I routinely hear the word "efficate" being used. For example, "The most powerful way to efficate a change in the system is to participate." I do not find entries for this word in common English dictionaries, but I do not have an unabridged dictionary. I have checked the OED (I'm not sure if it is considered unabridged), and it has no entry for "efficate". It does have an entry for "efficiate", which is used in the same way. Wordnik has an entry for "efficate" with over 1800 hits, thus providing some evidence for the frequency of use. I personally like the word and find the meaning very clear and obvious when others use it. If it's not currently an "officially documented" word, perhaps its continued use will result in it being better documented.
Post a Comment
Read more