Title: Some random math problems/puzzles
mpn - April 16, 2004 05:24 AM (GMT)
If you guys are interested, I'll start posting math (loosely defined) puzzles to this thread. After each is solved, a new will be posted.
Let's start with this one:
At a recent math competition, medals were given out to the winners of event. The medal was designed with three equations etched into the front:
| CODE |
x = (-b +- sqrt(b^2-4ac))/(2a)
Integral(a, b, f(x))dx = g(b)-g(a)
(f(10)-f(2))/(10-2) = 672/8 = 84
|
I found the third interesting, and decided to try and figure out a way to make it true.
The problem:
Find a function f(x) such that f(10)-f(2) = 672
How did you do it?
Seth - April 17, 2004 02:51 AM (GMT)
Heh, what did you win @ SMSU? I got 2 golds, a silver, and a bronze.
Have you solved this one yet?
*Seth whips out TI-89 and paper
mpn - April 17, 2004 03:42 AM (GMT)
A very surprising first place in Algebra II Restricted :). Paul and I got third in the programming contest. Oh, and our team (FHHS) won first on the challenging problems. Did you guys turn them in? Most weren't too hard. My favorite was the graph of [x]^2 + [y]^2 = 1. I heard your name a lot - nice job. Of course, it wasn't exactly surprising.
Regarding the question I posed: Yes, I figured it out during the car ride home. However, I did it by trial and error. I don't know if there is a better way.
mpn - May 2, 2004 07:08 PM (GMT)
If anyone is actually interested in this idea, let me know, and I'll find some problems that require more creative thinking or perhaps some that require more mathematical ability and less trial-and-error.
Polarris Delsan - May 2, 2004 10:13 PM (GMT)
There is probably some way to do it using matrix transformations, I'm thinking.
Of course, there is an unlimited number of solutions to that one, you know :P
mpn - May 15, 2004 05:26 AM (GMT)
Yes, and I want them all!
asloenxg - May 16, 2005 11:19 PM (GMT)
easiest thing ever. why would you need a calculator for this?
Two points define a line, the easiest function is thus a linear one:
f(x) = mx + b
f(10) = 10m + b
f(2) = 2m + b
subtract:
f(10) - f(2) = 8m, m=84
f(x) = 84x
but that was already more work than needed, since given the original equation (AKA the difference quotient), the derivative should be = 84, take the indefinite integral: f(x) = 84x + C gives all linear solutions
next question.