Recent content by Nimz

Ax+By=C, A>0 is often called the "standard" form of a line. Personally, I find y=mx+b (slope-intercept form) to be of much greater utility. Usually the slope is either given or can be found using the formula Hootenanny cited. In this particular example, both intercepts are given. b is the y...

Bijective means both injective and surjective. Or, in other parlance, one-to-one and onto, respectively. Wiki can be very helpful: http://en.wikipedia.org/wiki/Bijective

That's terrible. Conversation Starter #176 One theme that comes up in many of my lectures is "The Fourth Dimension: It's not just 'time' anymore." To illustrate, I tell the story of the herb distributor who wanted to use a vector space to keep track of orders. There would be one...

You want to show that (x-a) is a factor of f(x). Do you see how this is related to showing that x is a factor of p(x)=f(x+a)? Or perhaps showing that t is a factor of f(t+a)?

These integrals are sweet! \int dy \int_{-C}^y dt Q: What is a proof that is based on two prior results called? A: A dilemma. "Once I thought I was capable of making mistakes, but then I found out I was wrong."

In case anyone is interested, the June 2006 issue of Scientific American has a Sudoku article.

Actually, something like \sum_{k=0}^m \prod_{i=0}^n ki + n + \frac{3}{2} + j has a definite meaning, but it probably doesn't mean what is intended. As written, its meaning is the same as \sum_{k=0}^m \left( \prod_{i=0}^n ki \right) + n + \frac{3}{2} + j. Clarity is usually what counts the...

The way an expression is written can depend on context. This is no different from your example of how spelling and grammar works in English. Two grammatically correct sentences can say the same thing in very different ways. Sums usually have their limits written above and below the summation...

Looks like he means numbers that are simultaneously square numbers and triangular numbers. E.g. 36 = 6x6 = 1+2+3+4+5+6+7+8

Something else that might help is the Rational Zeros Theorem. If you have any polynomial with integer coefficients, anxn+an-1xn-1+...+a1x+a0=0, all the rational zeros will be of the form p/q, where p is a factor of a0, and q is a factor of an. So if p/q is a zero, there is a corresponding...

If you get both positive and negative values for the function from various choices of the variables, the function is neither positive (i.e. nowhere negative) nor negative (i.e. nowhere positive). There are regions where it is positive, and regions where it is negative. Since plugging in points...

One candidate method for how to express the relative gender bias would be to consider the probability a person is in a category given that they are male, and the probability given that they are female. To use the numbers in your op, that would be 21/772 and 70/3255 (2.72% and 2.15%)...

If you have f(x,y)=g(y,x), then your system of equations is f(x,y)=0 and f(y,x)=0. If there are solutions that are not of the form y=x, there are related solutions obtained by switching x and y. I see no guarantee that you will always get "nice" real solutions (that is, solutions that can be...

Looks to me like you omitted one case for when there are 4 scientists on the 1st project. There isn't any condition that says there has to be a scientist on the 2nd project, is there? By the way, you said you had trouble with two questions?

You could consider the expected value of picking N numbers. The expected value is how much you can win on average. Mathematically, it can be found as the probability of winning times how much you win minus the probability of losing times how much you lose. N=1 --> Expected value = -6 (13.8...