Recent content by mistermath

If Joe knows the answer, then the answer must be one of: (1,1), (2,2), (3,3),.. because otherwise he could get the x and y part incorrect. 1^2+1^2 = 2 2^2+2^2 = 8 3^2+3^2 = 18 4^2+4^2 = 32 etc.. so we have as the only possibilities for V to be: 2, 8, 18, 32, 50, 72, 98, 128, 162, 200...

The problem with what you've said (or maybe you did not finish) is of the final 4 choices: (5,5), (7,1), (7,6), (8,1) it could also have been: (5,5), (1,7), (7,6), and (1,8) the only one that works perfectly is (5,5). Since Joe must not only know what the two numbers are, but he must know...

I like that. It makes it even easier because any number squared is greater than or equal to zero. And -2x is always less than zero for x > 0. Both should be pretty easy to prove.

For question 2 you use trial and error to find your N (the point at which the function becomes monotonic). You cannot prove that a general function is eventually monotonic.. because not every function is. (Take sin(x) for example, it fluctuates forever!)

Did you do your algebra wrong? First one is: x^2+1 Second one is: x^2 + 2x + 1 Third term is: 2x^2 + 2 Subtract x^2 from every one you get: 1 less than 2x+1 less than or equal to x^2+2 Subtract 1 from every one you get: 0 less than 2x less than or equal to x^2 + 1 Now I would...

You're substituting x = a sin (t) so plug your limits into x then solve for t. Ex: 0 = a sin(t) -> 0 = sin(t) -> arcsin(0) = t -> t = 0. for upper boundary plug in x = a you get: a = a sin(t) -> 1 = sin(t) -> arcsin(1) = t -> pi/2

What does it mean for a function to be monotonic? It's either constant (everywhere or at some intervals), and at the intervals that it is not constant it is either: 1. increasing or 2. decreasing but this is an exclusive or, meaning if at some interval it is increasing, it will never be...

49+1 = 50 25+25 = 50 I bet this is the only time you get the same # that's up to you to figure out. However, this shows you one scenario that you're looking for. If you get V = 50, Bob doesn't know which one of the answers worked, the other guy will know V = 50 so he will look at U, if U...

You read my mind, thank you for the correction.

The problem with looking at the complement is that it makes it even harder. The complement of none is at least 1. In this case, you'd need 1-P(One couple)+P(Two Couples)+P(Three Couples) + P(4 Couples). But ouch, P(3 Couples).. what's that mean? Is it possible to have 3 couples and the 4th...

Homework Statement Four couples go to a party. They decide to split randomly into groups of 2. What is the probability that no group has a couple that came together. Homework Equations I actually have an MS in math; feel free to use mathematics at any level. The answer is supposed to be...

If it turns out out that a,b are supposed to be members of R, then it makes sense that (5, infinity) is not an open interval (because open sets are the ones of the form (a,b) where both a AND b are in R. (infinity is not in R).

What you're looking for is called a function that is one to one. It is also called injection/injective. A typical example is: f(x,y) = a^x * b^y where a, b are primes that don't equal each other. Ex: let f(x,y) = 2^x * 3 ^ y It should be easy to see that f(3,4) = 2^3 * 3^4 is a...

I don't think regular, undergraduate Calculus is enough to learn topology. You really need either: 1. A proofs class or 2. A logic class and knowledge of sets

What are a and b? Most likely, the book wants a,b to be elements of R.