Recent content by Mathechyst

I hate to be the bearer of bad news but B is the correct answer. Before I explain why you should reread the section on quantifiers and see if you can come up with an explanation. By the way, the ordering of quantifiers is very important. Doug

It is this fundamental mathematics that I consider to be part of a transition course. Such a course should also include all the nitty gritty about functions, relations, and a few other things as well as how to write a proof. Unfortunately, all too many schools still don't insure students know...

I find it easier to include the units conversion along with the rest of the solution. It's just a matter of multiplying by 1. For example, to convert km/hr to km/s you multiply the km/hr by the number of hours in a second, namely 1/3600. \frac{25 km}{hr}\cdot\frac{hr}{3600 s}=\frac{25...

Since we're giving out the answer, we should show how it is solved: m=\frac{2K}{v^2}=\frac{2\cdot1\cdot10^6 kg\cdot{m^2}}{s^2}\cdot\frac{hr^2}{25^2 km^2}\cdot\frac{3600^2 s^2}{hr^2}\cdot\frac{km^2}{1000^2 m^2}=\frac{2\cdot3600^2}{25^2}kg=41472kg Hmm. A 45.6 ton car. Still, it looks...

It doesn't look like you accounted for the fact that the velocity is given in km/hr.

Do you know what mass is in terms of velocity and energy? Doug

It doesn't but (a-3b)+c is even if a-3b and c are both even. Doug

Why worry about a-3b=2k? Why not just remember that the sum of two even numbers is an even number? Doug

I calculate .0184s by solving the equation {\Delta}y_1+{\Delta}y_2=18 where {\Delta}y_1=\frac{1}{2}at^2=1250t^2 is the distance traveled while the puck is in contact with the hockey stick and {\Delta}y_2=vt=2500t(0.4-t)=1000t-2500t^2 is the distance traveled while the puck is not in...

Aha. A contradiction. :smile:

I would say there's only one: (\emptyset,\emptyset,\ldots). Doug

The proof would be trivial if P(\emptyset)=0 but that too is a fact that must be proved. Doug

I hate it when a fact is so obvious that it isn't obvious how to prove it. Like showing that a subset of a finite set is finite. So ... here goes: A probability measure P on a \sigma-field \mathcal{F} of subsets of a set \Omega is a function from \mathcal{F} to the unit interval [0,1] such...

Where is this UTexas thing? Doug

Can you supply a sample problem? Doug