Recent content by magicarpet512

Yes, thank you. I've tried that... unless I'm missing something? A as the union of disjoint sets is A = (A \cap B) \cup (A \cap B^{c}). So, P(A) = P((A \cap B) + (A \cap B^{c}). When i plug this in and do some rearranging, i just get right back to where i ended up in the original post?

Homework Statement Let A \subseteq B \subseteq S where S is a sample space. Show that P(A \setminus B) = P(A) - P(B) Homework Equations A \setminus B denotes set difference; these are probability functions. The Attempt at a Solution I have, P(A \setminus B) = P(A \cap B^{C})...

sorry, i didnt mean to say that! As spamiam is hinting, how do you get \theta?

Your <u,v> must be a vector, not a scaler.

Anyways, it looks like you've got a simple homogeneous equation here: y'' = 2y' + 4y in which the 1st thing you need to do is find the eigenvalues.

Is this the variable x or 2 times y'(x)?

And here is a very interesting article to wrap up The Great Debate of twofish and shackelford! Written by the 2008 Nobel Prize for Economics winner Paul Krugman. It really puts into perspective the history of clashes between Austrian & Keynesian economics. I think twofish would side with this...

I think we can find the sum of a series only if it is a geometric series or a telescoping sum, and from a quick glance this doesn't look like either one. Otherwise we would need some math software to approximate the sum.

I should of thought about this earlier, but to some people might not think that "by substitution property of equality" makes sense. The grader might count off and say "by substitution and equality of what?" I'm sure you will come across some kind of Uniqueness & Existence theorem one of...

TylerH: In your intro to proofs class you will quite often find yourself being pretty wordy in your proofs by using phrases such as " by substitution property of equality, it follows that." This is perfectly fine, and I would encourage you to be wordy like this, it will help you see what needs...

For the second part of the question (equation of line from the intersection of the planes), take the cross product of the normal vector from the 1st and 2nd planes (this will give you a new normal vector that is perpendicular to the normal vectors of the two planes, or in other words this new...

What do you need to come up with an equation of a line? You need a point and a slope. A point P is given in the problem, and you can think of your normal vector as a slope. Now its just a matter of putting these things together in a multivariable point slope formula to get the equation of a plane.

z is defined as a function of x and y here. Why or how are you thinking that it is something different?

absolutely

Are these always necessary at the end of a proof? I hardly ever use these on homeworks or exams, unless I have more than one proof on one page. But of course i see the importance of using these in a more formal setting like writing a paper.