Homework Statement
In probability if they say that for instance " if one or more ____ are found" Why wouldn't it be x≥1?
Homework Equations
The Attempt at a Solution
If n is odd n^2 would be odd as well. n2=2(2R2+2R)+1 n=2R+1
That tells us that even ^2 gives you even, and odd squared gives you odd.
It helps us because it tells us something directly about n, for instance since they are telling us explicitly that n^2 is even. We know that n is even as well...
I get what you're saying, but I'm confused on how to express that. From the other post I started with n is even, then n^2 is even. So now I have to start if n^2 is even then n is even.
n2 is even, then n2=2R.
and n=√2R , where R is any integer. This is rational so I'm not sure how this...
If n^2, n is even. I can prove that simply by,
Suppose n is even, then n=2R where R is any integer.
n^2=4R^2=2(2R^2) which is also even.
Oh So would I have to do a sub step, and prove that if n is odd, then n^2 is odd?
Thank you for all the replies.
I noticed that a proof by contradiction might have been the worst way to go. So I tried two different methods direct, and contrapositive.
1. Direct: First I rewrote the problem if n2 is even then n2 is divisble by 4.
since n2 is even, then n2=2R, where are...
Homework Statement
Hello Guys, can you check my proof.
Problem statement: Let n be an integer such that n2 is even. Prove that n2 is divisible by 4.
Proof by contradiction:
Suppose n2 is not divisible by 4, thus n is odd. Such that n=2p+1, and n2=4p2+4p+1. Factoring out 2 we have...
Oh because since it is below the xy plane that would mean it would be in either quadrants 3 or 4, but would that mean it should be γ>180 not 90?. I do understand though that the max a triangle can be is 180 I just don't understand that relation.
For the projection of the 30 degree triangle I...
γ is measured from the z axis to F2. It seems that F2 is below the xy plane. For the projection what I mean was for the 30degree the way my mind analyzes it is that we get the x components of both triangles e.g 30 and 45 degree.
Which would mean that 450*cos(45) would be the x component for the...
Homework Statement
Hello everyone,
I have a few questions regarding the problem below.
1. I did the process for solving γ correct however I took the 60° angle instead of the 120° angle. The below solution states that γ>90°. Why must is be greater, than 90°, and when would it have been...
Homework Statement
Hello, I was working on the following truth table problems
1.P→(Q→R)
2.(P→Q)→R
and wanted to know why I got different truth tables it seems that we could use the associative law to rewrite 1. in the same manner as 2.
Or am I missing something?
Thanks
Higgenz...
It isn't homework. I even linked you the answer lol.
The problem statement is to compute the integral 0<x<(1/2)∏ ∫cos^2(x)dx in your head.
The example wanted you to use symmetry so if you were able to picture the graph in your head you see that both cos(x) and sin(x) both are symmetric on...
Homework Statement
Hello guys,
I'm studying for the Putnam, and I'm going over problem solving strategies involving symmetry. I got the symmetry portion correct, but their conclution to solving the integral is what confused me. I'm not sure how they got they got from...