Recent content by Amad27

If $K$ is the set of strings of 1s and 2s with the number of 1s $\equiv3\bmod4$ and with any amount of $2$s, find a recursive definition of $K$. For example, $1112112121$. I'm in need of some hints. The string can be empty, have no 1's or have 1's equivalent to 3 mod 4...

Thanks. Okay:$$0.01\sin(3.6) = m\lambda$$ so m=1, and thus $$\lambda = 6.279*10^{-7} m$$ Then by De Broglie, $$\lambda = h/mv$$ Thus, $$v = \frac{6.63*10^{-34}}{(9.1*10^{-31})(6.279*10^{-7})} = 1.16 m/s$$ Is this right?

Homework Statement Suppose that visible light incident on a diffraction grating with slit distance (space) of $0.01*10^{-3}$ has the first max at the angle of $3.6^{o}$ from the central peak. Suppose electrons can be diffracted with this same grating, which velocity of the electron would create...

I see. qv is negative right? So that is why you flip the direction?

Okay. I see this now. So in general, should I always put the back of my hand on the page? For any problem? And then for the electron, just flip the direction while keeping the others same?

I am actually very unfamiliar with that right hand rule. I use this one: So using this, I had the index pointing down and thumb pointing left, but that still had my middle finger pointing into the page?

The charge is negative, but I already accounted for that by flipping the force and pointing my thumb to the left?

Homework Statement **Question** Is the magnetic field directed into the page or out of the page?Homework Equations Right Hand Rule The Attempt at a Solution My index finger is pointing downwards, and since the magnetic force is towards the right and this is an electron (negative) my thumb...

>Let $R$ be the set of all possible remainders when a number of the form $2^n$, $n$ a nonnegative integer, is divided by $1000$. Let $S$ be the sum of all elements in $R$. Find the remainder when $S$ is divided by $1000$. Here is my working:$2^{\phi(x)} \equiv 1 \pmod{x}$ such that $(2, x) =...

The Annual Interplanetary Mathematics Examination (AIME) is written by a committee of five Martians, five Venusians, and five Earthlings. At meetings, committee members sit at a round table with chairs numbered from $1$ to $15$ in clockwise order. Committee rules state that a Martian must occupy...

No, because in the first one, we multiply by $\binom{n}{k}$ because the order matters, doesn't the order also matter in the second one? I think I am messing this all up. Are you using these definitions to solve probability like this? Like the definition of hypergeometric distribution...

A test consists of 10 multiple choice questions with five choices for each question. As an experiment, you GUESS on each and every answer without even reading the questions. What is the probability of getting exactly 6 questions correct on this test? The answer is: $$\binom{10}{6} (0.2)^6...

From Vieta's Formulas, I got: $a=2r+k$ $b=2rk+r^2+s^2$ $65=k(r^2+s^2)$ Where $k$ is the other real zero. Then I split it into several cases: $r^2 + s^2 = 1, 5, 13, 65$ then: For case 1: $r = \{2, -2, 1, -1 \}$ $\sum a = 2(\sum r) + k \implies a = 13$ Then for case 2: $r^2 + s^2 = 13$, it...

@RUber, is my proof correct though?

Homework Statement Assume that $f(x)$ has two derivatives in $(0,2)$ and $0<a<b<a+b<2$. Prove that if $f(a)\ge f(a+b)$ and $f″(x)\le 0$ $\forall x \in (0, 2)$, then: $$\frac{af(a)+bf(b)}{a+b} \ge f(a+b) \tag 1$$ Homework Equations Below The Attempt at a Solution**MY PROOF:** If $(1)$ is...