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1. Algorithm for creating unique groups of elements

Homework Statement so for a side task I'm supposed to assign people to groups for an icebreaker in python, can anyone give me links to theories that I could read up on or give me suggestion X number of people at my company signed up for a dinner roulette as a way to meet new people. Everyone...
2. Find where one graph is bigger than the other

Homework Statement My question is part of a bigger one that I'm using in a graphical proof. I have two functions, tanh(ap) and 2a/(1+a^2). The a is the input and p is a constant. I'm trying to find the value for p which is the bridging point between the two functions having 1 intersection...
3. Basic sturm liouville boundary problems

Wow such careless errors haha, but thanks for finding where I went wrong. I got the answer and everything seems good!
4. Basic sturm liouville boundary problems

Homework Statement Compute the eigenvalues/functions of the given regular S-L problem f''(x)+λf(x)=0 0<x<π f(0)=0 f'(π)=0 2. The attempt at a solution First off, why is π not included in the given boundary if it tells you f'(x) at π? Now for my attempt: assuming λ=0...
5. Thermal expansion (and the Michelson Morley experiment)

Ah I see, I completely forgot that only one arm was being affected. I understand what you're saying, but I'm having trouble expressing it mathematically. How do I know which arm to lengthen? The same change in L will affect the parallel and perpendicular arms differently (different denominators...
6. Thermal expansion (and the Michelson Morley experiment)

Homework Statement (B) http://imgur.com/VL4aG although I showed the rest of the problem for context if needed Homework Equations ΔL=αLΔT The Attempt at a Solution I'm a little confused by the wording of the problem. When we find the shift in ΔN, are we actually finding Δ(ΔN)...
7. Simplifying boolean expressions

I tried to use X(N)OR and this is what I came up with: From =a'b'c'+ac+bc I can multiply ac and bc by (1) in the form (x+x') =a'b'c'+ac(b+b')+bc(a+a') =a'b'c'+abc+ab'c+abc+a'bc Get rid of one of the two abc (redundant) =a'b'c'+abc+ab'c+a'bc Factor =bc(a+a')+b'(ac+a'c') =bc(1)+b'(aXORc)'...
8. Simplifying boolean expressions

It doesn't say we can't and we did cover it, however it doesn't show up in any of the other problems or examples so far
9. Simplifying boolean expressions

Homework Statement Simplify the following Boolean expressions to a minimum number of literals (a+b+c')(a'b'+c) 2. The attempt at a solution Whenever I tried this I made no progress in reducing the number of literals, I just reordered the expression. (a+b+c')(a'b'+c)...
10. Identifying parallel elements in a circuit

Okay I see, thank you very much for clarifying that for me.
11. Identifying parallel elements in a circuit

So say we have a square circuit, with one resistor on the top and 3 resistors in series on the bottom (nothing on left and right) Only the outer 2 of the 3 bottom resistors would be parallel with the top? Not the middle one? edit: also, going by what you said my answer for series seems to be...
12. Identifying parallel elements in a circuit

In the following circuit, a) identify all combinations of 2 or more circuit elements that are connected in series and b) Identify pairs of circuit elements that are connected in parallel. http://imgur.com/keorO a) Seems easy enough, the 4 and 6 ohm resistors are in series, and so are the 5...
13. Uncertainty Relations & Wave Packets

PROBLEM: Laser pulses of femptosecond duration can be produced, but for such brief pulses it makes no sense to speak of the ‘color’ of the laser. To demonstrate this, compute the time duration of a laser pulse whose range of frequencies covers the entire visible spectrum (4.0*10^14 Hz to...
14. Power disspated in a circuit

ahh I see, I don't actually need to find the value of I P=2000I^2=R*(I/2)^2=R*(1/4)I^2 meaning R must be 4 times 2k, or 8kΩ. And both R1 and R2 are equal so 8k for both, which I think is what the solutions said cool, thanks!
15. Power disspated in a circuit

P=I^2*R right? but R is still R1 or R2, and I don't know the current numerically. I know it's half of I1, but what's I1? The only way I can think of finding it is I=V/Req, where V is 10 and Req is 2k+R_1/2, which for R1 I don't know either and leads me in a circle
16. Power disspated in a circuit

http://imgur.com/WO1zq I tried the loop rule method but I couldn't get it to work since I had 2 unknowns (currrent and R1/R2) I know that for resistors in series, the current through both are the same. Also, R1 should equal R2, beecase they need to dissipiate the same power. This means the...
17. Determine is the set is a real vector space (and say why if it isn't)

anyone have any idea?
18. Determine is the set is a real vector space (and say why if it isn't)

-set of all nonnegative real numbers -set of all upper triangular nxn matrices -set of all upper triangular square matrices from the book, the answers are: yes, no(need to be the same size to define addition), and yes for the set of all nonnegative real numbers, doesn't it fail closure...
19. To double the energy stored by a capacitor, you should:

a) double the voltage b) double the capacitance WIth the equation U=(1/2)CV^2 doubling the voltage quadruples U and doubling the capacitance doubles U. However if you double the capacitance in the expression (1/2)Q^2/C you half U instead. Also, doubling the voltage doubles U in the...

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21. Potential Energy between molecules

Does anyone even have an idea of how I could approach this problem? If i was simply dealing with a system of 3 charges on a line, would I find the potential energy by adding the 3 possible potential energies together? (kq1q2/r, kq1q3/r, kq2q3/r)?
22. Potential Energy between molecules

Homework Statement The two sides of the DNA double helix are connected by pairs of bases (adenine, thymine, cytosine, and guanine). Because of the geometric shape of these molecules, adenine bonds with thymine and cytosine bonds with guanine. The figure shows the thymine–adenine bond. Each...
23. Proton Velocity (potential/field/charge)

Homework Statement (background info) The source of the sun's energy is a sequence of nuclear reactions that occur in its core. The first of these reactions involves the collision of two protons, which fuse together to form a heavier nucleus and release energy. For this process, called nuclear...
24. To double the power dissipated by a resistor you can

Ahhh I see. Thank you very much for clarifying that.
25. To double the power dissipated by a resistor you can

Homework Statement 1) double the potential difference, ΔV 2) double the current, I 3) reduce the resistance, R, by 1/2 Homework Equations The Attempt at a Solution These problems are usually straightforward but I'm a little confused this time because I keep seeing all of the...
26. Laplace transform IVP 2nd order

Homework Statement y''+6'+10y=0 y(0)=2 y'(0)=1 Homework Equations The Attempt at a Solution Laplace everything and I get s^2*Y(s)-2s-1+6s*Y(s)-12+10Y(s)=0 isolate Y(s) Y(s)=(2s+13)/(s^2+6s+10) split into 2 terms, bottom can be rearranged by completing the square...
27. Laplace transform - step function

You replace the discontinuous point with a right? Which happens to be one in this problem because it has a value of 0 whe greater than 1 and a value of 1 when between 0 and 1. So the discontinuous point would be at 1? Which you replace with a?
28. Laplace transform - step function

f(t) is 0 when t>1 and 1 when it is between 0 and 1, inclusive. so for ua(t) wouldnt I just replace the 1 with a?
29. Laplace transform - step function

I thought there was a step involving replacing the discontinuous point with a
30. Laplace transform - step function

Homework Statement f(t)= 1 if 0≤t≤1 ; 0 is t>1 find the laplace transform Homework Equations The Attempt at a Solution I know u(t)= 0 for t<0 and 1 for t≥0 I know I have to shift it and get u_a(t)=u(t-a)= 1 if 0≤t≤a, 0 if a>1 am I even going the right way? then I think...