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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

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...
4. 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)...
5. 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)...
6. 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...
7. 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...
8. 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...
9. 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...
10. 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...
11. 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...
12. 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...
13. 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...
14. 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...
15. 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...
16. Laplace transform of te^t

Homework Statement f(t)=te^t, find laplace Homework Equations The Attempt at a Solution I started doing integration by parts and after doing it three times I wasn't sure if I was going in the right direction/making any progress. I'm not supposed to use a table to solve this (I...
17. ODE - annihilator method?

Homework Statement y'' + 4y' +4y = 5e^(-2x) y''+9y=2sin(3x) Homework Equations combined with 3 The Attempt at a Solution For the first one, I started off by finding the general solution. r^2+4r+4=0 r=-2, double roots y=c1*e^(-2x)+c2*x*e^(-2x) And then when solving for the...
18. DiffyEQs - Undamped motion of spring

Homework Statement A 1 kg mass is attached to a spring with constant k = 16 N/m. Find the motion x(t) in amplitude-phase form (2.37) if x(0) = 1 and x′(0) = −1. Ignore damping forces. Homework Equations combined with 3 The Attempt at a Solution So I know m=1, k=16, c=0, x0=1, and...
19. Lagrange multpliers

Use lagrange multipliers to find max/min of f(x,y)=x^2+6y subject to x^2-y^2=5 grad f =λgrad g 2x=2xλ, λ=1 6=-2yλ, λ=-3/y 1=-3/y, y=-3 x^2-(-3)^2=x^2-9=5 x^2=14 x=+/-√14 two points are √14, -3 and -√14, -3 plugging both points into f(x,y) gives me the same answer. now what?
20. Will my physics experiment work?

For homework, I'm supposed to design an experiment and work it out using estimated values. I didn't really have an idea till I got to my swim practice later on. I heard my coach saying that you should try to dive off of the blocks at a 45 degree angle in order to maximize your distance. I...
21. Volumes of revolution

A log having the shape of a right circular cylinder of radius a is lying on its side. A wedge is removed from the log by making a vertical cut and another cut at an angle of 45 degrees, both cuts intersecting at the center of the log. Find the volume of the wedge. And as soon as I finish...
22. Buncha polar graph/integral stuff

Homework Statement 1. put in polar form x2+y2-3x+4y=0 my work: x2+y2=3x-4y r2=3rcos\theta-4rsin\theta r=3cos\theta-4sin\theta 2. put in cartesian form r2=tan\theta r2=y/x r=sqrt(y/x) 3. find slope at \theta=\pi/2 then find points where tangent line is horizontal...
23. Find the area of the region inside both polar graphs

Homework Statement r1= 1+sin(theta) r2= 5sin(theta) Homework Equations see above? The Attempt at a Solution totally stumped. usually i would set the two curves equal to each other, but i have no idea how to do that. using my ti-89's solve function just gives me a weird answer...
24. Parametrics - intersection and collision

Homework Statement x1t= 2-cos(pi*t) y1t= 3+7sin(pi*t) x2t= 3t+2 y2t= -(7/15)(3t+1)2 + 157/15 Find points of intersection and collision Homework Equations above? The Attempt at a Solution Well, to find the intersection I think I need to eliminate the parameters for both...
25. Parametrics (collisions/intersections)

Homework Statement curve1: x=5t^2-3, y=9t+2 curve2: x=8t^2-12, y=7t+4 find points of collision or intersection, if any Homework Equations see above The Attempt at a Solution I set the x functions or both curves equal to each other and got t=+/- sqrt(3) I did the same with...
26. Basketball player shoots a ball, find angle, parametrics

Homework Statement A basketball player shoots a ball with a speed off 25 ft/sec from a point 15 ft horizontally away from the center of the basket. The basket is 10ft away above the the floor and the player releases the ball from a height of 8ft. At what angle should the player shoot the...
27. Parametrics/phyics question

If a rock is thrown from a point 3 ft above the ground with a horizontal velocity of 90ft/sec and a vertical velocity of 47 ft/sec, how far away will it land if nothing is obstructing its path? If there is a 7'9" fence in front of you, will the rock sail over the fence? Actually, this is a...
28. What book to get for Physics?

I wasn't really sure where to put this topic, so feel free to move this if needed. Anyways, I'm a rising Junior (HS) right now, and would like to take the Physics SAT II at the end of my Junior year. The thing is, I would have to self study because of a scheduling conflict. I took an Intro...