Search results

1. Maxwell's Speed Distribution

Homework Statement Given Maxwell's probability distribution function, P(v) = 4\pi\ (\frac{M}{2\pi RT})^{3/2} \cdot v^2 \cdot e^{\frac{-Mv^2}{nRT}} Where v = velocity, M = molar mass, R = Universal Gas Constant, n = # of mols, T = temperature, solve \int P(v) dv =1 from 0 to...
2. Experimental Proof of Electrical Charge

Hi, I have a question about the transfer of electrical charge from object to another. Basically, my professor stated that if you rub a rod with certain matierials, the rod will become charged. This is due to the convention that Ben Franklin came up with called the triboelectric series. So...
3. Find the Potential as a function of position

Homework Statement A rod of length L carries a charge Q uniformly distributed along its length. The rod lies along the y-axis with one end at the origin. Find the potential as a function of position along the x-axis Homework Equations dV=\vec{E}\cdotp d\vec{l} V=\frac{kq}{r}...
4. Explaination of Curvature

Homework Statement Find the curvature of y = x³ Homework Equations k(x) = \frac{f"(x)}{[1+(f'(x))²]^{3/2} The Attempt at a Solution k(x) = \frac{6x}{(1+9x^4)^{3/2} I got the answer numerically, but I am looking for an explaination of the graph itself. I chose a relatively...
5. General initial value problem (DE's)

Homework Statement a) Consider the initial value problem \frac{dA}{dt} = kA, A(0) = A_0 as the model for the decay of a radioactive substance. Show that in general the half-life T of the substance is T = -\frac{ln2}{k} b) Show that the solution of the initial-value problem in part a) can...
6. DE with an initial condition

I am asked to solve this DE with the initial condition of y(1) = 1. (x+y)^2dx + (2xy + x^2-1)dy = 0 So, after working the problem out, I came to this as an answer: F(x,y)=\frac{1}{3}x^3 + x^2y + xy^2-y My question is what do I do with the initial condition. I assume that I am just...
7. Explanation of this Partial?

\frac{\partial_P}{\partial_y}(2ysinxcosx-y+2y^2e^{(xy^2)} I worked the first part no problem, but the second part I needed a little help from my calculator. This is what I got: 2sinxcosx-1+4ye^{(xy^2)} My question is, why does the partial of 2y^2e^{(xy^2)} come out to 4ye^{(xy^2)}...
8. Did I solve this DE correctly?

If someone has a chance out there, could you please check my math here and let me know if I am doing this correctly or not. Problem: Solve: (2x-1)dx + (3y+7)dy = 0 I would like to solve this using the "Exact" method for solving DE's, so: \frac{\partial_P}{\partial_y}(2x-1) = 0...
9. Ok, so now how do you separate this one?

\frac{dy}{dx}=\frac{xy+3x-y-3}{xy-2x+4y-8} I want to solve this DE using the separation technique. Any ideas on how to start? And just for myself, and maybe anyone else. Is there a sort of systematic approach to finding out how to start these problems? It seems like I will work a few no...
10. Idea of how to separate?

Problem: (y-yx^2)\frac{dy}{dx} = (y+1)^2 So, the first thing I tried was just dividing the whole equation by (y-yx^2) and then factored out the y to get \frac{dy}{dx} = \frac{(y+1)^2}{y(1-x^2)}. Next I expanded the numerator on the right side of the equation and then split them all into...
11. Help with a simple Diff Eqn

Here is the problem: Solve, (x+1)\frac{dy}{dx} = x + 6 Here is what I tried: I moved all the x's to one side and left the dy on the left of the equal sign to solve with the separation of variable method. I got, \int{dy} = \int{\frac{(x+6)}{(x+1)}dx} So here I just solve the...
12. Force of gravity if the Earth's radius, r = r/2

Problem: Suppose that the Earth retained its present mass but was somehow compressed to half its present radius. What would be the value of g at the surface of this new, compact planet? My work: So, this seems pretty simple, and I get the right answer, but I seem to be off by a lot of...
13. Newtons Law problem

Hello, I have a question with a simple Tension - Mass problem. Here is the question: For the systems in Equilibrium, find the unknown tensions and masses. a) http://answerboard.cramster.com/answer-board/image/ed663c5fcb01e8fb6c7522cf963b49f1.jpg [Broken] b)...
14. Particle pierces a sphere (vector)

A particle starts from point (-2,1,2) with velocity vector v = < 1,1,0 > and hits the plane x + z = 2 and bounces off and penetrates through a sphere x² + y² + z² = 25 at two points, P and Q. What is the angle between OP and OQ. This was a question on one of my exams that I did not get. I...
15. Vector Triangle Proof

Hello, I tried doing a search for this one here, but I didn't seem to come up with much... Homework Statement Prove that the three altitudes of a triangle meet at one point. Homework Equations Well, I am not really sure, but I know that Ceva's theorem might help me prove this...
16. Vector Rhombus Proof

Homework Statement Prove that the diagonals of a paraelogram are perpendicular iff the parallelogram is a rhombus. Homework Equations a (dot) b = 0 The Attempt at a Solution This is how I started: By definition, a rhombus is a quadrilateral with all sides equal in length. So this...
17. Vector Trouble

Homework Statement Given a plane S: x+y+z=8 and two points A(6,5,3) and B(10,5,-1), find the point P on plane S such that a line from point A bounces off of the plane S at point P and passes through point B. Homework Equations The Attempt at a Solution If I know that the angle...
18. Series Proofs

Homework Statement The question asked was to "Show that..." with regards to the equations stated below. Homework Equations http://album6.snapandshare.com/3936/45466/862870.jpg [Broken] sorry for such a large image... I am not too savvy with the latex yet, so i just linked an...
19. Cross and dot product problem

Ok, this one has really got me... Suppose that u \centerdot (vXw) = 2. Find (a) (uXv) \centerdot w (b) u\centerdot(wXv) (c) v\centerdot(uXw) (d) (uXv)\centerdotv Once I understand the what to do with the information given, I am sure the rest of the problems will fall into place...
20. Intersection of a sphere and plane problem

Hello, I was wondering if anyone could offer some advice on this one. I have a multi-part problem, in which I can't get the second part. It starts like this: (a) Find the equation of the sphere passes through the point (6,-2,3) and has a center of (-1,2,1). So I did this find and...
21. Just want to say Thank you

Just want to say Thank you!! Hello, I just wanted to say thank you to all the people that have been helping me over the past couple of days. I just had Math Midterm today and all of your work with me really paid off as I went in with a much greater understanding of the concepts and...
22. Last vector-plane problem for the night

I would like to show that two planes are || and then find the distance between the two planes. I think I have the distance between the two planes covered pretty good, but I am not sure about the || part. For example: P_1 = 4x-2y+6z=3 and P_2 = -6x+3y-9z=4 then \vec{n}P_1 = <4,-2,6>...
23. Find the line of intersection between 2 Planes

Hello, I am trying to find the line of intersection between these two planes: P_1 = x + 2y -9z = 7 P_2 = 2x - 3y + 17z = 0 I found the direction vector needed for the line of intersection between these two points by taking the cross product of the P_1 normal vector and the P_2 normal...
24. Another Vector question Quick one!

So I am given this: If l has parametric equations x = 5-3t y = -2+t z = 1+9t find parametic equations for the line through P(-6,4,-3) that is parallel to l. So, my question is this: for the two lines to be parallel, they have to have the same direction vector right? In this case...
25. Quick Vector intersection question

So, I am to find a parametric equation for the line through P_1 and P_2 and then determine (if possible) the points at which the line intersects each of the coordinate planes. P_1 (5,-2,4) P_2 (2,6,1) \vec{P_{1}P_{2}} <-3,8,-3> x = 5-3t y = -2+8t z = 4-3t So I got this far, but...
26. Basic Kinematics Question

Hello, I am having an issue with this simple kinematics problem. I have the question visualized, well, at least I think I do. Here is the question: Two cars are traveling along a straight road. Car A maintains a constand speed of 80 km/h; car B maintains a constant speed of 110 km/h...
27. Starting a Mixture problem

Hello, I think this is a pretty easy question here that I think I may be just overlooking. I am asked this huge drawn out DE problem about a tank being filled with water and brine and I am asked to solve all these different parts. My problem is that the first part of the quesiton asks to...
28. Newton's Law of Cooling Help

I have a question about Newton's Law of cooling. Basically I understand that the equation, http://album6.snapandshare.com/3936/45466/853596.jpg [Broken] Comes from the DE, dT/dt = K(T-To) Using this, I am to solve this problem: A thermometer is taken from an inside room to the outside...
29. Population Modeling using DE's

Hi, I was wondering if anyone out here on a Friday night could help me understand population modeling. Here is what I have as a problem (this is pretty simple because my goal here is to understand the thinking behind the madness :rolleyes: ) - The population of a certain community is...
30. Solving for an initial condition with a DE

Hi, I was wondering if anyone could clarify some things for me here. The problem tells me to solve the given DE subject to the indicated initial condition. In this case, the initial condition is y(1) = 3 Here is the equation. http://album6.snapandshare.com/3936/45466/852805.jpg...