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...
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...
Homework Statement
A rod of length L carries a charge Q uniformly distributed along its length. The rod lies along the yaxis with one end at the origin. Find the potential as a function of position along the xaxis
Homework Equations
dV=\vec{E}\cdotp d\vec{l}
V=\frac{kq}{r}...
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...
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 halflife T of the substance is T = \frac{ln2}{k}
b) Show that the solution of the initialvalue problem in part a) can...
I am asked to solve this DE with the initial condition of y(1) = 1.
(x+y)^2dx + (2xy + x^21)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^2y
My question is what do I do with the initial condition. I assume that I am just...
\frac{\partial_P}{\partial_y}(2ysinxcosxy+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:
2sinxcosx1+4ye^{(xy^2)}
My question is, why does the partial of 2y^2e^{(xy^2)} come out to 4ye^{(xy^2)}...
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: (2x1)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}(2x1) = 0...
\frac{dy}{dx}=\frac{xy+3xy3}{xy2x+4y8}
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...
Problem: (yyx^2)\frac{dy}{dx} = (y+1)^2
So, the first thing I tried was just dividing the whole equation by (yyx^2) and then factored out the y to get \frac{dy}{dx} = \frac{(y+1)^2}{y(1x^2)}. Next I expanded the numerator on the right side of the equation and then split them all into...
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...
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...
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/answerboard/image/ed663c5fcb01e8fb6c7522cf963b49f1.jpg [Broken]
b)...
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...
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...
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...
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...
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...
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...
Hello,
I was wondering if anyone could offer some advice on this one. I have a multipart 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...
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...
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 = 4x2y+6z=3 and P_2 = 6x+3y9z=4
then \vec{n}P_1 = <4,2,6>...
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...
So I am given this:
If l has parametric equations
x = 53t
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...
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 = 53t
y = 2+8t
z = 43t
So I got this far, but...
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...
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...
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(TTo)
Using this, I am to solve this problem:
A thermometer is taken from an inside room to the outside...
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...
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...