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1. Quantum Wire and Tunneling

Hello, I'm having trouble imagining a specific portion of a homework problem. Heres the problem: "Consider a ligand stabilized gold nanoparticle. The gold nanoparticle itself can be considered as “box” and the ligands as the “walls”. If the de Broglie wavelength of the gold...
2. Voltmeter Voltage and Error

Homework Statement A voltmeter will be used to measure the voltage vA in the circuit below. Assume that the voltmeter has a resistance of 100[ohms] and a full-scale voltage of 20[V]. a) What will the voltmeter read? b) What is the percentage error in making this reading? Homework...
3. Least Squares Fit

What procedure would I use to find a and b? I know about the error...would I convert the sum of the errors squared into normal equations?
4. Least Squares Fit

Homework Statement For the following data, find the least squares fit of the given form x=1,2,3,4,6 y=14,10,8,6,5 h(x)=ae^x+be^(-x) Homework Equations The Attempt at a Solution So I tried to linearize the equation by taking the natural log of everything...
5. Quick Question: Matrix added to Differential

Such as a vector U(0)=(1;1)
6. Quick Question: Matrix added to Differential

so what if it included a initial solution, would that change anything?
7. Quick Question: Matrix added to Differential

I wrote the question a little wrong.... I meant U'(t)=A u(t)+V Where A is just a regular 2X2 matrix and V is a 2x1 vector. like this U'(t)=(1,2;3,4)U(t)+(1;e^t) I already know how to solve systems such as U'(t)=Au(t) by using the eigenvalues & eigenvectors of A but I haven't learned...
8. Quick Question: Matrix added to Differential

Hey guys, I have a quick question about adding a vector to a system of differential equations. Like U'(t)= Ax+V Say A is a 2x2 matrix and V is a 2x1 vector. Can you all explain how I could handle that V vector? Should somehow include it into A?
9. Multi-Step linear systems problem - Build ODE, impulse response, systems balance

Remember Integration by Parts has "tricks"? Try setting your equation to \int exp(t/10)sin(t)dt =20et/10 - et/10cos(t) - (1/10)et/10sin(t) - (1/100)\int et/10sin(t)dt
10. Multi-Step linear systems problem - Build ODE, impulse response, systems balance

Yeah sorry about that, I forgot. :eek: Multiply both sides by exp(.1t). The integration is harder now but its still the basic concept.
11. Inverse of a matrix with an X

Thanks for all your help I understand now. I really appreciate it!
12. Multi-Step linear systems problem - Build ODE, impulse response, systems balance

Try my way... e^(.1t)x'+.1e^(.1t)x=2+sin(t) The left side is just the product rule. So if you do this: d/dt(e^(.1t)*x)=2+sin(t) Then you can do a really simple integration. But you could also do it Dick's way. :)
13. Inverse of a matrix with an X

The multiplicative inverse is 1/(x-3), this does not apply when x=3... Hmm... I was thinking about this before but I felt it wasn't right. Should I multiply row 3 by the multiplicative inverse ?
14. Inverse of a matrix with an X

Here is my process: 3, 0, 6, 1, 0, 0; 1, -2, x, 0, 1, 0; 1, 2, 1, 0, 0, 1; I multiplied -1/3 to r1 and added to r2 and got 3, 0, 6, 1, 0, 0; 0, -2, x-2, -1/3, 1, 0; 1, 2, 1, 0, 0, 1; I then did the same and added to r3 and got 3, 0, 6, 1, 0, 0; 0, -2, x-2, -1/3, 1, 0; 0, 2, -1, -1/3, 0, 1; I...
15. Multi-Step linear systems problem - Build ODE, impulse response, systems balance

You're on the right track. Remember you have a dx/dt on the left so the equation would be (dx/dt)+.1x= 2+sin(t) by turning this into a different notation you get: x'+.1x=2+sin(t) So then you can now multiply by the integrating factor and get e^(.1t)x'+.1e^(.1t)x=2+sin(t) Does the left side...
16. Inverse of a matrix with an X

Ok, I reworked it and I got this: 3, 0, 6, 1, 0, 0; 0, -2, 1, 1/3, 0, -1; 0, 0, (X-3), -2/3, 1, 1; So would this matrix not have an inverse since I can never get the Identity on the left? It seems like it I'll keep getting number when I do row reduction after this...
17. Multi-Step linear systems problem - Build ODE, impulse response, systems balance

I learned this recently in my class. Try moving all the x factors to the left and see if you can do something there.
18. Inverse of a matrix with an X

Hi everyone! Homework Statement Find the inverse of the following using row reduction. If it does not exist, indicate clearly why. 3, 0, 6; 1, -2, x; 1, 2, 1; 2. The attempt at a solution I started by augmenting with a 3 by 3 Identity matrix: 3, 0, 6, 1, 0...
19. Cylindrical Capacitor

Even though the homework assignment passed, I would still like an answer to this. :)
20. Cylindrical Capacitor

Oh I'm sorry, I forgot to add something. He wants us to find a cylinder's radius that contains half the stored electric potential energy. Yea theres a picture he showed us, a long cylindrical capacitor. The picture shows a cross section of the cylinder. The smaller cylinder within the...
21. Cylindrical Capacitor

Homework Statement Hey guys, My prof asked us to find the radius of a cylinder within a cylindrical capacitor with 2 radii a and b. I know we use the Capacitance formula for a cylinder but I cant seem to get pass the q that shows up when I plug it into the 1/2 c*V^2 EDIT: He wants us to find a...
22. Least Square Solution(zeros in one row)

not in precise terms...I know the columm space of A is 3x2. I looked up rank in wikipedia...
23. Least Square Solution(zeros in one row)

Does anyone have any clue???? If it helps, I tried to set the third variable as a number and first and second as equations in terms of each other (i.e 1st in terms of 2nd).
24. Least Square Solution(zeros in one row)

Homework Statement Give a least squares solution to Ax=C and give the residual error A= -1, 1, 2; 1, -1, 0; 1, -1, 2; C= -1; -1; 2; Homework Equations Residual Error= |Ax-C| The Attempt at a Solution I have done an RREF on the Transpose of A times A...
25. The Molar Specific Heat (internal energy)

I figured it out... but now I need to find the work done and the total heat entered into the system. I know it has to do with U=Q-W and the use of the other path(ABC).
26. The Molar Specific Heat (internal energy)

\DeltaU=n*Cv*\DeltaT
27. The Molar Specific Heat (internal energy)

Homework Statement One mole of an ideal diatomic gas undergoes a transition from. a to c along the diagonal path What is the change in internal energy? Homework Equations The Attempt at a Solution I've tried to use the two other paths since the internal energy is the same both...
28. Symbolic Acceleration Problem

oh wow that explains a lot thanks!
29. Symbolic Acceleration Problem

Homework Statement When force F(force is at an angle Theda) is not too large, box m1(smaller top box) moves with box m2(bigger bottom box) without sliding. Find the magnitude of the acceleration of the two blocks.(see attachment) Homework Equations F=ma The Attempt at a Solution...
30. Limit with integral

so the integral would be zero as n approaches inf. since the limits of integration go from zero to zero, right?