Recent content by joe_cool2

Ah, I see that I accidentally used the norm of u2 instead of v2 to normalize v2. The book confused me by switching up u's and v's. Checking to see if the norm of the final vectors is one would also be a useful trick.

Ok. So I gather that my answer is not technically wrong? How can I verify that my original answer is in fact an orthonormal basis spanning the same subspace? I guess if I make computational errors, it will be unlikely that all the dot products in some generated set of vectors is zero. Right?

Homework Statement Let R2 have the Euclidean inner product and use the Gram-Schmidt process to transform the basis {u1,u2} into an orthonormal basis. u1 = (1,-3) u2 = (2,2) Homework Equations Gram-Schmidt process: \\v_1 = u_1 \\v_2= u_2 - \frac{\left ( \left \langle u_2, v_1\right \rangle...

The heat involved in 1 -> 2 is actually leaving the system. So, QH is just the heat we put in during the isothermal and isochoric legs. So, the heat associated with the isobaric process, nCPΔT, does not enter into the expression for QH. Yes, there were brackets missing. Let me clarify as to...

Homework Statement A heat engine uses the closed cycle shown in the diagram below. (Figure 1) The working substance is n moles of monatomic ideal gas. Find the efficiency of such a cycle. Use the values for pressure and volume shown in the diagram, and assume that the process between points...

Homework Statement I give the entire question for context’s sake, but I am primarily concerned with A and B: Suppose you have the network shown below. We want the Thevenin equivalent for the part of the circuit that surrounds R1. A) Find Rth by zeroing sources and reducing the...

Homework Statement We're given two solenoids with identical currents and turns per unit length. But the solenoids have different diameters. Would a metal BB experience a larger acceleration in the smaller diameter tube, assuming we use the same BB in both solenoids it accelerates along the...

Homework Statement a) The average distance an electron travels between collisions is 2.0\mum. What acceleration must an electron have to gain 2.0 x 10-18 J of kinectic energy in this distance? b) What force must act on an electron to give it the acceleration found in part a? c) What strength...

Okay, I got it now. If I ask other questions, should I do each one in a different thread? If I stuck to this thread, it would be less messy on the subforum... Thank you Pranav and rl.bhat! :)

Pranav: Yeah I forgot a delta in that expression. Whoops. But that's what I meant, delta q. rl.bhat: So what you're saying basically is that I forgot lambda? Thanks, I'll try it soon.

You're right. That is the equation for a point charge. As the problem continues, I integrate to come up with an infinite amount of point charges from y=0 to y=L. The reason I labeled that part Exi is because it is just one point charge out of N, as N approaches infinity. I encourage you to...

Homework Statement FIGURE P27.43 shows a thin rod of length L with total charge Q. Find an expression for the electric field at distance x from the rod. Give your answer in component form. Homework Equations Equation for an electric field: E= \frac{KQ}{r^2} The Attempt at a...

Oh, dear. It's 3n, isn't it? Sorry, it's been about six months since the beginning of my Calc II class last semester. Thanks for your patience. EDIT: Solved.

Okay I changed them to minus signs. I see where I messed up there. But as far as I remember, you can pull factors out of the sums as long as no terms have an "i" in them. Why can I not do it in this case? I basically did split it up like: (12/n) Ʃ 3 - (12/n) Ʃ (6i/n) - (12/n) Ʃ 1 When I said...

Alright. Well here's the updated version using the correct formula. lim as n→∞ of Ʃ from i=1 to n of: f[(12i/n)+2]*(12/n) pulling out 12/n from under the summation sign: lim as n→∞ of 12/n * Ʃ from i=1 to n of: 3 - (6i/n) - 1 pulling 36/n out from underneath the summation sign because it has...