Recent content by praecox

Homework Statement Find a recurrence relation for Tn, the number of ways to write an integer n as the sum of terms, each of which is 2 or 3, and the order matters. [So 2+3 and 3+2 are different sums for 5.]Homework Equations (if I had one, this would be easier) The Attempt at a Solution So I...

You can see my frustration then. I checked to make sure I copied the problem word for word. I'm so confused by it - it's making me crazy. The only thing I can think is ζ is a rotation (as it had been used before). So it makes sense to me that ζ\bar{c} = -c, where ζ rotates the conjugate...

So this is the problem as written and I'm totally lost. Any help or explanation would be greatly appreciated. "Viewing ℂ=ℝ2 , we can identify the complex numbers z = a+bi and w=c+di with the vectors (a,b) and (c,d) in R2 , respectively. Then we can form their dot product...

Ok. I feel a little dumb for asking, but I'm working on a abstract algebra proof and this has got me stuck: \left(\sum_{i=1}^{n}a_ib_i\right)\left(\sum_{i=1}^{k}a_ib_i\right) where n,k are some positive integers. I feel certain that it's not just a sum to n+k or nk, but I could be wrong...

That makes so much sense now! Thank you so much! :D

Hey, guys. I'm having a hard time with a 2nd ODE reduction of order problem. The DE is t2y'' - 4ty' + 6y = 0, with y1 = t2. So I set up my y = t2v(t); y' = t2v' + 2tv; y'' = t2v'' + 4tv' + 2v. I then substituted back in and got: t4v'' = 0 This is where I'm getting stuck. The book...

Homework Statement A banked circular highway curve is designed for traffic moving at 56 km/h. The radius of the curve is 203 m. Traffic is moving along the highway at 51 km/h on a rainy day. What is the minimum coefficient of friction between tires and road that will allow cars to negotiate...

Oh, yes. That was just a typo. when I did the calculation, I did it with 11.5 - 0 = 4.4t + 2.3t2.

Homework Statement A moderate wind accelerates a pebble over a horizontal xy plane with a constant acceleration = (4.60 m/s2) + (7.00 m/s2). At time t = 0, the velocity is (4.4 m/s). What are magnitude and angle of its velocity when it has been displaced by 11.5 m parallel to the x axis...

That's a great explanation... but I'm still a little confused. I see how you got the final equation that we're going to use, but what do you mean "LE system"? I'm not sure how to solve for two variables at the same time... :/

Homework Statement A red car and a green car, identical except for the color, move toward each other in adjacent lanes and parallel to an x axis. At time t = 0, the red car is at xr = 0 and the green car is at xg = 220 m. If the red car has a constant velocity of +20 km/h, the cars pass each...

! Thank you so much. I knew it was something silly I was messing up. :blush:

Homework Statement From t = 0 to t = 5.00 min, a man stands still, and from t = 5.00 min to t = 10.0 min, he walks briskly in a straight line at a constant speed of 2.5 m/s. What is his average acceleration aavg in the interval 2.00 min to 8.00 min? Homework Equations I know that in...

AHA! Thank you so much! I had a feeling I was messing up something like that. Thanks again, Vela! :)

Thanks for replying, Vela. I didn't realize how off track I am. ack. So it could work to find the rotations/sec. Then that "sec" would cancel the one from the total seconds in 30 days, yes? Just to make sure I'm doing it right: (I realized I was multiplying wrong earlier) [and just to clarify...