Recent content by benji55545

Thanks for the reply. We talked about the binomial approximation when we were learning about about the relationship between spacetime and proper time, but I didn't think to apply it in this case. Thanks for the help.

Homework Statement About how many femtometers shorter than its rest length is the length of a car measured in the ground frame if the car is traveling at 30 m/s in that frame? Assume for the sake of argument that the car's rest length is 5.0 m. Remember that 1 fm = 10^-15 m. Homework...

Oooh okay. I guess I was getting caught up with incorporating the exponential n in the final equation. Δx/x + Δx/x + Δx/x ... Δx/x is all the uncertainties added together, each which is dependent only on x. I think I got it, thanks for the help.

I'm afraid I don't see why that's true... What is n representing in this case?

Well yeah. So the original question asked for a general equation for fractional uncertainty where q(x)=x^n. But that's not the answer obviously. If you just take the reduced form of the propagation of uncertainty, you get Δq/q=Δx/x. So... q(x)=(Δx/x)1. That doesn't seem right. Maybe I need to...

Right, the propagation rule for multiplication says Δq/q=sqrt[(Δx/x)2+...(Δz/z)2] But if it's only for one variable, it reduces to Δq/q=sqrt[(Δx/x)2] ---> Δq/q=Δx/x right? xn results in n multiplications... of what, though, beside x? Thanks.

Homework Statement Using the error propagation rule for functions of a single variable, derive a general expression for the fractional error, Δq/q, where q(x)=x^n and n is an integer. Explain your answer in terms of n, x, and Δx.Homework Equations The uncertainty of a function of one variable...

Thanks for the reply. I still cannot seem to get the correct answer. I solved the double integral you provided and was incorrect, then changed the limit on the integral with respect to u to 3pi like the limits given, but still no luck. Any suggestions on what I'm doing wrong? Thanks.

Homework Statement Evaluate ∫∫S √(1 + x^2 + y^2) dS where S is the helicoid: r(u, v) = ucos(v)i + usin(v)j + vk, with 0 ≤ u ≤ 4, 0 ≤ v ≤ 3π The Attempt at a Solution What I tried to do was say x=ucos(v) and y=usin(v), then I plugged those into the sqrt(1+x^2+y^2) eq, which I ended...

I'm afraid I don't follow what you mean by take the g integral and do the change of variables. Do I somehow take the g integral first? I think my biggest stumbling block is the lack of concrete numbers... and for the limits in x and y, would they be 0<y<(+-sqrt(144-x^2)) -6<x<6 so u and v...

Hey there, this is my first post, hopefully I don't screw anything up. Homework Statement Suppose that ∫ ∫D f(x, y) dA = 4 where D is the disk x2 +y2 ≤ 16. Now suppose E is the disk x2 + y2 ≤ 144 and g(x,y) = 3 f( [x/3], [y/3] ). What is the value of ∫ ∫E g(x, y) dA?Homework Equations The...