Homework Statement
Try to apply the First Isomorphism Theorem by starting with a homomorphism from a polynomial ring R[x] to some other ring S.
Let I = \mathbb{Z}_2[x]x^2 and J = \mathbb{Z}_2[x](x^2+1). Prove that \mathbb{Z}_2[x]/I is isomorphic to \mathbb{Z}/J by using the homomorphism...
Hmm, I'm not quite sure where you believe I added velocities. I used Lorentz transformations to find that v_x'=0, v_y=c/2, v_z=c/2. Where v_x' = \frac{v_x-u}{1-\frac{uv_x}{c^2}} = \frac{c/2-c/2}{1-\frac{(c/2)(c/2)}{c^2}} = 0 and v_y' = v_z = \frac{v_y-u}{1-\frac{uv_x}{c^2}} =...
Homework Statement
A particle of rest mass m_0 is moving the S-frame at a velocity of u=(c/2, c/2, c/2) . Calculate:
a) its energy E and its momentum p in the S-frame
b) E' and p' in the S'-frame moving at v=(c/2, 0,0) relative to S
Homework Equations
v_x = \frac{v_x-u}{\sqrt{1-(v_xu)/c^2}}...
Homework Statement
What must the emf ε in the figure be in order for the current through the 7.00 ohm resistor to be 1.75A? Each emf source has negligible internal resistance.
Homework Equations
Kirchhoff's Rule:
\sum I=0 junction rule
\sum V=0 loop rule
The Attempt at a Solution...
I have finished my first year of my undergraduate, taking an Honors BSc in Math with a minor in Physics. I am planning on going to grad school after my undergraduate, and I want to be sure I am not taking too many first year classes. How many first year courses (100 level) courses would you...
Homework Statement
I have a final coming up and I am a bit fuzzy on how to create a matrix that represents a rotation or reflection about a certain plane (in R3). Say we are given a rotation/reflection about either a plane or a line through two points T(v)=Av and we are told to find A. Do we...
You're right, for some reason I plugged in half λ. It should have been x^2+40000 = (m+1/2)^2λ^2+2(m+1/2)λx+x^2 which would reduce to x=\frac{40000-(m+1/2)^2λ^2}{2(m+1/2)λ}. Thank you so much! You were a huge help!
No worries - thank you for your help!
I first tried answering with 34.94,69.53,113.7,175.78 before I realized that was the distance less than 200m rather than the correct m≤3. Next, I tried answering 175.78,277.1,496.4,1540 and this was also wrong, but I can't find any errors in my computation.
\lambda = \frac{c}{f} = \frac{3.0*10^8}{5.80*10^6} = 51.7m
So the separation represents 3.86 wavelengths, meaning there will be a maximum of 3 path differences.
As I was thinking further, I drew another right triangle with the distance between the sources being 200m, the hypotenuse being r1...
Homework Statement
Two radio antennas radiating in phase are located at points A and B, 200m apart. The radio waves have a frequency of 5.80MHz. A radio receiver is moved out from point B along a line perpendicular to the line connecting A and B.
At what distances from B will there be...
Homework Statement
Find the volumes of the solids revolution obtained by rotating the region about the x-axis and the y-axis.
y=2x-x^2, y=0
The Attempt at a Solution
I know how to get the volume of a function that is rotating around one axis, but the "y=0" is confusing me. Because...
So if v_L=\sqrt{Y/\rho} and v_t=\sqrt{F/\mu} then
\sqrt{Y/\rho}=30\sqrt{F/\mu} which is equivalent to Y=\frac{900F\rho}{\mu}
Y=\frac{Fl_0}{Al}
so \frac{F}{A}=\frac{Yl}{l_0}=\frac{900Fl\rho}{l_0 \mu}
but l\rho = A and \mu = \frac{mass}{length} ~~so~~\mu l_0=mass
so...