Recent content by 6c 6f 76 65

Thank you for the reply! Sorry if I'm wasting your time, but I don't get what you mean by copy? (Is ⊕ the same as ×?) And ##A[X, Y]/(XY)## means, as far as I know, all polynomials, with coefficients from A, of variable X and Y. Mod XY means, XY = 0, so shouldn't the new ring be functions of only...

Homework Statement My textbook says that A[X, Y]/(XY) is a subring of A[X]⊕A[Y], but aren't they isomorphic? (A is any commutative ring) Homework Equations 1st Ismorphism Theorem The Attempt at a Solution I can construct the map φ: A[X, Y] → A[X]⊕A[Y] f(X)+g(Y)+h(X, Y)*X*Y → f(X)+g(Y), this...

Have you typed the the first equation correct? Because if not w_φ=0, and for the rest: remember that when you differentiate / integrate with respect to r you may have lost a function of θ.

Correct! Correct! Almost correct, what is the height of the "inner cylinder"? Well, you can make it a little simpler by saying the volume you're interested in finding is composed by: - Volume bounded by: x=1, x=2, y=0, y=\frac{1}{2} then get V_1=\pi\int_0^\frac{1}{2} (2^2-1^2)dy =...

Seems like you're heading in the right direction! As you creatively thought removing the cylinder is the key, now in order to compute the whole volume divide it into: - The volume of the "large thin cylinder", bounded by x=0, x=2, y=\frac{1}{2} (is the radius constant here?) - The volume of the...

Exactly!

Imagine seeing the rotated figure from above, it kinda looks like a volcano. Try to make a radius from the origin: one from the O to the yellow line, and one from O to the green line. How long will both of these radii be (as a function of x, then make the substitution y=\frac{1}{x})?

Think of it this way: You'll get the volume of the figure if you first find the volume under the purple line and the remove the volume between the purple line and the blue curve

Homework Statement Calculate the zeta function of x_0x_1-x_2x_3=0 in F_p Homework Equations Zeta function of the hypersurface defined by f: \exp(\sum_{s=1}^\infty \frac{N_s u^s}{s}) N_s is the number of zeros of f in P^n(F_p) The Attempt at a Solution My biggest struggle is finding N_s...

I was looking for a more analytic expression like \sum_{i=1}^n i = \frac{n(n+1)}{2}. Maybe it's possible to find yet another connection to the Bernoulli numbers? But thank you nevertheless!

Good evening dearest physicians and mathematicians, I recently came across the so-called "Svein-Graham sum", and i wondered: is it possible to find a simple formula for evaluating it? \sum_{i=0}^k x\uparrow\uparrow i = \left .1+x+x^x+x^{x^x}+ ... +x^{x^{x^{x^{.^{.^{.^x}}}}}}\right \}k

I=\frac{1}{2}m R^2, thank you so much!

Thank you so much! Here's what I got: \frac{dK}{dt}=-\frac{B^2 R^4 \omega^2}{4 R_\Omega}=-\frac{B^2 R^2}{2 m R_\Omega}K, used that K=\frac{1}{2}m \omega^2 R^2 Solution for diff. equation: K=K_0 e^{-\frac{B^2 R^2}{2 m R_\Omega}t} \frac{1}{2}=\frac{K}{K_0}=e^{-\frac{B^2 R^2}{2 m R_\Omega}t}...

\frac{dKE}{dt}=-\frac{(\frac{B R^2 \omega}{2})^2}{R_\Omega}

Sorry, I don't quite know what you mean. The KE and the electrical power produced is linked via the angular velocity with the formula: W=\frac{(\frac{B R^2 \omega}{2})^2}{R_\Omega}t=\Delta KE