Recent content by iwonde

Homework Statement Let R and S be rings. Show that \pi:RxS->R given by \pi(r,s)=r is a surjective homomorphism whose kernel is isomorphic to S. Homework Equations The Attempt at a Solution To show that \pi is a homomorphism map, I need to show that it's closed under addition and...

Homework Statement Let J be the set of all polynomials with zero constant term in Z[x]. (Z=integers) a.) Show that J is the principal ideal (x) in Z[x]. b.) Show that Z[x]/J consists of an infinite number of distinct cosets, one for each n\inZ. Homework Equations The Attempt at...

Homework Statement Show that for any natural number K, there is an n large enough so that (2^n) > K. Homework Equations The Attempt at a Solution K is a natural number -> the smallest possible K would be 0 (lower bound?) and the smallest 2^n is 1 when n = 0, and the upper bound...

Homework Statement Prove that for any two integers a and b, a+b=b+a. You may use the face that this holds for natural numbers. Homework Equations The Attempt at a Solution a=(x,y), b=(u,v) x,y,u,v are natural numbers a+b = (x,y)+(u,v) = (u,v)+ (x,y) = b+a I'm not sure if my...

Homework Statement Let S be a nonempty set and F a field. Prove that for any s_0 \in S, {f \in K(S,F): f(s_0) = 0}, is a subspace of K(S,F). K here is supposed to be a scripted F. Homework Equations The Attempt at a Solution I don't know how to approach this problem. I know the three...

Homework Statement Let V = {(a1,a2,...an): ai \in C for i = 1,2,...n}; Is V a vector space over the field of real numbers with the operations of coordinatewise addition and multiplication? Homework Equations I know that V is a vector space over C. The Attempt at a Solution I...

Homework Statement A 5.00-m, 0.732-kg wire is used to support two uniform 235-N posts of equal length (see figure). Assume that the wire is essentially horizontal and that the speed of sound is 344 m/s. A strong wind is blowing, causing the wire to vibrate in its 7th overtone. What are the...

I'm still a little confused about the energy approach in part (d).

for d) I'm thinking that part (a) can be found by using the energy approach because K_max = (1/2)m(v_max)^2, from v_max, you can find a_max; part (b) cannot be found by using the energy method because energy doesn't deal with what happens in the beginning and end; part (c) cannot be found using...

Homework Statement While on a visit to Minnesota, you sign up to take an excursion around one of the larger lakes. When you go to the dock where the 1500-kg boat is tied, you find that the boat is bobbing up and down in the waves, executing simple harmonic motion with amplitude 20cm. The boat...

Homework Statement A rocket is accelerating upward at 4.00 m/s^2 from the launchpad on the earth. Inside a small 1.50-kg ball hangs from the ceiling by a light 1.10-m wire. If the ball is displaced 8.50 degrees from the vertical and released, find the amplitude and period of the resulting...

Homework Statement A 1.50-kg, horizontal, uniform tray is attached to a vertical ideal spring of force constant 185 N/m and a 275-g metal ball is in the tray. The spring is below the tray, so it can oscillate up-and-down. The tray is then pushed down 15.0 cm below its equilibrium point (call...

[SOLVED] Simple Harmonic Motion Homework Statement A cheerleader waves her pom-pom in simple harmonic motion with an amplitude of 18.0 cm and a frequency of 0.850 Hz. Find (a) the maximum magnitude of the acceleration and of the velocity; (b) the acceleration and speed when the pom-pom's...

Homework Statement A box of negligible mass rests at the left end of a 2.00-m, 25.0-kg plank (see image). The width of the box is 75.0 cm, and sand is to be distributed uniformly throughout it. The center of gravity of the nonuniform plank is 50.0 cm from the right end. What mass of sand...

A wheel is rotating about an axis that is in the z-direction. The angular velocity w_z is -6.00 rad/s at t=0, increases linearly with time, and is +8.00 rad/s at t =7.00s. We have taken counterclockwise rotation to be positive. a.) Is the angular acceleration during this time interval...