# Thread: Problem Of The Week #301 Feb 13th, 2018

1. Hello, MHB Community!

anemone has asked for me to fill in for her while she's away on holiday.

Here is this week's POTW:

Find all quadruples $(a,b,c,d)$ of real numbers that simultaneously satisfy the following equations:$$\left\{\begin{array}{rcl}a^3+c^3 & = & 2 \\ a^2b+c^2d & = & 0 \\ b^3+d^3 & = & 1 \\ ab^2+cd^2 & = & -6 \end{array}\right.$$

Remember to read the to find out how to !

2.

Hello, MHB Community!

It has been brought to my attention that the problem posted this week has been used in the past, found here:

Problem of the week #277 Aug 28th, 2017

I apologize for that...here is the solution with which I was provided:

So, I am going to post another problem, from my old physics homework.

A uniform rod of mass $M$ and length $d$ rotates in a horizontal plane about a fixed, vertical, frictionless pin through its center. Two small beads, each of mass $m$, are mounted on the rod such that they are able to slide without friction along its length. Initially the beads are held by catches st positions $x$ (where $x<d/2$) on each side of the center, at which time the system rotates with an angular speed $\omega$.

Suddenly the catches are released and the small beads slide outward along the rod. Find:

• (a) the angular speed of the system at the instant the beads reach the ends of the rod
• (b) the angular speed of the rod after the beads fly off the ends

Remember to read the to find out how to !