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  1. Pessimist Singularitarian
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    #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. Pessimist Singularitarian
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    #2 Thread Author
    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 !

  3. Pessimist Singularitarian
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    #3 Thread Author
    No one answered this weeks POTW...my solution follows:


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