Recent content by ack

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    What is the velocity of the COM of a falling rod at a given angle?

    Homework Statement Given a rod of length 'l' placed upright on a smooth floor.A slight disturbance causes it to fall.Now required is the velocity with which the COM falls down when the rod makes angle θ with horizontal. The Attempt at a Solution now let the middle portion of the rod be...
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    What is the Remainder When a Polynomial is Divided by a Product of Linear Terms?

    Id like you to consider this eg: let p(x)=x and when you divide this by x-a,x-b,x-c you get a,b,c as remainders and when you divide this by their combined product you get x ie p(x) itself as the remainder.So I think your remainder will be p(x) in your question ie the degree of p(x) is < 3.
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    Undergrad The number of positive integral solutions is to be found

    Supposing we were to find all integral solutions?
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    Undergrad The number of positive integral solutions is to be found

    Oh!...then the answer would be 9P7/(3!)^2. thanks a lot!
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    Undergrad The number of positive integral solutions is to be found

    Oh!...then the answer would be 9P7/(3!)^2. thanks a lot!
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    Undergrad The number of positive integral solutions is to be found

    I already tried that.x can be 2^0,2^1,2^2or2^3 that is 4 ways ,2ways for 3and 4ways for 5.But what about y? I thought of another method , using AM>GM, x+y+z>=43 and max can be 3002 (when one of them is 3000 nd the other two 1 each.) Then use multinomial theorem.Can this be done?
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    Undergrad The number of positive integral solutions is to be found

    I am preparing for an entrance and I came across this sum.The equation given is xyz=3000. we need to find how many positive integral solutions are there for x,y and z. Please help.