solve the problem from the clue?

a certain solid is immersed in a vessel of water ,such that the water will rise through a series of distances, four inches ,one inch,one- fourth of an inch and so on.

what is the maximum number of inches that the water will rise?

2 Antworten

Relevanz
  • Anonym
    vor 8 Jahren
    Beste Antwort

    The Distances are decreasing in a multiple of 4.

    So the Progression factor is (1/4)

    1st step has value 4 inch, then 1 then (1/4) and so on....

    The formula for infinite series addition is

    Sum=(a)/(1-r)

    where,

    a=1st number

    r=progression factor

    so the total length or max length possible is

    S=(4)/(1-0.25)

    =4/(0.75)

    =5.333333inches

    So the water rises to a max of 5.33333 inches

  • If the question is clear to me then the vessel must be a conical vessel with vertex downwards. Further if you go on immersing the same solids 1st and then the 2nd and then the third and so on so that the height of water level rises through a series of heights 4,,1, 1/4, 1/4^2, 1/4^3 and so on then the maximum height will rise is given by

    4 + 1 + 1/4 + 1/4^2, + 1/4^3......

    = 4 + ( 1 + 1/4 + 1/4^2, + 1/4^3.......... )

    = 4 + ( 1 - 1/4)^(-1) = 4 + (3/4)^(-1)

    = 4 + 4/3 = 16/3 inches

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