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Math Help - Components

  1. #1
    Member aldrincabrera's Avatar
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    Smile Components

    ,.hi everyone,.i need ur help with this problem,.

    when a set is not connected, the separate pieces that it comprises are called components,.how many components are there to the set S= {all (x,y) with x^2 -3xy + y^3 < 0 }?

    i really don't know how to solve this problem,.,.thnx
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  2. #2
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    Re: Components

    Quote Originally Posted by aldrincabrera View Post
    ,.hi everyone,.i need ur help with this problem,.

    when a set is not connected, the separate pieces that it comprises are called components,.how many components are there to the set S= {all (x,y) with x^2 -3xy + y^3 < 0 }?

    i really don't know how to solve this problem,.,.thnx
    Consider a plot of x^2 -3xy + y^3 = 0: plot x&#94;2 -3xy &#43; y&#94;3 &#61; 0 - Wolfram|Alpha
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  3. #3
    Member aldrincabrera's Avatar
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    Re: Components

    ,.,i've seen the graph,.,thnx sir,.,.but what does the graph tells me??does the blue shade indicate that there are two partitions or rather 2 components??
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  4. #4
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    Re: Components

    Quote Originally Posted by aldrincabrera View Post
    ,.,i've seen the graph,.,thnx sir,.,.but what does the graph tells me??does the blue shade indicate that there are two partitions or rather 2 components??
    You are meant to interpret this graph in the context of the inequality. The graph provides a boundary ....
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  5. #5
    Member aldrincabrera's Avatar
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    Re: Components

    yes sir,.i changed the equal sign to inequality,.,then i obtained a graph with blue shades,.is that the component???
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  6. #6
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    Re: Components

    Quote Originally Posted by aldrincabrera View Post
    yes sir,.i changed the equal sign to inequality,.,then i obtained a graph with blue shades,.is that the component???
    I don't know, I can't see your "graph with blue shades". It should not be difficult to find convenient 'test points' in each region defined by the boundary and then make a conclusion.
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