Thread: 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

Originally Posted by aldrincabrera

,.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

,.,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??

Originally Posted by aldrincabrera

,.,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 ....

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

Originally Posted by aldrincabrera

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.