Step-by-step explanation:
If X is a finite Hausdorff space then every two points of X can be separated by open neighborhoods. Say the points of X are
. So there are disjoint open neighborhoods
and
, of
and
respectively (that's the definition of Hausdorff space). There are also open disjoint neighborhoods
and
of
and
respectively, and disjoint open neighborhoods
and
of
and
, and so on, all the way to disjoint open neighborhoods
, and
of
and
respectively. So
has every element of
in it, except for
. Since
is union of open sets, it is open, and so
, which is the singleton
, is closed. Therefore every singleton is closed.
Now, remember finite union of closed sets is closed, so
is closed, and so its complemented, which is
is open. Therefore every singleton is also open.
That means any two points of
belong to different connected components (since we can express X as the union of the open sets
, so that
is in a different connected component than
, and same could be done with any
), and so each point is in its own connected component. And so the space is totally disconnected.
If it takes an hour to fill 1 tank in 1 hour 1 tank will be full
So this is the volume of a cylinder:
V=hπr^2 to solve for h, divide both sides of the equation by πr^2
h=V/(πr^2)
For 2.5 hours of service, the costs charged by the two companies will be same.
Step-by-step explanation:
Given equation is;
75+50x=25+70x
Arranging alike terms together;

Dividing both sides by 20

For 2.5 hours of service, the costs charged by the two companies will be same.
Keywords: linear equation, division
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