This equation is separable,
Integrate both sides and solve for 
:
Solve for 
using the initial value.
Then the particular solution is
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.
Answer:3
Step-by-step explanation:
Answer:
7 days
Step-by-step explanation:
Answer:
Step-by-step explanation:
g(7) = 7^2 - 3(7) = 49 - 21 = 28
f(28) = 4(28) + 4 = 112 + 4 = 116
