a museum has a collection of 75 sculptures. of those sculptures 15 are from greece what percent of the sculptures are from greec
2 answers:
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All the components in the state vector need to sum to 1. You're given that component corresponding to state 1 is 0.2, and that the component for state 3 is 0.
That leaves states 2 and 4, for which you're told that the component for state 2 is four times as large. If
is the component for state 
, then you have
which means
. So the state vector is 
.
That leaves states 2 and 4, for which you're told that the component for state 2 is four times as large. If
which means
Compute the necessary values/derivatives of at
:
Taylor's theorem then says we can "approximate" (in quotes because the Taylor polynomial for a polynomial is another, exact polynomial) at
by
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Another way of doing this would be to solve for the coefficients in
by expanding the right hand side and matching up terms with the same power of .
