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Mar
28
comment Analytical question on year calculation.
@Medex well, it grows to 25 in 6 and tasks each year to double. So to grow half the height must have taken one year because it was half the height and then doubled in one year to reach the full height, so half the height was at 6-1=5 years
Mar
27
comment First order ODE with $f'(x) = 810(10)^x$
@recursiverecursion I found out what $f(x)$ was first and then took the derivative.
Mar
27
comment First order ODE with $f'(x) = 810(10)^x$
@recursiverecursion please see the edit
Mar
27
comment Finding Power Series Representations
Clever - partial fractions to geometric series.
Mar
27
comment Analytical question on year calculation.
@Medex I do. I also found an easier way to solve it. The hint is, it doubles in value each year and you need to find how long it took to grow to half the height at 6 years.
Mar
27
comment Degeneracy number of a ring graph
@triomphe yes, i am now confused too. the definition on wiki does not restrict graph size. need to look more into it, i am sorry.
Mar
27
comment Degeneracy number of a ring graph
@triomphe your last formulation is wrong, degeneracy is $$\min\{\max \mathrm{deg}(s) | s \in S\}.$$ This way, tree is 1-degenerate and cycle is 2-degenerate and star is 1-degenerate also. I got confused myself also, sorry.
Mar
26
comment Mixed integration problem
very nice trick
Mar
26
comment How do I do Linearization at a point that lies on a curve?
@Cozen $a=1$, so when all is done you get a linear function of $x$, hence the name linearization.
Mar
26
comment Double integral of $e^{x^2+y^2}dydx$?
Do you know about polar coordinates? Do you know about the Normal distribution? In what context are you asking this question, for which class is this the homework for?
Mar
26
comment Degeneracy number of a ring graph
@triomphe Yes, exactly.
Mar
26
comment What kind of a mean value is this?
@user3085931 That it is an average means that some actual values could (and likely will) be higher and some could (and likely will) be lower. Average must be in the middle, so it cannot be some will match exactly and others will be all higher or all lower. You should have a mix.
Mar
26
comment What kind of a mean value is this?
@user3085931 I am not familiar with your process's terms, but if I had to explain to someone in English what that quantity was, this is the term I would use.
Mar
26
comment Understanding Integral
Generally, $\int dF(x) = \int F'(x) dx$ which is sometimes written as $\int f(x) dx$ where $f(x) = F'(x)$. But I've never seen $\int dF(x) = \int F(x)dx$.
Mar
26
comment How to show a subset doesn't span a space?
This is an example of something on the span of the first set that is not on the span of the second set. Thus, the second span must be included in the first but the first is larger
Mar
26
comment Find a change in variable that will reduce the quadratic form to a sum of squares
after you are done with arithmetic you end up with $(...)^2 + (***)^2$ so change variables to have $a = ...$ and $b = ***$ and you get $a^2 + b^2$
Mar
26
comment Find a change in variable that will reduce the quadratic form to a sum of squares
Yes, rename $\left(x_1,x_2,x_3\right) \to (x,y,z)$ for convenience, then add and subtract $y^2$ and then factor out the $-$ in front of the $y,z$ terms.
Mar
25
comment Is determinant of matrix multiplied its transpose always positive?
@Pouya just like a square matrix can have complex eigenvalues, the rectangular matrix can have complex singular values, which would make the final result task but negative
Mar
25
comment Is determinant of matrix multiplied its transpose always positive?
@nam Yes, for square matrices this holds. For rectangular, you have to use similar value decomposition
Mar
25
comment Is determinant of matrix multiplied its transpose always positive?
Well, $\det(A)$ is not exactly defined for non-square $A$, and here $A$ is definitely rectangular, you cannot assume $m \neq n$