/sci/ - Science & Math

>>15166797
>>15166828
This is a type of problem called a recurrence relation, or a difference equation. You can google that but the wikipedia explanation seems decent:
>https://en.wikipedia.org/wiki/Linear_recurrence_with_constant_coefficients#Order_2
(starts at “Order 2” and ends before “In the case of complex eigenvalues…”). It looks like part (a) is asking you to do two things:
i) find out what kind of [math]\lambda_1,\lambda_2[/math] could result in growth to infinity; and
ii) figure out what [math]a[/math] values make the given equation [math]\lambda^2 = a\lambda + 0.5[/math] have roots [math]\lambda_1,\lambda_2[/math] that fit the criteria you found for the first part (i).

I think (b) will be easy after (a) is done

>>15080106
>compounded vs compounded continuously
This originates in basically a scam from hundreds of years ago. Look at some examples, say it’s a loan with a $1000 principle
>30% compounded annually
works as expected, after 1 year it’s $1300, after 2 years it’s $1690 etc.
>30% compounded monthly
actually means it’s 2.5% per month, so that after 1 year it’s 1000(1.025)^12=$1345 and after 2 years it’s $1808
>30% compounded daily
about $1350 and $1822

it doesn’t make sense but then it doesn’t have to, because again, it was a scam designed to rip people off who didn’t read the fine print. But it got people wondering: if you keep making the interval shorter and shorter, does it approach a limit? It turns out there is a limit which we call “compounded continuously”, and it turns out to be connected to this famous number [math]e[/math]. In fact, as far as I know, this question about the theoretical limits of a financial scam is how [math]e[/math] was first discovered

>>14728125
>German word
shouldnt it be a capital K then

>>11129152
You are not expected to understand, but to perform the operations you memorized to pass the examination, to show your conformity to the norm.

>>11064660
>sleeping on pizza
>not eating pizza
This is why we need genetically engineered catgirls.

>>10779235
>>10779450
>what did he mean by this?
[math]{\rm Spatial~intelligence} \times {\rm Musical~intelligence} = - {\rm Verbal intelligence}[/math]

>>10068490
Phimosis is the next stage in human evolution.

How come gays exist if they can't reproduce?