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What Should I Do In This Situation/cut Off

VERY simple cutoff frequency question?

I am an idiot. I can't calculate the cutoff frequency. Where am I going wrong?

Simple Lowpass filter, like on Fig 1 of wiki page for LPF.

G = Zc / ( R + Zc ) = 0.5^0.5
--Voltage Divider, G=sqroot of 1/2

= 1 / ( R / Zc + 1)
--Divide num&denom by Zc

Zc = 1/(j*w*C)
--impedance of a cap

1/(jwRC + 1) = 0.5^0.5

1/(0.5^0.5) = jwRC + 1

There is an error. The answer for w should be w = 1 / (R*C)
Where did the 'j' go? (imaginary part)? I am loosing my mind maybe

w = (2^0.5 - 1) / (j * T) where T=R*C

Please help!

Should I cut my nose off to spite my face situation?

I'm gonna make this as short as possible, because it's a long story.
So, I kind of 'left' my friendship group, because people were leaving, new people were moving in (if you know what I mean) and I was just fed up. They were all really bitchy and had changed so much, I just really didnt enjoy their company. This decision meant leaving my 2 (ex sort of) best friends. I still talk to them a lot, but they've moved on, which of course, I understand and respect, as I have done the same.
However, my problem is that one of these friends I still talk to (who's a guy) ALWAYS chooses somebody else over me, it's ridiculous.
I feel lonely at the moment as I'm between friendship groups, and in just tagged on as an 'extra'. I'm getting kinda fed up of it actually.
What my question is- Next time he asks me to go out (which is always when everyone else has turned it down), should I go out or stay in? I'm sick of always coming second with him.
When he does, I'm definitely going to rip into him for it
Thanks!

If I cut off my finger and don't cover it, how long would it take to bleed to death?

I am not a medical person, but there are no large veins or arteries in your fingers. You probably would be fine after a while.There are other places on the body that will bleed out alarmingly quickly.

I just cut my arm OFF WHAT DO I DO?

Won't even dignify this with a real answer.

Do paramedics cut off the patients underwear?

Absolutely if they feel there is a need to. In fact they are supposed to strip a trauma patient to do a full exam... obviously if a woman is giving birth or something of that nature they need to have the area exposed... Or if a person has or could have an injury to his/her genitalia or buttocks it also needs to be examined. We try to do this with as much privacy and discretion as the situation allows but remember you should only be seeing a Paramedic in a true emergency and truly emergent situations are often not ideal situations

Is it illegal to cut off your own arm or other limbs?

It is legal to cut off own arm or other limbs to save own life, if the situation so demands.
It is unlawful to cut off own arm or other limbs , and a capable public prosecutor can easily argue it as "attempt to take away own life" !

How do I give my friend legal consent to cut off and eat my finger?

Would it be illegal if he gave me money in order to convince me to let him cut off and eat my finger? Any other weird legal issues surrounding this kind of situation I should know about?

This is in America and we are both citizens of the US but willing to travel within reason/if necessary. Would rather stay in the US if possible though.

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