Recent content by iScience

In school I learned about impedance: where.. $$Z^2 = R^2 + X_{net}^2$$ but this was the only triangle I recall learning about. The picture below I definitely do not recall. from this Link The only quantity I am familiar with is the x-axis (Power). If someone could explain...

Consider the expression:$$A = \frac{ M! }{ r_1!\ r_2! }$$ where M = r_1 + r_2 , where r_1 = (M - 2r_2) $$A = \frac{ (r_1 + r_2)! }{ r_1!\ r_2! } \\ \ \\ \ = \frac{ ((M-2r_2) + r_2)! }{ (M-2r_2)!\ (r_2)! } \\ \ \\ \ = \frac{ (M-r_2)! }{ (M-2r_2)!\ r_2! } $$ Then, for a...

Is measuring pressure for a compressible fluid system angle dependent?For a compressible fluid, Bernoulli's Law gives us a relation between two points along a closed system. More specifically it gives us the relation between two cross sections belonging to two distinct points in the closed...

Thank you!

I know this is kind of a dumb question but please forgive me it's been awhile. Is it enough for a particle to merely "feel" an external force F to state that "F is acting on the particle"? ie if the particle was confined in a potential well and experiences F but does not move. or does...

Our professor did a demonstration today for our physics II class. She was demonstrating electromagnetic induction with a solenoid and a metal ring. When she slid the ring down the solenoid and passed alternating current through the solenoid, the metal ring was flung upward off the solenoid. My...

What is it about acceleration that makes it less fuel efficient?

Sorry if this is more of a HW question (if so then moderator please move my question. Thanks!) Hi, I'm trying to get an expression for a best fit curve of the combination formula (##_nC_r##). As far as I can tell, the curve is a simple parabolic curve, and its shape doesn't change. It's just...

oops, sorry, here's the other side ##\frac{log(stuff)}{8t} < 1 ## ##\frac{stuff}{10^{8t}} < 10 ##

The title more accurately should have been "How do you cancel floors and ceilings in discrete functions" For instance, ##\frac{log{\frac{3x}{-6(z)}}}{8t} < 1## If I wanted to get rid of the log, I'd just raise the expression by base 10. ##\frac{(\frac{3x}{-6(z)})}{10^{8t}} < 10^1## But what...

I know I stated that simplification was my goal. But I suppose that's not the only way to achieve my "true goal", which I'm still getting closer to.. (sorry) I postulate that there is a relationship between the numbers in the given set, that dictates its closeness to the value 1. I just want to...

##\{100\ ,\ 1\}## yields... ##numerator: log_2{ \frac{ 101! }{ 100! \cdot 1! } } = log_2{ \frac{ 101! }{ 100! } } = log_2{101} =7## ##ratio: \frac{7}{102} = 0.0686## (remember the numerator is logged by base 2)

For any set of values I've tested so far, the ratio has not exceeded the value 1. In fact i haven't found it to ever reach 1. I wanted to know what properties of a given set determined its closeness to the value 1. I hope this makes sense.

The fraction within the log is always greater than or equal to one, and only gets larger and larger with increasing ##R## and ##\bar{r}##. But I don't know how I would go about expressing the rate of change with respect to the denominator of the ratio. Hmm, I guess... what I'm looking for is...

Sorry in advance if I've posted in the wrong section. given the set ##\{r_i, r_{ii}, r_{iii}, ... , r_R\}## where ##r \ \epsilon \ \mathbb{Z}_+ \ , \ r_i \geq r_{i+1}##How would you go about finding the bounds of something like this, or determining if it even has any? ##( \...