Recent content by iScience

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    I Discrete Optimization Problem?

    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...
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    I Measuring Pressure For Compressible Fluid Systems?

    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...
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    B What Does It Mean For A Force To Act On A Particle?

    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...
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    I Why does a metal ring, slid onto a solenoid, fly off?

    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...
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    I Why are accelerating cars less fuel efficient?

    What is it about acceleration that makes it less fuel efficient?
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    B Best fit curve associated with the combination formula

    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...
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    I How do you move floors and ceilings in discrete math?

    oops, sorry, here's the other side ##\frac{log(stuff)}{8t} < 1 ## ##\frac{stuff}{10^{8t}} < 10 ##
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    I How do you move floors and ceilings in discrete math?

    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...
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    A Finding the bounds of a ratio

    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...
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    A Finding the bounds of a ratio

    ##\{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)
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    A Finding the bounds of a ratio

    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.
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    A Finding the bounds of a ratio

    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...
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    A Finding the bounds of a ratio

    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? ##( \...
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    Simplifying a Product

    Homework Statement This is a child thread I'm creating from a previous topic: In that thread, I was helped to come up with the expression for the number of arrangements of R distinct types of objects given the...