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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?

    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

    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...
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    Combinatorics Problem

    Homework Statement I have: 4 Blue pens 16 Green pens 7 Red pens 11 Yellow pens If I lay out all the pens in a single row, how many different arrangements does this system have? Homework Equations $$_nC_r = \frac{n!}{r!(n-r)!}$$ The Attempt at a Solution Procedure: Basically the number of...
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    I Solving This Polynomial

    I want to keep this question conceptual and qualitative (for now). I have the following polynomial $$\frac{(ar-1)(ar-2)(ar-3)(ar-4)(ar-5)}{(r-1)(r-2)(r-3)(r-4)(r-5)} = P$$ where r is the variable I'd like to solve for and P, a are just real constants. I was wondering whether or not I could use...
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    I What's The Discrete Math Derivative Equivalent?

    $$ƒ = b^n$$ $$ b,n,I ∈ ℤ $$ Condition: Upon choosing a base value b.. $$ n | b^n ≤ I $$ (n is determined based off the value of b to yield the highest ƒ without going over I) $$1<b<L , L<<I$$ where I is some large number, and L is also sufficiently large such that we want to avoid going...
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    How Signals Are Sampled and Stored As A Fourier Transform?

    This question is a little basic but.. how are signals stored in a Fourier Transform function f(t)? In my PDE class we were always given a base function to put in terms of sin and cos. But when taking a bunch of samples, all I end up with is a table/array over some time T. How might I use this...
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    I Alternative Ways To Find The Remainder of A/B?

    I guess this would be a Number Theory question. Short of actually going through the division process, is there another way to find the decimal remainder of an arbitrary set of integers { A , B } $$\frac{A}{B} , A > B$$
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    Which is more processor-intensive?

    What's more process intensive: 5465411784154564 / 3 or 5465411784154564 / 5746845218 ie a big number / small number or a big number / big number? does it matter if I want to take the modulus instead? ------------------ EDIT: Accidentally messed up my title, if a moderator could change it...
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    Optimization Problem -- Can a number always be expressed as the ratio of two other numbers?

    Take a number r that is n-digits long where n is finite. so if r =2385813... $$r_1r_2r_3...r_n$$ $$r_1 = 2$$ $$r_2 = 3$$ $$r_3 = 8$$ etc.. I postulate (since I don't know this is true): Every such number can be expressed as a division between two other numbers, say a and b. $$r = \frac{a}{b}$$...
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    Number of bits it takes to represent a number

    Is this accurate? $$x = some\_number$$ $$bits(x)= \frac{log(x)}{log(2)}$$
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    Is it possible to construct a thermally isolated system?

    If I'm just trying to design a system to minimize heat loss, would the following suffice? The system or object would be magnetically levitated inside a vacuum chamber. The interior lining of the vacuum chamber would also be covered in a sheet of radiation reflecting material.
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    Exponential growth problem

    Homework Statement There are initially two cells seen through a microscope. every hour, a computer was tasked with taking a cell count through the microscope. Taking the sum of all the cell counts after the 7th hour, the total cell count was 280 cells. Find the exponential growth rate...
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    What does the potential barrier energy measure?

    The energy of an incident charged particle refers to its kinetic energy. What does the potential barrier energy refer to qualitatively? EDIT: Is it just in reference to the "potential barrier" in the classical sense? where if the particle has less than the energy V, then it doesn't go through...
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    Thermal energy distribution of an object?

    Hey all, I just wanted confirmation. The thermal energy distribution of molecules in a system corresponds directly to its blackbody curve right?
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    Combinatorics with repetition

    Homework Statement if there are k spots for n balls, what are the number of possible arrangements? each spot can hold n number of balls and each ball is indistinguishable from one another. Homework Equations $$\frac{n+k-1}{k!(n-1)!}$$ The Attempt at a Solution I just wanted to know if this...
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    Finding a function that goes through given points

    Homework Statement Find a function of a decaying logarithmic trend that passes through a set of 3 points (at x=1,2,3) whose sum is S, where S>0. Homework Equations The Attempt at a Solution starting point: i assumed the equation had the form: $$y= -kln(x+1)+S$$ with the condition that must...
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    Thermodynamics: why is freon a "good" coolant?

    I always thought that a working substance / coolant with a high heat capacity is better since it can take in more thermal energy. why then are some of the most common heat exchange fluid chemicals ones with low heat capacities? acetone and freon for example, are commonly used heat exchange...
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    Overpowering my laser makes it dimmer, why?

    I bought some laser diodes on amazon. They're the typical small red 5mW lasers. Just wanted to see if the diode handle more power so i put about 20 - 30mW through it. Nice bright red dot on the wall, but then it dims and dims. The diode didn't get super hot it just got a little hot. But I've...
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    Do dimensions of a piezoelectric material affect voltage?

    Consider a block of a piezoelectric material sandwiched between two parallel plate conductors, sort of like a parallel plate capacitor with a piezoelectric material as its "dielectric." If applying the same pressure to two of these configurations, does the thickness of the piezoelectric block...
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    Why does the Darlington configuration work the way it does?

    I know the Darlington configuration is supposed to sky rocket the beta value of the system, but this is only assuming the pair can handle that current right? It's a silly question but I just wanted to confirm... I have two low current capacity transistors (I_max= 0.2A). so the setup can only...
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    Am I confusing input & output impedance?

    Homework Statement design a common-emitter amplifier with an output impedance of 4.7kOhms and again of-10 using a transistor with a beta=200 powered by a 12V DC supply. Homework Equations v=ir The Attempt at a Solution ------------------------------------------------------ rest of the...
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    Potential energy term in Schrodinger's equation?

    consider a 1-D problem where a charged particle travels along +x with a bound state energy. the vertical potential energy axis is displaying information about the force that is parallel to the particle's axis of motion. is this correct? so then this would be an accurate representation...
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    What's the color temperature for LEDs indicate?

    Specifically what does the color temperature on light bulbs it indicate? because, it clearly does not indicate the wavelength of max intensity.