What is Coefficient: Definition and 1000 Discussions

In mathematics, a coefficient is a multiplicative factor in some term of a polynomial, a series, or any expression; it is usually a number, but may be any expression (including variables such as a, b and c). When variables appear in the coefficients, they are often called parameters, and must be clearly distinguished from those representing other variables in an expression.
For example,




2

x

2



x
+
3


{\displaystyle 2x^{2}-x+3}
, has the real coefficients 2, -1, and 3 respectively, and




a

x

2


+
b
x
+
c


{\displaystyle ax^{2}+bx+c}
, has coefficient parameters a, b, and c respectively assuming x is the variable of the equation.
The constant coefficient is the coefficient not attached to variables in an expression. For example, the constant coefficients of the expressions above are the real coefficient 3 and the parameter represented by c.
Similarly, the coefficient attached to the highest multiplicity of the variable in a polynomial is referred to as the leading coefficient. For example in the expressions above, the leading coefficients are 2 and the parameter represented by a.
The binomial coefficients occur in the expanded form of



(
x
+
y

)

n




{\displaystyle (x+y)^{n}}
, and are tabulated in Pascal's triangle.

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  1. L

    I Finite potential well transmission coefficient

    In the last page of this image, the formula for the transmission coefficient, i'm not sure exactly what it means. The page says there is no reflection when the sine term is 0 cuz T=1), but for scattering states E>0 anyways? So won't it always pass through? Or is there a chance for a particle...
  2. bremenfallturm

    Test question: What is true for a mechanical impact?

    TL;DR Summary: I'm trying to figure out why this answer is not correct for a mechanical impact: "Conservation of energy and conservation of momentum can be used to find the relative velocities after the impact" Hi! I have a multiple choice test that asks...
  3. S

    GRIN Lens - Gradient Coefficient Expression

    z= the length of the lens, P is the pitch and g is the gradient constant. I attempted to solve for g using the radius and delta, but I think I am missing a key function. The units of g should be 1/mm. P=0.23 delta = 0.05 nmax = 1.6 nmin = 1.6 - 0.05 = 1.55 r = 1.0 mm z = (2*pi/g) * p Attempt...
  4. C

    ODE with constant coefficient ##b##

    For this problem, I can confused why they don't include the case where ##b = 0## since ##b < 0##. That is, why don't they include ## λ^2e^{λt} + e^{λt} = 0## when solving the associated homogenous equation? This gives the commentary solution ##u_h = \cos t + \sin t## which is not included in...
  5. E

    Calculating ballistics coefficient from two velocities

    Homework Statement: I am trying to figure out how to calculate the BC from two velocity readings with a known distance between the two readings Relevant Equations: BC = (AirDensity * Distance) / ( SQRT(Velocity0) - SQRT(Velocity1)) In long range rifle shooting, knowing your true ballistics...
  6. E

    Drag Coefficient -- What is the constant K?

    As I understand, the drag coefficient looks as follows: CD=CD0+CL/πAe however, the professor threw in a new constant, K, and I am having trouble understanding what this means. The formula now looks like this: CD=CD0+k1CL+k2CL^2 could someone help? Thanks!
  7. SSJBLOOD

    Find the coefficient of friction and acceleration with masses given

    I tried to use the energy route but the acceleration was not a plausible one. It was just way too big.
  8. cutielollipop

    Coefficient of Friction question for a cart going down a wooden ramp

    (mentor note: moved from Classical Physics forum hence no template) Hello, I am having trouble with this question: Imagine in real life there was a coefficient of kinetic friction of 0.4 between the plastic wheels of the cart and the wooden ramp. If there is only friction on the flat part of...
  9. F

    I Coefficient sign flip in linear regression with correlated predictors

    Hello Forum, I have read about an interesting example of multiple linear regression (https://online.stat.psu.edu/stat501/lesson/12/12.3). There are two highly correlated predictors, ##X_1## as territory population and ##X_2## as per capita income with Sales as the ##Y## variable. My...
  10. A

    A Standard error of the coefficient of variation

    What is the standard error of the coefficient of variation in an exponential distribution?
  11. Roger Dalton

    Dependence of Hall coefficient on temperature in semiconductors

    My first assumption is that the temperature dependence on the mobilities can be neglected, and so we would have: $$R_H(T)= \frac{1}{e} \frac{p_v(T)\mu_h^2-n_c(T)\mu_e^2}{(p_v(T)\mu_h+n_c(T)\mu_e)^2}$$ The expression for the electron and hole densities could be derived from...
  12. C

    How to find coefficient of friction of a body sliding down the slope?

    So basically I need to find the coefficient of friction given the listed information. What bothers me is that I am getting two different accelerations for two different approaches. When I calculate acceleration using Fg=mgsin60 I do it this way: Fg=mgsin60 -> ma=mgsin60 ->a=gsin60 -> a=8.66. But...
  13. Daniel Guh

    Mechanical Physics: Coefficient of Friction

    First of all, the pulling force is 300N cos(30) = 260 N At this point, I try to find the friction force Fn = mg = 20kg * 9.81 m/s^2 = 196.2 N Then, Ff = μ * Fn = 0.5 * 196.2 N = 98.1 N So after canceling the horizontal forces, 260N - 98.1N = 161.9N And the acceleration will be 161.9N / 20kg =...
  14. chwala

    Calculate the correlation coefficient in the given problem

    Unless there is another alternative method, i would appreciate...ms did not indicate working...thought i should share my working though... Let Waistline= ##X## and Percentage body fat =##Y## and we know that ##n=11## ##\sum X=992, \sum XY=13,772## and ## \sum Y=150## Then it follows that...
  15. M

    A Practical use of an overall heat transfer coefficient?

    Say I have a real counter flow heat exchanger using air and water. I run a test so I know every parameter; mass flow rate of both fluids, surface area, and in and out temps. This is great. Now I can calculate the heat transfer rate, my log mean temperature difference, and overall heat...
  16. F

    I Expected coefficient change from simple to multiple linear regression

    Hello forum, I have created some linear regression models based on a simple dataset with 4 variables (columns). The first models simply involve one predictor variable: $$Y=\beta_1 X_1+\beta_0$$ and $$Y=\beta_2 X_2+ \beta_0$$ The 3rd model is multiple linear regression model involving the 3...
  17. prithika

    I Effect of vent ratio on the drag coefficient of round parachutes

    For my 12th grade school project, I'm planning to research on the effect of vent ratio on the drag coefficient of round parachutes. My idea was to make small model parachutes and drop them from a height, and derive the drag coefficient after certain assumptions. But I also thought it'd be...
  18. Austin_Tx_Rockets

    Does the discharge coefficient of an injector depend on the fluid?

    The discharge coefficient is the ratio of the actual discharge to the ideal discharge and can be measured experimentally. If one were to experimentally measure the discharge coefficient using water, would this value be constant for all incompressible fluids? What does the discharge coefficient...
  19. T

    Coefficient of rolling resistance

    Hi, What is the formula or methodology for finding the Crr? There are many of those tests done on the internet, but none state the procedure of calculation. I'm trying to find the correlation between tire pressure and distance and want to use Crr as one of the key factors influencing it. Maybe...
  20. Argonaut

    Find the Coefficient of Kinetic Friction

    Young & Freedman 13th ed, Exercise 7.81 Starting with the crate, here is its free-body diagram: In accordance with Newton's First Law: $$ \Sigma F_y = 0 = n+(-w_c \cos{\alpha}) $$ Thus ## n = w_c \cos{\alpha} ##. And according to Newton's Second Law: $$ \Sigma F_x = m_c a_x = w_c...
  21. F

    A Coefficient correlation between 2 cosmological probes

    Hello, I have the demonstration below. A population represents the spectroscopic proble and B the photometric probe. I would like to know if, from the equation (13), the correlation coeffcient is closed to 0 or to 1 since I don't know if ##\mathcal{N}_{\ell}^{A}## Poisson noise of spectroscopic...
  22. Arwing

    Can't remember equation for coefficient

    We did a lab in class on how to calculate it but he collected it and its days later, can't remember how to attempt it.
  23. H

    What is the relationship between entropy and pressure in thermodynamics?

    Hi, Starting from dS in term of H and P, I'm trying to find ##(\frac{\partial H}{\partial P})_t## in term of ##P,V,T, \beta, \kappa, c_p##. Here what I did so far. ##ds = (\frac{\partial S}{\partial H})_p dH + (\frac{\partial S}{ \partial P})_H dP## ##ds = (\frac{\partial S}{\partial H})_p [...
  24. Faisal Moshiur

    The diffusion coefficient in a vacuum

    J = Φ.n, where n is a unit vector normal to the flow of flux.
  25. E

    A Why is this C-G coefficient always zero?

    From calculating a few CG-coefficient tables, it occurred to me that when we add two angular mometa ##j_1=l## and ##j_2=1## (with ##l## whole integer), the resulting ##|j=l,m=0\rangle## state always has zero C-G coefficient with ##|j_1=l,j_2=1;m_1=0,m_2=0\rangle## component, i.e., ##\langle...
  26. T

    I What is the difference between the resistance force and the friction coefficient?

    Hi I have been wondering what is the difference between resistance force and friction coefficient. While doing research online I could not find a clear answer. Maybe someone here will now:bow:
  27. N

    I What is the expected (squared) coefficient of variation of a sample?

    I've been trying to figure this out, but am not getting anywhere and was hoping someone here might know. Say I have a distribution of which I know the variance and mean. I then take samples of n random variables from this distribution. Without knowing anything more about the distribution, can...
  28. chwala

    Calculate the rank correlation coefficient of the given problem

    Find the problem and solution here; I am refreshing on this topic of Correlation. The steps are pretty much clear..my question is on the given formula ##\textbf{R}##. Is it a generally and widely accepted formula or is it some form of improvised formula approach for repeated entries/data? How...
  29. P

    Absorption coefficient and Linear Optical Susceptibility

    ##\alpha## is considered to be the absorption coefficient for a beam of light of maximum intensity ##I_0##. It's related to the complex part of the refractive index as we have shown above. Now, I have a doubt. Should I solve for ##k## from the quadratic equation in terms of the linear optical...
  30. Vladimir_Kitanov

    Impact and the Coefficient of Restitution

    Last post with picture, after this i will use Latex. She say that correct answer is 41 ft/m. Is this correct?
  31. E

    Potential and Kinetic energy equations including drag coefficient

    1. Golf ball initial potential energy uncertainty (110-5kg 0.01 m 0.01m/s2)= 110-9J4.31210-5=4.31210-14j 2. Golf ball initial potential energy calculation (4.4 x10-4kg 9.8 m/s2 0.609 m)= 4.31210-54.31210-14j 3.Golf ball final potential energy uncertainty ( 110-5kg 0.0 m0.01 m/s2)= 0.0 J 4...
  32. Erwinux

    I Calculating the thermal coefficient between the insulated interior of a telescope instrument package and the cold ambient air outside

    I've built an insulated chamber to protect a sensitive instrument at freeze temperatures in the winter. The instrument is mounted on a telescope, so the heat inside the chamber will slowly dissipate in the ambient. A digital PID thermostat is used to keep the temperature at a safeguard level...
  33. kasnay

    Question about these thermal expansion coefficient units (m/mK)

    so I have never seen this unit before. 10^-6m/mK for the thermal expansion (linear expansion). I believe this unit is micrometers divided by mili kelvins?
  34. Samama Fahim

    Limits of Integration in the Transmission Coefficient

    Initially '0' is the upper limit and ##a = \frac{Ze^2}{E}## is the lower limit. With change of variable ##x = \frac{Er}{Ze^2}##, for ##r=0##, ##x=0##, and for ##r=\frac{Ze^2}{E}##, ##x=1##, so 1 should be the lower limit. However, he takes 1 as the upper limit, and without a minus sign. Why is...
  35. E

    A Wilson Coefficient Values for b->s l l in the Standard Model: What Do We Know?

    Hi, does anyone happen to know a paper somewhere with a list of the standard model wilson coefficients for effective field theory? I see the same basis everywhere and I can find the new physics corrections, but nowhere seems to have an actual number for the standard model value? Specifically...
  36. E

    Yes! Calculating Friction Coefficient

    Fg = m * g: Fg = 30 * 9.8 = 294 N Fnet = m * a: Fnet = 30 * 1.2 = 36 N Fax = Fnet + Ff: Fax = 36 + 10 = 46 Fa = Fax / cos(angle): Fa = 46 / cos(25) = 50.75 Fay = Fa * sin(angle): Fay = 50.76 * sin(25) = 21.45 Fn = Fg - Fay: Fn = 294 - 21.45 = 272.55 Ff = mu kinetic * Fn, solving for...
  37. MathMan2022

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  38. mark_bose

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    Hi all, I'm trying to derive fuel temperature coefficient in a TRIGA reactor using a monte carlo code. When i do that, if i assume a radial temperature profile along the core, i obtain smaller value (-7pcm/K) than the one achieved with uniform temperature (-9pcm/K). More in detail: in my case...
  39. Leo Liu

    [Aerodynamics] Bernoulli's equation and Pressure Coefficient

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  40. A

    Help Identifying Source of Sliding Adhesion Coefficient Equation

    Hello all, I am a graduate student working on a thesis in tire dynamics and simulation. I have came across the following equation for sliding adhesion coefficient for the HSRI tire model (source: Schramm et. al. Vehicle Dynamics, Modeling and Simulation, pg. 182): Unfortunately, Schramm et...
  41. rudransh verma

    Coefficient of friction and normal force

    The answer should be no change but we know ##F=ma##. In this eqn when acceleration increases mass decreases for same force. So why not here? If normal is doubled ##\mu## should be halved.
  42. J

    What is the physical dimension of transduction coefficient in photonics?

    I am studying Tunable couplers with Programmable Integrated photonics by Jose Capmany. In this textbook, what is the physical meaning of signal s1 and s2? Is it an electric field intensity or the phase of electromagnetic wave? And what is the physical dimension of transduction coefficient here?
  43. barryj

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  44. Send-Help

    Find tangential velocity given radius and the coefficient of friction

    I have attempted to solve for the velocity by setting the centripetal force (mv2)/r to the normal force pointed to the center of rotation (mg). This approach seems to give the incorrect solution and I am unsure of my misunderstandings.
  45. Einstein44

    I Coefficient of rolling friction for a lab cart

    I was looking for a way to calculate the friction arising from the axle and wheel of a standard lab cart. I came across this research paper: https://www.usna.edu/Users/physics/mungan/_files/documents/Publications/PhysEd4.pdf That derived the following equation for the coefficient of rolling...
  46. J

    Equation calculations about the coefficient of kinetic friction

    I need an expert to verify equations about the coefficient of kinetic friction.
  47. L

    MHB What is the Minimum Number of Friends Needed for Unique Dinner Invitations?

    Hello all, I am trying to solve this one: John has n friends . He wants to invite in each evening (365 days a year) three of his friends for dinner. What should be the size of n, such that it will be possible not to invite the same triplet twice ? What I did was: \[\binom{n}{3}\leq 365\]...
  48. pasta-lord

    Effect of Surface Area on the Drag Coefficient of a Parachute

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  49. questionmonkey123

    Will this increase the Coefficient of performance of my refrigerator?

    If I orient my refrigerator such that the condenser coils at the back are facing a glass door (least insulation in room, cold outdoors) will CP increase? CP=Qc/(Qh-Qc) so Qh-Qc will be smaller thus CP larger. Could this damage refrigerator?
  50. S

    The relationship between angle and static coefficient

    I know you find the static friction of an incline by raising it until it begins to move and then measure the tangent of that angle, but I'm not sure how I'm supposed to show a relationship or create a procedure based off that.
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