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.
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...
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...
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...
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...
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...
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!
(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...
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...
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...
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...
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 =...
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...
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...
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...
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...
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...
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...
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...
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...
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 [...
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...
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:
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...
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...
##\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...
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...
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?
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...
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...
The following IVP
diff(T(x), x) = v/200*(45 - T(x)) + 0.015*(22 - T(x)) where T(0)=39
Describes the tempetatur T in celcius at the time x of a tub filled with water. A tub which is filled with hot water at rate of v l/min.
Lets say I am told that a guy takes a 40 min bath, and during those 40...
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...
We know that the definition of the pressure coefficient is $$C_p=\frac{p-p_\infty}{q_\infty}$$, where ##p## is the pressure at a point, ##p_\infty## is the ambient pressure (free-stream), and ##q_\infty## is the free-stream dynamic pressure.
We also know that the Bernoulli's equation is...
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...
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.
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?
Is this a polynomial? y = x^2 + sqrt(5)x + 1
I was told NO, the coefficients had to be rational numbers. I this true?
It seem to me this is an OK polynomial.
I can graph it and use the quad formula to find the roots? so why or why not?
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.
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...
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:
\[\binom{n}{3}\leq 365\]...
Summary:: Does the surface area of a parachute affect its drag coefficient? If so, how?
I have been trying to figure out the effect of surface area on the drag coefficient of a parachute. I have designed a lab in which parachutes of different surface areas are dropped and the terminal velocity...
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?
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.