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.
I have some time series data of the absorbance of Br2 formation using UV Vis spectroscopy and I need to figure out the extinction coefficient/ absorptivity.
The overall reaction is
BrO3-+5Br- +6H+-->3Br2+3H2O
which is expcted to go to completion
I know that the equation relating absorbance to...
Homework Statement
This is for differential equations with nonconstant coefficients and I wasn't so great at series and sequences in calculus so when I came across this example problem I wasn't sure how they got to their final form. If someone could explain it to me that would be really...
Hi.
I'm trying to get the Lyapunov coeficient for a Lorenz System (namely, a laser, using the Lorenz-Haken model) but I'm not getting the plots that would be expected. This is how two trajectories with near identical initial conditions behave (only one of the variables):
And here's the...
I have a problem with Discharge Coefficient of Valve equation which is described in book 'advanced water distribution modeling and management'
let me say:
I think the expression V^2 in Discharge Equation (P. 618 of the book mentioned) is extra and the equation must be changed to:
I)...
Hello everyone,
I am predicting the altitude of a model rocket based on some testing I did where I found the impulse of a little single stage model rocket motor. I am wondering how to incorporate drag into my calculations to make it more accurate. I know D=Cd*rho*v^2*A and I can definitely find...
Homework Statement
I am trying to prove that the coefficient of static friction is equal to the tan of the angle of incline. (You can find the proof of this from )
I set the angle of incline as my independent variable and had an angle range from 10 to 37.5 degrees. After setting the slope to...
Homework Statement
Two boxes each weighing 900 N are stacked on a horizontal floor. Box A is on the bottom, box B is on the top. The coefficient of static friction between box a and the floor is 0.3. A worker applies a force of 600 N to box b parallel to the floor, and the stack moves together...
Homework Statement
In an ideal refrigeration cycle, the temperature of the condensing vapour is 40oC and the temperature during evaporation is -20oC. Determine the coefficient of performance of this cycle for the working fluids; R12 and ammonia.
Homework Equations
C.O.Pc = TL/(TH-TL)
The...
Given the Laplace's equation with several boundary conditions. finally i got the general solution u(x,t).
One of the condition is that:
u(1,y)=y(1-y)
After working on this I finally got:
∑An sin(π n y )sinh (π n) = y(1-y)
However, i was asked to find An, by not using Fourier series...
Hi all, I am very confused by this concept. As I searched online, all respondents say that friction decreases as angle increases because normal force decreases. BUT, they don't explain this phenomenon:
A block on a ramp is static at certain angle, and after the ramp is raised by a certain...
Homework Statement
Homework Equations
Rd = retardation factor = (1 + (ƥbKd / n))
log(Koc) = -0.55logS + 3.64
Kd = Koc*foc
The Attempt at a Solution
Part C is the only part I feel sure on. I simply plugged 1480 mg/L into the log(Koc) equation above to solve for Koc. Then I multiplied Koc...
What kind and value is the friction coefficient of tank tracks on the move, when force is applied forward in the direction of the tracks movement?
Is the friction coefficient in that case, closer to kinetic/sliding coefficient or to a rolling resistance coefficient?
What about the sideways...
Homework Statement
The Clebsh Gordon coefficient is < 11;00 |11> = < l_1,m_1;l_2m_2 | kq >
Homework Equations
My professor determined the CG to be 1
The Attempt at a Solution
How do we look up these numbers in the table? What is the direct product basis? 1x1? What is JM and what is m_1 and...
Homework Statement
The problem requires me to find the overall mass transfer coefficient or Kg.
Homework Equations
$$N_{1}=\frac{1}{\frac{1}{k_{p}+\frac{H}{k_{x}}}}(p_{1}-Hx_{1}), (1)$$
$$N_{1}=k_{p}(p_{1}-p_{1i}), (2)$$
$$N_{1}=k_{x}(x_{1i}-x_{1}), (3)$$The Attempt at a Solution
So, I...
Starting a car: the voltage drops from 12V to 7.2 V, it is 0 degrees out, and 150 amps are pulled from the car. What is the temperature coefficient of the resistor?
I have NO idea how to do this. Help please!
hi every one
can you tell me how to calculate the absorption coefficient of a thin film using the absorption and the transmittance spectrum plotted as a function of the wavelength (knowing that i don't know the thickness of the film )
Anyone can explain me this example?
I substitute value for
e = 1.602*10-19;
m0 = 9.1*10-31;
pi = 3.14;
and calculated value for μav in matlab.
I received 1.7104*10-19. But in exam this value is 0.68*10-25.
What is i wrong?
please help me.
Thank you.
Hi everyone!
I would like to confirm if heat-transfer coefficient α units in SI are W/m2 K. I have to use heat-transfer coefficient α in this formula:
Heat-transfer resistance: 1/k = δ/λ + 1/α
Where δ is material thickness and λ is thermal conductivity
Thank you!
For the calculation of cn u have to multiply the equation
∑ cn * ejnx
by
e-jmx
what is the reason for this? in my textbook it says nothing about it and on some sites it just said "without justification"
i guess what I am asking is why does this do what we want?
ps: how do u properly make...
1. Homework Statement
m = 4.00 kg
theta = 30
v = 1 m/s
compression of the spring by the block , x = 0.3 m
d = 5 m
Homework Equations
rule : Fk = μ k * N
i must find Fk first to find μ k using conservation energy, [/B]
The Attempt at a Solution
First find N,
N = m x g x cos theta
N = 4 *...
Homework Statement
A particle of mass M is released from rest on a rough inclined plane, which makes an
angle of 30° with the horizontal. It is observed that the particle moves a distance of 3 m
in 3 s. What is the particle’s acceleration? Draw a properly labelled free body diagram.
Calculate...
Not a formal course - just a question I decided to try to tackle with what I've gleaned from Stanford's lectures on Youtube, but still putting this here on account of this.
So, I've been watching the Stanford GR series, and I have two motivations for messing around with this type of metric;
1...
Homework Statement
A 1790N force pull a 266kg load up a 17º incline. what is the coefficient of static friction between load and incline.
Homework EquationsThe Attempt at a Solution
Tried several times on notebook but I haven't seemed to solve the problem.
I've attached the equation for the transmission coefficient of a particle going through a potential barrier and E < V. I was simply wondering in the limit V --> E, why does T --> 0 (i.e. the V-E term --> 0 and thus the denominator would approach infinity, making T --> 0)? Shouldn't it be...
Homework Statement
You are trying to slide a sofa across a horizontal floor. The mass of the sofa is 200 kg, and you need to exert a force of 350 N to make it begin to move.
a) Calculate the coefficient of static friction between the floor and sofa
b) after it starts moving, the sofa reaches a...
In Griffith's "Introduction to Quantum Mechanics, second edition" he states: For the delta-function potential, when considering the scattered states (with E > 0), we have the general solutions for the time-independent Schrodinger equation: $$\psi(x) = Ae^{ikx} + Be^{-ikx}~~~~\text{for }x<0$$ and...
Homework Statement
plot the magnitude |r| of the reflection coefficient as a function of incident angle from 0 to 90 degrees with a step size of 1 degree for the following cases: (ill only post one)
A transverse electric plane wave in incident from air to glass
Homework Equations
r = (n1cosθi...
Homework Statement
i gt stucked here ... how to continue ? what's wrong with my working ? i found 2 values for D , whcih is wrong
Homework EquationsThe Attempt at a Solution
Hello,
I am taking some microwave engineering courses and was trying to explain the concept of reflection coefficients to my friend, but he asked me a question I am unable to answer...
So we know that given a transmission line with characteristic impedance Z_0 terminated with a load impedance...
Homework Statement
why the author consider the coefficient of discharge as the z here ? what is exactly coefficient of discharge?
Homework EquationsThe Attempt at a Solution
Homework Statement
Cooling of a food from 293K (20 ⁰C), freezing it at 272K (-1⁰C), and further cooling to 253K (-20 ⁰C); using cooling water rising in temperature from 293K (20 ⁰C) to 303K (30 ⁰C) to accept heat. The specific heat of the unfrozen food is taken as 3.2 kJ/kg K, that of the...
Homework Statement
As shown in the figure below, small object A (mass: M) collides with small object B (mass: m), which is initially at rest, on top of a horizontal stand fixed to a horizontal floor. Both A and B proceed to shoot horizontally off the stand and fall to the floor. Horizontal...
Hello physics forums,
I recently carried out an experiment testing the coefficient of friction of different grit sandpaper
My data supports that when you raise grit you decrease the cof.
My problem is WHY, why does the size of the grit have any impact on the coefficient of friction. Any ideas...
Suppose a wire made from an unknown alloy and having a temperature of 20.0°C carries a current of 0.529 A. At 52.4°C the current is 0.378 A for the same potential difference. Find the temperature coefficient of resistivity of the alloy.
tempinital = 20C
tempfinal = 52.4C
currentInital = .529A...
I've been stuck over this integral for around an hour while studying the derivation of the second coefficient of the virial equation:
∫∫dx1d x2 γ(x1,x2) where γ(x1,x2) is 1 when x1 - x2 < constant.
= V∫ dx2 γ(x1,x2) where V is the integral of dx1.
Given: periodic boundary condition: x1 + V = x1...
Homework Statement
A ball is dropped from a height of 9.02 m. After hitting the ground, the ball then rebounds to a height of 1.78 m. What is the coefficient of restitution associated with the ball and ground impact?
Homework Equations
e=(V'-v')/(V-v)
The Attempt at a Solution
I thought maybe...
Homework Statement
Electrons are pushed into a grounded metal tube A by the kinetic energy of 100 eV. After having gone through the tube it passes into another tube, B, at some distance from A. Tube B is kept at a potential of -50V. Calculate how many of the electrons are reflected back into...
Homework Statement
So we are doing a lab that is basically finding the coefficeint of restituion, what we did in this lab is drop a tennis ball from an initial height (recorded that height) and timed it until it stopped bouncing. So we have the time it stopped bouncing at and the height, and...
I have a peculiar problem of calculating a trapezoidal bar (used as sacrifical anode) in offshore substructures. Can anyone advise me how to calculate the Cd value of such a section. Flow is along the length of the bar.
Homework Statement
So far i know that the uncertainty of the force of friction is +/- 0.1 and the uncertainty of the force normal is +/- 0.1 also.
Homework Equations
Force of friction=(myoo)(force normal)
Myoo= force friction / force normal
The Attempt at a Solution
My data is
Force of...
Please go to this Wikipedia article on Lift Coefficients, and behold the first formula. The last part of the equation has a "S" which is supposed to stand for "relevant plan area". Now, there was no explanation of what this "relevant plan area" is or means. I was guessing that it means the...
Its for my final project. We are doing a sliding a textbook down an *incline plane* and we are expected to find coefficient of static friction without using Newton guage, and we are also now allowed to use kinematics. I just need some infomration on how to do this, like a formula or something in...
hi,
i'm student in a university. I do not understand the definition of these concepts, and I would like to know the properties of these and it depends
questions like
They depend on the material used?
the atomic number?
thanks for answering
capisko,
Hi All,
I have a situation were I need to evaluate the heat transfer coefficient of a horizontal surface. The surface has tubes within although I first used "flow across a bank of tubes", this has been untrue due to the air flow coming from above the surface flowing vertically (and...
In Newmann-Penrose formalism, a Null rotation with ##l## fixed is
$$l^a−>l^a\\
n^a−>n^a+\bar{c}m^a+c\bar{m}^a+c\bar{c}l^a\\
m^a−>m^a+cl^a\\
\bar{m}^a−>\bar{m}^a+\bar{c}l^a$$
Using this transformation, how to prove?
$$π−>π+2\bar{c}ϵ+\bar{c}^2κ+D\bar{c}$$
Ref: 2-Spinors by P.O'Donell, p.no, 65
Hi - an example in my book shows that FS coefficiants can be arrived at by minimizing the integrated square of the deviation,
i.e. $ \Delta_p = \int_0^{2\pi}\left[ f(x) - \frac{a_0}{2}-\sum_{n=1}^{p}\left( a_nCosnx + b_nSinnx \right) \right]^2dx $
So we're looking for $ \pd{\Delta_p}{a_n}...
Homework Statement
Exercise: Hexachlorobenzene (C6Cl6) is a highly toxic waste product of pesticide manufacturing. It is resistant to biodegradation. Sediments at the bottom of a reservoir in the Upper Mississippi River catchment have been found to contain high C6Cl6 concentrations. The...