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.
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...
I am currently trying to understand the mass attenuation coefficient (MAC) with regards to photoelectric absorption. Consider this graph:
Why does this have a negative gradient? Why does the MAC decrease as the photon energy increases?
From what I understand, the MAC is the rate of energy...
Homework Statement
I'm having trouble finding the coefficient of kinetic friction for a lab using spring scales.
Mass=.411kg
Normal Force=4.0278
Average Pull Force=.46N
Frictional Force= -.46NHomework Equations
μ k = Fk / N.
The Attempt at a Solution
μ k = -.46N/4.0278
μ k = -.1142
Determine the partition coefficient of chlorpromazine in DMSO and n-pentane
I'm a physics student and doing a course in biophysics. I would really appreciate it, if you would take some time and provide some hints as to how to design a more concrete plan. Especialy, how do I find out the...
Hi All!
I have an assignment from University that involves finite element analysis of a glass lifting body using Catia. Problem is in order to set the value for loading correctly, I need the frictional coefficient for glass when in contact with rubber.
I tried looking online and couldn't get...
Hi,
I am working on a video capture project in which i am videoing the projectile of a ball that is being thrown in the air and trying to fit it to a curve for the expected trajectory of a projectile with quadratic drag.I am running into the issue that in order for my expected trajectory to fit...
I would like to solve the steady-state one dimensional heat equation for a two piece material system. The thermal conductivity in each segment is a linear function of temperature, where ##\kappa_1=a_1T+b_1## for material 1 and ##\kappa_2=a_2T+b_2## for material 2. ##a_1, a_2, b_1, and \;b_2##...
A few decades ago my algebra teacher showed how to construct the expression for binomial coefficients. If I start with Pascal's recursion, and propose C(n,k)=n!/k!(n-k)!, I can prove it to be so through induction. But that doesn't give me that happy feeling that comes with understanding.
It...
Homework Statement
Hey new to forum here... Grade 11 physics student... Love physics and math! But this one question seems easy but I can't seem to get through... Here it is : A 1100kg car accelerates at 3.40 m/s. If the wheels exert a force of 5600N on the road, calculate the force of friction...
Homework Statement
A small block sits at the midpoint of a 2.0 m plank lying on a level floor. A student slowly raises one end of the plank until the block starts to slide. At that instant, the raised end is 0.55 m above the floor. Find the coefficient of static friction between block and...
Homework Statement
A child pulls a friend on a sled. The child maintains a constant tension of 29.4 N in the rope. The combined mass of the friend and sled is 30.0 kg, and the coefficient of sliding friction between the sled and snow is 0.1. How far can the child pull her friend in 6 sec...
I am trying to design a heat exchanger for a stratified hot water tank which means that the heat transfer on that side of the exchanger will be totally dependent on free convection. I plan on using a shell and tube set-up but I have no idea on how to calculate the required mass flow rate from...
I am having my students do a lab to calculate the coefficient of static friction along a ramp. They are calculating the coefficient of static friction between felt and the table to be something like 0.40, yet when i did this lab, but along a horizontal surface, and not with a ramp, i get a...
Mod note: Moved from technical math section, so no template was used.
Hey! So the complex Fourier transform of the square wave
$$
f(x) = \begin{cases}
2 & x \in [0,2] \\
-1 & x \in [2,3] \\
\end{cases}, \space \space f(x+3) = f(x)$$
is ##C_k = \frac{3j}{2 \pi k}( e^{-j \frac{4 \pi k}{3}}...
Consider the following chemical equation:
2IO3-+wH2O2+xH+=>I2+yO2+zH2O
Which of the following is the correct combination of the reaction coefficient y and z?
A) 4&5
B) 5&4
C) 5&6
D) 6&5
How to obtain the answer? Thank you~
To simplify my question I would like to use a random example (although, the issue holds regardless of the numbers you pick). Suppose two objects collide (head-on) in one dimension. The initial parameters are as follows (units are irrelevant):
m1=1;m2=2;u1=3;u2=-4;
Also, suppose that exactly...
How do you prove that the maximum value of 2*cov(x,y) can be is equal to var(x) + var(y).
Moreover, how do you prove that the correlation coefficient, cov(x,y)/(sigma(x)*sigma(y), can only be between -1 and 1.
How can I find an equation to calculate the lift coefficient on a basketball at different launch velocities?
I looked at different papers explaining the physics of basketball throws but all i could find was an equation for the drag coefficient: -mv +1/2 ρ A Cd v^2 = mv
Homework Statement
A force P acts as shown on a 200kg block placed on an inclined plane. The static coefficient of friction between the block and plane are Us= 0.5 . Determine the force of P to ensure he block is in the verge of moving down. The ans given is P = 560.4 N
i have done in 2 ways...
Homework Statement
An electric motor is used to pull a 125 kg box across a floor using a long cable. The tension in the cable is 350N and the box accelerates at 1.2m/s2 (forward) for 5.0s. The cable breaks and the box slows down and stops. Calculating the coefficient of kinetic force?
Given...
Homework Statement
y''+10y'+25y=x+2+3e-5*x
Homework EquationsThe Attempt at a Solution
F(D) = D2+10D+25 zeroes: -5
yc= C1*e-5*x + C2*e-5*x *x
yp = ax+b + C*e-5*x
yp = ax+b + C*e-5*x*x2
I just want to know if my yc and yp is correct, after that I know how to do it.
I have a long-standing puzzle about the Kubo formula of thermopower S=L_{21}/L_{11}.
The electric conductivity (L_{11}) can be expressed in terms of real time current-current correlations.
Similarly, the heat conductivity can be expressed in terms of real time correlations
of heat currents...
Homework Statement
What is the minimum coefficient of friction needed between the tires and the ground so you make the turn safely?[/B]
Car= 1394.7kg
You=75kg
Radius of turn = 40m
Velocity = 20m/s
Homework Equations
Fnet = MAc (Ac = centripetal Acceleration) = Force of friction
Force of...
Homework Statement
A 1000N crate is being pushes across a level floor at a constant speed by a force (F) of 300N at an angle of 20 degrees below the horizontal, what is the coefficient of kinetic force?
Homework Equations
Fk= uk*N
uk= Fk/N[/B]
Fk=F2
The Attempt at a Solution
in the back of...
Homework Statement
If a rubber ball is dropped from the height of 120 cm from the floor, and rebounds to a height of 80 cm, what is the value of e, the coefficient of restitution? Show your reasoning and justify your solution.
initial distance 1= 120 cm
final distance 1= 0 cm
initial distance...
Homework Statement
A horizontal force of 150 N is used to push a 50.0 kg packing crate a distance of 5.00 m on a rough horizontal surface.
The acceleration of gravity is 9.81 m/s2 .
If the crate moves with constant velocity, calculate:
a) the work done by the force. Answer in units of J.
b)...
The Joule coefficient, μJ, is defined as μ = (∂T/∂V)U. Show that μJ CV = p – αT/κ
Relevant equations
Cv=(∂U/∂T)v
κT=-1/V*(∂V/∂p)T
α=1/V*(∂V/∂T)p
dV(T,p)=(∂V/∂T)pdt+(∂V/∂p)TdpWhat I have attempted was to make μ = (∂T/∂V)U=(∂T/∂U)V(∂U/∂V)T=(∂U/∂V)T*Cv-1.
Then α/κT=(∂V/∂T)p/(∂V/∂p)T because the...
Homework Statement
A lab I've performed was measured using forces. As the mass increases, the force does as well. The inclined plane is at an angle of 30 degrees. Now, finding the coefficient, should the kinetic and static friction be decreasing on a plane? I've measured the frictions on a flat...
Question: The coefficient of restitution for ball colliding with steel is 0.95. If ball is dropped from height h sub o above steel plate, to what height will the ball rebound?
Please help me with this one, Is there a formula for this? all I know is e equals velocity of the first object...
Homework Statement
A car moving at 50mph coasts to a stop while traveling a distance of 150ft on level ground. what is the size of the friction force needed to bring this car to rest?
Homework Equations
vf^2 = vo^2 + 2a(xf-xo)
F=ma
Fk=un[/B]
The Attempt at a Solution
I first converted...
I've read that drag coefficient depends on the shape of the object but I am confused as to what shape means. Does it mean geometric shape or is area included in that? Say I have one sphere of radius r and keep fluid velocity, density, and viscosity constant and find its drag coefficient. Would...
Homework Statement
1. A pulley 150 mm diameter is driven directly by an electric motor at 250 revs min–1. A V-belt is used to transmit power from this pulley to a second pulley 400 mm diameter against a load of 200 Nm.
The distance between the centre of the pulleys is 600 mm, the included...
Hi all, I encounter an un-explainable question during my lab, so I figured it would be a good shot asking here. Also, my English isn't perfect, so if there is anything unclear, say it out and I'm happy to clarify it.
In the lab, we placed a sled on a track and slowly lifted one end of the track...
Hi all, Great forum.
I really don't know if this is the proper place for this,
so if it is not please forgive me.
I have been researching reflective coefficients in transmission lines. I understand everything except steps 4 -> 5.
Perhaps it is a lacking in my math skills but could someone show...
Hi all,
I've been a long time reader of this forum but haven't signed up for whatever reason.
So thanks for the wealth of information and solutions to my headaches.
I'm trying to figure out a coefficient of temperature equation and I'm having a hard time with the manipulation
for some reason...
Homework Statement
Homework Equations
Newton's 2nd Law
The Attempt at a Solution
I was wondering if anyone could verify that I have all the correct vectors or if I am missing any. I just wanted to check before I started trying to derive the equations.
[/B]
Is it possible to predict the damping coefficient of a string using a mathematical simulation that included the string's diameter, length, frequency (and therefore tension), material density, and elastic modulus (if not also its Poisson's ratio) as opposed to simply looking at the amplitudes of...
Hey everyone! This is my first time posting here, so my apologies if I'm doing things wrong...which I probably am.
So for my modern physics lab report, we're investigating the Hall effect. We measured Hall voltages as we adjusted a DC current source. The first question in my manual is to...
Homework Statement
The top of a ladder of L and mass m is connected to a wall by a horizontal cable. The ladder makes an angle Θ=60 with the horizontal. A woman of mass 2m finds that as she climbs the ladder, the ladder begins to slip when she is one-third of the way up the ladder.
Find the...
Homework Statement
The polynomial of order ##(l-1)## denoted ## W_{l-1}(x) ## is defined by
## W_{l-1}(x) = \sum_{m=1}^{l} \frac{1}{m} P_{m-1}(x) P_{l-m}(x) ## where ## P_m(x) ## is the Legendre polynomial of first kind. In addition, one can also write
## W_{l-1}(x) = \sum_{n=0}^{l-1} a_n \cdot...
The fact that energy in a laser can propagate without much loss over long distances is quite shocking !
It's a renowned fact that energy is dissipated when propagation takes place through any medium...
(I'm fully aware that laser is an exception)
But I have quite a difficult time understanding...
What to do here if D=d/dx
(D2+2D+4)y= x2e2x ?
How to find particular integral by method of undetermined coefficient?
if R.H.S would have been x2+ e2x then we could have taken
yp= Ax2+ Bx+C + De2x
but here in product, what to do?
Hi,
I have some modelling code that uses data from Hitran 2012 (https://www.cfa.harvard.edu/hitran/Download/HITRAN2012.pdf). I want to use some data from Lifbase but unfortunately the absorption coefficient units do not match.
Lifbase units are given in m3 J-1 s-2 whereas Hitran units are...
Homework Statement
A 4.30 kg block is pushed along a floor by a constant applied force that is horizontal and has a magnitude of 43.0 N. The figure gives the block's speed v versus time t as the block moves along an x axis on the floor. The scale of the figure's vertical axis is set by vs =...
Homework Statement
A baseball is hit at a height of 3 ft off thte ground. It leaves the bat with an initial speed of 165ft/sec, at an angle of 10 degrees from the horizontal. The linear drag coefficient is k=0.38; gravitational acceleration is 32 ft/sec^2
Homework Equations
[/B]
Find a vector...
I'm trying to get my head around the calculation for coefficient of friction: COF = Friction/Normal force. And what happens if you vary normal force.
Am I right in saying:
The COF is a constant - every pair of materials has a specific COF which is independent of how hard they are pressed...