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.
A car traveling at 97 km/h can stop in 48 m on a level road
a.) Determine the acceleration of the car
b.) Determine the coefficient of friction between the tires and the road
Homework Equations : Vf^2=Vo^2 +2aΔx
μ=Ff/mg[/B]
3. I have part A, I got -7.53 m/s^2, but I can't seem to...
Homework Statement
I have a homework assignment that requires me to use the coefficient of static and kinetic friction for rubber on wood. I cannot locate this value anywhere so far.
Homework Equations
None.
The Attempt at a Solution
I have searched and searched and I cannot find the...
Homework Statement
By means of a Maxwell relation derived from the Gibbs free energy and making use of the third law of thermodynamics, prove that the thermal expansion coefficient β must be zero at T = 0. I tried but I got something funny.
Homework Equations
$$G=U-TS+PV$$
$$dG=\mu...
Does coefficient of friction change in regard to clamp force applied to parts?
If you imagine a bench vice, clamping a plate with a weight attached.
Can the clamp force required be calculated to hold a specific weight?
I'm asking because I have an excavator mounted hammer EMV outside. It...
I would really like a logical explanation for some of the factors that affect convective heat transfer coefficient. I have only found mathematical one.
For example:
1) Properties of the fluid:
1)Velocity: My professor said that the lower the velocity the more time the fluid gets to interact...
In an experiment involving electron scattering from a finite rectangular well of depth 4 eV, it is found that electrons of energy 5 eV are completely transmitted. What must be the width of the well? At what next higher energy can one expect to again observe T = 1?
My Attempt:
I used the...
Hey Guys,
I'm on a rocket team at my university and we are attempting to figure out the force of opening acting on some of our parachutes. Typically this is done using the following equations, in particular, the one in the top right corner.
This is where our trouble begins. In the Recovery...
A 10.0 kg box rest on a horizontal board. One end of the board is slowly raised to 12.8° with the floor, the box slides at a constant velocity. (Use this information to find the kinetic coefficient). Find the magnitude and direction of the acceleration of the box when the board is raised to an...
Homework Statement
13.49 The flatbed railway car travels at the constant speed of 80 km/h around a curve
of radius 55m and the bank angle 15deg. Determine the smallest static coefficient of friction between the crate and the car that would prevent the crate of mass M from sliding.
Homework...
1. Homework Statement
https://i.imgur.com/tG9unNs.png
2. Homework Equations
in picture below
3. The Attempt at a Solution
https://i.imgur.com/egZC3Ay.jpg
I calculated the angle of attack is "7", yet the answer is "1", which implies the coefficient of lift is about 0.2 from the answer. I...
[note from mentor: this was originally posted in a non-homework forum, so it lacks the homework template.]
Hi guys,
I need your help with the last part of following problem please.
A soccer player with 70kg mass slides for 0.75 seconds on the grass to stop a soccer ball.
1) Acceleration...
Homework Statement
A ball of mass m hits the floor with a speed v making
an angle of incidence theta with the normal. The coefficient
of restitution is e. Find the speed of the reflected ball and
the angle of reflection of the ball.
The Attempt at a Solution
I know that momentum is conserved...
Homework Statement
Using the results from problem 2.18 for the setup shown in the Figure below show that if the system is to remain at rest, then the coefficient of friction:a) between the stick and the ground must satisfy
$$
μ ≥ \frac {sin(Θ)cos(Θ)} {(1+cos(Θ))(2-cos(Θ))}
$$
Homework...
I am not sure how to approach a problem involving the friction coefficient when only given initial velocity, final velocity, and distance traveled. I could combine the friction and kinematic equations, but I am only familiar with doing that for one velocity...
Here is the specific problem I had...
I'm trying to understand the concept of Butler-Volmer equation and its kinetic derivation. What I don't know and didn't find it anywhere is related to the charge transfer coefficient.
Let's have a reaction coordinate during electrode reaction with a transfer of electrons:
Can anybody explain...
Homework Statement
Ans: c)
Homework EquationsThe Attempt at a Solution
I can solve this problem if only I understand the setup . I am sure the diagram is missing something .
Can someone help me understand the problem statement in context of the setup ?
Hi,
I can't find my inductance calculations book. Say that you were considering magnetic flux linkage more from a geometric perspective:
-Does the mutual coupling coefficient for a series of coils all on the same steel core add up to a maximum total of ~1?
Because I tried simulating a three...
Hello i need to recreate these chebychev coefficents given the initial value of X_0=1.853 as shown in the photo bellow.
i have tried to follow the iterrative algorithm shown in the photo bellow.
please help me understand where did i go wrong?
thanks
I have few (more or less) general questions:
1. I know that: "The coefficients of friction are nearly independent of the area of contact
between the surfaces".
I understand this, but I know from everyday life, when car tire tread is worn off, braking distance increases and maximum acceleration...
Homework Statement
[/B]
A hockey puck travels across the ice at 6.5m/s. the puck travels a total of 7.6m. What is the coefficient of friction between the puck and the ice.
Homework Equations
[/B]
fnet=ma
Ffr= coefficient of friction x force normal
The Attempt at a Solution
[/B]
I found my...
I am currently studying collisions in high school and my teacher told us that, in order to calculate the direction of each object after a 2-body collision, we could change the values in the relative velocity terms of the equation of the coefficient of restitution to the components in x and y. Is...
Hello, I am doing Dittus Boelter correlation for Nusselt number accroding to my measured data. Coefficient (or constant) M that is related to Re has (in my case) value of 1.12. Is it physically possible to get value greater than 1? In my previous research, I've only met with a value of less than...
May I use function f(x) = 1/(1+x) to investigate chaos?
I am trying to understand chaos using this function, but things are not going as I expected...
Could you please advice me how I can calculate Lyapunov coefficient for this function?
I'm interested in finding out what the coefficient of friction would be for a few different materials such as:Copper on aluminum
Copper on graphite
graphite on aluminum
I'm not sure if it matters if the order is reversed such as Aluminum on copper vs copper on aluminum..
also I've seen that...
Hi all,
i ask in advance sorry for my bad english, i hope you will understand my question.
I'm studying the motion of a plume fluid in a fluid ambient, with ρ(plume) > ρ(ambient).
Afterwards there si a transport of fluid ambient as an effect of the turbolence caused by the viscosity between...
We know that the solution to the Legendre equation:
$$ (1-x^2)\frac{d^2 y}{dx^2} - 2x \frac{dy}{dx} + n(n+1) = 0 $$
is the Legendre polynomial $$ y(x) = a_n P_n (x)$$
However, this is a second order differential equation. I am wondering why there is only one leading coefficient. We need two...
A couple of questions today. First. I am running a panel data regression test. First I check the correlations between the independent variables and the dependent variable. these are the results.
The D/(D+Em) is the dependent variable, and the independent are the 4 variables most adjacent...
Homework Statement
The pV-diagram in Fig. P20.51 (See attached file) shows the cycle for a refrigerator operating on 0.850 mol of H2. Assume that the gas can be treated as ideal. Process ab is isothermal. Find the coefficient of performance of this refrigerator.
Homework Equations
K = QC/|QH -...
Let's say that the correlation coefficient between X and Y were swapped so that the correlation coefficient between Y and X. If we were to compared the correlation coefficient between X and Y and Y and X. Based on my understanding of correlation coefficient, it doesn't matter if f X and Y were...
Homework Statement
If the slope of the regression line is negative and the correlation coefficient is -0.5, coefficient of determination is:
Homework Equations
coefficient of determination: r2 = 1 - SSE/SST
correlation coefficient: r = Sxy / (√Sxx * √Syy )
The Attempt at a Solution
r =...
Homework Statement
WE have a thermally insulated metallic bar (from enviroment/surroundings) . It has a temperature of 0 ºC. At t=0 two thermal sources are applied at either end, the first being -10 ºC and the second being 10 ºC. Find the equation for the temperature along the bar T(x,t), in...
Is it true for all material that if young's modulus is high then melting point will be high and coeff of thermal expansion will be lower? Any example that doesn't follow the above statement.
Many Thanks
Homework Statement
A 1.0x10^3 kg elevator carries a maximum load of 800kg
Velocity = 3m/s
Distance = .01km
Net work = 13640J
Homework Equations
Force of friction = (m)(mu)(gravity)
The Attempt at a Solution
Gravity = friction
9.8 = (mu)(17640)
.001 = mu
Homework Statement [/B]
I am looking for help with part (d) of this question
2. Homework Equations
The Attempt at a Solution
I have attempted going through the integral taking L = 4 and t0 = -2. I was able to solve for a0 but I keep having the integrate by parts on this one. I've tried it...
Homework Statement
I have a Force Normal vs Force Friction Graph and I wan to find the coefficient of friction from the graph.
Homework Equations
The Attempt at a Solution
I have tried the formula ff= uFN but my teacher is looking for me to do it using the graph
Homework Statement
I need to find the coefficient of a refrigerator that uses a monatomic gas and only has two steps.
I know the:
initial pressure of the refrigerant
initial temperature
initial volume
and final pressure
Every formula I know requires 4 steps or a knowledge of the outside and...
In my experiments, on a flat plane, when I incrementally increase the normal force acting on a rubber block, I am measuring a decrease in the static coefficient of friction. I am also measuring the friction force, which increases as normal force increases BUT this is not a proportional increase...
Let's say you two objects with weight of 2 kilograms but one is narrower and one wider. They are said to be similar coefficient of friction against a surface.. but what if the surface is rough? Won't the wider object has more friction?
Or still the same?
If still the same.. what if the...
Homework Statement
A child is playing with their Hot Wheel cars. They have set up a track which is initially horizontal but then ascends to a second horizontal section which is 50 cm higher than the initial track. The track is friction-less until the car reaches the upper section of the track...
Hello guys. i know i shouldn't be doing this, but I am asking you if you can help me with a problem for my younger sister, because my major is something else (biology, genetics) and she need this and doesn't know how to solve it..
1. Homework Statement
At an upper end of the slope inclined at...
This issue was the subject of this old post, now closed.
The question is: can a coefficient of friction (static) be larger than one?
I see confusing replies. Someone talks about glue, but I'm not convinced about that. It's a bit like wondering about the coefficient of friction of a wooden plank...
Homework Statement
Let ## f(x) = \frac{a_0}{2} + \sum_{n=1}^{\infty} (a_n \cos nx + b_n \sin nx) ##
What can be said about the coefficients ##a_n## and ##b_n## in the following cases?
a) f(x) = f(-x)
b) f(x) = - f(-x)
c) f(x) = f(π/2+x)
d) f(x) = f(π/2-x)
e) f(x) = f(2x)
f) f(x) = f(-x) =...
Homework Statement
I am investigating a scenario where a pendulum with a bob attached is released from an angle and pushes a box to a certain distance. My goal is to find the coefficient of friction between the box and the surface it moved on.
I have measurements for:
- mass of the bob (125...
From what I have understood about Pearson correlation coefficient I have created a visual illustration, I would like to know if this understanding looks correct.
Say I have a sample with 5 data points:-
x y
8 6
16 8
20 16
28 12
32 20
My goal is to...
Hello, I have this simple COR problem that I seem to be a bit stuck on.
Homework Statement
A 1.25 kg squash racquet swung at 37 m/s contacts a ball moving at 42 m/s in the opposite direction. Immediately after impact the racquet has a velocity of 25 m/s and the ball has a velocity of 50 m/s...
ΔL=LαΔT
The concept is interesting and applying its formula isn't even tedious, but what are the real factors that determine α here? I understand that thermal expansion is a direct consequence of the average separation between atoms. And that the coefficient can be found through different...
Dear Experts,
I am looking for the variation of magnetic permeability of the plain carbon steel wire grade 1000 to 1095 with respect to the ambient temperature ranging from -40 deg C to 200 deg C. Any leads will be appreciated. Thank you!
three spheres of mass 1kg,2kg and 3kg move in the same line with velocities 5i,i and 3i respectively. the smaller masses are the first to collide.if only one collision takes place find the maximum value for the coefficient of restitution between the smaller masses.
what I've got so far...
Homework Statement
An disk has a radius of 0.2 meters. A lump of putty with a coefficient of static friction of 0.9 is stuck on the edge of the disk.
Let's say the disk starts at rest and gradually speeds up. At what speed will the putty just barely be able to stay in place on the edge of the...