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.
Hi!
Sorry if this isn't a good question, but for an experiment, I wanted to try measuring the coefficient of friction of frozen solutions, but wasn't sure how to do it? I thought that since ice would have a low coefficient of friction, it would be interesting to see if solutions with water and...
Homework Statement: The Task is to calculate the Transmission coefficient with the WKB Approximation of following potential: V(x) = V_0(1-(x/a)²) |x|<a ; V(x) = 0 otherwise
Homework Equations: ln|T|² = -2 ∫ p(x) dx
I have inserted the potential in the equation for p(x) and recieved
p(x) =...
Summary: Hello, I have a task to calculate the air drag coeficient experimentally. I have a cone which I had dropped from height of 1.5 m and measured the time. Then I derived the equation of of velocity and acceleration but they are very complicated. Is there any simpler method?
a=g-k/m*V^2
Hello, I have a question with regard to equipment design.
How do I calculate the overall heat transfer coefficient for a large pipe who has smaller pipes in it? Say I have water flowing on the large pipe, and inside it there are three pipes with hot acid in them. Assuming they flow concurrently...
GR (bold = mathematical convention)
m = 3.2kg
|applied force| = + 22.8 N
|acceleration| = + 3.02 m/s^2
FBD-hypothetical
^ normal force
|
friction force <-----*-----------> applied force
|...
I tried using coefficient of friction = friction / Normal force, but needed a value for friction. I then tried to find the friction using a = f/m, but was unsure of which value to plug in for force. Simply finding the force given a and m will not yield the correct answer; the net force must be a...
Problem:
We wish to find the temperature and the diffusion coefficient of water by measuring the velocity of pollen grains in the medium, due to brownian motion and other forces.
Attempt:
We have a video clip and are using the program Tracker to measure the position of the pollen grains over...
i tryed putting all the number into that equation but it does not work, i have no clue if i need to include the angle to solve this or not and if i do i have no clue how i would
(New thread following up to a conversation in another thread).
I'm using SimFlow 3.1 with OpenFOAM 5 on Linux to try to evaluate the drag coefficient of a water rocket body, constructed from a 2-liter Coke bottle with a conical nose, traveling through air at 77 m/s.
This should be a simple...
Hi there,
I have modeled with MAXSURF a few variations of a prehistoric logboat in order to test a few theories. Now, I am trying to look at resistance-performance over a range of speed. To do so, I need to include a constant drag coefficient without knowing the drag force and velocity (both...
I am totally confused about whether it even makes sense to speak of n and p-types materials, when referring to whether the majority of charge carriers are electrons or holes.
We can read all over the place that the Hall effect can tell us whether a material is p or n-type, just by checking the...
Could you please explain the term 'co-efficient of static friction'?
why do the banking of roads or tracks depend of co-efficient of static friction?and not on the co-efficient of kinetic friction?
The Hamiltonian of the system I'm working on is in the form :
##\hat H=\dfrac{p^2}{2m}-\dfrac{\partial_z^2}{2m}+V(z)+\gamma V'(z)(\hat z \times \vec{\mathbf p})\cdot \vec{\sigma}##
There is translational symmetry in the x-y plane.
##\vec{\mathbf{p}}## is the two dimensional momentum in the x,y...
Dear all,
For an assignment, I am trying to find the relationship between the Sherwood number and the Reynolds number in a channel for different laminar velocity profiles, where there is a concentration of a species at both the top and bottom wall which is transported to the fluid. For this, I...
Fg = mg
= 50 * 10
= 500 N
Fn = mg-ma
= 500 - (50.0)(1.0)
= 500-50
= 450
I don't necessarily know if this is right and I can't seem to find the Ff or coefficient of friction either. Please Help!
Since the integrand is spherically symmetric I use spherical coordinates
\int d\vec{r} = \Omega_d\int_{0}^{\infty}dr r^{d-1}
where \Omega_d is the solid angle i d dimensions. Since I am to plot as a function of 1/\beta U_0 (= k_bT/U_0) , I introduce a new varible \Theta = 1/\beta U_0...
Basically, the way I did this problem was to use a table with a known ##n## and ##k##. In this case, I fixed ##n=5##, and ##k=3##. I wanted to find the number of terms with three ##x##'s and two ##y##'s. I labeled each ##x_i##, ##1\leq i \leq 5##; the ##y_i## are labeled the same way. Anyway...
Homework Statement
Hello. I have slope = 45 degrees, at distance 36.4cm (0.364m) object gains 2m/s speed. Need to calculate friction coefficient. Correct answer is ( 0,2). How to calculate?
Homework Equations
1) t = s/v "t" - time; "s" - distance "v" - speed
2) S =...
Homework Statement
Hello, I have a problem with my data analysis from my lab. My goal is to find drift velocity of the electron and it's diffusion coefficient. The experiment looked like this: I've measured the time difference between signals on two gaseous detectors. The source of the signal...
Hi, I was recently tasked to build a mini-sumo robot (10x10cm. 500g. the objective is to push your opponent out of a 75cm. diameter arena or dohyo), and I was wondering about the tires that I'm going to use. I want to increase the friction coefficient as much as I can, so I was wondering how to...
Homework Statement
The static friction coefficient on an inclined plane is equal to tan(θ). The problem requires me to prove this also works by using an x-axis parallel to the ground rather than parallel to the incline. I understand how to get tan(θ) using the incline as the x-axis, but I don't...
Homework Statement
At a construction side, a small crane is raising two boxes of nails on a plank to the roof. One box has already been opened and is half full, while the other box is new. The boxes, including the nails, weight 10 kg and 20 kg, respectively, and are the same size.
Diagram...
Homework Statement
##b_2## is the second virial coefficient
Homework Equations
Virial expansion:
$$P = nkT(1 + b_2 (T)n + b_3 (T)n^2...)$$
$$b_2 = -\frac{1}{2} \int dr f(r) $$
r is the distance vector.
$$f(r) = e^{-\beta \phi(r)} - 1$$
The Attempt at a Solution
$$b_2(T) = 2 \pi r^2...
What is the coefficient of drag on a flat surface?
Note:
The body is in free fall
The object has 2 wings planform (it's a paper helicopter), which is flat
The object's wing spin in a circular motion (anti-clockwise) during free fall
Homework Statement
Prove that the Clebsch-Grodan coefficients (in the notation ##\langle j_1j_2m_1m_2|j_1j_2jm\rangle##) for the decomposition of the tensor product of spin ##l## and spin ##1/2## to spin ##l+1/2## are
$$\left\langle l,\frac{1}{2},m\mp \frac{1}{2}, \pm \frac{1}{2} \Bigg\vert l...
I am learning binomial theorem now on my long journey to calculus. I noticed that in older textbooks, the binomial coefficient looks like
C(n on top,k on bottom)
I don’t think that I can display it here
and in newer ones,they look like
##\binom{n}{k}##
is the old notation outdated?or this is...
Homework Statement
I have the following circuit: The two inductors are connected in series are characterized by internal resistances R1 and R2 and self-inductances L11 and L22. The magnetic coupling factor between the inductors is k = 0.75. The inductors carry the same current i. What is the...
I have been attempting to calculate a Ballistic Coefficient (BC) from two velocities of a known distance using the formula:
BC = (AirDensity * Distance) / ( SQRT(Velocity0) - SQRT(Velocity1))
for example
AirDensity = 0.0751265 lb/ft³
Distance = 100 yards
Velocity0 = 3000 fps
Velocity1 = 2772...
Homework Statement :
A sled starts from rest at the top of a snow-covered incline that makes a 20° angle with the horizontal. After sliding 68 m down the slope, its speed is 17 m/s. Use the work–energy theorem to calculate the coefficient of kinetic friction between the runners of the sled and...
Homework Statement
I need to find the explicit formula for the following recursive sequence:
##v_n=\frac{2}{1+q^n}v_{n-1}## where ##0<q<1## is a constant
Homework Equations
I found the following method to solve it...
I learned that there are two different definitions for the coefficient of restitution: e = final relative velocity / initial relative velocity and e = √(final KE/initial KE). However, I don't understand how these two definitions will always give the same value.
If one particle with mass m...
Homework Statement
So in physics we have this lab. Its simple, I'm just bad at physics...so bare with me.
The objective of the lab is find the coefficient of friction (on a flat surface not on inclined planes and such not sure if this makes a difference (I should know if it does but I don't and...
Why is the absorption coefficient (##\alpha##) of water is always given using the units ##\text{length}^{-1}##, while for other materials it is often given by ##\text{length}^{2}.\text{mass}^{-1}##?
For instance, this paper uses ##cm^{-1}## for water and yet ##cm^2 / \mu g## for other...
Homework Statement
A man pushes a 50 kg box up a 20-degree ramp at constant velocity. If the pushing force is parallel to the ramp, and the coefficient of friction is 0.4, how much force is he pushing with?
Homework Equations
u=Fs, max/Fn Not sure if this equation is needed.
The Attempt at a...
Homework Statement
Homework Equations
[/B][/B]
3. The Attempt at a Solution
Here's my solution attempt:
NOTE: Evolution 2 to 3 is really an isothermic process, but in the diagram shows as an politropic process.
4. Further Questions
But it isn't giving me logical values of COP...
Consider this Ito proces: $$dX_t = \mu(X_t,t)dt+\sigma(X_t,t)dW_t$$ with W_t being a wiener process. My question: What is the diffusion coefficient of X?
My motivation for asking: A lot if financial literature refer to "diffusion coefficient" and I haven't understood by googling it, because...
Homework Statement
In a particular fibre, the attenuation coefficient for Rayleigh scattering is measured to be 0.30 dB/km at 1.20 μm.
(a) How large would it be expected to be at 0.80 μm?
(b) Ignoring other sources of attenuation, if a signal of a certain initial power was sent over a...
I was wondering that if rolling resistance is basically caused by slight deformation of a body, we must have formulas in place to relate it to the physical and material properties of a body. But when I went ravaging for it in library or internet, everything was experimental. I wished to know...
Homework Statement
Coefficient of xy(z^-2) in (x-2y+3(z^-1))^4
Homework EquationsThe Attempt at a Solution
[/B]
I was wondering if anyone could give me an explanation for my answer?
The coeffecient of xy(z^-2) does not = 4 where I would be able to use the multinomial theorem.
So since I...
Hi all,
I have a suspended seat with a scissor mechanism like the following: This seat is composed of coil spring and a hydraulic damper. My aim is to develop a multibody model of that seat. Actually, my model is quite complete, only the parameters of damper are missing (i.e. the damping...
I have conducted an experiment that measures the velocity of an object that is moving on a flat surface. The object rolls on four fixed caster wheels. The wheels are made of some kind of rigid material. Maybe nylon, maybe hard rubber. The total mass of the object, including the wheels, is...
I'm having trouble with trying to find the expansion coefficients of a superposition of a Gaussian wave packet.
First I'm decomposing a Gaussian wave packet
$$\psi(\textbf{r},0) = \frac{1}{(2\pi)^{3/4}\sigma^{3/2}}\text{exp}\left[ -\frac{(\textbf{r} - \textbf{r}_0)^2}{4\sigma^2} + i\textbf{k}_0...