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 box slides down a 30° ramp with an acceleration of 1.20 m/s^2. Determine the coefficient of kinetic friction between the box and the ramp
ok so the only equations I know are μk= Fk(kinetic friction)/Fn(normal) and that Fn=mass x gravity
so i don't know how to get Fk or mass... so help on...
1. Here is the problem http://i.imgur.com/WH0Z4ko.png
So I've set up a Free Body Diagram and I think I have it right. I have the two Forces of Weight (8.82N and 21.27N), the force of 12.8 that is pulling the .9kg box, and then the Force Normal (just the opposites of the two Forces of...
Homework Statement
There's no specific problem statement but I have to explain how I would find out the coefficient of kinetic friction given the angle (θ) of the inclined plane and mass of the object sliding down, nothing else.
Homework Equations
ƩF = ma
μk = Fk (kinetic friction) / Fn...
Hello,
For my Classical Mechanics Lab, my fellow students and I are to calculate the coefficient of air-resistance of several objects dropped from the roof of our science building. We are assuming that the air-resistance is linear in nature. The first method by which we calculate the drag...
Homework Statement
Find the coefficient of x8 in the expansion of (x2-3)7
Homework Equations
This one:
(n n-j) an-jxj
The Attempt at a Solution
Hi!
Well, I know that
x= x2
a= -3
n= 7
and apparently, j=8.
This is what confuses me. n-j is a negative number.. how would...
Homework Statement
A block is projected up an inclined plane that makes an angle
θ to the horizontal. It returns
to its initial position with half its initial speed. What is the coefficient of kinetic friction
between the block and the plane in terms of the angle of the incline...
Homework Statement
You are to lower a safe of mass 260kg at constant speed downs skids 20.0m long, from a truck 2.0m high.
a) If the coefficient of friction between the safe and the skids is 0.25, do you need to pull the safe down or hold it back?
b)How great a force parallel to the skids is...
Homework Statement
I have a box on a horizontal plane.
Given data: mass = 0.25kg
height of object = 14 cm
width of object = 9cm
Calculate the coefficient of static friction.
Homework Equations
μs = Ff/N (N is the normalforce)
F = Ff = μ*N
mg = 2.45 Newton
The Attempt at a...
Hi all,
This is my first post here. As a bit of background I have a keen interest in mathematics, but I'm not necessarily strong in it...
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Quantum -- Find the formal expression of the coefficient cn(t=o)
Hello everyone,
I'm really stuck on the first question of an exercise, so I can't start! :cry:
Homework Statement
ψ(x,t) a wave function normalized and solution of Shrodinger equation for a given potential.
I the...
Hello physics forum! I come to you with a binomial coefficient problem I am stuck on. Here is the question
1. Suppose an airport has three restaurants open, Subway Burger King and McDonalds. If all three restaurants are open and each customer is equally likely to go to each one, what is the...
A road vehicle equipped with mechanical wheel brake e.g drum or disc brake ,driving at a speed of 100Km/hr is braked to a stand still with a deceleration of 1G (3.2m/sec^2),How large must be the coefficient if friction between wheel and road at least be to enable that.
Options:
1)At least...
Homework Statement
I need to calculate molar extinction coefficient for Albumin at 280nm.
Homework Equations
A=ε*c*L
ε=A/(c*L)
But since L=constant, I can just say ε=A/c
The Attempt at a Solution
The given molecular mass of albumin is 66,5kDa, which equals 66500g/mol. I do...
Homework Statement
A man of mass m is applying a horizontal force to slide a box of mass m' on a rough horizontal surface. It is known that the man does not slide. The coefficient of friction between the shoes of the man and the floor is ##\mu## and between the box and the floor is ##\mu'##...
Hi,
Will I have a higher slipping force / torque by increasing the width of my brake shoe and drum? Though my instinct says it is possible, textbook says it's only the coefficient of friction that controls the slipping force. Can you pl help me understanding this? Thanks.
Homework Statement
a block with a mass of 0.310kg at a constant velocity , calculate the coefficient of kinetic friction on an incline plane
Homework Equations
f=ma
fg=mg
fparallel= mg* sin30 degreesThe Attempt at a Solution
I found the FN which is 2.60 and the f parallel to be 1.52. i...
Lately, I have conducted an experiment where I dragged various circular cylinders through water in order to find the resistance, and hopefully also the drag coefficient. It seems to me that this coefficient is dependent on what is called the Reynolds number. Using some sources, I can easily find...
A hockey puck on a frozen pond with an initial speed of 12.3 m/s stops after sliding a distance of 198.9 m. Calculate the average value of the coefficient of kinetic friction between the puck and the ice.
So I started with finding the acceleration. I divided 12.3m/s by 198.9m then took the...
Homework Statement
Prove that ##\binom{-1}{k}=(-1)^k##
The Attempt at a Solution
Using induction on ##k##,
##\binom{-1}{0}=1## which is true also for ##(-1)^0=1##
Assuming ##\binom{-1}{k}=(-1)^k##, then ##\binom{-1}{k+1}=(-1)^{k+1}##
Indeed when ##n=-1##, we can write...
So I've been stuck on this type of question, please help!
You are pushing horizontally on a 3.0 kg box of wood, pressing against a wall. If the coefficient of static friction is 0.60, how much force must you exert on the block to prevent it from sliding down?
Homework Statement
What is...
Dear Everyone,
I have a problem to be solved now. how to calculate the symplectic group SP(3,R) non-compact induced by the SU(3) group? Any reference provided will be appreciated.
Homework Statement
A steady stream of 5 eV electrons impinges on a square well of depth 10 eV. The width of the well is 7.65 * 10^-11 m. What fraction of electrons are transmitted?Homework Equations
The following equation for the transmission coefficient, T, is given:
T = [1 + \frac{V_0 ^2...
Hey all,
I'm trying to simulate a simple chip-heatsink situation in SolidWorks using their thermal modeling suite. I have found an ideal set of parametric values for the chip to work at a reasonable temperature, but I need to figure out what the convection coefficient means in terms of air flow...
Hi There
Does anyone out there know a good estimate or any real values for the total heat transfer area for the hot and cold sides of a domestic refrigeration system? i.e. the sum of the areas of the evaporator and the condenser.
For the Evaporator:
QL=UL.AL.(TL-T1)
AL=heat transfer...
I am looking for an exact value of absorption coefficient of aluminium for microwaves, but I can not find it in the internet. Anyone knows where I can find it?
Homework Statement
This problem is from a homework assignment. The professor says that the the ping-pong ball will go up if the cd = 0 and will go down if the cd is much larger than one. Is this logic correct? I keep thinking about how if an aerodynamic car is pushed by wind, the car...
Homework Statement
##| \ X \in \mathcal P(\{0,1,2,3,4,5,6,7,8,9\}) : |X|= 4 \ | = \ \ ?##
Homework Equations
There's no wording in the exercise , just what I wrote above.If I understood correctly , they asked me to find the cardinality of the set of all subsets of {0,1,2,3,4,5,6,7,8,9} that...
Homework Statement
This one is trickier than the problem in my other thread in my opinion.Twenty-one people are to be divided into two teams , The Red Team and the Blue Team.There will be 10 people on Red Team and 11 people on Blue Team.How many ways to do this?
I am not sure how to solve...
Homework Statement
A department consists of 5 men and 7 women.From this department you select a committee with 3 men and 2 women.In how many ways can you do this?
Homework Equations
Since the "overall set" (the entire department) is composed of both men and women and each has a specific...
Homework Statement
So the problem gives you the compressibility factor Z. It gives two equations, one for ideal gas and other one for non-ideal gas.
The question states:
The second Virial coefficient B(T) depends on the temperature T and is related to the intermolecular potential B(T) =...
Homework Statement
I am conducting an experiment to determine the coefficient of static and kinetic friction between 2 objects I've arbitrarily chosen. I have a block and a plank of wood. I have been raising the plank to an incline to determine at what angle the block will begin sliding.
I...
Hi I was looking at how to calculate the GINI coefficient and saw two different statements from two websites.
Statement 1:
It has been shown that the sample Gini coefficients defined above need to be multiplied by in order to become unbiased estimators for the population coefficients...
https://www.khanacademy.org/math/probability/regression/regression-correlation/v/r-squared-or-coefficient-of-determination
Homework Statement
So, when determining how effectively a best-fit line describes the variance of a given set of measured data, the Coefficient of Determination is the...
Can someone please look at this and tell me what's going on here?
I'm trying to understand the coupling coefficient k between two wire coils some d distance apart.
I found this but I am lost!
Please help!
Hello,
I was competing calculations for a simple machine lab, and I got a different mu_k for 3 separate inclines of 20,30 and 40 degrees.
But a question asks says ,"explain why the coefficient of kinetic friction should be independent of the inclination angle of the inclined plane."
How do I...
Say if an iron disk slides down a non ferromagnetic conductor ramp and we get a certain time. And then we have an iron disk with the same mass but MAGNETIZED slide down the same ramp and get a longer time (because of of magnetic braking). The calculated acceleration of the MAGNETIZED disk will...
Physics coefficient of friction question!
A 17kg box is being pushed by a 150N force. If the box is accelerating at 2.3m/s2. What is the coefficient of friction on the ground?FNet=μFn
Fn= 9.8x17= 166.6N
How can I find the fnet?
Hello,
I am stuck on this question, I don't understand what to do. Any help would be great! I know that I have to use Newton's Second Law in the x and y directions.
Greezy is pushing a very large crate of 50 kg across the floor at a constant velocity with a force of 200N. He is pushing on...
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Given a certain muzzle velocity, how do I use that to calculate velocity at some point downrange?
Homework Statement
f(x) = 1, 0<x<1
Extend f(x) t generate an even function P(x) and find Fourier coefficients
Homework Equations
an = 2/T ∫ P(x)cos(2nx/T) dx
The Attempt at a Solution
P(x) = 1, -1<x<1
0, -2<x<-1 , 1<x<2
even function so b0 = 0
Average of P(x)...
Homework Statement
I´ll show the problem with a picture:
Homework Equations
M=rxf
Sum Forces = 0
Sum Moments= 0
The Attempt at a Solution
I recognize that I am completely lost with this problem, so I´ll try to analyze every force acting on every body to show where are my doubts.
When...
Homework Statement
A 3 kg block slides down a 30 degree inclined plane with constant acceleration of 0.5 m/s2. The block starts from rest at the top. The length of the incline is 2 m.
Homework Equations
Vf^2=Vi^2 +2ad velocity is 1.414
Fg=3 x 9.8=29.4
Fn= cos(30) (9.8 x 3) = 25.5...
I want to solve a depressed quartic:
ax^4 + bx^2 + cx + d = 0
Assume |a|\ll |b|,|c|,|d|.
I would like to find the solutions by expanding around the solution to the quadratic. If you try to solve in, say, Maple, and expand around a in a series you get something that blows up. That seems silly...
Hey all,
I'm trying to design a clamp that has to hold onto a hollow carbon fiber tube, approximately 2.5 inches in diameter. The clamp will be bearing a 15-20lb load. The carbon fiber will be at angles from 20-70 degrees from a vertical axis.
I'm curious if there is a polymer that can be...
Homework Statement
Homework Equations
r=\frac{S_{xy}}{S_{x} S_{y}}
S_{x}=\sqrt{\Sigma(x-\bar{x})^2}
The Attempt at a Solution
I have calculated the value of Sx several times and I got 43.3 but the answer key said that Sx = 11.2
1. Is my formula correct?
2. If yes, is my...
The coefficient of variation tells us about the consistency in the data. I know that the lower the coefficient of variation is, the higher will be the consistency in the data. What I don't understand is what is being meant by 'consistency' here. Could someone please explain that?
Homework Statement
You do 2.2 kJ of work pushing a trunk at a constant speed 3.1 m along a ramp inclined upward at 22 degrees. What is the frictional coefficient between the trunk and the ramp?
Homework Equations
W = F*d
Ff = μmg * cos(θ)
Fg = mg * sin(θ)The Attempt at a Solution
To find the...
Okay I got to wonder about this: Why is the multinomial coefficient independent of if you start by taking out n1, n2, n3 etc. or n2,n1,n3 or n3, n2, n1... etc.. I mean intuitively from actually doing the combinatorics by counting it seems obvious that the order should not matter. But can this be...
what is the max free air heat transfer coefficient(film coefficient)? at 1000 c?
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let say a cylinder(steel) is 6 cm diameter and length of 3.5 cm length. and is heated to 1000 degree c.
in a room of free air and room temperature of 20.
will convective heat transfer dominate? it radiation is negligible?
what would the convective heat transfer be?
what power(watt)...