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 ! First at all thanks for read, I'm new in the forum ...
So the problem is, I would calculate the drag coeff of a car but in the coeff formula I would like to know which AREA is considered for this.
drag coeff is given by = 2F / ρ(V^2) A
Where :
F is the drag force
ρ is the mass...
Definition: Proth number is a number of the form :
k\cdot 2^n+1
where k is an odd positive integer and n is a positive integer such that : 2^n>k
My question : If Proth number is prime number are there some other known relations in addition to 2^n>k , between exponent n and coefficient k ?
Homework Statement
"A 1250 kg slipper hippo slides down a mud covered hill inclined at an angle of 18 degrees to the horizontal. A) If the coefficient of friction is 0.0900, what force of friction impedes the hippo's motion down the hill? B) If the hill were steeper, how would this affect the...
Homework Statement
The original problem is determining the dispersion relation of an ordinary wave in plasma damped by collisions. That part was easy enough but the next part is to find the damping rate (-Im(ω)) of the wave, assuming k is real and \nu << \omega where \nu is the collision...
At the bottom of a hill, a snowboarder with a velocity of 16m/s (FWD) skids to a stop after moving a distance of 9.4m. The mass of the board and rider is 71kg, and the magnitude of the force of kinetic friction during the skid is 950N.
Determine the coefficient of kinetic friction during...
The problem:
A car traveling on a flat (unbanked) circular track accelerates uniformly from rest with a tangential acceleration of 1.60 m/s2. The car makes it one quarter of the way around the circle before it skids off the track. Determine the coefficient of static friction between the car and...
So there's this graph in chemistry with a curved negative slope shape.
(x, y)
(0.16, 104.61)
(0.26, 39.62)
(0.35, 21.86)
(0.56, 8.54)
(0.70, 5.47)
(0.98, 2.79)
The equation is y=KX^N
1) What is the value of N for which the graph would be a straight line?
2) What is...
Homework Statement
I'm trying to solve this DE: 4xy''+2y'+(cosx)y=0 using a series solution.
Homework Equations
The Attempt at a Solution See attached PDF. I tried writing the cosine term as an infinite series, but that gives me a messy double summation. And in the end, I get an...
A() 61 kg child stands at the rim of a merrygo-round of radius 1.05 m, rotating with an
angular speed of 1.87 rad/s
The acceleration of gravity is 9.8 m/s^2
What is the child’s centripetal acceleration?
Answer in units of m/s
What minimum force between her feet and
the floor of the...
Homework Statement
Calculate the energy generation coefficient ε (J s^-s kg^-1) in the center of a 50 Solar mass Main Sequence star, assuming that all luminosity is generated in a constant density core containing one tenth of the total mass of the star.
Homework Equations
L=M^3.3...
Hi all:
Now I have a question about the concept of diffusion coefficient in two cases: the diffusion equation (J=DdT/dx) and the random walk (tao^2=6Dt). My quesion is the two D in two equations are the same or different. If they are different, is there any relationship between them?
Best
Xu
Hi,
I am trying to get my head around the temperature coefficient of resistance; that is, the fact that the resistance of a metal (in this case, copper) will change as the temperature of the metal changes. This coefficient is given a value (for copper this is usually given as around 0.00393...
Homework Statement
A block is projected with a speed of 3.0 m/s on a horizontal surface. if the block comes to rest in 1.5 m, what is the coefficient of kinetic friction between the block and the surface?
Homework Equations
M=Ff/N
(Fapplied-Ff)=ma
I'm not really sure which...
Homework Statement
A uniform 7.7 m tall aluminum ladder is leaning against a friction-less vertical wall.
The ladder has a weight of 291 N.
The ladder slips when it makes a 59.0◦ angle with the horizontal floor.
Determine the coefficient of static friction between the ladder and the floor...
Hi, I'm currently taking a Discrete Mathematics class and cannot seem to work out this one problem, we need to find the x^10 term in order to determine its coefficient of the equation f(x)=(x+x^2+x^3+x^4+x^5+x^6)^3 I know the answer is to be 27 from a previous problem (we are to use this method...
a. A very large reservoir of pressurized air feeds a contraction and forms a free jet of air of circular cross section and diameter 60 cm in a laboratory, where the ambient pressure is atmospheric. A Pitot static tube is arranged in the jet and attached to a vertical U-tube manometer containing...
a. A very large reservoir of pressurized air feeds a contraction and forms a free jet of air of circular cross section and diameter 60 cm in a laboratory, where the ambient pressure is atmospheric. A Pitot static tube is arranged in the jet and attached to a vertical U-tube manometer containing...
If we set a ball rolling on a loop-the-loop track,why do we say that we need infinite friction coefficient for the ball to complete the loop. This seems illogical because f=kN. Since f and N are finite how can k be infinite ?
Homework Statement
Julia is delivering newspapers. Suppose she is driving at 15 m/s along a straight road and wants to drop a paper out the window from a height of 1.00m so it slides along the shoulder and comes to rest in the customer's driveway. At what horizontal distance before the...
Homework Statement
If a mass of 609 kg travels in a circle with a radius of 102 m, and the μ= .13, and the acceleration of gravity is 9.8 m/s^2. What is the max velocity that the mass can go without canceling out the force of friction?
Homework Equations
?
The Attempt at a Solution...
I remember doing an experiment in Physics class to find the coefficient of friction with gravity.
We set an object with a flat surface on top of a ramp, and adjusted the ramp angle so that the object would move down the ramp at a constant velocity. Then we measured the angle of that ramp to find...
Hi everybody.
I am going to exam on Monday. I would like to make a experiment on how to measure the coefficient of friction.
I know, that I can find the mu(s), by taking the tan to the angle α.
μs = tan(α).
Is there somebody, who has some others ideas how to measure that? Somebody...
Homework Statement
When three blocks are released from rest, they accelerate with a magnitude of 0.500 m/s2. Block 1 has mass M, block 2 has 2M, and block 3 has 2M. What is the coefficient of kinetic friction between block 2 and the table?
(The blocks are arranged with block 1 hanging from...
Homework Statement
A box with mass 2kg is on the edge of a circular platform of radius 6.0m. The coefficient of friction between the platform and the box is 0.3. The platform accelerates. Determine the speed when the box slips off the edge.Homework Equations
Fs = μsN
F⃗ net=ΣF⃗ =ma⃗
a(t) =...
Homework Statement
This is what I was given:
A block is placed on a rough wooden plane it is found that when the plane is tilted 30° to the horizontal, the block will slide down at a constant speed.
Homework Equations
I'm not sure which equations to use other than sinΘmg but I'm not getting the...
Okay, this is a long post so buckle up (not sure if this counts as Homework Help or not - technically it WAS homework, but now it's basically exam revision).
I was wondering if anyone would mind helping me with a few physics problems I have? It was originally for a mastering physics...
Hi friends,
I have been trying to solve the ode of second degree below with respect to z:
d2y/dz2=(i/a*z+b)*y
i is the complex i, a and b are constants
i ended up with the summation of bessel functions of first end second kind. Then I checked with MATLAB ode solver it gives no...
Homework Statement
1st problem: If and object has a weight of 100 N and a frictional force of 50 N exerted on it, what is the coefficient of friction?
2nd problem: A Block with a mass of 50 kg, is pulled with a force of 10 N at an angle of 10 degrees to the horizon, if the coefficient of...
I seem to be getting some arbitrary values from my Scilab code for a function. I have to generate a graph showing the dependence of the transmission on the air gap separating two higher refractive index materials i.e. I want to plot "T" as a function of "d".
T = \frac{1}{1 + \beta \sinh^2...
Homework Statement
A physics student slides a 2.0kg textbook along the laboratory bench to her friend. She imparts to the book an initial velocity of 2.70m/s. μ=0.20. How far away is her friend if the book comes to a stop right in front of her friend
Vi= 2.70m/s μ=0.20 m=2.0kg Vf= 0m/s...
Homework Statement I'm trying to determine R_0 and alpha (temperature coefficient of resistance) from results I obtained through an experiment. We have been given the first equation and been told that R_T is the resistance at temperature T in kelvin. R_273 is the resistance at temperature 273K...
A flight attendant pulls her 70.0 N flight bag a distance of 269 m along a level airport floor at a constant speed. The force she exerts is 32.0 N at an angle of 52.0° above the horizontal.
(a) Find the work she does on the flight bag.
_5299_J
(b) Find the work done by the force of friction...
Homework Statement
Find a general solution to \frac{d^2x}{dt^2}-2\frac{dx}{dt}=1-4t+e^t
Homework Equations
None really.
The Attempt at a Solution
I know that a complimentary solution is x=c_1+c_2e^{2t}
But when I try to guess say: x_p=At+B+Ce^t and plug into the DE, I do not get...
I need to find the coeffcient of friction on an incline plane. I need the equation to find the coefficient for any givien angle. It part of a lab where I'm required to create the procedure and am stuck with how to create the equation. We can use a protractor or trigonomic functions to find the...
A 10.2 kg block is being pulled at constant speed in the positive x-direction along a flat surface with which it has a coefficient of kinetic friction. It is pulled by a rope at an angle of 30° above the horizontal, and the tension in that rope is 50 N. Normal force is 75 N.
Ok so I'm in college upgrading, and doing my physics 20. I have a hand in assignment due Wednesday and I can't for the life of me figure out these two questions.
6. The 4.0kg block shown accelerates across a frictionless horizontal table at 1.5m/s2.
Find the mass of object m1
A. 0.61kg B...
Homework Statement
A 500kg box is being pushed across a floor, with an applied force of 8400N, at a constant velocity, at an angle of 35 degrees below the horizontal. What is the coefficient friction between the floor and the box.
Homework Equations
I really do not know where to...
An object on a 30 degree inclined surface with force applied up the ramp,
weight of object = 6.9N,
applied force on object = 3.13N
My answer was -0.05, but I'm not sure if this is right so I want to make sure with someone's help
Thanks
Hi,
I'm doing research on the Coefficient Of Friction using a forceplate. I'm trying to determine the coefficient by pulling several objects over the plate, and using the frictional force and normal force to determine the coefficient of friction (measured by the force plate).
When I pull...
I've been reading about calculating dissolved gas concentrations in water at varying temperature and salinities using an equation of the form:
ln(β)=exp(A1 + A2*(T/100) + A3*ln(T/100) + A4*(T/100) + S*(B1 + B2*(T/100) + B3*(T/100)^2
where β is in units of mL/L, and A# and B# are...
I'm currently working on a project that requires me to model depressurization of a gas through an outlet. I need to find the time for complete depressurization of a pressurized chamber as a function of opening cross-sectional area A. I scoured the forums, and found the extremely helpful link...
Homework Statement
A 100 kg bale of hay falls off a truck traveling along a level road at 24.4 m/s. It lands flat on the road and slides 100m before coming to rest. Assume the acceleration is constant, compute the coefficeient of kinetic friction between the road and the hay.
Homework...
Homework Statement
The Attempt at a Solution
I found the acceleration using kinematics equations.
I don't know how to find the coefficient of friction though.
I need help answering pard b c and d
If you could give me the equations and explain.
Just knowing how to do this one...
Homework Statement
A block weighing 9.3 N requires a force of
3.7 N to push it along at constant velocity.
What is the coefficient of friction for the
surface
Homework Equations
Ff=μ*Fn
The Attempt at a Solution
So the 3.7 N to push is the Force of friction so 3.7=μ*9.3...
The data came from my lab involving friction between wooden block with metal weight on it and a metal table. The wooden block is moved from rest and the force is measured using a force meter and Logger pro.
Homework Statement
Force of peak static friction = 23.285N. Normal force is...
Homework Statement
An object is moved with a speed of 2m/s on one side of a 1m table to the other, it stops right at the other and of the table without falling off. Does it have wheels or not?
Homework Equations
The teacher gave this just to me and said we havnt learned about it yet...
A 5.00-kg block is placed on top of a 12.0-kg block that rests on a frictionless table. The coefficient of static friction between the two blocks is 0.600. What is the maximum horizontal force that can be applied before the 5.00-kg block begins to slip relative to the 12.0-kg block, if the force...
Homework Statement
A car is sliding down an icy hill inclined at 1.6 degrees, find the coefficient of friction.
Homework Equations
f_k=\mu_k*n
The Attempt at a Solution
Don't know how to begin it only given the angle of the hill.
Homework Statement
A block(7 kg) is released from rest on an inclined plane of 23 degrees and moves 2.8 m during the next 4.7 s. The acceleration of gravity is 9.8 m/s^2. What is the magnitude of the acceleration of the block? What is the coefficient of kinetic friction for the incline...
Let's say there is a conducting plane of conductivity \sigma. Boundary conditions for above and below such plane are:
E_1^t = E_2^t
(D_2 - D_1 ) \cdot n = \rho
i.e. tangential components of E field are continuous and perpendicular components of D are discontinuous because of surface charge...