Linear Definition and 1000 Threads

Homework Statement a= eD/R*T*G make a linear equations and calculate the value for D and G R=8,3 and constant D,G=constant T= variable Homework Equations y=ax+b y=numberax*bThe Attempt at a Solution ax= E/(R*T) x= 1/T a= E/R y= (E/R)*x+G I don't know how to move on and if this is even correct/

Are there any linear quantum gravity theories out there with respect to the wave function?

Hello, I have a set of data, two columns, and each datum has its measurement error like illustration shows below: x | y --------------|----------------- x1+/-xe1 | y1+/-ye1 . | . . | ...

Hi and thanks to everyone for his/her attention. I have to minimize a function that depends on several parameters. The aim of minimizing that function is to actually guess these parameters, which are unknown. The thing is that the author of the pdf from which I have to make the calculations...

Consider the case where a basketball rotating about its center of mass strikes a wall head-on. The velocity given it parallel to the wall due to the spin is caused by the friction between the wall and the ball as the ball is sliding against the wall during the collision. Friction is proportional...

This isn't really a homework question, I just need help understanding the example: ===================== ==================== So transformation takes complex n-tuple as input, and it seems output is also a complex n-tuple (which is what makes it "operator"). But permutations of n entries is...

Homework Statement In the circuit above ##E_1=E_2=E_3##, ##Ig_1=Ig_2=Ig_3## and ##R_1=R_2=R_3=R_4##. In the case when the switched is closed the power of the ideal generator ##E_2## equals ##P_{E_2}=-30W##. Then the switch opens. Calculate the ##ΔP_{E_1}##. Homework Equations 3. The Attempt...

I have some understanding of Liner Energy Transfrom (LET), but when I compare it with other terminologies such as momentum, then it gets little contradicting. For example, I know that if talk about particles and ions, then a gold ion (AU) has much higher LET than an Iron particle (Fe). And...

I am given the equations of Lorenz with respect to deterministic non-periodic flow: \frac{dX}{dt} = Pr(Y-X), X(0)=X_{0} \frac{dY}{dt} = -XZ + rX - Y, Y(0) = Y_{0} \frac{dZ}{dt} = XY-bZ, Z(0) = Z_{0} where Pr is the Prandtl number, r = Ra/Rac is the ratio of the Rayleigh number to its...

I encountered several times the following problem: Say I have a variable y dependent in a nonlinear way on m parameters ##\{x_i\}##, with ##i \in \{1,m\}##. However there is a linear relation between n>m functions ##f_j\in{x_i}##, i.e., ##y=\sum_j z_j f_j##. So I can get a solution of my problem...

Is there a difference between the linear independence of ##\{x,e^x\}## and ##\{ex,e^x\}##? It can be shown that both only have the trivial solution when represented as a linear combination equal to zero. However, the definition of linear independence is: "Two functions are linearly independent...

I don't quite get this question, how is it done ?

Homework Statement given a linear transformer rated for 50kVA, 11000V/120V How do I find the maximum apparent power? The prompt is to maximum apparent power while keeping the Load RMS voltage between 114V and 126V. Vsource has a peak voltage of 11000*sqrt(2). The circuit looks something like...

I am a Physics teacher. I made a linear track of length 2m with 400 holes(two rows of 1mm dia). Somewhere I read household vacuum cleaner can be used as a blower. But it does not create sufficient pressure to lift the cart. What should be the specifications of the blower which can be used...

I am trying to calculate and draw a relation between (IL) and the Growth rate (m). I have used Il as range from 10^15 to 10^18 in the calculation and when I draw the relation (x-axis ) is Il and (y-axis ) is m. I converted the IL to be in log scale. I noticed unacceptable output. So, I am...

Homework Statement How exactly they combined equation1 and equation2 and got that system? I don't get that part. Homework Equations A*(dy/dt)= -k*y eq1 A*(dz/dt)=ky-kz eq2 The Attempt at a Solution I tried substituting the 1st ky in the 2nd equation and then differentiating but I don't...

Homework Statement system of equations is as follows x+y=1 2x+y-z=1 3x+y-2z=1 ##\begin{cases} x+y=1 |*(-1)\\2x+y-z=1\\3x+y-2z=1 \end{cases}## Homework Equations Gaussian elimination method technique The Attempt at a Solution ##\begin{cases} x+y=1 \\ x-z=0 |*(-2)\\ 2x-2z=0 \end{cases}##<=>...

[SOLVED] Find the diameter of a circle given linear velocity? Hello all! I need help with a certain type of problem. I do not know how I can find the diameter of a circular object given it's linear velocity. Here is an example problem, and I would love any explanation you could give me! Thanks...

Linear work is F*D and rotation is 1/2Iω2, but if a problem as me rotational energy (Rotation worl = KE?) of a wheel and I have the linear work, can I just set Wrotation=Wlinear?

Homework Statement Solve sin (x + pi/4) = √2 cos x Homework EquationsThe Attempt at a Solution sinx*cos(pi/4) + cosx*sin(pi/4) = √2 cos x √2/2 sinx + √2/2 cosx = √2 cos x not sure if I am on the right track? or where would I go from here? would I bring √2 cos x to the left side?

Homework Statement This is an ordinary differential equation using the differential operator. Given the system: d^2x/dt - x + d^2y/dt^2 + y = 0 and dx/dt + 2x + dy/dt + 2y = 0 find x and y equation Answer: x = 5ce^(-2t) y = -3ce^(-2t) Homework EquationsThe Attempt at a Solution We change...

I am not a student. This is not a homework question. I am a 64 year old man who wants to understand a principle of physics. Suppose there is a large block of matter, designated as m2, which lies on a flat surface that initially is at rest. At some point in time a small block of matter...

The transfer function of a linear system is known in the sinusoidal frequency domain. It is given in its final form as a complex function of the angular frequency ω (not jω ). How to obtain the step response? Thanks in advance.

The question is : Is it true that two matrices with the same characteristic polynomials have the same trace? I know that similar matrices have the same trace because they share the same eigenvalues, and I know that if two matrices have the same eigenvalues, they have the same trace. But I am...

My background is in mechanical engineering, but I'm working on a project for which I need to design a control system for a linear actuator. I want to design the actuator using a roller screw mechanism, which in turn will be conected to a 3 horsepower electric motor through gear reduction. I need...

Homework Statement You are asked to measure the moment of inertia of a large wheel for rotation about an axis perpendicular to the wheel at its center. You measure the diameter of the wheel to be 0.600 m. Then you mount the wheel on frictionless bearings on a horizontal frictionless axle at...

I've been studying graduate level Linear Algebra from Steven Roman's Advanced Linear Algebra (Springer, GTM). It is a terrific book, but many of the concepts are extremely abstract so that I find it difficult to retain what I've learned. Can anyone point me to some books/reading on the...

Homework Statement How can I show that if a vector (in a vector space V) cannot be written as a linear combination of a linearly independent set of vectors (also in space V) then that vector is linearly independent to the set? Homework Equations To really prove this rigorously it would make...

I'm currently an applied math major. I'm creating a schedule for my next semester and I have the choice to take either complex variables or vector analysis with linear algebra and a college geometry course(elective of choice), but I don't know which pairing will be less stressful. I am currently...

Homework Statement True or False: If u, v, and w are linearly dependent, then au+bv+cw=0 implies at least one of the coefficients a, b, c is not zero Homework Equations Definition of Linear Dependence: Vectors are linearly dependent if they are not linearly independent; that is there is an...

I want to understand which of these is computationally expensive (in the sense of computational time) which is more accurate. Also I want to understand which of these two problems (computations time + accuracy) of iterative methods are addressed by multi-grid methods?

Hey! :o We have the vectors $\overrightarrow{a_1}=\begin{pmatrix}1 \\ 2 \\ 3\end{pmatrix}, \overrightarrow{a_2}=\begin{pmatrix}-1 \\0 \\ 2\end{pmatrix}, \overrightarrow{a_3}=\begin{pmatrix}7 \\ 8 \\ 6\end{pmatrix}$. I have shown that these vectors are linearly dependent: $\begin{bmatrix}...

Hello PF, I have just finished my first semester in college and did Calc. 3. Now for the spring semester i have to take differential equations and i have been given the advice that linear algebra comes in handy when dealing with DEs. So can anyone recommend a good introduction for linear algebra...

Hi! First off, I am actually a math / econ major. I hope I'm still welcome here I am trying to figure out if it's worth it to take both of these courses or just one of them. I have not taken LA before. Course 1: Addition, subtraction and scalar multiplication of vectors, length of vector...

We were going over linear independents in class and my professor said that if y1 and y2 are linearly independent then the ratio of y2/y1 is not a constant, but he never explained why it is not a constant.

Hi I've collected few sets of data and obtained significant different linear regression (R^2) in 2 particular sets of data . Does that indicates the 2 sets of data is not validated which might due to data collection error? For example, 20 sets of data contain linear regression of 0.900+...

In a problem I am working on, it is given that $V_1, V_2, ... , V_n$ are mutually perpendicular vectors in a space defined with a certain scalar product. I need to prove or disprove that $V_i$ are linearly independence regardless of any definition of scalar product. I think the solution should...

Homework Statement A very long cylinder of linear dialectric material is placed in an otherwise uniform electric field ##E_0##. Find the resulting field within the cylinder. (The radius is ##a##, the susceptibility ##X_e##, and the axis is perpendicular to ##E_0##) Homework Equations Boundary...

Homework Statement Consider a two-layered cylindrical wire with inner-layer permeability μ1 and outer-layer permeability μ2. A line current I runs through the center in the z direction. Calculate the bound currents and the magnetic field produced by the bound currents. Homework Equations [1]...

In the image above, a centroid with radius 1 is depicted. F1 is pointing directly at point A (which is the center of the circle), and F2 is pointing directly at point B. The radius for finding the torque would be the perpendicular between the center of the object and the force vector, so r1...

Homework Statement I'm not sure how to approach this. The question involves linear operators and a non-homogenous differential equation. Here is the question: https://s15.postimg.org/cdmw80157/Capture.png Homework Equations They are given in the question The Attempt at a Solution I really...

xy'' + 2xy' - y = 0 Honestly no clue where to start, Wolfram Alpha gives a rather complex answer lol (http://www.wolframalpha.com/input/?i=xy%27%27%2B2xy%27-y%3D0)

Hello all. I have a question about linear dependency. Suppose we have a set ##S## of functions defined on ##\mathbb{R}##. ##S = \{e^x, x^2\}##. It seems very intuitive that this set is linear independent. But, we did something in class I'm unsure about. Proof: Let ##\alpha, \beta \in...

Homework Statement Homework Equations The Attempt at a Solution I set up the Wronskian?? and compare them?

Good evening! I'm having trouble completing an assignment related to inelastic collisions and momentum. Homework Statement Here is the statement: You are in great shape on this hot July morning. You are working as an intern for the Montreal Police (SPVM) Collision Investigation unit. You...

if A and B are 3x3 matrices such that: ABC = I, |3A|=81 and |C^T|= 2 , how to find |B^-1| I couldn't solve this because there is not much given.

Homework Statement Does a linear transformation ##g : \mathbb{R}^2 \rightarrow \mathbb{R}^2## so that ##g((2, -3)) = (5, -4)## and ##g((-\frac{1}{2}, \frac{3}{4})) = (0, 2)## exist? Homework EquationsThe Attempt at a Solution For a linear transformation to exist we need to know if those two...

The problem I am trying to write the equation for the plane on the following form ## ax + by + cz + d = 0 ## $$ \begin{cases} x = 1 + s - t \\ y = 2 - s \\ z = -1 + 2s \end{cases} $$ The attempt ## s, t ## are the parameters for the two directional vectors which "support" the plane. $$...

Hi! I have a question about Linear Energy Transfer for electrons. According to the definition the linear energy transfer is equal to the energy dE which a charged particle loses at a distance dl. But what does dl mean in case of electrons? Is LET calculated per unit of full path length or per...

We learned that the condition of a linear transformation is 1. T(v+w) = T(v)+T(w) 2. T(kv) = kT(v) I am wondering if there is any transformation which only fulfil either one and fails another condition. As obviously, 1 implies 2 for rational number k. Could anyone give an example of each...