Linear Definition and 1000 Threads

Homework Statement I did an experiment on how stretching a rubber band, affects the range or distance of a projectile shot. Variable list: Independent Variable Amount of stretching Dependent Variable Range or distance I created my catapults on my own and used two different rubbers bands...

Homework Statement If ##A## is an ##n \times n## matrix, show that the eigenvalues of ##T(A) = A^{t}## are ##\lambda = \pm 1## Homework EquationsThe Attempt at a Solution First I assume that a matrix ##M## is an eigenvector of ##T##. So ##T(M) = \lambda M## for some ##\lambda \in \mathbb{R}##...

Homework Statement T/F: Let ##T: V \rightarrow W##. If ##\{v_1,v_2,...,v_k \}## is a linearly independent set, then ##\{T(v_1), T(v_2),..., T(v_k) \}## is linearly independent. Homework EquationsThe Attempt at a Solution This seems to be true, because we know that ##a_1v_1 + a_2v_2 + \cdots +...

The function ƒ(x) is a linear function and g(x) is a rational function. These functions have the following values: ƒ(3) = 7 g(3) = 5.6 ƒ(4) = 5 g(4) = 6.7 There is a solution to the equation ƒ(x) = g(x) between x = 3 and x = 4 that must be closer to 3 than 4. TRUE or FALSE?

Can i Use a standard F-test on longitudinal data for a linear multiple regression? Mons

Homework Statement http://prntscr.com/eqhh2p http://prntscr.com/eqhhcg Homework EquationsThe Attempt at a Solution I don't even know what these are, it is not outlined in my textbook. I'm assuming I am is image? But how do you calculate image even? As far as I'm concerned I am has to do wtih...

Say I want to see if a continuous variable, say strength, is associated with another continuous variable, say height. Clearly I can just use linear regression with height as the response variable and strength as the predictor variable. But I can also split height into a tall category and a...

Hi, I'm currently doing my extended essay for the IB in physics and I'm basing mine around the Gauss gun (similar post that explains it really well here https://www.physicsforums.com/threads/physics-behind-gaussian-accelerator-magnetic-linear-accelerator.320389/). What I was wondering was how I...

Hey. I am doing a project where I am studying a set of companies over a 7-year period. I am doing a multiple linear regression analysis either with fixed or random effects (so, it's a panel study). What I am wondering is if the general assumptions/requirements apply when using the fixed/random...

Let D represent the differentiation of a single-parameter holomorphism, with respect to its parameter x. It's clear that for any sequence of holomorphisms g on x, sigma[k=0,inf](g[k](x)*D^k) is a linear operator on the space of holomorphisms. Is this a complete parameterization of the linear...

Can i have help with this linear differential equation ? First, i divided by (1-x^2) to be like dy/dx + p(x)y= q(x). But i could not obtain Q(x). Any help will be welcomed.

Homework Statement A 500g putty ball moving horizontally at 6m/s collides with and sticks to a block lying on a friction-less horizontal surface. If 25% of the kinetic energy is lost, what is the mass of the block? Homework Equations initial (i) = final (f) m1v1+m2v2 = m1v1+m2v2...

Homework Statement Find the general solution of y^{(5)}-y(1)=x The Attempt at a Solution I found the complementary function by substitution of the solution form y=e^{kx} giving k=0,1,-1,i,-i, so y_{cf}=a_0+a_1e^x+a_2e^{-x}+a_3e^{ix}+a_4e^{-ix} Now for the particular integral, the general...

Hi the parameter $\lambda$ in linear integral equations say Fredholm that appears in front of the integral containing the kernel i.e. $y(x)=f(x)+ \lambda \int_{a}^{b} \,k(x,t) y(t) dt $ can $\lambda$ be adjusted for the convergence of the method like in using Picard's successive...

Homework Statement [/B] A uniform cylinder with radius r is rolling down an incline without slipping as shown in diagram below. It's angular acceleration is α and acceleration of it's center of mass C is a. What will be the linear acceleration of point of contact P and another point Q on the...

I have been studying structural physics lately, in particular the linear elastic eqns, governed by the equation of motion. https://en.wikipedia.org/wiki/Linear_elasticity I am trying to solve these equations numerically. I was thinking of a scenario of a rod being compressed on one end by some...

I'm in a bit of a dilemma. At my university, Calc 2 is a prerequisite to Linear Algebra. However, I have been told that it's totally doable to take both at the same time. What do you guys think? Do most universities wave this requirement if you take them concurrently? Thanks!

<Moved from a technical section and thus a template variation> 1-) Question: Let f, g and h be differentiable everywhere functions with h(1) = 2 , h'(1) = - 3 , g(2) = -1 , g'(2) = 5 , f(-1) = 4 , f'(-1) = 7. Approximate the value of function F(x) = f(g(h(x))) at point x= 1.001 2-) My...

I have the linear equation ##a + (2a - b) \sqrt{2} = 4 + \sqrt{2}##. I commonly hear that for linear equations, if we have two variables and one equation, then the system is undertermined and there are infinitely many solutions. However, how does that jive with this example, where there is one...

How do I solve this? Which of the following ordered pairs (x,y) satisfies the system of inequalities below? y>-3x+5 y≤ x-2 Choices: (2,1) (1,4) (4,1) (3,-6) Please. Thanks.

You can work a total of no more than 41 hours each week at your two jobs. Housecleaning pays \$6 per hour and your sales job pays \$9 per hour. You need to earn at least \$252 each week to pay your bills. Are the answers: x+y\le 41 6x+9y\ge252 How would you solve this? Thanks

Hi everyone! So I'm working on project where I have to design a hinge system for a hard lid that is fitted onto the back of a pickup truck. In this system, I will be using 2x linear actuator(s) that will need to lift a total weight of roughly 95kg. At the moment, I've got a selection of 600N...

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...

Homework Statement Find the first-order corrections to energy and the wavefunction, for a 1D harmonic oscillator which is linearly perturbed by ##H'=ax##. Homework Equations First-order correction to the energy is given by, ##E^{(1)}=\langle n|H'|n\rangle##, while first-order correction to the...

Homework Statement [ Homework Equations I found this is about linear quadrupole and these are potential of it. [/B] The Attempt at a Solution So, i solve the problem (a) by using potential. This is what I've done, I'm not sure if it is right though.[/B] And i have no idea how can i...

Homework Statement Homework EquationsThe Attempt at a Solution if there exists a set with 3 vectors, and all of them are linear independent, then by definition no linear combination of the 3 vectors can equal to 0. I believe that's an accurate definition right? So in this case, the answer...

I have two questions over linear and binary serch. 1. Homework Statement Q1: In binary search, after three comparisons have been made, only ___ of the array will be left to search. Q2: The maximum number of comparisons that a binary search function will make when searching for a value in a...

<mod note: moved to homework> Calculate the spectrum of the linear operator ##T## on ##B(\ell^1)##. $$T(x_1,x_2,x_3,\dots)=(\sum_{n=2}^\infty x_n, x_1, x_2, x_3, \dots)$$I think the way to do it is to find the point spectrums of ##T## and its adjoint ##T^*##. But I don't know how to calculate...

Let's say we have a set of eigenvectors of a certain n-square matrix. I understand why the vectors are linearly independent if each vector belongs to a distinct eigenvalue. However the set is comprised of subsets of vectors, where the vectors of each subset belong to the same eigenvalue. For...

Homework Statement Please bear with the length of this post, I'm taking it one step at a time starting with i) Let A: I → gl(n, R) be a smooth function where I ⊂ R is an interval and gl(n, R) denotes the vector space of all n × n matrices. (i) If F : I → gl(n, R) satisfies the matrix ODE F'...

Hi All, I am kind of confused at the fact that Excel uses the measurement of adjusted ## R^2 ## for simple linear regressions ; please see below. What does that even mean, what is the adjustment for?

Homework Statement Find the coordinates of each member of set S relative to B. B = {1, cos(x), cos2(x), cos3(x), cos4(x), cos5(x)} S = {1, cos(x), cos(2x), cos(3x), cos(4x), cos(5x)} I am to do this using Mathematica software. Each spanning equation will need to be sampled at six separate...

Are interpretations that are non linear with respect to the wave function (eg. GRW, transactional) compatible with string theory?

First of all I will use L to denote lambda the parameter of the distribution. X~Poission(nL), n$\in\Bbb{N}$, Y~Poisson(mL),m$\in\Bbb{N}$ with m$\ne$n S= aX+bY a,b real constants. Given observations x and y find the maximum likelihood estimator of L. The problem is I don't know what the pmf...

I have a particle that moves along a circular arc centered at origin in 2D plane. I have the following angular displacement function for time T0 through T3 and the following acceleration and velocity constraints in Cartesian coordinates. At t = T0, theta = 0, velocity = 0. At t = T3, velocity =...

kuruman submitted a new PF Insights post Frames of Reference: Linear Acceleration View Continue reading the Original PF Insights Post.

Okay here's the question: If you sell widgets for 2 dollars, you sell 300 per day. If you sell them for 4 dollars, you sell 200 per day. assume linear relat., between price (x) and # widgets sold per day (y), write linear equation relating x and y I'm thinking I plot the x,y pairs, then...

The answers is b) ab≠1, but I have no clue how to get to that answer... Can someone help me? :D

http://imgur.com/a/xIydC The answers is b) ab≠1, but I have no clue how to get to that answer... Can someone help me? :D

I am taking a linear algebra class, and it has a required lab associated with it. Here is the following problem that I must solve using Matlab 1. Homework Statement Write a function using row reduction to find the inverse for any given 2x2 matrix. Name your function your initial + inv(M), the...

Hey! :o To product a product $3$ square plates $A$ with measures $300\times 500$mm and $2$ square plates $B$ with measures $400\times 600$mm are needed. These plates must be cut out by two different workpieces with measres $1000\times 1000$mm (Type I) and $600\times 1500$mm (Type II). The...

Homework Statement A bullet of mass 0.011 kg is fired at a speed of 850 m/s. It embeds itself in a man of mass 90 kg. a) Find the momentum of the bullet before it strikes the man. b) Assuming it takes 0.1 seconds for the bullet to come to rest after hitting the man, calculate the average...

I am told that the trace function tr(A) is a linear transformation. But this function maps from the space of matrices to the real numbers. How can this be a linear transformation if the set of real numbers isn't a vector space? Or is it? Can a field also be considered a vector space?

I am trying to figure out the interaction terms in the Lagrangian which are linear in the top quark.I find that these terms can only be found in the charged-current interaction since the neutral-current interaction and the gluon-fermion couplings are quadratic in the top quark. Now, I find two...

Sorry If the thread name confuse you. I want to know if I want to find the Torque from deriving Kinetic Energy and the system has Object the Rotate and the rotating cause linear motion(v). Let's say it a Rolling Disc on the non-slope plane which has angular velocity ω and that ω cause it to move...

Homework Statement A mass of 0.5 kg is suspended from a flywheel as shown in FIGURE 2. If the mass is released from rest and falls a distance of 0.5 m in 1.5 s. Mass of wheel: 3kg Outside rad. of gyration of wheel: 300mm Radius of gyration: 212mm calculate: (a) The linear acceleration of the...

Hi everyone. Excuse me for my poor English skills. I did an exam today and my exam result was 13 of 40. I don't understand why it was my result, because while doing the exam I though I was doing it well, then the result was a surprise for me. I will write down the questions and after show my...

Hi everyone. Excuse me for my poor English skills. I did an exam today and my exam result was 13 of 40. I don't understand why it was my result, because while doing the exam I though I was doing it well, then the result was a surprise for me. I will write down the questions and after write my...

Hey! :o A national economy has $3$ sectors: fishing, forestry, boat building. One fishing boat is needed, to catch two tonnes of fish. To produce four tonnes of wood, one tonne of fish is needed to feed the forestry workers. Two tonnes of wood are needed, to build one fishing boat. There...

In particular, I would like a book that explains the theory of function spaces, linear transformations, to explain the ways one can interpret ODEs as linear transformations on function spaces. I need to read up on these for a project in my Intro to Differential Equations class. Any suggestions...