Inverse Definition and 1000 Threads

Homework Statement I need to prove that Q[√2,√3] = \{a+b√2+c√3+d√6: a, b, c, d \in Q\} is a field. Homework Equations The Attempt at a Solution I proved all axioms except the existence of inverses for nonzero elements. My problem is that multiplication is quite hairy. I ended up...

Homework Statement I have some problem finding the inverse laplace transformation of the function: \frac{s}{s^2+2s+5} Homework Equations http://math.fullerton.edu/mathews/c2003/laplacetransform/LaplaceTransformMod/Images/Table.12.2.jpg The Attempt at a Solution I tried to...

hey guys can you help solve this problem. $\displaystyle\int\frac{dx}{\sqrt{2x-x^2}}$ i know that i have to change the integrand into this form $\displaystyle\frac{du}{\sqrt{a^2-u^2}}$ can you please show me how. thanks!

Homework Statement I have that X is distributed with Gamma(a,b) and that Y = \frac{1}{X}. I found the pdf of Y to be \frac{1}{\Gamma(a)b^a} \left(\frac{1}{y}\right)^{a+1} e^{-1/yb} for y > 0. I need to use this to find the expected value. Homework Equations The gamma function is...

f(x)=(x^5)/x^2+6 and f(x)=2x^3-4x I tried x=(y^5)/(y^2+6) then x(y^2+6)=y^5 but idk after and y=2x^3-4x then idk what to do

Homework Statement The nonlinear, inherently unstable inverted pendulum is shown in Figure 1.15. The goal is to maintain the pendulum angle θ(t) = 0 by using a feedback controller with a sensor (encoder or poten- tiometer) for θ(t) and an actuator to produce an input force f (t). The...

Homework Statement I have two questions sin2x = 1/25 and this obviously becomes sinx= +-(1/5) I also have cos2-1.5cosx-0.54 and cosx = (-3/10) and (9/5) Now this is asking for me to solve for the x value in radians in the domain [0,2pi] and I have no idea how to solve these for exact values...

Homework Statement I'm stuck trying to find out the inverse Laplace of F(s) to get y(t) (the solution for the differential equation): Y(s) = 1 / [ (s-1)^2 + 1 ]^2 The Attempt at a Solution I tried using a translation theorem and then apply the sine formula, but the denominator...

Quoting from Wiki, bolded section mine: What exactly is going on here with the data rate? Is it just the strength of the signal that is falling off as distance increases? If so, how does that reduce the data rates that can be used? If not, what limits the data rates?

I need some help understanding inverse functions, we've had a 4-page chapter covering the basics of inverse functions and I understand that. But now we have suddenly gotten these task that I don't understand how to solve, I've read the part on inverses several times, but I still don't...

Within certain branches of analysis - both real and complex - the Inverse Tangent Integral (and its generalizations) can be quite useful. Similarly, it's much less well-known (= uglier? lol) cousin, the Inverse Sine Integral can be used to solve many problems. To that end, this is not really a...

1. Homework Statement A permanent electric dipole consisting of charges +q and -q separated by the fixed distance s. Charge +Q is distance r from the center of the dipole. We'll assume s << r. a) Use the binomial approximation (1+x)-n ~= 1-nx if x << 1 to show that the net force exerted...

q)give the converse ,the contrapositive and inverse of these conditional statements a)if it rains today,then i will drive to work b)if |x|=x then x>=0 c)if n is greater than 3,then n^2 is greater then 9

i know when you are dealing with limits you can take the inverse to fit the standard limit equations. how about integrals? can u take the inverse for instance: integral(f(x)dx) turn it into integral((1/f(x))dx)^-1) get the answer and then reverse it back? when can u or can't you take...

1. Which of the following is a group? To find the identity element, which in these problems is an ordered pair (e1, e2) of real numbers, solve the equation (a,b)*(e1, e2)=(a,b) for e1 and e2. 2. (a,b)*(c,d)=(ac-bd,ad+bc), on the set ℝxℝ with the origin deleted. 3. The question...

How does this work? I'm very confused about the phi is solved using inverse sin. knowing: A=(c^{2}_{1}+c^{2}_{2})^{1/2} and c_{2}= Acos(\phi) solve for \phi which yields: \phi=sin^{-1}\frac{c_{2}}{(c^{2}_{1}+c^{2}_{2})^{1/2}}=tan^{-1}\frac{c_{2}}{c_{1}} I'm not sure how we use the inverse...

Homework Statement Evaluate ∫(x^2-4)^(1/2) / x for x > 2 Homework Equations The Attempt at a Solution I was able to solve this problem via substitution, and my answer is: (x^2-4)^(1/2) - 2arcsec(x/2) + C. However, when I put the question into Wolfram Alpha, it gets this...

Homework Statement The problem can be found in Jackson's book. An infinitesimal Lorentz transform and its inverse can be written under the form ##x^{'\alpha}=(\eta ^{\alpha \beta}+\epsilon ^{\alpha \beta})x_{\beta}## and ##x^\alpha = (\eta ^{\alpha \beta}+\epsilon ^{'\alpha \beta})...

Homework Statement I have to turn this homework in online... I just want someone to check my work Convert from Cartesian coordinates to Polar coordinates (-1,-sqrt(3)) if r > 0 and if r < 0. Homework Equations The Attempt at a Solution if r > 0 then I believe the answer is...

I am reviewing some material on Laplace Transforms, specifically in the context of solving PDEs, and have a question. Suppose I have an Inverse Laplace Transform of the form u(s,t)=e^((as^2+bs)t) where a,b<0. How can I invert this with respect to s, giving a function u(x,t)? Would the inverse...

hi all, I have a TEC data and I got this TEC = \intNe ds How can I inverse this equation to get data for Ne. Thank you

I know the inverse of a function is found in two steps. Isolate the independent variable and then switch the variables like this: [y = x^{3} +1] = [x = \sqrt[3]{y - 1}] Then switch the variables to get: y = \sqrt[3]{x-1} However, when it comes to finding the derivative of the...

f(x) where x belongs to all real numbers inverse: f-1(x), where x belongs to all real numbers True or False: The inverse of f(x+3) is f-1(x+3) My ideas: I think that it is false given that when you usually find the inverse of a function, you switch the x and y variables and solve for y again...

Homework Statement Find the inverse of f(x)=ln(x^3-3x^2+3x-1) Homework Equations n/a The Attempt at a Solution y=ln(x^3-3x^2+3x-1) x=ln(y^3-y^2+3y-1) e^x=(y^3-y^2+3y-1) i looked around for inverse of cubic functions and i found a monster of a formula...

Homework Statement Find the inverse Laplace transform of e^(-3pi*s)/(s^2+2s+3). Homework Equations I know that you're supposed to factor out the e^(-3pi*s) and the other part becomes 1/(s+1)^2+2 but how do you get the answer? I'm confused. The Attempt at a Solution The answer is...

Homework Statement Which of the following is the solution set of the equation $$2\arccos(x)=\text{arccot}\left(\frac{2x^2-1}{2x\sqrt{1-x^2}}\right)$$ A)(0,1) B)(-1,1)-{0} C)(-1,0) D)[-1,1] Ans: A Homework Equations The Attempt at a Solution I start by rewriting LHS in terms of ##\arctan##...

Homework Statement The sum of the infinite terms of the series \text{arccot}\left(1^2+\frac{3}{4}\right)+\text{arccot}\left(2^2+\frac{3}{4}\right)+\text{arccot}\left(3^2+\frac{3}{4}\right)+... is equal to A)arctan(1) B)arctan(2) C)arctan(3) D)arctan(4) Ans: B Homework Equations The Attempt at...

Homework Statement I'm wondering how to find the inverse function of some f(x,y)? Homework Equations The Attempt at a Solution

Homework Statement Find the Inverse Laplace Transform of \frac{1}{(s^{2} + 1)^{2}} Homework Equations The Attempt at a Solution I tried using partial fractions but it didn't work. It looks like a cosine transform, but I don't know what else to do. Help please :(

Homework Statement Find the inverse Laplace transform of F(s)=(8s^2-4s+12)/(s(s^2+4)). Homework Equations A/s+(Bs+C)/(s^2+4) 8s^2-4s+12=A(s^2+4)+(Bs+C)(s)=As^2+4A+Bs^2+Cs=s^2(A+B)+Cs+4A 8=A+B C=-4 A=3 B=5 L^-1 (3/s)+L^-1 ((5s-4)/(s^2+4)) =3+ (Now I'm stucked.) The Attempt...

Basically I don't know anyone in real life that can help me with this, so I need help checking to see if my answers are correct :) Part B 2) Given the functions f(X) = 7x^2 - 5x and g(x) = 2x - 3 determine and simplify the following: a) (f-g)(x) My Answer: 7x^2 - 7x - 3 b) (f - g)(2) My...

Homework Statement Find the inverse Laplace transform of F(s)=(2s-3)/(s^2-4). Homework Equations I don't want to find the answer by looking at the Table. F(s)=2s/(s^2-4)-3/(s^2-4) The Attempt at a Solution The answer is f(t)=2 cosh 2t - (3/2) sinh 2t.

Hi I have a question regarding differentiation of inverse functions that I am not capable of solving. I want to prove that \frac{\partial}{\partial y} h_y(h^{-1}_{y_0}(z_0))\bigg|_{y=y_0} = - \frac{\partial}{\partial y} h_{y_0}(h^{-1}_{y}(z_0))\bigg|_{y=y_0}, where h_y(x) is...

Hello, I have the following matrix of matrices \mathbf{H}=\begin{array}{cc}\mathbf{A}&\mathbf{B}\\\mathbf{B}^H&\mathbf{A}\end{array} where each element is a square matrix, A is a diagonal matrix of real numbers, whereas B is not (necessarily), and the superscript H means conjugate transpose...

Write the inverse, converse, and contrapositive of the following statement: upside down A x E R, if (x + 2) (x - 3) > 0, then x < -2 or x > 3 Indicate which among the statement, its converse, its inverse, and its contrapositive are true and which are false. Give a conterexample for each that...

Let $$f(x) = k\ log_2 x$$ (a) Given that $$f^{-1}(1)=8$$, find the value of $$k$$ to get $$f^{-1}(x)$$ exchange $$x$$ and $$y$$ $$x=log_2 y^k$$ then convert to exponential form $$2^x=y^k $$ then $$2^{\frac{x}{k}} = y$$ so for $$f^{-1}(1) = 2^{\frac{1}{k}}= 8=2^3$$ then...

Do we have identities for the following $$\arctan(x+y) = $$ $$\arctan(x)-\arctan(y) = $$

Let's say we have a one dimensional single particle system that is described by a SE -\frac{\hbar^{2}}{2m}\frac{d^{2}}{dx^{2}}\psi(x)+V(x)\psi(x)=E\psi(x) We do not know what the potential energy function V(x) is, but we know that the eigenvalues spectrum is E_{n}=kn^{\frac{3}{2}}...

"All engineers have practical skills or are good at mathematics" to write down the converse, inverse and contrapositive for the above statement, I have to find the hypothesis and the conclusion of the statement. but how? is there any other way to write converse, inverse and contrapositive...

Checked around a buch and could not find any help. But I needed help with: Understanding that if I get the Inverse FT of K-space data, what is the scaling on the X-space (object space) resultant image/data i.e. for every tick on the axis, how do I know the spatial length? More detailed...

Having difficulty with L-1 {1/(s^2+s-20)}: Should I make it L-1 {1/(s+5)(s-4)}? I'm stuck.

Homework Statement Let L: V →V be a linear mapping such that L^2+2L+I=0, show that L is invertible (I is the identity mapping) I have no idea how to solve this problem or how to start,I mean this problem is different from the ones I solved before, the answer is "The inverse of L is -L-2 "...

what is the inverse laplace transform of (2s)(1/(s-2))? could i use the identity ∫f(T)g(t-T)dT=F(s)G(s)? i was hesitant so i figured i'd just ask before i continue..

Hi there, I'm learning about solitons and chanced upon this pdf talking about the inverse scattering method. However, I'm stuck trying to derive the coefficients using the LAX method (pg 5 of the attached pdf or from http://arxiv.org/pdf/0905.4746.pdf). Hope that someone can help shed some light...

If one has the mean and standard deviation of a population, is it possible to calculate (or estimate) the mean and standard deviation of the inverse population (ie. 1/(every value in the original population)? Thank you!

I can find inverses using an adjust for a 3X3 matrix. But My homework book asks us to find the inverse using an adj(A) for a 4x4 matrix. 1 3 1 1 2 5 2 2 1 3 8 9 1 3 2 2 it seems less time efficient to find the inverse using this method. Is it possible to reduce the matrix to a a simpler yet...

I have sets of 2d vectors to be transformed by an augmented matrix A that performs an affine transform. Matrix A can have values that differ at most |d| from the identity matrix, to limit the transformation, meaning that the min/max bounds for A are I_3 \pm dI_3 The problem is that i'd lke...

Is there a way without using the algorithm to find A-1 of a square matrix greater than 2x2? The question we are given in the books is: [-25 -9 -27] [536 185 537] [154 52 143] We are asked to find A-1 of the second and third column without computing the first column. (Sorry...

Homework Statement Find inverse of each. 1. y<x+1 2. y=2x/(x-2) Homework Equations Switch y and x? The Attempt at a Solution For 1. I switched y and x, so x<y+1. Do I have to switch the sign also? For 2. I switched y and x, so x=2y/(y-2). But I have to express the inverse...

Homework Statement Find the inverse Fourier transform of F(jω) = cos(4ω + pi/3)Homework Equations δ(t) <--> 1 δ(t - to) <--> exp(-j*ωo*t) cos(x) = 1/2 (exp(jx) + exp(-jx))The Attempt at a Solution So first I turned the given equation into its complex form using Euler's Formula. F(jω) = 1/2...