Expression Definition and 999 Threads

Homework Statement A particle has mass m = 0.1 kg , has a velocity which is given as: v = 3.2i+4.3j+5.4k m/s It's acted by force f = 7.1i+8.2j+9.3k The questions which arise are: i) Find the speed of the particle. ii) Write down a unit vector in the direction of the velocity. iii)Find...

Hey folks its me again! The problem at hand gives me a potential energy function ( V(x) ) that defines the height of a particle in motion. Next to the problem is a picture of a curvy graph that is y vs x. It asks to find the expression for the horizontal acceleration. This is what I did...

1. a) Prove the following holds for A A is a matrix [a b, c d] I is identity matrix. A^2 = (a+d)A-(ad-bc)I. b) Assuming ad-bc not equal to 0, use a) to obtain an expression for A^-1. The Attempt at a Solution I proved the first equation, but I'm not seeing where it relates to...

Homework Statement consider the cascading of two non identical amplifiers stages, each having a low-pass STC frequency response. STage 1 has a low freqency gain of ALF1 and a 3 dB frequency of f1. Stage 2 has a low frequency gain of ALF2 and a 3 dB frequency of f2. Derive a polynomial...

Hello, I'm prepping for a course I'm about to take and on the pre-course syllabus it said I should be able to: "Derive the equations for E and H fields in terms of magnetic current source M." It's been a long time since I've had an EM course, so I'm naturally lost. How would I go about...

Homework Statement Using Leibniz rule and integration by parts, solve \frac{\partial}{\partial x} \int_0^y u dy. Homework Equations u = U(x) f' (\eta) \eta = \eta(x,y) = y g(x)

Homework Statement I could not type it here, so i made a screenshot and posted it below. Homework Equations it's about complex numbers undergraduate level. I'm currently doing Euler's formula and De Moivre's theorem, although I'm not sure that the solution lies there. The Attempt at...

Homework Statement What will be the values of 'm' so that the range of the equation y= \frac{mx^2+3x-4}{-4x^2+3x+m} will be all real values i.e. y\epsilon (-\infty,\infty)given:x can take all real values. any help or hint will be appreciated. Homework Equations The Attempt at a Solution i...

The question states: Determine the negation of the expression. p -> q ^ r. I am having difficulty finding the negation. Below are the steps I have taken in an attempt to come to the solution. The - symbol will be the negate symbol. p -> q ^ r (-p OR q) ^ r -(-p OR q) ^ r...

Homework Statement 2/1+y-2 /2x^3+x its all over top of 2x^3+x Homework Equations The Attempt at a Solution should i multiply the top by 1+y, like the 2 and the -2.

Homework Statement simplify each expression: 2(4-h)^2-32/h Homework Equations The Attempt at a Solution I forget if I should multiply the 2 into the 4-h.

When we refer to terms in an equation, what EXACTLY are we referring to? Suppose for example we have: ab + bc + cd = A Suppose somebody refers to term "ab". Are they referring to the syntactical NAME "ab", the IMAGE of ab (i.e., it's value), or the ARGUMENT (a,b) which belongs to some...

[b]1. Homework Statement The swinging period T(θ) for a small amplitude simple pendulum, is given by T, a constant for a constant length pendulum. If the initial angle θ is large, then the amplitude becomes large and the period needs to be corrected. The correction to the large amplitude...

I have studied in my lower grades that work(w) done or energy is the product of force(f) and displacement(s).Till now I was thinking that this was true. I was not taught that it was the dot product of force and displacement. according to this definition, the work done when the force and...

"Scientific Thinking Graphing" -Determining the Mathematical Expression Homework Statement Ok, so I recently got an assignment for "Scientific Thinking Graphing Practice". Basically, I need to take a data table that will produce a curve shaped graph and turn it into a straight lined graph...

Homework Statement A square loop with side-length a is positioned at the centre of a long thin solenoid, which has radius r (with r > a), length l and N turns. The plane of the loop is perpendicular to the 5axis of the solenoid. A current I = I0 sin ωt flows through the loop. Derive an...

Homework Statement k(x) = x^2(2x^3+x)^1/3 Homework Equations I used the product rule and the chain rule to get to the point that i did. The Attempt at a Solution dy/dx(x^2)(2x^3+x)^1/3 + dy/dx(2x^3+x)^1/3(x^2) = (2x)(2x^3+x)^1/3 + 1/3(2x^3+x)^-2/3(6x^2+1)(x^2) I can't...

Homework Statement The series, 1 / (1 x 2) + 1 / (2 x 3) + 1 / (3 x 4) + ... + 1 / [n(n + 1)] + ... is not a geometric series. (A) Use the identity 1 / [k(k + 1)] = 1 / k - 1 / (k + 1) to find an expression for the nth partial sum Sn and (B) use it to find the sum of the...

Suppose a particle in frame S moves with acceleration a_{x} and velocity u_{x} at a given instance in the x-direction. I wanted to find the acceleration in a frame S' moving with velocity v in the positive x-direction with respect to frame S. To do this I used the following approach...

Homework Statement Find the vertical asymptote, if there is one, of this rational function. \frac{\sqrt{16x^2 + 3x + 6} -5}{x-1} Homework Equations The Attempt at a Solution This was actually a Calculus problem, I had to find the limit at infinity. I was able to do that easily; an extra...

Homework Statement \frac{d^2y}{dx^2} + (y^4-1)\frac{dy}{dx} = 0 Homework Equations \frac{dy}{dx} + (y^4-1) = 0 The Attempt at a Solution \frac{dy}{dx} = (1- y^4) \frac{dy}{1- y^4} = dx Then I get a horrible expression involving logs and inverse tan functions...

Homework Statement If a polygon has n>=4 sides, what is the probability, in terms of n, that a triangle made up of vertices of the polygon shares at least one side with the polygon. Homework Equations The Attempt at a Solution Treating vertices of polygons as possible outcomes...

Homework Statement (-3/x^(1/2)) / ((2/y^(1/2))-8) which, from my book, I see can be rewritten with radicals as: (-3/sqrt(x)) / ((2-8sqrt(y))/(sqrt(y)))The Attempt at a Solution Now, what I don't understand is how the denominator was rewritten. I understand that in the numerator, the 1/(...

My higher secondary book says that momentum[p] is equal to 'mv' where 'm' is mass and 'v' is velocity.Then it was also mentioned that the force[f] was dependent on the rate of change of momentum{[delta]p= m*[delta]v}. Though the book mentions various examples to support that momentum plays a...

lim as x -> 0, [(x+4)1/2-2]/x That's the limit I want to evaluate. I keep running into problems getting to the real limit (1/4). You don't have to give me the answer, but let me know if I'm missing something simple. Or you can just give me a hint.

I'm trying to find the general form for the nth derivative of f(x) = \frac{1}{x^m \log x} where m can be anything (set m = 1 for instance). For ease, you can take m to be integral. It sounds surprisingly simple, but the most I've been able to say is f^{(n)}(x) = (-1)^n x^{-(m+n)}...

Homework Statement n(n+3)(n+6)(n+9)=x-81 Show that x is a squared expression Homework Equations These are some examples they give you: 0*3*6*9=92-81 1*4*7*10=192-81 2*5*8*11=312-81 The Attempt at a Solution To be honest, I have know idea where to start. So, I'd like a push in...

Homework Statement Show that the change in internal energy of a simple system between states (V1, T1) and (V2, T2) is given by ∆U = \int^{T1}_{T2} C_v\ dT + \int^{V1}_{V2} T.\frac{\partial p}{\partial T}|_V - p \ dVHomework Equations dU=dQ-pdVThe Attempt at a Solution As U is a function of...

Hi, I'm getting used to the anti-symmetric bracket notation used with indices and I can't seem to find the Weyl Tensor written fully out. So I want to make sure I get it. Here is my attempt in dimension 4...

My problem is this: I have an algebraic expression, and I want to express it in terms of one variable divided by another. It's a fairly large expression, and I'd like to do it in mathematica before attempting it by hand. I've tried Simplify, FullSimplify and Solve, but none of these have done...

Hi,i ve problem about C.i should write a program that read expression from standart input take derivative and print. For example: input: (X^2-1)*tan-ln^2/X output: (((X*2)*tan+(tan^2+1)*(X^2-1))-(1/X*ln*2*X-ln^2)/X^2) I converted expression to postfix form by shuting...

Homework Statement \frac{d}{dx} x+\sqrt{x} Using the definition of a derivative, no rules allowed. Homework EquationsThe Attempt at a Solution \frac{d}{dx} x+\sqrt{x} \lim_{h\to0} \frac{(x+h)+\sqrt{x+h}-x-\sqrt{x}}{h} \lim_{h\to0} \frac{(x+h)+\sqrt{x+h}-x-\sqrt{x}}{h} \lim_{h\to0}...

Homework Statement Construct a circuit from the Boolean equation: Homework Equations P v (~P ^ ~Q) The Attempt at a Solution According to the textbook, I am supposed to go from right to left, working on the outermost part of the expression to the innermost part. I read this as...

I must construct a circuit from the following Boolean expression: P v (~P ^ ~Q) From my understanding I am supposed to go from right to left, working on the outermost part of the expression to the innermost part. I read this as saying even though the outermost part of the expression is on...

Homework Statement The plastic rod of length L shown in the figure has the nonuniform linear charge distribution λ =cx, where c is a positive constant. Find an expression for the electric potential at point P on the y-axis, a distance y from one end of the rod. V = ?Homework Equations V = 1/4πϵ

Is this expression (-5+12√3)/26 the same as (12-5√3)/26 ? Thanks

Homework Statement If n is an integer which leaves remainder one when divided by three, then (1+√3i)n + (1-√3i)n equals a) -2n+1 b) 2n+1 c) -(-2)n d) -2nThe Attempt at a Solution Multiply and divide each of the two expression inside bracket by 2. 2n(cosπ/3 + isinπ/3)n + 2n(cosπ/3-isinπ/3)n On...

Homework Statement For the following circuit, obtain an expression for the capacitor voltage, vC(t), for time, t (greater than or equal to) 0 if vs(t) = 10 V and vC(0) = 2 V. Homework Equations KVL Definite integrals, differentiation etc The Attempt at a Solution Right so I...

I need some help. I don't know how to make the intgral symbol, but here's the question. If somebody can get it started it'd be awesome. 1to e^10 1to e^6 1to e^2 1/xyz dxdydz

Homework Statement From Prussing and Conway (Q1.11): derive an expression for the eccentricity e in terms of the initial speed v, radius r, and flight path angle x (they use gamma). Homework Equations (1) h^2 = mu*a*(1-e^2) [a is semimajor axis, mu is gravitational parameter] (2) h =...

If a and b are real numbers, and we know that (2a-b-3)^{2} + (3a+b-7)^{2}=0, how much is 3a-7b Any ideas on this? I'm guessing the solution can go two ways: either i find a and b separately, or i calculate the expression above somehow and i'll be left with 3a-7b

Homework Statement x^2 + x + \frac{1}{4} Homework Equations This should be written in the form: (x+y)^2 Just to add a bit more info, the exercise is to "Write each of the following as the square of a binomial expression". So basically the book teachs to take the rook of x^2 and 1/2...

Hi guys, I am hoping you can either point me in the right direction here or show me how to do this a bit. the problem is as follows: "a particle with weight 86.8 N is positioned at r= (8.1t)i - (7.2t-9.4t2)j. t is in seconds. Find an expression for angular momentum, L and torque, T which act...

Homework Statement Find an expression for x(t) and plot on graph T < 0 < 3T v = 4 for t < 0 = 1 for t >= 0T is time const. Homework Equations Voltage across capacitor cannot change instantlyThe Attempt at a Solution Well the transfer equation is \frac{X}{Y}(jw) = \frac{2+jwC}{1+jwC}...

Homework Statement find the minimum value taken by the integral expression integral from 0 to pi/2 [(y')^2]-(y^2)+2xy dx y(0)=0 y(pi/2)=pi/2 The Attempt at a Solution using euler lagrange d/dx(2y')-(-2y+2x)=0 2y''+2y-2x=0 from here I'm stuck

Homework Statement The potential energy of a system of two particles is inversely proportional to their separation, d. Find an expression for the radial force that each particle exerts on the other. Homework Equations The Attempt at a Solution I'm really stuck on this one guys...

Homework Statement I'm trying to derive the \epsilon - NTU Expression for a double-pipe counter flow heat exchanger. I know what I need to do the only problem I am having is: I don't know how to algebraically go from ln( \frac{\Delta T2}{\Delta T1} ) = -UA ( \frac{1}{Ch} + \frac{1}{Cc} )...

I am working through a problem from a Fluid Dynamics course and I have gotten to a point on a problem where it says to "… expand the resulting expression for small values of a2/(bz) and for small z/b … " I am not so sure how to interpret this? The expression that I am supposed to expand is...

Hello, I have this expression: 2(x-3)(x+2) + (x-3)^2 It is simplified to: (x-3) (2x+4+x-3) I understand how the (x-3) has been separated to start the simplification process, but I cannot grasp how the rest was done. Can someone please tell me the rest was simplified ? Thanks...

very sorry, this does not belong in this forum.