Simplify Definition and 373 Threads

During solution of a PDE I came across following ODE ## \frac{d \bar h}{dt} + \frac{K}{S_s} \alpha^2 \bar h = -\frac{K}{S_s} \alpha H h_b(t) ## I have to solve this ODE which I have done using integrating factor using following steps taking integrating factor I=\exp^{\int \frac{1}{D} \alpha^2...

Hello everyone! I have this expression which I have to simplify: ∑i=1log(n) 1(log(n) - i) And my book apparently simplifies it to being log(n). I am struggling to figure out why this is the case. Could anyone help? Thanks!

Homework Statement I have to prove that the expression $$\frac{\omega C - \frac{1}{\omega L}}{\omega C - \frac{1}{\omega L} + \omega L - \frac{1}{\omega C}}$$ is equal to $$\frac{1}{3-( (\frac{\omega_r}{\omega})^2 + (\frac{\omega}{\omega_r})^2)}$$ where ##\omega_r= \frac{1}{\sqrt{LC}}##...

What exactly does it mean to simplify an expression. I understand that an expression becomes more simple when you combine like terms but what other conditions are there? Is x(5x+1) more or less simple than 5x^2 +x? Do square roots need to be moved to the numerator?

Homework Statement The answer in (algebraic form) is Homework EquationsThe Attempt at a Solution I'm not sure how to simplfy into the form required from here.

Hi I am to calculate Rab of the circuit and I have no idea on how to approach this problem. It would have been all nice and eaasy if it weren't for the vertival 30 ohm resistor. Because of this I'm in a dark spot. I will appreciate any help.

Hey guys, I am seriously confused by this problem. 3/4 [ 5/6 ( -18/25 ) + 1/2 ] I would appreciate it if someone shows me the step by step process. Thanks in advance :)

Homework Statement I need to simplify the following integral $$f(r, \theta, z) =\frac{1}{j\lambda z} e^{jkr^2/2z} \int^{d/2}_0 \int^{2\pi}_0 \exp \left( -\frac{j2\pi r_0 r}{z\lambda} \cos \theta_0 \right) r_0 \ d\theta_0 dr_0 \tag{1}$$ Using the following integrals: $$\int^{2\pi}_0 \cos (z...

Hello. I have been looking into trigonometric identities that helps to simplify a question in mathematics. But the question that I have is, why do I need to simplify a question? For instance: Sin(x) * Cos(x) means Sin(2*x)/2. I have no answer that tells me why I simplify Sin(x) * Cos(x) to its...

]Homework Statement Solving the cubic equation x^3 + 6x = 20 by using formula gives (10+ sqrt(108))^1/3 - (-10 + sqrt(108))^1/3 How do you show that this comes out exactly 2? No calculators allowed.Homework EquationsThe Attempt at a Solution Tried cubing the expression and tried using the...

Simplify sqrt{12x^7} Solution: sqrt{4•3•x^6•x} 2x^3(sqrt{3x}) Is this correct? Note 1: According to wolfram, the answer is 2sqrt{3}•sqrt{x^7} Note 2: The term x^3 in my answer comes from the breakdown of sqrt{x^7} as sqrt{x^6•x}. Isn't sqrt{x^6} the same as x^3?

Homework Statement Hello! Please, take a look at the following equation and help me to understand where the authors got the value of φ = π/3. I don't see where it is derived from as no additional conditions are given. Homework Equations x(t) = 5e(-t/5) cos(t) + 5e(-t/5) √3 sin(t) The...

Homework Statement ##G_{OL} = \frac{5}{s}## ##G_{CL} = \frac{KG_{OL}}{1+KG_{OL}}## Homework EquationsThe Attempt at a Solution It's pretty easy when the equation is so simple ##G_{CL} = \frac{K\frac{5}{s}}{1+K\frac{5}{s}}## ##G_{CL} = \frac{5K}{s+5K}## If the open loop equation is really...

Homework Statement The Attempt at a Solution The way i have simplified it: I do not know it is the way to do it. But if so, now I need to give the answer in cartesian form, and I think I need to use the formula: meaning it will look like: Anyone who can tell me if I am on the right...

Let's say I have two vector fields a(x,y,z) and b(x,y,z). Let's say I have a scalar field f equal to a•b. I want to find a clean-looking, simple way to express the directional derivative of this dot product along a, considering only changes in b. Ideally, I would like to be able to express...

Hi, I have ## 120 \sum \limits_1^\infty (\sigma_{3}(n))^{2} ## , where ## \sigma_{3}(n) ## is a divisor function. And I want to show that this can be written as ##120\sum \limits_{k=1}^{n-1} \sigma_{3}(k) \sigma_{3}(n-k) ## I'm pretty stuck on ideas starting of to be honest, since the sum is...

Can anyone simplify any of these questions?

Homework Statement http://prntscr.com/cpbr3f Homework EquationsThe Attempt at a Solution If I were to simply plug in 25 into the limit, i would get ((25)^(1/3) - 5)/25 Apparently the answer is 2/5. How the heck can you come to this conclusion?

What I mean by this is that I'm looking to see if there's any sort of software out there that has formulae that it "knows" and can reduce/expand back and forth for you. A simple example would be that I type "I*R" and it gets simplified to "V" using this software, or vice versa. I understand...

The problem I have been trying to solve a long problem but my answer differs from my books answer with just a few peculiar terms. My answer: ##x_1' \vee x_0'x_1x_2 \vee x_0x_1'x_2' \vee x_2## Book: ##x_1' \vee x_2 ## My question is: Is it possible to simplify ##x_0'x_1x_2 \vee...

Homework Statement I have to do nodal analysis and I was wondering if there is any transformations or simplifications I can do to the circuit. In this class we are supposed to be able to look at the circuit and input what we need into the matrix based on just looking at it. I am not sure that I...

Homework Statement I posted the entire question, but I am only conserned with part B. There was a circuit drawing on there but it is irrelevant for this part of the problem. One can solve it without knowing the circuit drawing. Homework Equations The application for Kirchoff's Voltage Law...

Hey everyone, I am in a discrete math course, and I was reading pre-reading the textbook (Discrete Mathematics with Applied Applications by Epp 4th Ed.), but didn't understand their example, I don't understand, specifically, the distributive portion. I don't see how they distributed it like...

Homework Statement I want to know how he simplified this expression to tan (theta) Homework EquationsThe Attempt at a Solution

lim_(h->0^-) (e^(x+h)/((x+h)^2-1)-e^(x+h)/(x^2-1))/h = -(2 e^x x)/(x^2-1)^2 I know how to differentiate the expression using the quotient rule; however, I want to use the limit definition of a derivative to practice it more.This desire to practice led me into a trap! Now I just can't simplify...

Hi, I have worked the problem but I am not sure that this is the correct answer, Please help. 3(-3) - (5)2^2 ____________ 8- SQRoot(36) +12 I got an answer of 11/14 but When I check on an online calculator to see if it is correct I am getting 5.5 ... 2^2 = TWO SQUARED SQRoot = Square...

When using the double integration method to solve for deflection, do you simplify the integral before integrating or do you just integrate it? When i tried it with simplifying and without simplifying, I get a different value for the constant which results in different answers. For example in...

I heard that if Aether was real it would simplify many things in science, what exactly would it simplify?

Simplify. Assume that $n$ and $m$ are positive integers, $a>b$, and $a>2$.$\frac{\left(a+1\right)!}{\left(a-2\right)!}$ was helping a friend with this but was clueless I know that n! $=n(n-1)(n-2) ... $

hi..how can i simplify this..i tried on mathematica but i am getting nothing but the same expression\noindent\(\pmb{-e^{-x} \left(1-e^{-x}\right)^{-1+\beta } \left(1-\left(1-e^{-x}\right)^{\beta }\right)^{-1+\text{$\alpha $1}+\text{$\alpha $2}} \left(-1+\left(1-\left(1-e^{-x}\right)^{\beta...

I would like to simplify this equation. It contains the same value of the outside and inside the exponential. how to simplify more it more.

Let f(x)=-4x+5. Find and simplify f(3a-4) I have the answer, but I don't know how to get there. Missed it on a test. Answer= = -12a+21

Homework Statement The sides of the biggest square have resistance ##R## and length ##L## (the amount of resistance in the wire is equal to the length), the smaller square is placed so that it's corners intersect midway through the sides of the larger square. Find the resistance between...

Homework Statement To simplify: ##\mid \vec b -\frac{\vec a*\vec b}{\vec a*\vec c} * \vec c \mid## ##\mid \vec b -\frac{(\vec a*\vec c)*(\vec b*\vec b)-(\vec a*\vec b)*(\vec b*\vec c)}{(\vec a*\vec b)*(\vec c*\vec c)-(\vec a*\vec c)*(\vec b*\vec c)} * \vec c \mid## Vectors may be any...

Homework Statement Simplify: 1/k [(k-1) x_n+ x^k/(x_n^(k-1) )]- 1/k [(k-1)x+ x^k/x^(k-1) ] where e_n = x_n - x x_n means x subscript n e_n means e subscript n It might be easier to look at the picture I typed out in MS Word...

Can someone please show me, step-by-step, how cos(θ)sin(θ+φ)-sinθcos(θ+φ) simplifies to sinφ? I know I have to use trig identities, and I got to cos2θsinφ-sin2θcosφ but I'm not sure where to go from there. Thanks

I don't understand why my instructor simplified this problem like he did. I get how we took out the square for the (e^t + e^-t)^2, but what happened to the 2 under the square root. Pic of solution is attached

Hey guys, I know it's pretty simple but after an hour of thinking on it i just can't get how to simplify this. Can someone help me? Thank you in advance!

Homework Statement Simplify (1/3 + 1/3y)/(1/y + 1/3) Homework Equations (1/3 + 1/3y)/(1/y + 1/3) = x In this case I am using x to represent the simplified expression The Attempt at a Solution (1/3 + 1/3 * 1/y)/(1/y+1/3) = (2/3 * 1/y)/(1/y + 1/3) = (2/3y)/(1/y+1/3) = (2/3y)/(3/3y + y/3y) =...

Homework Statement Q7.[/B] a) Express x^(n-1)⋅³√(y^2/2x^5) in its simplest, rationalised surd form. b) Given that the solution to part a) is 5, and that y can be expressed as 1/x^(6n+5)/4), determine the value of x. Again, express your answer in rationalised surd form. *Note, this is a...

< Mentor Note -- thread moved to HH from the technical math forums, so no HH Template is shown > cos(x-y)=ysinx My attempt: -sin(x-y(x'-y')=y'cosx.x' Yeah I'm stuck.. I know it is differentiation of implicit functions and I need to make y' the subject of the formula.

y=##sin^{-1}(\frac{x-1}{x+1})## My attempt: ##\frac{dy}{dx}## = ##\frac{1}{\sqrt{1-(\frac{(x-1)}{(x+1)})^2}}## . ##\frac{d}{dx}(\frac{x-1}{x+1})## = ##\frac{1}{\sqrt{(\frac{(x+1)^2-(x-1)^2}{(x+1)^2}}}## . ##\frac{(x+1)(1)-(x-1)(1)}{(x+1)^2}## = ##\frac{x+1}{\sqrt{x^2+2x+1-x^2+2x-1}}## ...

Homework Statement 3∜2 - ∜(2/81) + ∜32 - ∜162 Homework EquationsThe Attempt at a Solution 3∜2 - ∜(2/81) - ∜130 3∜2 – ∜2/3 - ∜130 exactly when i tried to calculate, i got problem with the next of this calculating, i confused. Can anybody help me for do the next of this calculating??[/B]

##m*\frac{G*16*π*ρ*ω}{c^2}*\int_{a_0}^{a_{1}}(da*a*\int_{y}^{H+y} (\int_0^R (\int_0^{2*π} (\frac{(r-a*Cos(α))*r^2}{(a^2+r^2+h^2-2*r(a*Cos(α)))^{3/2}}* dα)dr)dh))## This equation is related with this post https://www.physicsforums.com/threads/gravitomagnetic-experiment.824048/. It where helpful...

I would want to change this expression to another one that would have P easily accessible. \frac{\left \lceil (n+1)^{P} \right \rceil}{\left \lceil n^{P} \right \rceil} As an example of 'accessible'; given (n+1)^P / n^P, I can make P more accessible by using log(). Then it becomes P *...

Is there a way to simplify the proof of different vecot calculus identities, such as grad of f*g, which is expandable. And also curl of the curl of a field. Is there a more convenient way to go about proving these relations than to go through the long calculations of actually performing the curl...

$A=(\dfrac {1\times 4+\sqrt 2}{2\times 2-2})\times (\dfrac {2\times 5+\sqrt 2}{3\times 3-2})\times(\dfrac {3\times 6+\sqrt 2}{4\times 4-2})\times --------\times (\dfrac {2015\times 2018+\sqrt 2}{{2016}\times {2016}-2})$ please simplify $A$

A friend and I have been working on this problem for hours - how can the following expression be simplified analytically? It equals $\frac{1}{2},$ and we have tried the following to no avail: 1. Substitution of $x = \sqrt{5}$ 2. Substitution of $x = 2\sqrt{5}$ 3. Substitution of $x =...

Homework Statement [/B] I feel like I'm missing some theorem which is preventing me from finalizing this problem! It's been driving me nuts I feel like I'm missing something super basic! Ultimately they've given the solution, g/8, so I know this is how I should try to get the equation to look...

Homework Statement I'm trying to find Arc Length of F(x) = (e^x + e^-x)/2 0< x < 2]Homework Equations L = integrate sqrt ( 1 + (dy/dx))^2)The Attempt at a Solution (dy/dx)^2 + 1 = 1/4e^2x + 1/4e^-2x + 1/2] I don't know how to take the square root of the above function so I can be able...