Simplify Definition and 371 Threads

1. prove that: X'Y'Z + X'YZ' + XY'Z' + XYZ = (X⊕Y)⊕Z Homework Equations Use postulates and theorems. The Attempt at a Solution X'Y'Z + X'YZ' + XY'Z' + XYZ (original expression) X'Y'Z + X'YZ' + X(Y'Z' + YZ) (distributive) X'Y'Z + X'YZ' + X.1 (complement) X'Y'Z + X'YZ' + X (identity)[/B]...

Simplify $\left(\sqrt{3}\sec \dfrac{\pi}{5}+\tan\dfrac{2\pi}{5}\right)\tan \dfrac{2\pi}{15}$.

Hey! So we're deriving something in Daniel Schroeder's Introduction to Thermal Physics and it starts with this: \Omega \left( N,q\right) =\dfrac {\left( N-1+q\right) !} {q!\left( N-1\right) !} Both N and q are large numbers and q >> N. The derivation is in the book, but I am always...

Hi Folks, This loop code is working fine but I would like to simplify it further. Can anyone help? Basically, i need syntax to automate the numbers highlighted in bold. k is a 3*3 matrix, SE_ans is a 3*1 vector, A is a 3*3 identify matrix. The rests are just constants. for i=1:size(k,1)...

Homework Statement How to simplify 1-2*sqrt(x)*sin(sqrt(x))*cos(sqrt(x))? Homework Equations None. The Attempt at a Solution I know the identity that sin(2x)=2sin(x)cos(x).

Homework Statement 2. Evaluate the determinants ## \begin{vmatrix} 1 & 1 & 1\\ x & a & b \\ x^2 & a^2 & b^2 \\ \end{vmatrix} ## ## \begin{vmatrix} x & a & b \\ x^2 & a^2 & b^2 \\ x^3 & a^3 & b^3 \\ \end{vmatrix} ## and factorize both answers. Homework Equations Rules of determinants are...

Outer log could be any base.

Compute the Wronskian and simplify. So the first part was easy a) $y_1 = t^2 + 1$ , $y_2 = 3t^2 + k$ =$6t-2kt$ b) for what values of $k$ are the functions linearly independant so would I just solve for $k$? I'm confused What exactly does linearly independant mean?

Homework Statement find F(7) and F(a^2-2) (a≥2). Simplify.The Attempt at a Solution Not sure maybe F(7^2-2) therefore F(47)? Not sure what this question is asking me to do. Please help

I have attached the properties/rules that will aid in simplifying the 3 x 3 determinant so that it can be calculated with minimum effort. I am trying to understand rule (2) and (4). I am not so clear about the idea of linearity. Can anyone please explain these two rules with regards to example...

Are there simple governing equations for FETs like there are for BJTs, and if so, what are they? For example, in the BJT case we have IC = β×IB IE + IC + IB I'm sure it depends on the type - MOSFET, JFET, etc. - so anything anyone could contribute would be helpful. From what I understand, the...

Homework Statement Basically, I'm just trying to verify that I can do basic algebraic manipulation correctly. The objective: solve the charging equation of a simple RC circuit for (C), capacitance. Homework Equations v\left(t\right)={v}_{s}\left(1-{e}^{{-t}/{RC}}\right) The Attempt at a...

I just watched susskind video on EFE but he didnt show us how to convert curvature tensor(the one with 4 indices) to that of Ricci tensor. Can anyone help me with this? Try to simplify it as I just started this.

how does this aproximation reduse the integral

Homework Statement IF G, H and G+H are invertible matrices and have the same dimensions Prove that G(G^-1 + H^-1)H(G+H)^-1 = I 3. Attempt G(G^-1 +H^-1)(G+H)H^-1 = G(G^-1G +G^-1H + H^-1G + H^-1H)H^-1 = (GG^-1GH^-1 +GG^-1HH^-1 +GH^-1GH^-1 +GH^-1HH^-1) = GH^-1+I +GH^-1GH^-1 +GH^-1 =2GH^-1+...

Homework Statement Between two metal plates a metal strip is inserted as shown on the figure. a) Calculate the electric potential anywhere inside the capacitor. b) Simplifly ##U(x,y)## for ##x>>a##. c) Calculate the electric field in the middle of the capactior. Homework EquationsThe Attempt...

I managed to get it down to 2ab/(4a-3b)-b, but that doesn't seem very simplified to me. I also added and subtracted terms in the numerator to make it factorable, ect but nothings really worked out.

Two functions are defined as: f(x) = 1/(-10x+14)+17 g(x) = 1/(-4x-3) Find fg(x) and gf(x) and simplify answer into form (ax+b)/(cx+d) where a,b,c and d are numbers to be found. I know it is common practice to put in some of my own attempts onto here, but I am not even getting remotely close to...

Because on the test the answer given back says the correct answer for -2^2 is -4. Is there a difference between simplifying and solving?

Hello, I am having difficulty solving my math problems. Simplify the Expression and show how.. And kalkulate z²+w(2wz)²-(w+4z²-1)w³-(z+w²)(x-w²) And w=2 I know we have many ways doing it, an the more ways i can study, the bether i can understand this..

Hey there! This isn't actually a problem from a book or something. Its a problem I have stumbled upon when I did some physics. The problem I have come to this equation and I can't seem a way to simplify it $$Q_c^2 =Q^2 \frac{d_1^4+d_2^4}{(d_1d_2)^4} \cdot (d_1^2+d_2^2)^2 $$ The attempt...

Homework Statement I'm trying to simplify some trigonometric expressions, I'm attaching my work here. This comes from a famous physics problem i.e. the rod with two masses spinning on a circle. I've tried many times but I just can't get it. Any help on which identities to use would really...

Hellow I did these three math problems and I wonder if my answers are right. (1.03 : 10^-1 + 17) : (4.5^-1 + 5/18)^-2 my answer here is 3. (0.2 : 10^-2 -2 ) : (1/0.9 - 1)^-1 my answer here is 2. Now the last one 1/a^2+a - a+2/a+1 + a+1/a and here my anser is 2. Thank you.

$[\sqrt{4+\pi^2}-2\ln\left({\frac{2+\sqrt{4+\pi^2}}{2}}\right)]-[\sqrt{4+\pi^2/9}-2\ln\left({\frac{2+\sqrt{4+\pi^2/9}}{2}}\right)]$

Simplify $\tan x\left(1-\sec \dfrac{x}{2} \right) (1-\sec x)(1-\sec 2x)\cdots(1-\sec 2^{n-1} x)$ at $n=8$.

Helping my middle schooler and got hung up with this one. Simplify and solve: (630*137+2) / (316+315*136) I don't see it. Extract 2 from the numerator? Then what? Any guidance is appreciated.

Could someone please explain why the following sum simplifies to the following? = As far as I can see, this sum does not correlate to the formula for incomplete gamma function as a sum. I'd appreciate any help as the incomplete gamma function is somewhat beyond the scope of my current...

How do you simplify this? $$-2x[5x-(2x-7)]+6x[3x-(1+2x)]$$ Can someone show the steps? I keep getting the wrong answer.

5c) Simplify. $$\frac{2x}{3y} - \frac{x^2}{4y^3} + \frac{3}{5y^4} $$This is what I did, which is wrong according to the textbook. Could someone point out what I did wrong and how to correct it? Thanks. $$\frac{(2x)(4y^3)-(x^2)(3y)}{(3y)(4y^3)} + \frac{3}{5y^4}$$ $$\frac{8xy^3-3x^2y}{(12y^3)}...

Simplify 1) Simplify and state any restrictions on the variables: $$\frac{3a-6}{a+2} ÷ \frac{a-2}{a+2} $$ This is what I did. Can someone tell me what I did wrong? Thanks. $$\frac{3a-6}{a+2} ⋅ \frac{a+2}{a-2} $$ $$\frac{3a^2-12}{a^2-4}$$ $$\frac{(3a+6)(a-2)}{(a+2)(a-2)}$$...

Simplify and state any restrictions on the variables: $$\frac{2(x+1)}{3} ⋅ \frac{x-1}{6(x+1)} $$ This is what I did, which is wrong (according to the textbook). $$\frac{2}{3} ⋅ \frac{x-1}{6}$$ $$\frac{2x-2}{18}$$ $$\frac{2(x-1)}{18}$$ Can someone tell me what I've done wrong? Also, how...

Homework Statement Simplify sqrt(x^2+(y-sqrt(5))^2) = 8 - sqrt(x^2 + (y+sqrt(5))^2) The Attempt at a Solution I know squaring both sides, collecting like terms and simplifying gets the equation but in my solution manual they do it a different way that is a lot shorter and I need help...

I'm sure this is easy but it has got me baffled. I'm told that the binomial theorem can be used to simplify the following formula x = \dfrac{1 - ay/2}{\sqrt{1-ay}} to (approximately) x = 1 + a^2 y^2 / 8 if a << 1. Thanks for any help or pointers on this one in particular, and/or general...

Homework Statement In a paper I have found there is a simplification of an equation which I do not understand. How did they do this? Can someone explain this step by step? Homework Equations The euqation is as follows: X = e \cos\theta + \sqrt{(R^2 + e^2 \sin^2 \theta)} X =...

simplify: $\sqrt {21-4 \sqrt 5 +8\sqrt 3 - 4\sqrt {15}}$

Hi, Please see the attached pdf file. Equation 1 and equation 2 are equivalent. Can someone please help me understand how to simplify equation 1 to get to equation 2? Thanks.

I have some problems I am stuck on. The goal here is to simplify radicals in the denominator. I understand that when there is a binomial in the denominator, you need to multiply both sides by the conjugate. For some reason though, I seem to be having trouble doing that or am making a mistake...

Why can't the equation be simplified in the third step where it specifies that the equation is indeterminate? You could essentially have ln1/(ln1+1-1) if you substitute values in here. This then simplifies to just ln1/ln1 and then they would cancel to equal 1. Yet, the solution uses l'Hospital's...

I am currently stumped with a mental blackout, how do you simplify this again? (-192x^2(4x-3)-4(27-64x^3))/(4x-3)^2 Wolfram Alpha spits out -32x-12, but how do you get there? :(

1. The problem statement ( F(r) \frac{d}{dr} ( r^{2} \frac{d}{dr} ) ) g(r) 2. The attempt at a solution Does it just melt down to: ( F(r) r^{2} g(r) ) \frac{d^{2}}{dr^{2}}

Please refer to the attached image. My lecturer seems to have re-written $e^{-st}$ as $\frac{d}{dt}e^{-st}$ and taken out the $(-\frac{1}{s}$ which I do see is equivalent, but i am unsure how he goes from there onwards. Although, e is the derivative of itself. how does he split the integral...

Homework Statement I'm having a brain fart, how do you factor/simplify a fraction such as \frac{ab}{ab+cd} I keep thinking multiply by ab-bc but I'm not sure.

2h/h2 + 2h + 2 does the 2h cancel out?

Homework Statement Simplify the expression using boolean algebra postulates, laws, theorems. (\overline{\overline{x + \overline{y})(xz + \overline{y}}) + x (\overline{yz}}) The Attempt at a Solution (\overline{\overline{x + \overline{y})(xz + \overline{y}}) + x (\overline{yz}}) 1. ((x +...

Homework Statement Build the truth tables for the boolean expressions. (x + y' * z)' + (x * y * z' + (y + z)') + (y + (x * z')')' The Attempt at a Solution Given that the expression is so complex I believe that I need to simplify first then proceed to build the truth table? Work so...

Homework Statement I've been struggling with simplifying this circuit, eliminating a bunch of sources and moving around stuff in general. I'm still very unsure of how to handle nodes with multiple sources though. Like in the picture I've attached. I've got a voltage source and a current...

Homework Statement Solve: ##x\frac{dy}{dx}-4y=x^{6}e^{x}## Homework Equations ##x^{-4}\frac{dy}{dx}-4x^{-5}y=xe^{x}## is equal to ##\frac{d}{dx}[x^{-4}y]=xe^x## The Attempt at a Solution The second equation above simplifies to the third (according to my textbook) but I can't figure out...

I have the expression $$sin^{-1}(cosx)$$ I'm not sure how to simplify this at all. I've never done a problem like this and it's in my textbook as a review question. A quick boot in the right direction would help

Homework Statement sqrt((2-sqrt(3))/4) I tried to split whatever is under the radical sign into two separate parts, 1/2 and (-1/4)sqrt(3) I realized that 1.5 times 2 is 3 and 2-1.5 = 1/2 so it seemed like it fulfilled the requirements for solving a double radical. so I put down...

Mathematica -- how to simplify an output formula Hi all, Is there any more options to simplify an out put Mathematica formula. I used //Simplify but the expression still complicated and //FullSimplify too slow and didn't work. Bests, Safinaz