Simplifying Definition and 498 Threads

Homework Statement Expand and simplify algebraic expressions. Homework Equations (2a+1)(3a-1)(a-2) The Attempt at a Solution The problem is, we normally always do these problems with only two sets of brackets. I tried just multiplying each number will each other number but it...

I am trying to simply G1 = G1(1+F1) / (1 + G1F2(1+F1)) in terms of G1, G2, H2, and H3 where F1 = G2/(1-G2H2) and F2 = G3 / (1-G3H3) i got the result (G1(1-G2H2)(1-G3H3) + G1G2(1-G3H3)) / ((1-G2H2)(1-G3H3) + G1G3(1-G2H2) + G1G2G3) however, the book gives the result with a +1 in the...

Homework Statement It has been a while since I have really been involved in trig seriously, But I felt it appropriate to go in this particular forum because in my classes from years back "precal" was the title associated with trig (: The Problem: sin(X) / sin(X/2)...

When simplifying a circuit, can a parallel branch with a current source and a resistor in series be considered as just the current source? Also, if two parallel current sources 'point upwards' i.e. toward the positive rail, can I add them together as one source even if there are other...

Homework Statement So i think i found the general solutions to both these separable equations, but I am not sure if I am suppose to simplify any further to get it in explicit form, and how i can even do that. Homework Equations The Attempt at a Solution 1. \frac{dy}{dx} -...

Homework Statement Simplify this expression: csc(x)sqrt(sec^2(x)-1) with 0 less than or equal x less than pi/2. Homework Equations The Attempt at a Solution Not really sure what they want here, but would a good place to start be to square the entire expression to get rid of the...

This problem comes from an engineering exercise (hence the C/R which you can ignore). I want to see if I got it right. http://img51.imageshack.us/img51/3989/mama1h.jpg http://img851.imageshack.us/img851/3401/mam2.jpg

Homework Statement So I am a little rusty on my basic math and I am trying to simplify this expression. In case you were curious the expression came from a signal block diagram that I calculated the transfer function H(z) to then found the frequency response H(f) and I think i have done that...

Homework Statement f(x) = (x^3+6)^4 * (x^3+4)^6 Homework Equations f'(x) = (x^3+6)^4*18x^2(x^3+4)^5 + (x^3+4)^6*12x^2(x^3+6)^3 The Attempt at a Solution Obviously this expression can be simplified, but I haven't the slightest clue on how to do this. I would really appreciate...

Homework Statement I'm trying to find P_L \displaystyle{\not}p P_L for a left-handed particle. (I think the answer is zero...) Homework Equations P_L = \frac{1}{2} (1-\gamma_5) (the left-handed projection operator) \displaystyle{\not} p = \gamma_\mu p^\mu (pμ is the 4-momentum) (γμ, γ5 are...

Homework Statement Find the value of \lim_{x \to 0}\frac{cosx - \sqrt{1 + sin^{2}x}}{x^{2}} Homework Equations N/A The Attempt at a Solution The answer is 1/2, but I don't know how they got that. I've tried using double angle formulas and multiplying by the conjugate but I get...

Homework Statement I have a question with asks to solve a differential equation via power series and I've done everything up to finding the recurrence relation which is a_{n+2} = -\frac{a_{n}}{n+2} Given the initial conditions a_{o} = 1 and a_{1} = 0 I'm trying to simplify the series into a...

Homework Statement We are only given variables in this problem, that is: m1 travels at V, collides with 2m which is at rest results in m going off at 45° at V1 2m also goes off at 45° down at V2 Calculate V1 and V2 in terms of V Homework Equations Ʃρx-initial=Ʃρx-final...

Homework Statement We need to solve the double integral: 6 -2/3x+4 ∫ ∫ [12-2x-(3y/4)] dy dx 0 0 Homework Equations (a+b)2 = a2 + 2ab + b2 The Attempt at a Solution I've got to: 6 (1/4) ∫ [12y-2xy-(3y2/2)] evaluated at -2/3x + 4 and 0. 0 6...

I'm having a bit of a brain fart here. Given a positive definite quadratic form \sum \alpha_{i,j} x_i x_j is it possible to re-write this as \sum k_i x_i^2 + \left( \sum \beta_i x_i \right)^2 with all the ki positive? I feel like the answer should be obvious

Hello Guys I could not simplify the finite product bellow to another expression I hope I get an answer from you guys Thank you

Homework Statement A D0 meson (with a rest mass of 1.86 GeV/c2), initially at rest, decays into a K0 meson (with a rest mass of .51 GeV/c2) and a \pi0 meson (with a rest mass of .12 GeV/c2). What is the Kinetic Energy of the \pi0 meson? Homework Equations E=\gammam0c2 p=\gammam0v...

Homework Statement Find dy/dx. y=sin^{2}(3x-2) Homework Equations The Attempt at a Solution Using the chain rule, y=sin^{2}u y'=2sinucosu u=3x-2 u'=3 \frac{dy}{dx}=6sin(3x-2)cos(3x-2) Answer is: 3sin(6x-4) What am I missing here ?

How can ((n+1)^2(*n!))/((n+1)!*n^2) be simplified to (n+1)/n^2? My own answer is (n+1)^2/n^2, but its apparently wrong

Hi, I've already worked out the question until part (a) but I don't understand how they go from (a) to (b) right at the bottom of the image. How did they change -s + i to s - i ? [PLAIN]http://img64.imageshack.us/img64/9366/unledrze.png Thank you very much for your help.

Homework Statement I'm trying to simplify this polynomial ((s+1)/(2+s))/((s+1)+((s+1)/(s+2))(s+1)) It's more readable if you view it here: http://www.wolframalpha.com/input/?i=%28%28s%2B1%29%2F%282%2Bs%29%29%2F%28%28s%2B1%29%2B%28%28s%2B1%29%2F%28s%2B2%29%29%28s%2B1%29%29 It simplifies...

I have not been able to solve these 3 questions. (attached) I understand that parallel circuits can be identified by checking if there are branches at a particular point, but I am still unable to simplify these circuits and solve these questions. Any help would be greatly appreciated! Thanks! :)

Ok I have been going crazy and I think I must be making a simple algebra mistake. Basically in my book I read over an example dealing with a head on collision between 2 balls and the collision is elastic so the kinetic energy intial= final KE. The momentum is also conserved so i can use momentum...

Homework Statement Simplify the following xyz + x'(w+z') + yz(w+z') Homework Equations The Attempt at a Solution xyz + x'(w + z') + yz(w + z') xyz + x'w + x'z' + yz(w + z') xyz + x'w + x'z' + yzw + yzz' xyz + x'w + x'z' + yzw + 0 I got the answer xyz + x'w + x'z' + yzw...

Hi guys I need some strategies in simplifying this boolean equation please. ~=not My problem is: ~A~C + ~ABC + ~BC My first idea was to factor out ~A from the first two terms so I get : ~A(~C + BC) + ~BC) Any help would be appreciated. Thanks!

Homework Statement http://images.calcchat.com/solutionart/etf5e/03/d/se03d01063.png Homework Equations The Attempt at a Solution I get to the third row, but can't simplify (Sin2θ)(Cos2θ). I'm looking at the trigonometric double angle formulas, and still can't figure out how the...

Homework Statement http://images.calcchat.com/solutionart/etf5e/03/c/se03c01047.png Homework Equations The Attempt at a Solution What am i missing, because i get: 6/4 [(-1 + tanx*secx- (tanx)^2]

Hi, I was reading about surds and saw this: [PLAIN]http://www.mattvonfat.com/eq.png I'm probably not as familiar with simplifying fractions as I should be but I think I get that it's being split into two fractions and that √3/2 is the same as 1/2*√3 but I don't understand what's...

Homework Statement Where . or SPACE (" ") = AND + = OR ` = NOT (Complementary) Homework Equations I've been having problems with the second question of my assignment. Here's the equation: [( a + bc ) + ( b` + a'c )]' = F The Attempt at a Solution So far, all I've done is this...

Homework Statement simplify: (x^(a-1))/x^((3a+4)) Homework Equations i was really dumb to think laws of logarithms would help me, but obviously not... The Attempt at a Solution the only thing i know is that the a's can't cancel! i don't know what to do !

I was given the equation dp/ds = 4 + 1/e*d/de(e*dp/de) The derivatives in the equation are partial derivatives the values of p,s,e are dimensionless numbers. I am to assume that the solution is separable and then use finite difference method to solve for p, the finite difference method...

Thanks.

Homework Statement I've been studying trig. for my Precalculus class, and I decided to give 50 problems a try, though I got stuck in two of them: Reduce the first expression to the second in each of the following: 38.) cos2x-cos4x, cos2xsin2x and 68.) sec4θ - sec2θ, sec2θtan2θ...

Homework Statement I'm sure you all know deMorgans law on simplifying boolean expressions, I just can't seem to get it. It doesn't make sense to me, like ([not]x.[not]y) = [not]x + [not]y].2. The attempt at a solution I tried it and I don't know why it doesn't work for me ie. ([not]1.[not]0) =...

Homework Statement Use Factorization to simplify the given expression. Homework Equations (x^3 + 3x^2 + 3x +1)/(x^4 + x^3 + x + 1) The Attempt at a Solution I can't get to the first step. I forgot how to factor exponents higher than x^2.

ϵ-N proof Homework Statement Homework Equations The Attempt at a Solution I've tried to make the denominator smaller as is usual with ϵ-N proofs. But the sqrt(2) confuses me. Any help is much appreciated.

Hello, i have a question which is too hard for me to type in here, so I've scanned in the image. At the top, as explained in the image, i have the answer I've found in my lecture notes, but then I've worked it out for myself and i do not get the same answer. Can someone please tell me where...

Homework Statement EDIT: Ahhh, my apologies. At first, I thought it appropriate for the non-calculus sub-forum, but by the title it really does not, XD. I also can't seem to find how to remove it. The question really does not require calculus, though! Basically, the problem of finding the...

Homework Statement Greetings, I am having trouble understanding the solution to this DEQ equation. I am able to solve the equation using the variation of parameters technique, however, when it comes to simplifying the integral I am lost. It appears they are using the Fundamental Theorem of...

Why does (5 i)/(3 (1-i)) = -5/6+(5 i)/6

Homework Statement f(x) = 3x^2-6 We are asked to solve for the inverse function of the above function. Homework Equations The Attempt at a Solution y=3x^2-6 x=3y^2-6 \frac{3y^2=x+6}{3} y^2 = \frac{x+6}{3} \sqrt{y^2}= \frac{\sqrt{x+6}}{3} y=...

Hi, Wanted to know if anyone could explain why if you simplify an expression into a different equivalent form, the integrations are different depending on which form you use. For example: \frac{1}{\frac{5x}{7}+3} = \frac{1}{\frac{5}{7}(x+4.2)} \int\frac{1}{\frac{5x}{7}+3}dx =...

I'm having a discussion about blackbody radiation on one of the other forums. I'm trying to prove that two blackbody emitters combine to act like one blackbody emitter. Unfortunately the algebra is beyond me. What I need to show is the following: I want to show that...

Homework Statement (cos4x) + 2(cos2x)(sin2x) + (sin4x) Homework Equations All Pythagorean, reciprocal, and quotient identities. The Attempt at a Solution Okay, so I thought that maybe (cos4x) + (sin4x) might be the same as its Pythagorean identity (which would make that mess just...

Homework Statement Simplify: 1 + (cot2x) - (cos2x) - (cos2x)(cot2x) Homework Equations All reciprocal, quotient, and Pythagorean identities. The Attempt at a Solution I have spent SO much time trying to figure this out, the answer is "1" but I cannot get it! I managed to get "1 +...

Homework Statement find the nth term Homework Equations x/2+(x^2)/3+(x^3)/2^2+(x^4)/3^2+(x^5)/2^3+... The Attempt at a Solution the numerator clearly is x^n but i have problems with the denominator

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.

sqrt(65/7)/[2sqrt(2)] I know how to simplfy radicals but this one has me stuck. I tried to answer it and i got sqrt(65)/[2*sqrt(2)] is this right?

Homework Statement Fore each of the following functions, find the expression for [ f(x+h) - f(x)] / h. Simplify each of your expressions far enough so that plugging in h=0 would be allowed. ... (f). f(x) = √(x-1) (Hint: Rationalize the numerator) Homework Equations Nothing...