Simplifying Definition and 498 Threads

Homework Statement Tan(15deg)/(1-Tan^2(15deg) In my solution manual this is what they did... 2/2 * Tan(15deg)/(1-Tan^2(15deg) = 1/2Tan(30deg) Ok first off... I noticed they multiplyed by a fraction of one (2/2) which resulted in 2*tan(15) in the numerator... ( I did...

How would you simplify (2n+1)! Is the same as (2n-1)! ?

Homework Statement The figure here shows four penguins that are being playfully pulled along very slippery (frictionless) ice by a curator. The masses of three penguins and the tension in two of the cords are m1 = 13 kg, m3 = 17 kg, m4 = 22 kg, T2 = 112 N, and T4 = 224 N. Find the penguin...

I have the following function to differentiate: f(x) = x^\frac{4}{5} * (x-4)^2 My derivative is: f'(x) = x^\frac{4}{5} * 2(x-4) + (x-4)^2 * (\frac{4}{5}) * x^\frac{-1}{5} My calculator gives me: f'(x) = \frac{2(x-4) * (7x-8)}{5x^\frac{1}{5}} How does my expression simplify into...

I need to simplify this expression. How do I go upon that? cos(sin^{-1}(9x))

I'm really not sure how to approach simplifying something such as this. Could anyone offer any advice?

Help simplifying an equation - URGENT, PLEASE! Hello folks, I'm trying to simplify the following equation: V = (a(1+a^n)-Q(1+a))/((a^n)*(1+a)) I really need to eliminate the divisor. Thanks in advance, Estêvão

Homework Statement Expand and Simplify 6(x-1)(x+2)-(1-x)(2+x) Homework Equations The answer in the book is 7x^2+7x-14 The Attempt at a Solution I've tried several ways, but all of them give the wrong answer. I'm not sure what to do with the negative in the middle. I know it...

I'm not seeing how you get 1/4k = (1/2)k(1/2)k(1/2) I understand why you can factor out the (1/2). It's in each term of the sum. http://i111.photobucket.com/albums/n149/camarolt4z28/Untitled-2.png?t=1297227186 I haven't really looked at this crap in four years.

Homework Statement Find all solutions using Gauss-Jordan elimination: [ 0 0 0 1 2 -1 l 2 1 2 0 0 1 -1 l 0 1 2 2 0 -1 1 l 2] Homework Equations Switching rows, able to scale any row able to add non zero multiple to row The Attempt at a Solution What I did was...

Homework Statement I'm trying to understand an example in the book. They're simplifying the following expression: S=z \oplus (x \oplus y) =z'(xy'+x'y)+z(xy'+x'y)' I don't get how they go to this from the above =z'(xy'+x'y)+z(xy+x'y') =xy'z'+x'yz'+xyz+x'y'z Homework Equations DeMorgan law...

Homework Statement \sum\limits_{j=0}^\infty \binom{j}{r} p^r (1-p)^{j-r} (1-q) q^j where p and q are between 0 and 1, and r is a positive integer Homework Equations The Attempt at a Solution since \binom{j}{r}=\binom{j}{j-r} we can rewrite the summation as (1-q)\sum\limits_{j=0}^\infty...

Homework Statement [PLAIN]http://img802.imageshack.us/img802/9172/qns33.png Simplifying the circuit? Also find the power dissipated in the circuit? Homework Equations P=I^2R V=IR The Attempt at a Solution I tired to simply the diagonal by making it parallel with...

Homework Statement I am solving some convolutions, and i have come to these solutions. a)\sum2k, summing from -\infty to -1 b)\sum2k, summing from -\infty to n , where n <=-1Homework Equations the geometric series summation formula, from 0 to N \sumak = 1-aN+1 / 1-a , summing from 0 to N The...

Homework Statement trying to simplify (using dirac notation) QM: <E| (QH - HQ) |E> using H|E> = E|E> Homework Equations The Attempt at a Solution the textbook says that it simplifies to (E-E) <E|Q|E> = 0 but i can't see how :S

Homework Statement Find the derivative: F(x)= cos (x)* sin(5x^2 +7) Homework Equations The Attempt at a Solution I used the power rule and the chain rule and wound up with this: but i don't know how to simplify it... = -sin(x)*sin(5x^2+7)+(10x)*(cos x)*(cos (5x^2+7)

Homework Statement √(3+2√(2)) can be simplified into a fairly simple sum of two number: one is an integer and one is an irrational number . Find them and show you are correct by squaring both sides of the "equation" Homework Equations The Attempt at a Solution

The Attempt at a Solution I'm attempting to solve a question with a few unknowns, and I managed to get it to the following form: tanx(1-cosx)=0.25 I just can't seem to simplify it further and thus solve.. Any ideas?

Homework Statement In D3, simplify f = u R u R Homework Equations The Attempt at a Solution u(Ru)R=(uR)uR u(uR^2)R=(uR)u2 uR=R I am doing this for independent study, and the website I am using says the solution is 1=R I just got started on dihedral...

Hey, I need some help with simplifying these fractions. (3x-6)/(x^2-3x+2) - (x^2-1)/(x^2-4x+4) Im not quite sure what to do with the denominators. Am I supposed to change them to special forms? What is the process of making these a single fraction? Thanks in advance.

i have two boolean expressions that I'm simply stuck on. (any variable with the ' mark means NOT). i used http://hopper.unco.edu/KARNAUGH1.1/Function.html" to check my answers for both..apparently they are both supposed to equal 1. i have tried solving the expressions multiple times, and each...

Homework Statement we know dV/dt = a from the definition of acceleration multiplying by sides by V, velocity yields V dV/dt = aV Left side can be reduced to d/dt(V^2/2) so to be more clear, just looking at the left side V dV/dt = d/dt( V^2/2) I want to know what calculus topic...

Homework Statement Consider the following code fragment. for i=1 to n/2 do for j=i to n-i do for k=1 to j do output ‘‘foobar’’ Assume n is even. Let T(n) denote the number of times ‘foobar’ is printed as a function of n. (a) Express T(n) as three nested summations. (b) Simplify the...

Homework Statement Hey guys, having a trig brain fart here, can you point me in the direction of simplifying: \frac{6cos\vartheta}{2sin\vartheta-3cos\vartheta} or is it as simplified as it gets? \ Homework Equations Thought about using double angle formula The Attempt at a...

Homework Statement Attached is the problem, I don't like the math editor used on this site, so its a pdf. The only real problem I have is how to is how do you square a problem like square root of x over 2x?

Homework Statement How do i simplify the ln(3/sqrt(5)) + 2 into the ln(3)- (1/2)ln(5) + 2 Homework Equations The Attempt at a Solution

Homework Statement Express in simplest form. 1/2 – 4/d divide by 1/d + 3/2d Homework Equations LCF The Attempt at a Solution I know the LCD is 2d. But would you multiply this to the equation

Homework Statement Ok so I'm trying to simplify this (x-5)/(x+1) which is apparently equal to 1 - 6/(x+1) but I don't see how there equal like I don't know what was done to this (x-5)/(x+1) to get that 1 - 6/(x+1). I feel kind of dumb as fel as if I should know this but I can't make...

Homework Statement http://img96.imageshack.us/img96/9288/lagrangiansimplifcation.jpg [PLAIN]"[URL If you require more info in the derivation, it's on page 1: http://www.ph.qmul.ac.uk/~phy304/Homework/HW3sol.pdf Homework Equations L = T - V The Attempt at a Solution I...

Homework Statement F= A'C+A'B+AB'C+BC Express the function as sum of minterms, and find the ninimal sum of products. Homework Equations The Attempt at a Solution How do I do this? I really don't know. I know it is easy though. Any help is appreciated!

Ok, I have an Expression which is attached and it needs simplifying. What I have done is got 12logx But I don't think this is correct. Another possible place I got to is logx4/logx1/3 Which one is it?

Simplify the attached expression using any relevant logarithmic rules I haven't really done much with logarithms, so i didnt know where to start?

Homework Statement Describe the shape of each level curve for the following function: z= (5x^2+y^2)^.5-2x Homework Equations I would like to prove that the curves are elliptical by setting z as a constnat and algebraically putting the equation in standard for for an ellipse...

I'm finding the percent error in a S.R. problem and getting a really small number. How can I find the exact percentage? This is the result that needs to be simplified: 6.7x10^(-16) / (1 + 6.7x10^(-16)) If I do an order of magnitude approximation, then the bottom becomes 1, but that will...

-This is what I need to simplify. π((14-2x)/π)2 -This is what I got. (196+4x)/(π2) -This is the solution. (196-56x+4x2)/π Really unsure of where that -56x is coming from in the solution.

Homework Statement sin(α+45) = ? The Attempt at a Solution Dunno. Really dont. Need it in simplification.

Homework Statement Sketch the graph of x ^ (4/9) * e ^ (-x) Homework Equations None. The Attempt at a Solution My y' = -x ^ (4/9) * e ^ (-x) ( 1 - 4/9x ^ 1/9). I keep on getting a reaaally long derivative for y'' and thus cannot place it on my sign table. Could someone please...

EDIT: My apologies if I started this thread in the wrong forum! Homework Statement Z = P.Q.R + P.R Where . = AND + = OR ~ = NOTHomework Equations (Commutative Law) A+B = B+A, A.B = B.A (Associate Law) (A+B)+C = A+(B+C), (A.B).C = A.(B.C) (Distributive Law) A(B+C) = AB+AC...

Homework Statement I'll give an example. Ex: x'=[-1/2 1; -1 -1/2]x. Homework Equations Assume a solution of the form x=$ert for these type of problems. Euler's formula: ebi = cosb + isinb The Attempt at a Solution |A-rI|=0 ---> r= -1/2 +/- i ---> x= e-t/2 ( C1(cost...

1. ex*eh+e-x*e-h -ex -e-x/ 2h 2. This should simplify to (e^x-e^-x)/2. This is lim (h--->0) so in the end the h should become 0 (I think!) 3. I have absolutely no idea what to do!

Homework Statement Simplify (\log_a{b})(\log_b{c})(\log_c{d}) in terms of \log_x{y} Homework Equations The Attempt at a Solution well , the furthest i can reach is \frac{\log_xd}{\log_xa} , how do i express in terms of \log_x{y}

Homework Statement Simplify Sin[3θ] (no double angles) Homework Equations Sin[3θ]=Sin[θ+2θ] Sin[α + β] = Sin[α] Cos[β] + Cos[α] Sin[β] Sin[3θ] = 3sinθ - 4sin^3 θ Cos2θ = 1-2Sin^2θ The Attempt at a Solution Sin[3θ] = sin[θ+2θ] Sin[θ+2θ] = Sinθ Cos2θ + Cosθ Sin2θ Sinθ Cos2θ + Cosθ Sin2θ =...

Homework Statement (a) lim_{n\rightarrow\infty} (\sqrt{(n + a)(n + b)} - n) where a, b > 0 (b)lim _{n\rightarrow\infty} (n!)1/n2 Homework Equations The Attempt at a Solution I tried to use Limit theorems but nothing happened.

Homework Statement (2 CIS (pi/6))*(3 CIS (pi/12)) Homework Equations Also what is CIS? I believe it's Cos+i*sin but how do you use it? The Attempt at a Solution i simplified it to 6 CIS (pi/12) How do i turn it into cartesian?

Hi all...not sure if this should be here, perhaps in the precalc section =S but here goes anyways... 1. So the question asks to find the derivative of y = sqrt(arctan x), then to simplify wherever possible...my issue is not with the differentiation, but rather with the simplifying...oh and we...

Could someone please expain where I went wrong with this? expand and simplify the following: 1/8(6x - 12y) + 1/2(3x + 2y) I expanded the brackets like this: 0.75x - 1.5y + 1.5x + y and simplified like this: 2.25x - 0.5y But the right answer is: 2.25x - 2.5y

I got the following 2 questions in a recent maths test. Can anyone please explain the correct way to simplify these expressions? 4u to the power of 3 v to the power of 6 / 8u to the power of 2 v to the power of 3 3x to the power of 6 y to the power of 5 z to the power of 3 / 9x to the...

Homework Statement I have a quiz tomorrow and i know a problem like this is going to be on it and i need to figure out the process Homework Equations the expression is: (2x^2-3x+1)(4)(3x+2)^3(3)+(3x+2)^4(4x-3) The Attempt at a Solution i know the final answer(3x+2)^3(36x^2-37x+6)...

Homework Statement See attachment! 2. The attempt at a solution I multiplied by the LCD of (x+h-1)(x-1) and got 6h/h(x+h-1)(x-1) . I then got 6h/h^2+2hx-2h . However, my answer seems to be wrong. What is my error?

So I'm in the process of solving the following differential equation: \frac{dy}{dx}=2y^2 +xy^2 with initial condition y(0)=1 I worked it out until I got to the following equation: y^2 +y =x^2 -4 So now my problem is that I can't isolate y as a function of x in order to move on...