Simplifying Definition and 487 Threads

Homework Statement Show how to simplify (mBvB2 - mBvC2 - mCvC2)/(mBvB2) to mC/(mC + mB) Homework Equations vB is not equal to vC. vB = muzzle speed of a bullet = unknown value vC = speed of the clay block after it is hit by the bullet = unknown value vB = ((2gh)0.5(mB + mC))/mB vC =...

Express \frac{1+\sqrt{2}}{3-\sqrt{2}} as a+b\sqrt{2} where a and b are rational numbers. I started by \frac{1+\sqrt{2}}{3-\sqrt{2}} * \frac{3+\sqrt{2}}{3+\sqrt{2}} But, I obtain \frac{5}{7}-\frac{4}{7}\sqrt{2} I believe that, here, a and b are rational, but is there a more tidy version? I...

Homework Statement How do i solve for the subscript in: (log (sub5)) / 2 = log(sub x) Homework Equations -- The Attempt at a Solution the original question was: (log(subx)7)(log(sub7)5)=2 solve for x. however i don't get how to solve for a subscript...

I am having great difficulty grasping the concept of Lenz's law. As far as I am unware it is derived as: "any current driven by an induced e.m.f opposes the change causing it" I do not really understand what this means - help would be greatly appreciated :)

\frac{\sqrt{\sqrt{5}+2}+\sqrt{\sqrt{5}-2}}{\sqrt{\sqrt{5}+1}} What technique/method could I use to simplify that one fast? It was asked in a math contest here in our country and the question is only for 20 seconds. The answer is \sqrt{2}. You know any technique for that one guys?

I'm trying to follow some notes in class. so the original equation is: u= [ (x^2 – 1)^1/2 + ln (x + (x^2 – 1)^1/2 )] and we let x=z+1. Then by simplifying and approximating, u=z*2*2^.5 + higher order terms from my notes: (x^2 – 1)^1/2 = (2z)^.5*(1+z/2)^.5 ln(1+e) approximately = e

I have just been doing some algebra homework. The are just problems that I can't work out. I wonder if anyone can explain how to solve them? 3x + (-3) = x + 199 x = ? I know the answer is x = 101 but I haven't worked it out in the right way. I just did it by deduction which took ages. What...

Take this equation: f(x) = u0.5(2 - 2u) + (2u - u2)(0.5u-0.5) My lecturer simplified it to this: f(x) = (2u(2 - 2u) + (2u - u2)) / (2u0.5) = (6u - 5u2) / (2u0.5) My intuition tells me to simplify it like this: f(x) = 2u0.5 - 2u1.5 + u0.5 - 0.5u1.5 = sqrt(u)(3 - (5/2)u)...

I did a problem in class today that evaluated f(t)=e^{At} for A_{2,2}=\begin{bmatrix}2&1 \\-1&4 \end{bmatrix} to a matrix form. The answer I got was: f(t)=\begin{bmatrix}e^{3t}-te^{3t}&te^{3t} \\-te^{3t}&e^{3t}+te^{3t} \end{bmatrix} Factoring we have: f(t)=e^{3t}\begin{bmatrix}1-t&t...

Homework Statement Find the first derivative of the function y=cos[(8t-7)^{\frac{-6}{7}}] The Attempt at a Solution Here is my answer: \frac{dy}{dx}=\frac{48sin[(8t-7)^{\frac{-6}{7}}]}{7(8t-7)^{\frac{13}{7}}} How can I simplify this further?

Is it possible to simplify this? \frac{a}{2^a} It's actually part of a limit: 2\lim_{n\rightarrow\infty}(\sum_{a=4}^{n}\frac{a}{2^a}) The limit I'm hoping tends to 3/4 as n tends to infinity. It certainly appears to do so when I plotted a graph of a/(2^a). Any little hints? Tried...

Homework Statement I need to simplify the expression below. The absolute value is throwing me off \left[\left|(\alpha + k)^{2}e^{-2i \alpha a} - (\alpha - k)^{2}e^{2i \alpha a}\right|\right]^{2} Homework Equations I know \left|e^{ix}\right| = 1 The Attempt at a Solution I...

hello all, i am unaware of how to handle a delta function. from what i read online the integral will be 1 from one point to another since at zero the "function" is infinite. overall though i don't think i know the material well enough to trust my answer. and help on how to take the integral of...

simplify the following expression log2 4^3x-1 (2 is a subscript of log and 3x - 1 is a superscript of 4) i can rearrange this to 4log2 3x - 1, i am thinking after this it becomes 4 log3 + 4 logx, but i don't know what to do with the -1 please show all the steps and explain.

Homework Statement I need to simplify this: ((84/13)x4y - 4) / (-x + (21/13)x5)y)Homework Equations The Attempt at a Solution I don't know if it can be simplified further. I can't factor anything out that will cancel. I multiplied both the top and the bottom by 13 to get rid of those fractions...

If you have a 3d shape how do you simplify the problem using symmetry. eg with a sphere is symmetric along any axis therefore the centroid must be in the middle of it eg2 A cone sitting on the xy plane, where the pointy bit is points up the z axis. -nb it is sitting on point (0,0,0) where the...

Homework Statement F(x,y,z)=X'Y'Z + X'YZ+ XY'Z + XYZ' + XYZ The Attempt at a Solution F(x,y,z) = X'Y'Z + X'YZ+ XY'Z + XY (Z'+Z) F(x,y,z) = X'Y'Z + X'YZ+ XY'Z + XY I am stuck here l don't know how to further simplify it so that l can end up with F= XY + Z

Homework Statement Okay, I have question I was pondering about for a while... If I had the equation below and wanted to transform it into a K-Map, is the only way I can do it to expand it completely? Are there any shortcuts? Homework Equations This is just a random equation out of...

1.I can't figure out how the \sqrt{1+((x^2)/(4-x^2))} simplifies to 2 times\sqrt{1/(4-x^2)} I have tried rewriting it in different ways, but I can't see how it simplifies. \sqrt{x^2 + 1/4-x^2}

Homework Statement I'm not sure if you can ask about two questions in one thread; they are very similar. If it's not allowed I can make a second thread and edit this one. Simplify the expressions: 1. sin^3 theta + cos^3 theta / sin theta + cos theta 2. 2-tan theta / 2 csc theta-sec...

Homework Statement Show that: p(r'+e) \cong p(r')*exp( -3e2 / 2s2 ) for large D given that: p(r) = rD-1 * exp( -r2 / 2s2 ) r' = sqrt(D) * s Homework Equations This arises out of a D-dimensional gaussian distribution and r' is the radius at which the probability is maximized. The...

Homework Statement Simply these rational functions: [\sqrt{(X^2)+12}-4]/(X-2) (2-\sqrt{(X^2)-5})/(X+3) (X-1)/(\sqrt{X+3}-2) Homework Equations The only example in the book used the technique of multiplying the numerator and denominator by the function p(x) if p(x) is the function...

Homework Statement 2cos2x-2cosx...how do you simplify this further? Homework Equations The Attempt at a Solution 2(cos2x-cosx)..but i have to find 0=2cos2x-2cosx so this doesn't really help me.

Just a quick question. I finished an expectation value sum and noticed that the given solution had me stumped. Ive attached a quick picture of the simplifying process which was given as the solution. The only thing i don't understand is how to get the value iCm/(pi*hbar)^1/2. I don't know...

I'm looking at an equation where the integral of 1/x(1-x) is being taken, and it has been simplified to the integral of 1/x + 1/(1-x). I guess my brain has locked up on this one, because I can't see how the first equation was simplified to the second one. Can anyone point out what I'm missing...

I need to simplify these boolean expressions. Homework Statement Problem A: a`b`d+a`bd`+bc`d`+bcd`+ab`c`d+b`cd Problem B: a`b`cd+a`bd+abcd+a`b`d+acd+abd+ab`c`d Problem C: a`b`c`d`+a`b`cd`+a`bd+ab`c`d`+bd+ab`d`Homework Equations abc means a AND b AND c a+b means a OR b a` means NOT a The...

\Sigma_{n=1}^{ \infty} \frac{1}{(3n-2)(3n+1)} I simplified it to partial fractions to (1/3) / (3n-2) - (1/3) / (3n+1) Now what?

Homework Statement cosx/(secx+tanx) The Attempt at a Solution So far I have this: =cosx/(1/cosx + sinx/cosx) =cosx/(sinx + 1/cosx) =cos2x/sinx + 1 From there I don't know what to do. I've messed around with it for a while but don't seem to get anywhere. Any help is appreciated.

I was looking over a problem to make sure I hadn't messed up my arithmetic and I put the term (-SQRT(18-12SQRT(2))/6 into my calculator and it reduced it to (2SQRT(3)-SQRT(6))/6. I found approximate values for these two expressions and they were in fact equal. So my question is, how does one...

I've done a calculus problem. The LHS is my answer and the RHS is the answer in the book. \frac{2(x-1)^2}{(x^2-1)^2} = \frac{2}{(x+1)^2} What was done to simplify this equation?

Homework Statement Find the derivative of the function: f(x) = x^2((x-2)^4) Homework Equations f`(x) = (u)(y`) + (u`)(y) The Attempt at a Solution Via the product rule I got [x^2(4(x-2)^3)] + [(2x)(x-2)^4] the book then goes on to give the solution as 2x(x-3)^3 * (3x-2) I'm...

Homework Statement Simplify \frac{x^2 - \sqrt{x}}{\sqrt{x^5}} Homework Equations Unsure The Attempt at a Solution Tried to factorise the numerator and denominator. Not sure how to proceed given the subtraction in the numerator. Best effort so far...

Homework Statement (cube root \sqrt[]{}x^4 * \sqrt[]{}x^5)^-2 Honestly, I tried and my answer didnt make any sense...The answer is supposed to be 1/(x^23/3) How would I go about solving this? Any help would be appreciated :) Also how would I solve the cube root of 7 * the cube root of 49?

For some surds inside of surds, they can be converted into a more simple form: \sqrt{a+b\sqrt{c}}=e+f\sqrt{g} Such as: \sqrt{11-6\sqrt{2}}=3-\sqrt{2} However, there are some that cannot be simplified into this form (as far as I know). Such as: \sqrt{3+\sqrt{7}} I am curious to...

I am unable to simplify the tensor. I have the expression Bc.A(axb)+Bb.A(cxa)+Ba.A(bxc) In this capital letter is second order tensor and the small letter is vector.I have to simplify in the form like tr(Transpose(B)A)[a b c].Somebody can help me.

challeng ! in simplifying the Grammer It is a challeng grammer to be simplified by removing all useless, unit, and epsilon (empty string)-productions: S -> abAB |CD A -> aBA |epsilon (empty string) B -> ABb |A |epsilon (empty string) C -> bb |CD D -> bD if no one answer it :smile:

Homework Statement I'm trying to prove k*(k!)=(k+1)!-1 Homework Equations The Attempt at a Solution This is how far I've gotten: k[k(k-1)(k-2)...1)]

Homework Statement The equation is \int^{t}_{0}[SIZE="6"]e^{-t'\gamma}\int^{t}_{0}[SIZE="6"]e^{t''\gamma}f(t'')dt''dt'. f(t) is a random function with no known anti-derivative. I need to simplify this into a single integral of one variable. Homework Equations above. The Attempt at a...

Hi all, http://www.bsodmike.com/stuff/interpolation.pdf" I am going through some of my notes and quite a few books; they all skip the over the point I have marked with 3 red dots in the http://www.bsodmike.com/stuff/interpolation.pdf" . \begin{equation}\label{eq:solution}\begin{split}...

I understand that the square root of (for example)j^16 is j^8. But when you have an odd squared root, like the square root of j^19, would it be j^9square root of j? Another quick question 12 radical 36 would be 72? Sorry, I know this is basic algebra, but I really have forgotten how to do...

1. Variables Given a generalized basis in three dimensions: e_{1},e_{2},e_{3} and the standard Kronecker delta \delta_{ij}, and using Einstein summation. With the vector \textbf{x},\textbf{y},\textbf{z} I'm trying to simplify this problem: 2. Problem \delta_{il} . \delta_{jm} . x_{j} 3. My...

need to integrate the following equation from 1 to 3 \int\sqrt{4x^{6}+16x^{2}} what i tried to do was call x^2, y for example then what i have is (4Y^3+16Y)^0.5 which i don't know how to integrate. what else can i do, somehow need to play with the equation.

Homework Statement (sec^2 x - 1)/(sin^2 x) Homework Equations The Attempt at a Solution i know that the answer is sec^2 x, but i have no idea what steps to take to get there

is it possible to simplify this more?? Ln(log7-log76)= Ln(log77)

Homework Statement \frac{1 + \sqrt{\frac{1}{1 + \left(\frac{s}{u}\right)^{2}}}}{1 - \sqrt{\frac{1}{1 + \left(\frac{s}{u}\right)^{2}}}} Should equal \left(\sqrt{1 + \left(\frac{u}{s}\right)^2} + \left(\frac{u}{s}\right)\right)^{2} Homework Equations above The Attempt at a Solution...

Hey guys. So, complex numbers. Its been a while since I've dealt with them. I've been wondering a few things about them. When expressed in the form a + ib, is there a particular way that you square them? And when you have a rational number, with an i term on the bottom, how exactly...

Homework Statement (secx-1)/x^2 limit x--->0 Homework Equations secx=1/cosx (1-cosx)/x=0 The Attempt at a Solution I have done obvious thing, solved to make secent cosine and got common denominators in the top portion of the fraction, then subtracted. Ended up with...

Homework Statement Find the derivative of f(x)=2x^3+cos^2(x^3) The Attempt at a Solution f'(x)=6x^2+2cos(x^3)*-sin(x^3)*3x^2 f'(x)=6x^2-6x^2cos(x^3)sin(x^3) The book has a different solution since they always simplify, but how would I simplify it? I know it has something to do...

How could I go about expressing |x|-|x-6| without using absolute value signs?

isotropic equation, so k, ρ, and c are constant, where k is thermal conductivity, c is specific heat, and ρ is the density of the body. the equation boils down to \left( \frac{c\rho}{k}\right) \left(\frac{\partial u}{\partial t}\right) - \left(\frac{\partial^{2} u}{\partial...