Root Definition and 944 Threads

Homework Statement [PLAIN]http://www4a.wolframalpha.com/Calculate/MSP/MSP184619c56eg84971107d00001e292h4340heh8g4?MSPStoreType=image/gif&s=35&w=135&h=53 It is a definite integral between x=0 and x=20. I forget how to integrate with a square root. Do you just change it to a power of a...

Homework Statement Integrate : f(t) = t3/ sqrt(t2+1) Homework Equations The Attempt at a Solution t2* t / sqrt(t2+1)let u = sqrt(t2+1) u=(t2+1)0.5 u2 = t2 +1 t2 = u2 -1 -Eq 1u=(t2-1)0.5 du = t/sqrt(t2-1) dt dt = sqrt(t2-1)/t du -Eq 2 Hence Substituting 1 and 2...

Homework Statement Find the length of x=y^3/30+5/(2y) on 3 <= y <= 5 Homework Equations L = integral sqrt(1+(dx/dy)^2)dx The Attempt at a Solution I got to the integral upper bound = 5, lower bound = 3, sqrt(y^4/100+25/(4y^4)+1/2)dy. How do I actually solve the integral? It...

And if so, could I take the ith root of i?

How to solve recurrence relation with one real root and two complex roots ? The Example is ; Solve the recurrence relation a n-1 + a n-3 = 0 where n ≥ 3 and a 1 = 1 a 2 = 1 a 3 = 2 a n = nth order a n-1 = (n-1)th order. a n-3 = (n-3)th order. I've started the solving ; a n = r^n so...

sorry, I am using phone, owho i hope you can get it. suppose its rational. in the form a/b gcd(a,b)=1 and so and so and so and then they concluded that a^2=2 is a contradiction. but i cannot see what it conradict the assumption. help

hi, I am plotting a 1D graph in root (TH1F pointer). currently the y-axis gives the number of entries in each bin along my x-axis. how do i change it so that it is actually the number of entries in each bin divided by the total number of entries. thanks

Hi all, I am trying to find a nice back-of-the-envelope way to numerically-calculate nasty things like square roots and stuff. For instance: \sqrt {4.51} = ? I tried to use a linearization: \sqrt x = \sqrt {n + \varepsilon } = \sqrt {\left[ {{\rm{integer}}} \right] + \left[ {{\rm{decimal...

Hi there, I am having difficulty with one aspect of intergration by substitution where the substituion of a square root is U^2, wondering if anyone can help. Problem: Integral of: 2x√(3x-4) dx by substituting U^2 = 3x-4 Would du^2/dx = 3 therefore 1/3 du^2 = dx (I think...

Given a symmetric 2x2 matrix, what would be the way to calculate the square root of it? Here, http://www.jstor.org/stable/2689616?seq=2 , it is announced that a relatively simple formula could be applied for the resulting matrix entries, but I could not access it further. Thanks

Homework Statement Evaluate the next integrals, expressing it previously in the forms that contains \sqrt[ ]{a^2+u^2}, \sqrt[ ]{a^2-u^2} and \sqrt[ ]{u^2-a^2}, and then solve it using the integral table; The exercise which I couldn't solve...

Is square root a function in this way? f:\mathbb C\rightarrow\mathbb R^+ However contradiction can be drawn:\sqrt{x^2}=|x|\text{ and } i^2=-1 \sqrt{-1}=\sqrt{i^2}=|i|=1 \sqrt{-1}=1 ??What is the problem in the...

Homework Statement dP/dt=root of (Pt) Homework Equations P(1)=2 The Attempt at a Solution Well, I figure that the integrating factor is 1, since there is no P(x) value, so it's a matter of finding the integral of root(Pt). I can't solve this because the only method I know is...

1. square root of 144400 using Taylor series 2. I used the equation of sqrt(x) for x>2 given in http://www.understandingcalculus.com/chapters/23/23-1.php 3. I have tried it upto the 7th power and I got sqrt(144400)=1/0.209482810=4.773661 I know sqrt(144400)=380; and...

Homework Statement If Kp = 6.0 x 108 For equilibrium N2 <--> 2N Then what is the equilibrium constant of N <--> .5N2Homework Equations K= C^c/A^aThe Attempt at a Solution I tried finding the fourth root of 6.0 x 108 and that didn't give the right result. BTW the answer is 4.1 x 103, I'm...

Homework Statement Hi guys, I'm doing a rather long math modelling task. As part of the task, I have to investigate the following argument: There is a rectangle ABCD. It is sliced by the line EF, such that EF is parallel to AD and BC. M is the midpoint of BC. X is a point on the line...

Hi, I ve got two problems. 1) The problem i have is how to find an open loop transfer function that gives poles at -3, -6, -7+_ j5 and zero at -5. So i think that the numerator is (s+5), and denominator has (s+3),(s+6). and now I don't know how to carry on. Is it ( s+7+j5) and (s+7-j5)?. Am I...

Homework Statement Let q=p^e, where p is a prime and e is a positive integer. Let a be in GF(q). Show that f(x)=x^p-x+a is irreducible over GF(q) if and only if f(x) has no root in GF(q) Homework Equations The Attempt at a Solution One of the directions seems obvious. Namely, if...

Homework Statement Let F have prime characteristic p and let a be in F. Show that the polynomial f(x)=x^p-a either splits or is irreducible in F[x]. I was given a hit: "what can you say about all of the roots of f in a splitting field?"Homework Equations The Attempt at a Solution Suppose f...

Is it a right mathematical operation (a*b)^0.5 = a^0.5 *b^0.5 when a and b either both are negative or one of them is negative.

Homework Statement So I was doing the following relativity problem: An atomic clock moves at 1 000 km/hr for 1 hr as measured by an identical clock on the Earth. At the end of the 1 hr interval, how many nanoseconds slow will the moving clock be compare with the Earth clock? The problem...

Homework Statement Example: If the tension in a string is 25N, the square root of that tension would be 5 ...what?

Homework Statement I don't have the problem in front of me but it was something like "converge or diverge"?: \sum 5^n/(n+1) The Attempt at a Solution I would like to know that if I use the root test, would I get lim n-> \infty 5/(n+1)^1/n = 5/(n+1)^0 = 5/1 = 5 ? I suspect...

Homework Statement 9y'' + 6y' + y = 0 r^2 + 6r + 1 ( -6 +/- root 36 - 36 ) / 18 lamda = -6/18 = -(2/9) mu = 0 (this is the part I am unsure about, because if i end up with a zero under the root, then does this make the final equation into this: y = c_1*cos(0*x) +...

Homework Statement Hi, I have a problem in my book in which they use a method of making sqrt( 36 + x^2 ) a perfect square by simply making x = 3( t - 1/t ) and then we get 9( t + 1/t )^2 by substituting back into sqrt(36 + x^2). My question is that why did the chose 3( t - 1/t ), is...

Homework Statement Using the Newton raphson method with x0=6, find the root of x2- 2 to 3dp. Then estimate the number of iterations the bisection method that would be required to achieve the same accuracy. Homework Equations The Attempt at a Solution I have done the first...

Find six distanct sixth roots of -1 + i root 3 I want check my answer ==== > x = -1 y = root 3 r = 2 tan Q = 2pi/3 -1 + i roo3 = 2 { cos ( 2 pi / 3 ) + i sin 2 pi / 3 ) = 2 e ^2 pi i / 3 } now six root -1 + i roo3 = 2^1/6 e ( 2 pi/3...

Show that sq. root of 2 to power sq. root of 2 to ... N converges Sq. root of 2^sq root of 2 ^ sq. of 2...N Use monotonous convergence theorem to that it converges and determine what it converges to.

Homework Statement find the square root of: 4+4(sqrt3)i put the answer in a+bi form Homework Equations finding the nth roots: √(r(cos(theta)+isin(theta)))=√r(cos(theta+2(pi)(k)/(n))+isin(theta+2(pi)(k)/(n) where k=0,1 The Attempt at a Solution first i converted my...

I have some measurements from a physics lab experiment and I am coding in Matlab a fit for the data. [Note this is not a problem with Matlab, my problem here is theory] In normal regression of statistics the RMSE is given by: s=\frac{\sigma}{\sqrt{n}} =\sqrt{\frac{\Sigma (\epsilon...

My notes claim that the square root loop \sigma : S^1 \longrightarrow RP^1 ; z=\cos 2\pi t +i\sin 2\pi t \longrightarrow [\cos \pi t, \sin \pi t] is a homeomorphism, where [x,y] is an equivalence class given by the antipodal equivalence relation on the circle. However, this map doesn't even...

Using the root test find whether the series converges or diverges: Lim Sin (4/(3n+3)) / Sin (4/(3n)) n-> inf. I have no idea how to cancel out the sin terms

Homework Statement Let n be a nonzero integer and let a be an integer with gcd(a, n) = 1. We have two equivalent conditions which characterize primitive roots: (i) a is primitive modulo n if the order of a is \phi(n). (ii) a is primitive modulo n if for every element b with gcd(b, n) = 1 we...

Question is pretty simple : How do I know that square root 3/2 = 0.8660 or how can 0.8660 be converted into square root 3/2 more importantly. My calculator is out of style so it displays only numbers. Thanks

Homework Statement The matrix C is self-adjoint and positive definite on \mathbb{ C}^2. Determine \sqrt{\mathbb{C}} \in \mathbb{ C}^{2x2} . C=\left(\begin{array}{cc}5&-4i\\4i&5\end{array}\right) The Attempt at a Solution Characteristic polynomial: (5-\lambda)^2 - 16 = 0 What I...

Homework Statement Determine whether the series converges or diverges. \sum (\sqrt {k} - \sqrt {k - 1})^k Homework Equations The Attempt at a Solution (a_k)^\frac{1}{k} = \sqrt{k} - \sqrt{k - 1} What do I do here..? = \frac{1}{\sqrt{k} + \sqrt{k-1}} \to 0 ?

I have no idea how to go about this, except that we are supposed to use proof by contradiction to show that the square root of 3 is an irrational number. Any help or tips is appreciated. Thanks.

Homework Statement solve for x: [ x / sqrt(x^2 + h^2) ] = [ d / sqrt(d^2 + h^2) ] I need to solve for x. Homework Equations sq rt * sq rt = what is inside the square root square both sides of an equation The Attempt at a Solution Can anyone help me remember how to get...

Hello all, I'm attempting to find in literature a method of determining from a Lie algebra's full root system in an arbitrary basis which roots are simple. It seems there are many books, articles, etc on getting all the roots from the simple roots but none that go the other way. My task is...

I've struggled for days reading about square roots of complex numbers and I get most of the problems but not this one. I really want to understand what is going on in this problem, hope someone can help! 1. The complex number (C) is C = 1/\sqrt{i*x} . find the two roots of C. The solution...

Homework Statement Maclaurin series for square root (1+x) Homework Equations The Attempt at a Solution I attempted to find the maclaurin series for the function Square root of 1+x. F(0)=1 first term= 1 F'(0)=1/2 second term= (1/2)x F''(0)=-1/4 Third term (-1/4)x^2...

hi there, I'm trying to plot r against \phi by solving the following ODEs using runge-kutta. The problem I'm having is with the square root. How do I know when it will be positive and when it will be negative? If this is a simple question I apologise I'm not that great with the maths :). E and...

Let ∑ak be a series with positive terms. Ratio test: Suppose ak+1/ak -> c. If c<1, then ∑ak converges. If c>1, then ∑ak diverges. If c=1, the test is inconclusive. What if ak+1/ak diverges (i.e. ak+1/ak->∞)? Do we count this as falling into the case c>1? Can we say whether ∑ak converges...

I came across this weird graph from another thread: y=\left(x^2-6x+8+\sqrt{x^4-12x^3+52x^2-96x+64}\right)^2 It seems that there is a root y=0 for the domain x=[2,4]. I've never seen such weird behaviour on a graph before. How could analysis of this function (or not?) determine that there...

Homework Statement \int dx/(e^{x}\sqrt{1-e^{-2x}}) Homework Equations The Attempt at a Solution I have absolutely no idea of how to start the problem, any help is greatly appreciated! thanks!

Consider square root of 4. Can square root of 4 be +2 or -2? I asked that to my math teacher so he said: NO, square root of 4 is +2! But I can't really understand why it cannot be -2 since -2 squared is also 4. One thing I've imagined is: square root of 4 can be +2 or -2, but for...

Homework Statement This isn't really a homework question, but I was considering a different model of library fines... where the fine at the end of the 1st late day is $0.01, and it increases geometrically with a common ratio of 2, so it goes like $0.01, $0.03, $0.07, $0.15... Then I...

Homework Statement Does it converge or diverge? Sum n=0 to infinity : (n/(n+1))^(n^2) The attempt at a solution I know I need to use the root test. But what I get is ... Limit to infinity : (n/(n+1))^n It seems that the n/(n+1) would go to 1 because when you multiply the top...

Hello, I came across the following formula after asking for practical applications of math in finance and other sciences, it concerns mortgage payments A = Pi/1-(1+i)^-n The above denominator end part reads (1+i)^(-n) As a mathematical question, is it possible to rearrange the...

hi there, i have written a small program in C++ and if the user puts in the wrong values for some of the variables the operation will end up trying to square root a negative number and this returns that the answer is not a number can anyone show me how to write an if function that if...