Root Definition and 918 Threads

Hi, can you help me with this problem? a = \sqrt[3]{1 - 4b - 4c} b = \sqrt[3]{1 - 4c - 4a} c = \sqrt[3]{1 - 4a - 4b} Find \dfrac{1}{a} + \dfrac{1}{b} + \dfrac{1}{c} Thanks

Homework Statement (A) For what value of K does the equation 2x^2-10x +8 = K have a repeated root? Use the quadratic formula to find the root. (B) Choose a value for K so the equation has no real roots, Use the quadratic formula to prove that this equation has no real roots for your...

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I found a way to find the square root of an expression which is confusing to me. Is anyone familiar to this method? And my main question... will it be useful?

Homework Statement Re-arrange the open-loop transfer function and sketch the root locus for the system for variation of the parameter 'a' from 0 to infinity. Homework Equations G(s)H(s) = 10(s+a) / [s(s+1)(s+8)] The Attempt at a Solution my problem is that i don't know how to re-arrange...

Why arnt the two terms eqaul even though the square root of m was solved properly? And is this a general rule?

Homework Statement is there no square root for a negative number? is there no solution for this? q=-1 r=2 the square root of 2q - 5r The Attempt at a Solution 2x-1 - 5x2 = -12 sqaure root of -12? my calculator doesn't come up with a answer for the square root.

The square root yields only one value !? One guy advanced and asked me the question with an intention to judge my skill - " What is the value of x , if x2=4 " I , without any reluctance replied rather confidently - " Ha , its simple x will have 2 values : +2 and -2 " He laughed hard and said...

Hello, recently, I have found so called Batman graph and equation, which basically plots Batman sign. I have even found Python code that plots this implicit equation. Code can be found here: . And the equation is given here: [url]http://i.imgur.com/CNy9J.jpg If you look closelx...

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 Test for convergence and divergence. Homework Equations \sum_{i=1}^{n} \frac{n!}{3^n} \sum_{i=1}^{n} \frac{1}{{(log (n))}^{1/n}} The Attempt at a Solution For the first one I get \frac{(n+1)}{3} After applying the ratios. Taking the limit as n approaches infinity, it is...

Homework Statement Consider the following series (Baby Rudin Example 3.35): \frac{1}{2} + \frac{1}{3} + \frac{1}{2^2} + \frac{1}{3^2} + \frac{1}{2^3} + \frac{1}{3^3} + \ldots We have to apply the root test. 2. The attempt at a solution \sqrt[n]{2^{-\frac{n+1}{2}}} =...

Hi! Does anyone know how to solve the following integral analitically? \int^{1}_{0} dx \ e^{B x^{2}} J_{0}(i A \sqrt{1-x^{2}}), where A and B are real numbers. Thanks!

How to learn ROOT ?? What do i need to learn ROOT ? and what do i need in c++ to learn ROOT?

Homework Statement Prove that the function 111x^111+11x^11+x+1 has exactly one real root. The Attempt at a Solution Well, I know how to prove this. f is continuous because It's a polynomial. f(-1) equals -111-11-1+1 = -122 < 0 and f(0) equals 1. therefore, It satisfies all conditions...

Homework Statement I have a homework problem that asks the following: R^2 is a 2 dimensional vector. I know how to calculate vector norms, but I'm not sure how to approach the rest of the problem. Can anyone help me out with this problem or point me in the right direction?

I came across this question. How do you show that √N is irrational when N is a nonsquare integer? Cheers.

Hi all, Could anyone guide me on the following prove √2 = 1+1/(2 + 1/(2+ 1/(2+ 1/(2+···))))

I am doing the following practice problem in prep for an exam: sum from n=0 to infinity: (3^n)/(n+1)^n The book says to use the ratio test on it, which I did, but would the root test also apply to this?

Homework Statement Sketch the curve defined by g(x) = x^{1/3}*(x+3)^{2/3}Homework Equations First Derivative Second DerivativeThe Attempt at a Solution I attempted to use the algorithm for curve sketching: 1) Find the intercepts 2) First Derivative; look for extrema and points where f'(x) DNE...

Homework Statement integrate ln(cube root (2+y^3)) dydx with limits of y =sqrt (x) to 1 of x from 1 to 0 Homework Equations integral of ln x= x ln x. This ends up being very convoluted, haven't even begun to insert limits The Attempt at a Solution

We were having our maths class a weeks ago and while studying quadratic equations our teacher asked us if there was an difference between x^{1/2} and \sqrt{x}. Up until then I had always assumed them to be the same thing. However he said that there was a difference and said that he would tell...

Consider this function: (x^2)^0.5 My textbook considers this to be |x| (modulus of x). Is it correct? x^2 gives a positive quantity.On taking square root of that,we'll get either -x or +x. So why modulus? Also, (x^0.5)^2 This is modulus isn't it? Thank You

Homework Statement Given f\left(x\right) \in \mathbb{R}\left[x\right], if a + bi is a root of f\left(x\right), then a - bi is a root of f\left(x\right) as well. Homework Equations Factor Theorem: if f\left(x\right) is a polynomial over a ring with identity, then a is a root of...

I was told to plot a root locus(by hand) of the open loop transfer function: H(s)G(s)= (s+2)/(s^2 + 2s + 3) and for a value of k=1.33 determine the location of the root, then find the equivalent damping coefficient. After several attempts i was able to draw the...

i asked to find the root mean square speed of Methane in temperature of 50 degrees Celsius. so i have an dilemma which formula i need to use, so in the picture you can see the 2 formula that i have doubts. thanks.

Hello, this is my frist thread so I'm sorry if this is in the wrong place, but the other forums didn't seem to be as relevant. I'm trying to get a research position over the summer and I need to teach myself how to use Root, I have programming experience with Java (although it has been a...

\intop_{-\pi/2}^{+\pi/2}\sqrt{(144sin^2t+6)cos^2t}dt how to approach it?

Square Root of 6 <math>\sqrt{6}=\frac{sqrt{2}sqrt{3}}<\math>

\intop_{-\pi/2}^{+\pi/2}\sqrt{(-6sin2t)^2+\sqrt{6}(cost)^2}dt how to solve it? i tried by parts and it looks very bad and complicated edit sorry i copied the wrond integral now it fine

Homework Statement Does the series: sum from 1 to inf. (n+2)/(n+1) converge? If so does it converge absolutely? Homework Equations Ratio test for series The Attempt at a Solution I found this series to converge using the root test, (.jpg attached) however wolfram alpha...

Hi all, How to convert the root of an equation from symbolic form into an ordinary from? I have tried to use the N command, but still displaying in the symbolic form. Thanks

How is squareroot(x)*(1/x)= 1/square root x can somebody please explain this? I think I am having a brain lockup...

Hey all, I've run into a snag with research and it is partly related to taking the square root of a matrix. I've seen related stuff concerning matrices that can be diagonalized, however the 2x2 matrix in question is not diagonalizable. Can the square root of such a matrix be determined? If...

1. For n ≥2, n^(1/n) is irrational. Hint provided: Use the fact that 2^n > n2. This is probably familiar to many. By contradiction, n = a^n/b^n --> a^n = n(b^n) --> n|a^n --> n|a Am I trying to force the same contradiction as with 2^1/2 is rational, that is, that a/b are not in lowest terms? Or...

Homework Statement Let f(x)=x^{1/3} show that it is uniform continuous on the Real metric space. Homework Equations By def. of uniform continuity \forall\epsilon>0 \exists\delta>0 s.t for \forall x,y\in\Re where |x-y|<\delta implies |f(x)-f(y)|< \epsilon The Attempt at a Solution...

Homework Statement Our teacher was talking about something regarding two tangent lines on a circle who distance between the tangent lines is square root of 3 times the radius of the circle... She wanted us to find the proof of this but I am stumped on where to even look... Does anyone know...

As you can't take the square root of a negative number without introducing complex numbers, which would be the correct answer to this function: Equation: x = -2 f(x) = √x / (x(x-1)) Answer a) 1.41i / 6 or Answer b) 0

Homework Statement find the inverse of y=2x^2-8x x>=2 I am in calculus b but forgot some of the algebra so I am not sure how to treat the root Homework Equations The Attempt at a Solution I am skipping steps y=2(x-2)^2-8 (y+8)/2=(x-2)^2 I know that x >=2 so f(2) =-8 and...

Is there a way to simplify this? Is this a known function? tan(arccos(((x/y)-1/y )/ ((x/y)+ 1/y)))*((x/2)-1/2)=sqrt(x)

How to prove that root n is irrational, if n is not a perfect square. Also, if n is a perfect square then how does it affect the proof.

Prove that cube root of 6 irrational. Solution: I am trying to prove by contradiction. Assume cube root 6 is rational. Then let cube root 6 = a/b ( a & b are co-prime and b not = 0) Cubing both sides : 6=a^3/b^3 a^3 = 6b^3 a^3 =...

I'm trying to understand root systems better. They seem to be tied to what I've been working on. Any suggestions on books? here is an e8 root system http://upload.wikimedia.org/wikipedia/commons/thumb/f/fe/E8_graph.svg/500px-E8_graph.svg.png here is some of my root system. the prime...

Banging my head against a wall trying to prove to a coworker why the square root of three shows up in a three-phase voltage drop calculation...any ideas?

Homework Statement show that cos(2pi/n) + isin(2pi/n) is a primitive root of unity Homework Equations The Attempt at a Solution if i know z = cos(2pi/n) + isin(2pi/n) is an nth root and I'm trying to prove that z is a primitive nth root. is it correct to assume that z^k is not...

Is anyone familiar with this method of determining square roots? http://www.cs.cas.cz/portal/AlgoMath/Geometry/PlaneGeometry/GeometricConstructions/SquareSquareRootConstruction.htm I have an equation that I'm working on that expands on this a bit and I'd love some feedback.

Hey there, Square roots never have been my strongest point in maths, but I'm not seeing the trick in this example: I'm trying to find an alternate form of: sqrt(3+sqrt(8)) I get as far as: sqrt(3+2 sqrt(2)) But i know i want to/should end up with: 1+sqrt(2) I just don't know how...

well it is easy to construct sqrt(2) with a triangle with two sides of length 1. but what about sqrt(2 + sqrt(2)) or the iteration sqrt(2 + sqrt(2 + sqrt(2))). the question is how to construct a line with length sqrt(sqrt(2)) i guess(beginning with lines of length 1), but i am not sure.

I arrived at this problem while trying to find the length of a 3D http://en.wikipedia.org/wiki/Cubic_interpolation" . Basically, I'm having to figure out how to integrate ((At4+Bt3+Ct2+Dt+E)1/2)dt A,B,C,D, and E are constants which have to be plugged in after integration, I'm sorry to say...

Homework Statement Helium is used to fill a balloon of diameter 44 cm at 22 degrees C and 0.9 atm. The mass of a helium atom is 4.0026 u, the conversion factor from u to kg is 1.66 x 10^-27 kg/u, the conversion factor from atm to Pa is 1.013 X 10^5 Pa/atm, the universal gas constant is...