Root Definition and 944 Threads

Hello! My book explained how to take cube root of a number withou using calculator. I managed to extract the cube root of number less than a million. But when its higher like this one 12812904. I cannot extract it. Can you suggest an algorithm on how to go about this one? Thanks!

Hi, Having a bit of trouble with this question: "Assuming a proportional controller is used, determine the gain to achieve a damping ratio of 0.5, for the following transfer function. Hence calculate the associated natural frequency and oscillation period. G(s) = -4(s+0.4) / s^2+1.6s+14." I...

Hello! Is there a way to extract the square root of this expression without expanding? Please teach me how to go about it. $4\left((a^2-b^2)cd+ab(c^2-b^2)\right)^2+\left((a^2-b^2)(c^2-b^2)-4abcd\right)^2$ I tried expanding it and it was very laborious and I end up not getting the correct answer.

Homework Statement in a given activity: solve for z in C the equation: z^3=1 Homework Equations prove that the roots are 1, i, and i^2 The Attempt at a Solution using z^3-1=0 <=> Z^3-1^3 == a^3-b^3=(a-b)(a^2+2ab+b^2) it's clear the solution are 1 and i^2=-1 but i didn't find "i" as a solution...

I have been looking at various proofs of this statement, for example Proof 1 on this page : http://www.cut-the-knot.org/proofs/sq_root.shtml I'd like to know if the following can be considered as a valid and rigorous proof: Given ##y \in \mathbb{Z}##, we are looking for integers m and n ##\in...

I'm trying to find the answer to a question similar to this posted it earlier but in the wrong section I think and not explained well. $$ \sum_{{\rm n}=0}^\infty \left (-\sqrt x \right )^n \ \ \rm ?$$ Find the interval of convergence? I tried using the root test and got from 0 to 1 but when I...

I had a question similar to Σ0∞ (-1)^n (x)^(n/2) and attempted to solve it using the root test getting abs(√x)<1, but I've also seen some places answer it as √abs(x)<1 so am I skipping a step.

Prove that $\cos \dfrac{\pi}{7}$ is a root of the equation $8x^3-4x^2-4x+1=0$.

If one root of $4x^2+2x-1= 0 $ be $\alpha$ then show that other root is $4\alpha^3-3\alpha$

In chapter 7 of Spivak calculus, it is proved that if n is odd, then the 'n'th degree polynomial equation f(x) has a root. I do understand what goes into the proof and can follow steps easily. But, my question is 1.How did they think of a proof like that? 2.By trial and error, did they find...

What is the root mean squad (RMS) of a signal (or wave) and why is it important for electrical engineering? How do you Find it? What is it used for? Thank You All

Let ζ5 be e2πi/5. Find a monic polynomial of degree two in K(ζ + ζ−1) So, if E/F is a field extension, with α∈E then K(α) = {f(x)∈F[x] | f(α)=0} and m(x) is the minimal polynomial of α over F such that K(α) = [m(x)] where [m(x)] is the ideal generated by m(x). I was thinking maybe (x- ζ -...

Let $f(z)=z^{1/3}$ be the branch of the cube root whose domain of definition is given by $0<\theta<2\pi$, $z\neq 0$ (i.e. the branch cut is along the ray $\theta=0$.) Find $f(-i)$. Could someone please help me understand the question? I'm not too clear on "branches" and "branch cuts".

How is it equal to v in the end? I'm sorry for asking such questions. But I'm just trying to understand

i get the differentiation the halves cancel the 2 the h bar cancels the h bar square and to get rid of the root in the denominator the entire thing is squared But I cannot understand where the huge square root came from at the end where I circled. Can someone help me here

Let $1\lt a \lt 2$, $a$ is a root of the equation $x^5-x-2=0$. Prove that $\large a>\sqrt[9]{8}$.

Homework Statement Suppose a field F has n elements and F=(a_1,a_2,...,a_n). Show that the polynomial w(x)=(x-a_1)(x-a_2)...(x-a_n)+1_F has no roots in F, where 1_f denotes the multiplicative identity in F. Homework EquationsThe Attempt at a Solution Strategy: We have this polynomial...

One reads of cancer ever more these days, it seems like one can get cancer of anything, surly there must be a different switch to switch on breast cancer or prostate cancer.

Hello, Given the quartic: $$16x^4-40ax^3+(15a^2+24b)x^2-18abx+3b^2 = 0$$ where $a,b$ are certain real constants. My question is if there is a (simple) condition on $a$ and/or $b$ such that the quartic has at least one real root. Since the quartic has real coefficients the only possibilities...

I have three problems that I've been trying to tackle for a while now. 1) I have a code for the bisection method. I would like to use TLine *line = new TLine function to create the lines that you normally see in the bisection method. These lines from a to F(a) are the ones I am talking...

The following is invalid, since the operation is not defined when ##a, b < 0##: ##\sqrt{-1}\sqrt{-1} = \sqrt{(-1)(-1)} = \sqrt{(-1)^2} = \sqrt{1} = 1##. This is not correct, because ##ii = -1##. This shows that ##\sqrt{a}\sqrt{b} = \sqrt{ab}## is invalid when ##a, b< 0##. However, say we have...

Homework Statement Hello, I have to use the HP 10s calculator at my university, I have been used to my modern casio for the last 4 years but I have a problem. The square root symbol when pressed does not allow for continual calculation, such as when I am using the quadratic formula. It seems to...

I'm doing an online course in quantum information theory, but it seems to require some knowledge of linear algebra that I don't have. A definition that popped up today was the definition of the absolute value of a matrix as: lAl = √(A*A) , where * denotes conjugate transpose. Now for a...

Homework Statement [/B] 1. I've been tasked with forming a 10 x 10 matrix with elements 0, 1, 2, 3, 4, 5,... and have it display properly. 2. Then, take this matrix and make a 2d-histogram out of it. Homework Equations Here is my code void matrix6( const int n = 10) { float I[n][n]; //...

Hey, I am working on this problem over the root test but I am not sure if I am doing it right. I will attach my work to this thread and I really want someone to look over my work and see if I am doing it right. By the way I didn't finish the problem because I was not sure where to go from my...

Homework Statement The goal is to create two arrays that have the values a = { 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 } b = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} And then graph them so that a=mb slope m thus being 2. I am working on the first part before I graph them. Homework EquationsThe Attempt...

Tomorrow I embark on a new semester and this semester I have the pleasure of learning applied partial differential equations and the software of "ROOT" ROOT: https://root.cern.ch/ So I am here to solicite advice. 1. In regards to ROOT, is there anything that can set me up better for a more...

Homework Statement Find [(3 - 51/2)/2]1/2 Homework EquationsThe Attempt at a Solution My calculator says (-1 + √5)/2 I have no idea how. Rationalising doesn't really do much good. Just tell me where to start.

Given $a$ is the real root for $x^3-3x-3=0$, prove that $10^a\lt 127$.

Prove $\sqrt[3]{43}<\sqrt[3]{9}+\sqrt[3]{3}<\sqrt[3]{44}$

Show that $\sqrt{99}-\sqrt{98}+\sqrt{97}-\sqrt{96}+\cdots-\sqrt{4}+\sqrt{3}-\sqrt{2}+\sqrt{1}> 5$.

Is the principle square root just the positive and negative roots of any number (as opposed to just the positive)? I've seen some confusing definitions of this term online and thought I'd double-check with knowledgeable math people here. Lastly, if it is just the + and - roots of any number...

Homework Statement Find a double root of the equation ## f(x)= x^3+15.87x+24.34 ## correct to 3 decimal places. Homework Equations By Newton Raphson's Formula, ## x_{n+1}=x_n + \frac{f(x_n)}{f'(x_n)} ## ##f'(x)=3x^2+15.87 ## The Attempt at a Solution Does a double root means to find two roots...

Homework Statement If ##\sqrt{\frac{10+4\sqrt{6}}{10-4\sqrt{6}}}=a+b\sqrt{6}##, then a+b is ? A) 8 B) 7 C) 6 D) 5 E) 4 The Attempt at a Solution [/B] This is my attempt...

Suppose I have a collection of 40 directories, each containing 1, 2 ,3 ,4 or 5 .root files with histograms and trees. What is an optimal way to merge those .root files so I would end up with 40 directories and 40 root files with the histos added together? One way I thought of was to start typing...

Problem statement: Find the arc length of the curve defined by x = √t and y = 3t -1 on the interval 0 < t < 1attempted solution: dx/dt = 1/2t-1/2 , dy/dt = 3 and dx = dt/ 2√t dy/dx = 6√t length = ∫01 √(1 + (6√t)2) .dt/ 2√t = ∫01 √1 + 36t) dt/2√t now I'm stuck with a product that is very...

1. Integrate the following: (4x - x^2)^1/2 dx 2. Any assistance would be appreciated.3. Honestly don't know where to start.

Why is this true? It is bigger but it is not equal to

I have done this problem before but forgot how to get from one step to the next: let a>0. how is absval(x^1/2-a^1/2) equal to abval(x-a)/(x^1/2-a^1/2)?

I have one question (simple I hope). In the TMVA factory one can set global weights by typing: // global event weights (see below for setting event-wise weights) Double_t signalWeight = 1.0; Double_t backgroundWeight = 1.0; And use them afterwards by calling their names signalWeight...

Here's my equation y= sqrt (x+4)+1 I want to find the x intercept. Ok so i replace y with 0 and solve for x 0= √(x+4)+1 -1=√(×+4) (-1)2=×+4 1=×+4 -3=× So it looks like the x intercept is (-3,0) But then when i go back and plug in -3 in place of x... y=√(-3+4)+1 y=1+1 y=2 I now have a point...

Can someone explain me what SetDirectory actually does? I found the problem with a macro like that: #include<iostream> #include <TH1F.h> #include <TCanvas.h> #include <TFile.h> int histoSum(){ //create histograms to use TH1F* histo1 = new TH1F("histo1",";A", 100, 0,10); TH1F* histo2 = new...

Homework Statement If you take a 4th root of something, is that answer also plus or minus, just like if you are taking a square root? Ex. ##4^{\frac 1 2} = ±2## So following that logic, would that mean that: ##16^{\frac 1 4} = ±2## as well? Meaning, is the ± still present if you take a 4th...

I am stuck with this question: why can't we use the equation c(rms)=√(3RT/M) for problems when no of moles is not 1? Because I think the mole will be deduced as c(rms)=√(3nRT/nM) =√(3RT/M) For instance I found this problem, given atmospheric pressure is 10^5 Pa, molecular mass of Nitrogen...

Suppose I have a programme. In there I have the creation of histograms: signal: histo_s_Pt histo_s_v1 histo_s_v2 background: histo_b_Pt, histo_b_v1 histo_b_v2 iteration to fill signal/bckg from events j. So at this point I'm having the 6 above histograms filled. Now if I wanted to compare...

Can you help me question 1a?

Hello guys, How can I evaluate the following integral please? ##\int_{-\infty}^{+\infty}\frac{e^{i A x}}{\sqrt{x^2+a^2}}dx## Thank you

And what are the methods? This was stimulated by This question could be rephrased as "use the method for finding square roots you were taught in school to find √7 to 6 decimal places". If you were taught at school. If you were not taught at school you were luckier than me, I was. It has had...

Hi I'm just wondering: How does √(10^2+10^2) become 10*√(2) ? I also noticed that √(10^2+10^2+ 10^2) becomed 10*√(3) But how to you mathematically - ith more steps- go from √(10^2+10^2) to 10*√(2)? Kind regards, Christian

I am reading the text Group Theory A Physicist's Survey of Ramond, in particular chapter 7. He explains classical lie algebra structure using cartan generators and root generators. He sometimes uses reality condition of structure constant( i think he supposes that all generators are...