Root Definition and 918 Threads

find the positive square root of 70-20\sqrt{30}

Homework Statement I. 3*3 matrix A (8 2 -2, 2 5 4, -2 4 5) II. 3*3 matrix (1 2 0, -1 -2 0, 3 5 1) Homework Equations I. Solve Aexp 100 of 3*3 II. Find the 5th rooth of B matrix The Attempt at a Solution I. I got stuck at diagonalising the matrix. Is this OK 1st step ? If yes...

Homework Statement I've been trying for a week to understand root locus and how it works but what i got is a big confusion that's why I'm asking here for help. Why do we only look at open loop transfer function of the system when we are supposed to know the stability of the closed loop system...

I started by setting $\alpha= e^{2\pi i/3} + \sqrt[3]{2}.$ Then I obtained $f(x) = x^9 - 9x^6 - 27x^3 - 27$ has $\alpha$ as a root. How can I proceed to find the minimal polynomial of $\alpha$ over $\mathbb{Q},$ and identify its other roots?

HI EVERYONE I was thinking if we could find a cube root without using a calculator. square root was easy to find without calculator,but cube root i have no idea to find it. any help?? for example(cube root of 3 or 2)

hi guys i know all square root and any root(cubic...) rules sqrt(x)=x^(1/2) sqrt(x^2)=abs(x) sqrt(xy)=sqrt(x)*sqrt(y) sqrt(x/y)=sqrt(x)/sqrt(y) sqrt(-x)=isqrt(x) f'(x)=1/2sqrt(x) F(x)=2/3*(x^3/2) ..... my question is: is there any rules for this sqrt(x+y) or sqrd(x-y)?? any help please??

The characteristic equation is 1+K(S+1)/S2 Below is the root locus diagram. I don't get why there are two branches when there is only one pole, at 0. Does it count as having two poles even if it is the same because of s^2 ? If it does then why doesn't the angle of departure make sense? number...

Homework Statement Good day, I've been have having difficulties finding the roots of this: Find the roots of 3ix^2 + 6x - i = 0 where i = complex number i = sqrt(-1) Homework Equations quadratic formula (apologies for the large image) The Attempt at a Solution...

Homework Statement A high school experiment shows a plant immersed in a solution of nitrate ions. The beaker is closed but has an air vent passing into the solution. Q. Why is air bubbled into the solution Q. Why is the beaker covered with black paper Homework EquationsThe Attempt at a...

I don't know what to say. sqrt(4) = +/- 2, but constants are fixed. When written sqrt(4), it seems sqrt(4) is a constant, but not in the latter case. Help!

Homework Statement Find the solutions to z^{\frac{3}{4}}=\sqrt{6}+\sqrt{2}i Homework Equations de Moivre's theorem The Attempt at a Solution z^{\frac{3}{4}}=2\sqrt{2}e^{\frac{\pi i}{6}}=2\sqrt{2}e^{\frac{\pi i}{6}+2k\pi}=2\sqrt{2}e^{\frac{\pi +12k\pi}{6}i} z=4e^{\frac{4}{3}{\frac{\pi...

Homework Statement The task is to plot a 2-d surface of the potential and field lines calculated from a numerical method. In this case, there is a charged box (v = 1) @ r = 1 (it's not round, but each side is d = 2 and the center of the box is at the origin) and the edges of the box are v=0...

Homework Statement Hi, I'm new here. I'm really rusty, I resume my career this year, and I'm reading 'the spivak book', (for Calculus 1). Making some exercises, I get curious about how to solve this: x+e^x=4 I would love if someone could give me any trick Homework EquationsThe Attempt at a...

Homework Statement P(x)=x^24-2kx^6+k^2 Find all values of k so that (x-(sqrt(3)/2+i/2)) is a factor of P(x) Homework Equations The Attempt at a Solution Letting z=sqrt(3)/2+i/2 mod(z)=1 arg(z)=π/6 z^(24) gives e^(24π/6)i=e^(2πi)=1 z^(6) gives e^(6π/6)i=e^(π)i=-1 If (x-(sqrt(3)/2+i/2)) is...

I'm having trouble simplyfying this, I guess there's a trick but for the life of me can't remember what it is. Here is what I have so far: ##\omega ^{2} = f\left ( \frac{1}{m}+\frac{1}{M} \right )-f(( \frac{1}{m}+\frac{1}{M} \right ))^{2} - \frac{4q^{2} a^{2}}{mM})^{\frac{1}{2}}## so I divide...

I'm going through an explanation in a number theory book about Tonelli's algorithm to find the square roots of a quadratic residue modulo ##p## where ##p## is prime, i.e. I want to solve ##x^2 \equiv a \pmod{p}## with ##(\frac{a}{p}) = 1##. The book goes as follows: Let ##p - 1 = 2^s t##, where...

Hello This is not exactly a homework problem. I was browsing through an old book, "Elementary Algebra for Schools" by Hall and Knight, first published in England in 1885. The book can be found online at https://archive.org/details/elementaryalgeb00kniggoog . I was studying the process of...

I need help understanding this proof. The textbooks says, For every k∈{1,...,n} there exists an mk∈ℕ such that (n choose k) rn-k 1/mkk< δ/n His justification for this, is that for every real number x there exists an natural number n such that n≥x. I fail to see the connection between the two...

Hi! :o I'm stuck :confused: I was thinking I need to use the equation $f=kw^2$ but I'm really not sure.

Hi, I'm using partial derivatives to calculate propagation of error. However, a bit rusty on my calculus. I'm trying to figure out the partial derivative with respect to L of the equation: 2pi*sqrt(L/g) (Yep, period of a pendulum). "g" is assumed to have no error. I know I can use the...

The N-R (iterative) formula is: xi+1=xi - f(xi) / f '(xi). A textbook exercise states that the N-R method does not converge for an initial guess of x >~ 1. I wrote the required program for tanh and found the method diverges at x >~ 1.0886. But I don't understand why it is this value - the N-R...

((2+i)/(3-4i))^(2n) I know it converges with 1/5 < 0 but I don't understand how to obtain 1/5 unless somehow its like this (2+i)^2 = (4+1)=5 (3-4i)^2 = (9+19)=25 which is 5/25 which is 1/5 but that doesn't seem like the correct way to me

Hi guys. Firstly the answer to the requirement of the post is all in the picture (problem statement, relevant equations etc.). I'm just wondering if someone could tell me why they use the root -0.435 as the breakaway point? Like I know there's two real roots; -0.435 and -1.61, so obviously one...

I was going through some important points give in my textbook and I saw this: ##\log_e x < \sqrt x## How did they get this? I know calculus so you can show this using differentiation, etc. One possible way is that they took ##f(x)=\sqrt x-\log_e x## And tried to prove it is always greater than zero.

Digital root (adding a number's digits together repeatedly until a single digit answer is obtained) doesn't seem like a very interesting operation, but it has some weird properties. One of the first someone might notice is that dr(n) = dr(n+9) This is fairly easy to demonstrate. But after...

Find a real root of $x^5-10x^3+20x-12=0$.

Homework Statement [/B] From K=4 to infinity the Σ (-1)^k (k/e^k) Converge or diverge? Use: a) Ratio Test b) Root Test c) Integral Test d) Alternating series test Homework EquationsThe Attempt at a Solution For the alternating series test and ratio test I have the correct answer that it...

Homework Statement Find the critical points for the function g(x, y, z) = x3+xy2+x2+y2+3z2. Homework EquationsThe Attempt at a Solution I've come up with the following 3 equations (derivatives set so that they are equal to 0) (1) 3x2+y2+2x=0 (2) 2xy+2y=0 (3) 6z=0 From (3), z=0 From (2)...

Can anyone tell me why for example the speed of light is squared in "E=mc^2" ? Also what does square root mean and why is it in certain equations like for example time dilation? What happens if you exclude the square root and the y^x in a equation? I am still studying high school physics, but...

In a text, We have this: $\sqrt{2x^2 + 1}$ is equal to $x \sqrt{2 + \frac{1}{x}}$ I am confused as to how to factor out x from the original term.

Dear everyone, I have a question about a property of square root. $${\frac{1}{x}\sqrt{x^2}}$$$\implies$ $\sqrt{\frac{x^2}{x^2}}$=$\left| 1 \right|$ Is that property of a square root? Since $$\sqrt{x^2}$$= $\left| x \right|$.

$a+bi$ is a root of :$z(z+i)(z+3i)=2002i$ here :$a,b>0$ and $i=\sqrt {-1}$ please find :$a^2-b^2=?$

Dear All, Please help me understand how ## \sqrt{2} ## divide by 0 is rational as stated in the excerpt from alan F beardon's book?

A quiz at the end of Steven Krantz's Calculus Demystified includes the following problem: Find \lim_{x \to \infty} [ \sqrt[3]{x+1} - \sqrt[3]{x} ] I see how one can use the Maclaurin series to get \sqrt[3]{x+1} = 1 + \frac {x}{3} - \frac {x^2}{9} + \frac {5 x^3}{81} + . . . but trying it...

Prove that the order of 5 modulo $2^k$ is $2^{k-2}$ where $k$ is at least 3. I thought probably induction is best bet. For k=3 we can verify. So for inductive step we need to show the order of 5 modulo $2^{k+1}$ is $2^{k-1}.

Hi, In the attached image the roots are shown for the characteristic equation. I don't know how the roots were found. Anyone able to help? Thanks Splint

$$4\sqrt{n^{2}}+\sqrt{m^{2}n-\sqrt{4n^{2}}}-\sqrt{mn^{2}}$$ I don't even know where to start, I know the teacher said to distribute but distibute what?

I have: sq rt 2 +sq rt 2 over 2 , sq rt 5 + sq rt 5 over 2 I got (sq rt 4 over 2, and 0) = 1, 0 but the answer is actually (sq rt 2, 0) so is my answer still wrong?

solve a radical expression: 1.5r250 (*r denotes the radical symbol) in a radical expression where the index of the root is 1.5 and the number is 250 Use Calculator, Show Steps Homework Equations The Attempt at a Solution First of all, using a calculator the answer comes out to 39.685, but I...

Homework Statement These are the Points. X values: 0, 1.98, 3.96, 5.94, 7.92, 9.9 Y values: 1.98, 7.13, 9.08, 11.04, 12.57, 14.51 I need to find the original equation and the linear equation. I can't seem to find the line for square root graphs. 2. The attempt at a solution I know it's a...

I need to find the domain of this function.$$h(x) = 1 / \sqrt[4]{x^2 - 5x}$$ So, I understand that I need to set $$x^2 -5x > 0$$ from that I get $$ x(x-5) > 0$$ and $$ x > 5$$ However, the answer in the textbook is given: $$ ( \infty, 0) \cup (5, \infty)$$ Which mean that the graph has a...

How does this work? (Also, I am very math illiterate and do not understand even the most basic terms, if you could kindly speak as you would to a child I would GREATLY appreciate it.) sq rt sign over 13^2 - 12^2 (over both of it together) Now the answer is 5, because (13)(13) - (12)(12)...

Homework Statement Write code in Mathematica to find the root of f(x) = \int_0^x \frac{\sin (t)}{t} \, dt-\frac{\pi }{2} using the bisection method. I have attempted to do this using: f[x_] := N[-(Pi/2) + Integrate[Sin[t]/t, {t, 0, x}]] (*Plot[f[x],{x,0,2*Pi}]*) fg =...

I have a table with several quantities in it, and one of them is \sqrt{T} (T is tension) I have values for this table, and want to put the units next to the values. Something seems off to me about doing this, I guess because they're not integers. Is it correct to say the units are kg1/2m1/2s-1...

Easiest Method to Evaluate Imperfect Square Root up to 5 Decimals? Any ideas?

Is $$\mathbb{Q}(\sqrt[3]{3})=\{a+b\sqrt[3]{3}+c\sqrt[3]{9}\mid a,b,c\in\mathbb{Q}\}$$ a ring? If it is a ring, is it a field? I have shown that it is a ring; however, I am not sure that it is a field, since in my calculations it does not seem to be closed under inverses. But I read somewhere...

Homework Statement In this task we will show that √2 is irrational. Assume that √2 = a/b where both a and b are natural numbers. Let a = p1p2p3...pn, and b = q1q2q3...qm be the prime factors a) explain why 2q1q1q2q2q3q3...qmqm = p1p1p2p2p3p3...pnpn √2=a/b b√2=a...

PHP has some powerful arbitrary-precision (BC or binary calculator) arithmetic functions which seem to be greatly underused and only consist of the basic arithmetic operations, a square root function, a mod function and an integer power function. However, those basic operations can be used to...

Show that for every integer $k\ge 2$, the equation $x^k+\dfrac{1}{x^k}=1+x$ has a root in the interval $\left(1, 1+\dfrac{1}{k} \right)$.

Hello. How do I find the limit of this term? $$\lim_{{n}\to{\infty}}|\left(\frac{n}{n+1}\right)^{\!{n^2}}|^\frac{1}{n}$$ This is the working but I don't understand how to get the third line. r = lim(n→∞) |[n/(n+1)]^(n^2)|^(1/n) ..= lim(n→∞) [n/(n+1)]^n ..= lim(n→∞) 1 / [(n+1)/n]^n...