Root Definition and 944 Threads

In vascular plants, the roots are the organs of a plant that are modified to provide anchorage for the plant and take in water and nutrients into the plant body, which allows plants to grow taller and faster. They most often lie below the surface of the soil, but roots can also be aerial or aerating, that is, growing up above the ground or especially above water.

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  1. B

    How Do You Solve a Differential Equation Involving a Square Root?

    Hi all, I've been musing on a problem I came across whilst decanting some sloe gin (that time of the year here in the UK and all that). Essentially, I want to know given a vessel of known dimensions, open to the atmosphere at the top, with a hole in the bottom, and a pipe at the top filling...
  2. L

    Understanding the Derivative of y = 2x sqrt(x^2 + 1)

    y = 2x square root of (x^2+1) I'm not exactly sure how to start off this problem. Am I supposed to use the chain rule or some other rule? I really need help on understanding this, so if anyone is kind enough to provide detailed steps, I thank you so much.
  3. L

    Show a function has at most one Root (IVT & Rolles [quick question])

    show x^3-15x+c=0 has at most one root on the interval [-2, 2]. My work/attempted solution. Using the IVT i determined that there is a possible root (N=c) within the interval of [-2,2]. because c is my constant i decided to Use [d] as my letter for explanation. f(x)=x^3-15x+c...
  4. T

    Prove that of sum square root of 2 and square root of 3 is not rational

    prove that the square root of 2 plus the square root of 3 is not rational? does always the sum of two not rational numbers is a not rational number? i know the proof 2 = a^2/b^2 i separately proved that square root of 2 and square root of 3 are irrational how two prove that the sum...
  5. K

    Which Interval Contains the Root of the Equation?

    Homework Statement Find an interval of length 1 that contains a root of the equation xe^{x}=1 Homework Equations The Attempt at a Solution I'm not quite sure how to find these intervals... Homework Statement Find an interval of length 1 that contains a root of the equation...
  6. W

    Proof that linear operator has no square root

    Homework Statement Suppose T \in L(\textbf{C}^3) defined by T(z_{1}, z_{2}, z_{3}) = (z_{2}, z_{3}, 0). Prove that T has no square root. More precisely, prove that there does not exist S \in L(\textbf{C}^3) such that S^{2} = T. Homework EquationsThe Attempt at a Solution I showed in a...
  7. E

    Proove that the cubic root of 2 + the square root of 2 is irrational

    How do you show that the cubic root of two + the square root of two is irrational? I can easily show that each of these numbers is irrational, but not the sum :/.
  8. K

    How to use Rolle's Theorem to prove exactly ONE REAL ROOT

    Homework Statement Show that the equation 2x-1-sin(x) = 0 has exactly one real root. Homework Equations The Attempt at a Solution I first used the Intermediate Value Theorem to prove that there exists at least one c such that f '(c)=0. The next step requires Rolle's Theorem to...
  9. S

    Finding the 6-decimal Root of e^-x=lnx in [1,2]

    Homework Statement to six decimal places the root of the equation e^-x=lnx over interval [1,2] The Attempt at a Solution (e^-x)-lnx=0 F'(x) = (-e^-x)-(1/x) x(subcript(n))-(e^-x)-lnx/(-e^-x)-(1/x) the problem I am having is getting it to six decimal places. do i have to go int0...
  10. E

    How to Analyze Root Locus in Matlab for DC Motor Control?

    Homework Statement I'm trying to analyze the root locus of this transfer function in Matlab to control a DC motor: mysys=tf([0.022],[0.00000000007 0.0000000626 0.000493]) The Attempt at a Solution Using: %[Kp,P]=rlocfind(mysys) %rltool(mysys) rlocus(mysys) I get a root locus...
  11. S

    Proof of uniqueness of square root

    Homework Statement Let G be a finite group in which every element has a square root. That is, for each x\epsilon G, there exists y \epsilon G such that \(y^2=x.\)Prove that every element in G has a unique square root. The Attempt at a Solution Proof: Assume not. Let k be the order of G...
  12. M

    Show that complex conjugate is also a root of polynomial with real coefficients

    Homework Statement Suppose that f(x) is a polynomial of degree n with real coefficients; that is, f(x)=a_n x^n+ a_(n-1) x^(n-1)+ …+a_1 x+ a_0, a_n,… ,a_0∈ R(real) Suppose that c ∈ C(complex) is a root of f(x). Prove that c conjugate is also a root of f(x) Homework Equations...
  13. P

    Simple square root addition question

    I know this must be an easy question, but I can't seem to remember how to do it: \sqrt{z^2+R^2 - 2zR} - \sqrt{z^2+R^2 + 2zR} Can someone go through step by step how to solve this? This isn't a homework question but I've been running into this problem more often in multiple courses. So far...
  14. E

    What is the square root of zero?

    1. describe the square root of 0 from the following perspectives: A. Algebraic B. Complex Numbers C. Limits
  15. N

    Multi-dimensional root finding

    Hi all, Consider that one has several functions, say 3, of the form f(x,y,z) and g(x,y,z) and h(x,y,z). You know the form of these equations and they are non-linear, long, messy equations. f', g' and h' are even longer and messier and therefore assume that they cannot be found. Now...
  16. C

    Integration Involving Square Root

    Homework Statement \int \sqrt{t^8 + t^6 } dt Homework Equations The Attempt at a Solution I'm not sure what to do next, can someone point me in the right direction? Thank you.
  17. tony873004

    Square Root of N Law of Random Counts

    "Square Root of N" Law of Random Counts According to my lab manual, "Theory says that radioactive decay obeys statistics for which the standard deviation of the counts per time interval is equal to the square root of the mean number of counts for that interval, for cases when the mean is a...
  18. N

    How to find Pressure and Root Mean Square Velocity

    Homework Statement The average kinetic energy of a 2.35g sample of argon gas in a 7.00L container is 2.58E-22 j/atom. Homework Equations a) What is the pressure of the gas? b) What is the rot mean square velocity of teh argon atoms under these conditions? The Attempt at a Solution...
  19. M

    Primitive 5th root of unity extension

    Hi, Let E = Q(a), where a is a primitive fifth root of unity. Find a basis for E as a vector space over Q, and express a/a-3 in terms of this basis. I can find a basis for E: {1, a, a^2, a^3}, but am not sure how to express a/a-3 in terms of this basis. Any help much appreciated.
  20. J

    What is the intuition behind root mean square?

    From this website, http://www.analytictech.com/mb313/rootmean.htm It seems to it is more intuitive to just inverse all the sign to calculate the mean. But I can't get the idea of root mean square (equation can see here http://en.wikipedia.org/wiki/Root_mean_square) How is this idea...
  21. T

    Conversion of root mean square or interval velocity into average

    I really ain't sure whether my problem is mathematical or related to Physics but i most probably think it has a mathematical solution. I am have a situation where I have subsurface seismic velocity windows at certain Depth points. In the window I have been given the two-way time in seconds...
  22. Evo

    Root Canal Today: My Numb Eye, Gnats & Cravings

    Ok, I finally broke down and had a root canal done on my other tooth. This doctor really believes in going heavy on the local anesthetic. So much so, even my eye started to get numb, which concerned me a bit. Now I am in that gawdawful time when the anesthetic is wearing off and it feels...
  23. D

    Derivative of a square root fraction.

    I need help finding the derivative of the following equation. This may look a little messy because it involves a square root and a fraction. y = square root of: 1 + x2 / 3 + 3 - x / 5 My first thought is to change the equation to look like this: y = (1 + x2)1/2 / 3 + 3 - x / 5...
  24. J

    Are all root systems defined with respect to a bilinear form?

    When root system is defined on some vector space V, the definition uses numbers \langle x,y\rangle = 2\frac{(x,y)}{\|y\|^2},\quad x,y\in V where (\cdot,\cdot) is the inner product. This number is handy, because a reflection of vector y with respect to a hyper plane orthogonal to x is...
  25. J

    Show equation has Exactly one real root

    Homework Statement show that the equation 1 + 2x + x^3 + 4x^5 = 0 has exactly one real root Homework Equations The Attempt at a Solution i don't know what to use to find out that it has exactly one real root. i know you use the intermediate value theorem for roots but what do...
  26. S

    ANGAMWhat is the Integral of Cube Root of Cot(x)?

    Hi, I just registered on to the forums, and I have to say it is a very good job. I am currently a senior at High School and aiming for an Engineering Course. While solving some integrals, I got stuck upon this one, and even after a lot of attempt, my friends and I could not solve it. Hence I...
  27. R

    Solving x^3 +5x -4 to Get Root 0.3274

    I am on my final part of my C3 coursework, doing the comparison of methods, i have found the root using the change of sign method, and the Newton raphson method but i am struggling with using the rearranging method. the equation i am using is x^3 +5x -4, i have tried rearranging it to get the...
  28. P

    Definite integral involving base e and square root of variable as exponent

    Homework Statement Calculate \int_{0}^{4}\sqrt{x} e^{\sqrt{x}) The Attempt at a Solution At first I tried substitution, but this didn't bring me anywhere since the integral is not of the form \int f(g(x))g'(x) My attempt at integration by parts also leads to an endless loop...
  29. D

    Analogue Square Root: Practical Output Explained

    Hi everybody... http://www3.0zz0.com/2008/07/02/08/264668819.jpg As shown in the previose figure, the output from the op amp is sequre root the input signal. Since the feedback of our circuit is sequare the feedback signal ( the output), we shall expect the output to be sequare root for...
  30. J

    Using a differential to approximate a cube root

    Homework Statement Use the differential dy or L to approximate cubed root 1.03 Homework Equations L(x)= f(a) +f'(a)(x-a) The Attempt at a Solution I have no clue how to start so that would be the most help, do i just find the derivative of cubed root 1.03 first?
  31. D

    Can the 0.5 constant in the asymptote of sqrt(x*(x-1)) be found?

    Hi. I'd like to show that sqrt(x*(x-1)) has the asymptote x-0.5. The coefficient on "x" is found by saying \lim_{x\rightarrow\infty}\frac{\sqrt{x(x-1)}}{x}=1 but how does one find the 0.5 constant?
  32. E

    Constant determining a double root

    Consider the function y=x^3 - 2x^2 + k, where k is a constant. Explain why k=0 ensures that f(x)=0 has a double root. A double root is a bounce and I thought that when k=0, the x^2 can be immediately common factored out of the function, so you have (x^2)(x-2)=0. Therefore, you will always have a...
  33. J

    Square Root of a Negative Number?

    I'm pretty sure it's not possible but if anybody has any kind of theory on finding the square root of a negative number go ahead share. Sorry if I sound a bit imature or "noobish". I'm new here and probably younger then a majority of the users here. Example: -100
  34. Holocene

    Can you take an even root of a negative number?

    Actually, can you take a root of any negative number?
  35. F

    Prove 7th root of 7 is irrational

    1st I assume it is rational so: 7^(1/7) = m/n then 7 = (m^7)/(n^7) implies m^7 is a multiple of 7. Means m^7 = 0 mod 7 So, using fermats little theorem.. m^7 = m mod 7 for m to be in the class of 0 it has to be a multiple of 7. Now set m = 7k, so 7n^7 = 49k^7 But...
  36. K

    Equilibrium problem involving cube root

    Homework Statement The reaction 2Fe3+ + Ni(s) = 2Fe2+ + Ni2+ has equilibrium constant K = 1.5E34. What is the concentration of Fe3+ at equilibrium if a lot of Ni(s) is added to a 0.1 M solution of Fe3+ that initially contains no Fe2+? The Attempt at a Solution K = 4x3/(0.1-2x)2 My...
  37. B

    Root Locus: 4 Open Loop Poles at s=-2

    If have a system with 4 open loop poles, all at say s=-2, how would the locus approach each of the four asymptotes? thanks
  38. K

    Defining the Square Root: Why Do We Only Consider the Positive Number?

    Homework Statement I have been doing elementary algebra for a couple of weeks now, and gotten quite used to the idea that the square root of n gives +- n1. Then moving on to arithmetic and n-roots / powers, I was given the current definition of the square root: The square root of a...
  39. S

    Questions about imaginary number and root of 4

    I am thinking that if the imaginary number is bigger than the other number, is it right to say that: i> 5 ? 7i> 3i ? Does i has magnitude? if Z_1=4+5i then Z_2=1-3i whether Z_1>Z_2 or Z_2>Z_1 is true? If we say Z_a is bigger than Z_b, does that means the absolute value of these complex...
  40. Schrodinger's Dog

    Re: Integral involving square root of e^x

    [SOLVED] Re: Integral involving square root of e^x Homework Statement \int \sqrt{1-e^{-x}} Homework Equations Sub rule. The Attempt at a Solution I realized that it's fairly obvious I can use u=e^-x/2 to give \sqrt {1-u^2} but I'm kind of looking at the answers and I'm not seeing how I...
  41. P

    Can a 4x4 matrix with two vanishing eigenvalues have a square root?

    If one 4\times 4 matrix have two vanishing eigenvalues, does the matrix have a square root?
  42. M

    Finding Point c on f(x) = kx^n for Equal Area Between 0 and c

    Ok, so doing a physics problem the other day I had to find a point c on a graph such that there was an equal amount of area between 0 and c and c and a point b > c. I found that for the graph f(x) = kx, the point was b over the square root of 2. This intrigued me so I looked for a...
  43. R

    Square root of an imaginary number

    Where on the imaginary number axis do i graph sqrt(3i)? At sqrt3?
  44. C

    Antiderivative of square root function

    1. find the antiderivative of sqrt(81-x^2) in the bounds 0 to 9/2 okay so the first thing i did was sin substitution. where I made x = 9sin(t) dx = 9cos(t) where t is theta. then after some manipulating i got that that new integral was 9cos^2(t) i then used the double angle formula and...
  45. P

    Root of the symmetric equation

    Homework Statement Solve this equation, and find x. 6x^5-5x^4-29x^2-5x+6=0 Homework Equations if x= \alpha is root of the symmetric equation, then x= \frac{1}{\alpha}, is also root of the symmetric equation The Attempt at a Solution I tried first to write like this...
  46. I

    How Do You Calculate the Interest Rate for Compound Interest Problems?

    Have this question in relation to some investment exam I am doing, I am a maths novice being some years since leaving school etc, ok enough of the excuses. Example FV = future value PV = present value R = interest rate N = number of compounding periods my PV is 6000 and my FV is...
  47. C

    Prove that the square root of 3 is not rational

    Homework Statement Show that the square root of 3 is not rational Homework Equations The Attempt at a Solution A number is irrational if χ is not ε. Q=p/q: p, q ε z and q is not=0, z=integers If p/q: p, q is not ε or q=0, then square 3 is rational. If p=square root of 3 and q...
  48. E

    Complex Variables. Complex square root function

    Homework Statement Proof that f(z)=\sqrt{z}=e^{\frac{\ln z}{2}} with logarithm branch [0,2\pi). Then f maps horizontal and vertical lines in A=\mathbb{C}-\{\mathbb{R}^{+}\cup\{0\}\} on hyperbola branches. Homework Equations I have that \ln_{[0,2\pi)} (z)=\ln\vert z\vert+i\mathop{\rm...
  49. P

    Root mean square velocity of CO2 molecules

    Homework Statement If the translationa speed of the water vapor molecules (H2O) in ir is 648 m/s, what is the translational rms speed of the carbon dioxide molecules in the same air? Both gases are at the same tmperature. Homework Equations V^2 = (3kT)/m The Attempt at a Solution...
  50. cepheid

    Principal nth Root of a Real Number

    According to Wikipedia, if n is odd, then every real number A has a unique real nth root having the same sign as A and known as the principal nth root of A. It is denoted by \sqrt[n]{A} My question is, how do we know that this is true i.e. that \sqrt[n]{A} exists for all real numbers...
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