1. A

    Invariant Subspace proof

    I am having some trouble with part (ii) of the following question, part (i) is fine; Let V be a finite dimensional vector space and let f, g : V -> V be linear maps such that f∘g = id_V. Prove: (i) g∘f = id_V (ii) a subspace of V is f-invariant if and only if it is g-invariant I've tried the...
  2. N

    Solve for x+y+z

    if 36/11=3+1/(x+1/(y+1/z)) , where x,y,z are natural number Answer is 6 but i want steps ....
  3. F

    Why this equation is true? Can someone explain?

    Can someone explain why this equation is true? I came up with it some time ago and did not understand why it's true: Is there some specific rule for that? Maxima CAS could not tell if it's true, but it is.(Surprised) \frac{2 \tan{\left( \frac{\alpha }{2}\right) }}{\tan{\left( \alpha \right)...
  4. O

    Finding solution for natural logarithm equation

    Hi, Can someone please explain to me why when solving for $2\ln{x} + \ln{x+2} - \ln{x^2 + 2x} = -\ln{2}$ the solutions for x are 0, 1/2, and -2,but when you substitute these values back into the equation, only x = 1/2 works? There may be some elementary concept relating to systems of...
  5. I

    Steps of deriving a complicated algebra equation

    Hello guys, I am currently working on a physics paper, and in it there is an equation I need to show how to derive. The equation is (it's not in its original form because it has variables containing two letters, and even though one might say it makes no difference, it actually makes the...
  6. N

    factoring polynomials - I have been stuck for a while

    2.x9 + 1 3. 2m4 - 2mn3 4. 3a4 + 81a B. Can These Be Factored using the methods (GCF, squares, cubes) discussed in thislesson? Yes or No? Explain why or why not in a complete sentence? 5. 7x5 - 64y 6. a4 + 1 7. a4 – 64 C. Factor completelyusing Grouping 8. xy – 5y – 2x + 10...
  7. F

    Binary relation

    Hello, i've been given this problem at University and I need some help with the formulas. From already thank you very much. Let A = {1,2,3, ..., 365} be the set of the days of the year 2018, numbered from 1 (January 1, 1018) to 365 (December 31, 2018). Let R be the binary relation in A given by...
  8. D

    Mininum Variance Portfolio of Two Risky Assets

    So I have a question: I need to derive an expression for the share of wealth allocated to Asset 1 in a portfolio that has the minimum possible variance. The following is known: Two risky assets: 1 and 2 Returns: r1 and r2 Variance: σ12 and σ22 Covariance: σ12...
  9. B

    How does this fraction simplify into that?

    -----> Huh? (Drunk) The first equation is the original, the second one is the answer. A hero is needed to assist me in this strange paradise of problem!
  10. R

    Demonstration by Induction

    Hi, I've been trying to demonstrate this(Worried): I know that $d_1=1, d_2=10, d_3=50, d_4=248$ and for $n \geq 5 ,d_n = 5d_{n-1} - 4d_{n-4} $. Demonstrate for all $n \in \mathbb{N} $ that: $$P(n): d_n < n \cdot 3^{n+1}. $$ I need to demostre this using the induction principle. My doubt is...
  11. A

    How to arrange a football team and substitutions

    Hi all, First time on the forum for me, looking for some help on a practical problem! Basically me and some colleagues have a football match tomorrow, and we would like to figure out how we can all spend the same time on the field, given some restrictions: Strikers: Iago, Javier Midfielders...
  12. O

    Algebraic manipulations and solutions

    Hi, Can someone help clarify why the solution to this expression does not result in both solutions equating to 2 when substituted in for x? I'm referring to when x = 4, since (4) + (4)^(1/2) does not equal 2. What is going on here? Please let me know! - otownsend
  13. S

    Algebra problem

    I am stuck at a question after trying a lot,plzz help me Q. If the equation $\dfrac{x^2}{(1+x^2)^2}+\dfrac{ax}{1+x^2}+3=0$ has two real and distinct roots then a lies in the interval $(-\infty,a)\cup(b,\infty)$. Then find the value of $\displaystyle{\frac{a+b}{13}}$?.
  14. J

    Simultaneous Equations

    A journal is planning to increase the price of its magazine. According to a recent survey, 1250 magazines will decrease for each 0.025 dollars increase of the magazine price. What is the price of the magazine that will increase the revenue of the journal to its maximum. The normal price of the...
  15. C

    position vector of the point to the intersection of the line

    Find the position vector of the point of intersection of the line x→= ⎛⎝⎜⎜⎜28110⎞⎠⎟⎟⎟ +t ⎛⎝⎜⎜⎜-120-1⎞⎠⎟⎟⎟ and the plane x→= ⎛⎝⎜⎜⎜-253-18⎞⎠⎟⎟⎟ +λ⎛⎝⎜⎜⎜-10-2-1⎞⎠⎟⎟⎟ +μ⎛⎝⎜⎜⎜-130-9⎞⎠⎟⎟⎟ The syntax for entering the column vector ⎛⎝⎜⎜⎜abc⎞⎠⎟⎟⎟ is < a,b,c > .
  16. M

    factorisation of determinant

    help please
  17. S

    Adding a fraction to a whole number in an algebraic equation

    Hello! :) I am going over another answer for a question on an online test: The only question I have is, how did they get 9/2? The way I'd go about solving this is making the -4 a -4/1, and then adding -1/2 to get 4/2. Where am I going wrong? Thanks in advanced! :) -Neo
  18. W

    Complicated equation with 3 unknowns - please help!

    Hi all, I'm doing my final year maths project, and it has appeared to be a bit beyond my limits... It would be great if you helped me somehow! So, I have 3 points from a graph and a general equation. With this data, I have to find a, b, and c of this equation. The equation is: While the...
  19. M

    eigen value and vector using properties help

    i know how to find eigen values and vectors but i'm having difficulties in questions 2 3 and 4 (part 2 and 3)
  20. S

    Distributed Discount.

    Hi All, Wasn't to sure what to title this with, I would like to apply a discount for multi-qty's orders of Items. More Specifically, for every Six (6) ordered, One (1) Item is Free. So Ordering Twelve (12), would get Two (2) for Free BUT I would like Qty Breaks for 1,2,6 & 12. 1 - £22.00 2 -...