# algebra

1. ### Computing velocity of wind

Hello, Going against the wind, a domestic plane can travel 5/8 of the distance it can travel in one hour if it is going with the wind. If the plane can fly 300 kilometers an hour in calm air, what is the velocity of the wind? Answer:- There are five answers given by the author to choose...
2. ### 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...
3. ### 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 ....
4. ### 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)...
5. ### 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...
6. ### 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...
7. ### 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...
8. ### 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...
9. ### 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...
10. ### 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!
11. ### 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...
12. ### 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...
13. ### 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
14. ### 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 $\displaystyle{\frac{a+b}{13}}$?.
15. ### 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...
16. ### 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 > .