2
votes
1answer
60 views

Can polynomials with degree at least 2 over $\mathbb{R}$ have finite number of solutions in $End(\mathbb{R},+)$

Consider a polynomial of degree at least 2 with all coefficients in $\mathbb{R}$. We are concern with set of solution for the polynomial in $End(\mathbb{R},+)$ - the endomorphism ring of the abelian ...
0
votes
1answer
40 views

Finding equations when given new center of a circle

$y = −x + \sqrt{2}$, $y = −x − \sqrt{2}$, $y = x + \sqrt{2}$, and $y = x − \sqrt{2}$. These equations determine lines, which in turn bound a diamond shaped region in the plane. Construct a diamond ...
0
votes
1answer
48 views

Convert this scenario into algebra equation

Sales for the month minus the VAT @ 20% = (x). 20% of (x) is profit margin (y). 5% of (y) is commission earned (c). How can I write an equation that demonstrates the above please? I.e x - 20% of y ...
0
votes
0answers
100 views

integral equations - i need help to expand the function [duplicate]

I have the following integral equation to solve: $$\int_{0}^{2\pi} (\cos^2(x+y)+1/2) \phi (y) dy$$ So, I need to find $\lambda$ where $\lambda$ is the eigenvalues's function. Well, my main goal is ...
0
votes
1answer
94 views

Plotting temperature over time excel

I am doing an uni assignment and have worked out a linear equation which plots temperature over time. I have this in a graph now but that required me to use a lot of calculations in the spreadsheet. ...
5
votes
2answers
343 views

Are all multiplicative functions additive?

Suppose $cf(x)=f(cx)$ and $f:\mathbb{R}\to\mathbb{R}$. I believe it follows that $f(x+y)=f(x)+f(y)$. Proof: There is some $c$ such that $y=cx$. Then ...
5
votes
2answers
239 views

Cauchy's functional equation for $\mathbb R^n$

Suppose $f(x+y)=f(x)+f(y)$. If $f:\mathbb R\to \mathbb R$ and is measurable, then $f(x)=cx$. This is referred to as Cauchy's functional equation. Suppose $f:\mathbb R^n\to \mathbb R^n$ instead. Does ...