All Questions
0
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0answers
2 views
How to find 'x' of this equation?
I'm doing some equations and I'm not sure how to find x. Any idea? Step by step answers please, it's like my first time.
2(3x^2+x-5)(2x^2-7x+3)=0
0
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1answer
7 views
Maximal number of leaders in the tournament.
Let's call a leader in the tournament such participant $L$, that won with every other participant directly or indirectly. Show that a leader always exists. Find the maximal number of leaders in the ...
1
vote
0answers
15 views
Using definitions instead of axioms.
Lets take (classical) first-order logic for granted, including an equality symbol and its associated axioms.
Given all this, a rigorous work of mathematics will typically begin with a signature - ...
0
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0answers
9 views
left handed and right handed cartesian coordinates ?
during my reading in Vector analysis - Edwin wilson - when i reached to the part of "unit vectors i , j , k" page 20 he stated a introduction of solid cartesian coordinates stating that regular ...
1
vote
0answers
10 views
The elliptic curve $x^4+y^4 = 193z^2$ and its friends
Given
$$x^4+y^4 = (u^6+v^6)w^2\tag{1}$$
let $u,v = 3,4$ then we have,
$$x^4+y^4 = 25\cdot 193w^2$$
or simply,
$$x^4+y^4 = 193z^2$$
and one solution is $x,y,z = 18, 31, 73$, and an infinite more. ...
0
votes
0answers
8 views
Find the standard matrix of the transformation $T:\mathbb{R}^2\to \mathbb{R}^2$ that corresponds to the reflection through the line
Find the standard matrix of the transformation $T:\mathbb{R}^2\to \mathbb{R}^2$ that corresponds to the reflection through the line $x_2=2x_1$ followed by reflection through the line $x_1=3x_2$
I am ...
1
vote
2answers
17 views
Continous value of integrals
Let $$f:(a,b] \rightarrow \mathbb{R} $$
if the riemann Integral$$ F(c):= \int_c^b f(x) dx $$ for all $$ c \in (a,b) $$ exists and the improper integral $$ F(a)=\int_a^b f(x) dx$$ exists too. Does this ...
0
votes
1answer
15 views
Why is a prime number needed for the Diffie-Hellman key exchange? (modular arithmetic)
I'm writing a cryptography essay, and am wondering why you need a prime number for the deffie-hellman key exchange? Any help would be appreciated :)
this is a link to a previous post which quickly ...
3
votes
0answers
13 views
Are large cardinals bi-interperable with type theory?
"Sets in Types, Types in Sets" establishes that the calculus of constructions is bi-interpretable with ZFC + infinitely many inaccessibles.
Are there any more results like this higher up the large ...
0
votes
1answer
16 views
Math question partial derivatives?
I have to find ∂z/∂x and dz/dx if z=ln(e^x+e^y) ,y=x^3
Awesome.Now, I write ∂z/∂x=(∂z/∂y)*(∂y/∂x) .I find ∂z/∂y=e^y/(e^x+e^y) ..but how do I find ∂y/∂x? what is its value?
0
votes
0answers
8 views
Converting a system of ODE to a single higher order ODE
If we have the system of differential equations:
$$x^{(2)}(t)=\alpha(y(t)+\frac{x(t)-2x^3(t)}{7})$$
$$y^{(2)}(t)=x(t)-y(t)+z(t)$$
$$z^{(2)}(t)=-\frac{-1}{100}y(t)$$
How do I convert it to a single ...
1
vote
1answer
24 views
Prove that for every $p>0$, $\lim_{n\rightarrow∞}\int_n^{n+p}{sinx\over x} = 0$
Got stuck with this question:
Prove that for every $p>0$, $\displaystyle \lim \limits_{n\rightarrow∞}\int_n^{n+p}{\sin (x)\over x} = 0$.
Thanks in advance for any help!
1
vote
2answers
16 views
Solve the quadratic congrunce
Solve the following quadratic congreunce
$x^2+ 7x + 10 \equiv 0$ (mod $11$).
I want to know a general and easy method how to solve this kind of questions.
0
votes
0answers
6 views
Are my definitions of cotangent space, differential and differential forms and coboundary operator correct?
Define the cotangent space $T_a^*\mathbb{R}^n$. Define the differential of a dunction $f$ at the point $a, df \in T_a^*\mathbb{R}^n$. Write down the explicit formula for the deffertial $df$ in ...
0
votes
0answers
18 views
Triangle inequality: $\vert\vert a+b\vert^q-\vert a\vert^q\vert\leq \varepsilon\vert a\vert^q+C(\varepsilon)\vert b\vert^q$
I am having difficulty in proving the following inequality for $1\leq q<\infty$:
\begin{equation}
\Big|\vert a+b\vert^q-\vert a\vert^q\Big|\leq \varepsilon\vert a\vert^q+C(\varepsilon)\vert ...
