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If $f(x)=x^{2}$ and $g(x)=x sin x+cos x$; Find out the no of intersecting point

Question from an entrance paper If $f(x)=x^{2}$ and $g(x)=x sin x+cos x$ then A. $f$ and $g$ agree at no point B. $f$ and ...

Mathematics Asked on 2 years ago

How to factor $x^k -1$?

Is there any way to find the degrees of the irreducible factors of a polynomial $x^k - 1$ over the field$Bbb F_q $, andover $Bbb Q$, in...

Mathematics Asked by Aspiring Mathematician on 2 years ago

Additional condition needed for a binary operation to have inverse, apart from the necessary condition of having a two-sided identity.

Is it needed that if two sided identity exists for a binary operation (on a set), still need to check if inverse exists or not. I request a reason for...

Mathematics Asked by jiten on 2 years ago

$Bbb{R}^n$ and $Bbb{R}$ are isomorphic as vector spaces over $Bbb{Q}$.

Show that $Bbb{R}^n$ and $Bbb{R}$ are isomorphic as vector spaces over $Bbb{Q}$.My attempt:Let $c=$ cardinality of $Bbb{R}$. Then we know that $Bbb{R}$ over ...

Mathematics Asked by user598858 on 2 years ago

On k-regular functions

My father asked me the following question: A real function $fcolon mathbb{R}to mathbb{R}$ is called $k$-regular if for each $yin mathbb{R}$, the equation $f(x)=y$ has precisely...

Mathematics Asked by Mathematician 42 on 2 years ago

Should I use the absolute value of a correlation coefficient?

I have calculated the Pearson correlation coefficient for two sets of values using excel. I got the value in the negative number. I know that the idea of getting a...

Mathematics Asked by LSG on 2 years ago

Integral with exponent and trigonometric functions

How do I solve the following integral?$$I = int_0^{pi} e^{-frac{1}{2}cos x} cos left( 3x + frac{1}{2} sin x right) dx$$ I suppose this can be solved...

Mathematics Asked by Denis Korzhenkov on 2 years ago

Axis of reflection

Is there any way to get the equation of axis of reflection given two intersecting lines without sketching?Example question: The image of the line $p:; y-2x=3$ is the line...

Mathematics Asked by Ham Tesh on 2 years ago

Skew-symmetric bicharacters on $A$ and $H^2(A,mathbb{C}^{times})$

Let $A$ be a finite abelian group. I have read that there is an isomorphism of abelian groups between the group $H^2(A;mathbb{C}^{times})$, and the group of skew-symmetric bicharacters...

Mathematics Asked on 2 years ago

An area preserving diffeomorphism between a disk and an ellipse

This is a self-answered question. I post it here since (embarrassingly) it took me some time to realize that the solution is obvious. Let $D subseteq mathbb R^2$ be...

Mathematics Asked on 2 years ago

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