I came across the following problem: Show that if $x$ and $y$ are real numbers with $x <y$, then there exists an irrational number $t$ such that $x <...

Given that P(A and B)=0.1 and P(A and B')=0.4 find P(A or B') if A and B are independent. The ans is 0.9 Please tell me the rule you use in the ...

My son's homework sheet says to solve problems like: (5) / (15/4) and to write the "quotient" in its "simplest" form. The crux of my question is, whi...

This could be primary school stuff. But I want to ask it. In factoring $x^2+bx+c$ (i.e. $a = 1$ in $ax^2+bx+c$), we find $m$ and $n$ such that $m+n = b$ a...

What I mean by that is, suppose say I have a circle centered at some point in the Euclidean space for which a certain property $P$ is true. How can I conc...

I was studying calculus and I had doubts about this problem: (this is not homework) A circular wire expands due to heat so that its radius increases with ...

Hello I' am stuck on how to get the final result of the laplace transform of $f(t)=tsin(at)$using (a is a constant) only the definition of $$\int_0^{...

I am stuck on what seems to be an easy exercise. We have $f(x,y) = x^2 + 4xy + y^2 \mbox{ for all } (x,y)$ in $\mathbb{R}^2.$ Now we are supposed to find ...

$$\dfrac{x_1^2+ x_2^2 + \cdots + x_n^2}n \geq \left(\dfrac{x_1+x_2+\cdots+x_n}n\right)^2$$ I don't think AM, GM can be used here. And simple expansio...

I want to solve a Lagrange multiplier problem, $$f(x,y) = x^2+y^2+2x+1$$ $$g(x,y)=x^2+y^2-16 $$ Where function $g$ is my constraint. $$f_x=2x+2, \ \ \ f_y...