Let $x = \sin10^\circ$. The formula for $\sin3\theta$ shows that $3x - 4x^3 = \sin30^\circ = \frac12.$ So $8x^3 - 6x + 1 = 0.$ If $y=2x$ then $y^3 -...
Another way of looking at this is to visualize $\int_0^\infty c\,dx$, where $c>0$. Now make a drawing, including the $x$-axis, of what this integral...
Each term in the series can be represented by $5+9n,\,0\le n\le240$. In order for a term to be divisible by $5$, $n$ must be divisible by $5$. Hence...
Sometimes editing a thread title is an issue, but the issue is with vBulletin. If you ever want to change a thread title, and can't, just let me know...
Perhaps there are differences in terminology...I was taught that a function is concave up on an interval when its second derivative is positive, and...
"People assume that time is a strict progression of cause to effect, but *actually* from a non-linear, non-subjective viewpoint - it's more like a big ball of wibbly wobbly... time-y wimey... stuff." -Dr. Who, "Blink"