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What is the value of $\arctan(1/2)+\arctan(1/5)+\arctan(1/8)$?
What is the value of : $$\arctan(1/2)+\arctan(1/5)+\arctan(1/8)?$$ I tried to do geometric solution:: Where in the angles we are looking for are shown, bu...
Apr 12, 2026
Archive: News
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Completing the square for quadratic equation
I'm learning algebra (at age $66$) with home schooling materials. I am doing well and enjoying it. My question is this: The material says I can use "...
Apr 12, 2026
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Why have we chosen our number system to be decimal (base 10)?
After learning about the binary number system (only 2 symbols, i.e. 0 and 1), I just thought why did we adopt the decimal number system (10 symbols) after...
Apr 12, 2026
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Is it possible to take the absolute value of both sides of an equation?
I have a problem that says: Suppose $3x^2+bx+7 > 0$ for every number $x$, Show that $|b|<2\sqrt21$. Since the quadratic is greater than 0, I assume ...
Apr 12, 2026
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How to determine if two lines are parallel/ almost parallel?
I have $2$ lines in this form Line $1$: $(x_1,y_1)$ $(x_2,y_2)$ Line $2$: $(x_3,y_3)$ $(x_4,y_4)$ I want to detect if the two lines are parallel or almost...
Apr 12, 2026
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How to Find Moore Penrose Inverse
I have a matrix: $$A= \begin{bmatrix} -1 & 0 & 1 & 2 \\ -1 & 1 & 0 & -1 \\ 0 & -1 & 1 & 3 \\ 0 & 1 & -1 & ...
Apr 12, 2026
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Proof of Heron's Formula for the area of a triangle
Let $a,b,c$ be the lengths of the sides of a triangle. The area is given by Heron's formula: $$A = \sqrt{p(p-a)(p-b)(p-c)},$$ where $p$ is half the p...
Apr 12, 2026
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What does "relatively closed" mean?
Let $S\subset U$. What does it mean to say that $S$ is relatively closed in $U$? Also $U\subset\mathbb{R}^{n}$ is open and bounded, but I don't know ...
Apr 12, 2026
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Find points on graph at which slope of tangent line is equal to 4
Find the points on the graph of $y = x^{2}+2x+6 $at which the slope of the tangent line is equal to $4$ Just starting to learn calculus. This is what I ha...
Apr 12, 2026
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Proper divisors of 1?
What are the proper divisors of 1? I understand proper divisors do not include the number itself, but is 1 an exception or does it have no proper divisors?
Apr 12, 2026
