I'm trying to solve the following $x^2 + 3x + 7 \equiv 0 \pmod {37}$ What I've tried - I've tried making the left side as a square and then...

I have been trying to prove that $9^n-8n-1$ is divisible by $8$ for all $n$ integers greater than 1. My progress: Let $n = 2$. This gives us the expressio...

I am currently enrolled in a General Relativity course, and was taught about the connection but I can't really wrap my head around it qualitatively. ...

Background: Vieta's Theorem for cubic equations says that if a cubic equation $x^3 + px^2 + qx + r = 0$ has three different roots $x_1, x_2, x_3$, th...

$$ A = \left( \begin{array}{ccc} 10 & 29 & 41 \\ 23 & 27 & 42 \\ 24 & 28 & 48 \\ \end{array} \right) $$ $\det (A) = -1748$. Now $B...

Given bases $a$, $b$, and the height $h$. Get the $M(x,y)$ coordinates formula from point $O(0,0)$, where $M$ is center of mass. Wiki has a formula for $M...

As we know cross product of any two vectors yields a vector perpendicular to plane containing both the vectors so is it same for the vector operator del c...

I have a rectangle with a known area and a known ratio of length/width. How do I calculate the length and width. Area: 1500 sq ft Ratio: 241 / 625 = .386 ...

In pre-calc, we're doing trigonometric identities, and I have a question but my teacher isn't available right now. We have to verify trigonometr...

sketch the region enclosed by the given curves and find its area: $$y=\frac 1x,\; y=x,\; y=\frac x4,\; x>0.$$ I have no problem sketching the area betw...