What is the extraneous solution of $$\sqrt a=a-6$$ The roots are $9$ and $4$. So I'm assuming that $4$ is the extraneous solution because when you pl...

I am trying to plot a 3D surface like the picture below to help depict the relationship between some variables. I have been fiddling with Google Search bu...

This is a question I have regard the proof of the cancellation law for addition in Apostol's Calculus. We are told that the sum of two real numbers x...

It seems the definition of a parallelogram is locked to quadrilaterals for some reason. Is there a reason for this? Why couldn't a parallelogram (giv...

My textbook states that $f(x)$ can always be written as $$f(x) = q(x)g(x) + r(x)$$ but it doesn't provide any proof of this and I cannot seem to find...

Is there any software that lets one explore group theory, ring theory, and category theory visually and theoretically that is tailored for education purpo...

I understand that this looks exactly like a "Do my Homework" kinda question but trust me, I've spent hours(I won't go into detail as it's o...

Can someone provide an example of a covariance matrix for any set of data? For example, if given: 2 3 4 5 1 8 9 7 6 how would I take this 3x3 matrix and c...

I'll use the following definition: (Def) A functor $F$ is exact if and only if it maps short exact sequences to short exact sequences. Now I'd l...

I've got a function $$g(x,y) = \| f(x,y) \|_2$$ and I want to calculate its derivatives with respect to $x$ and $y$. Using Mathematica, differentiati...