news

Finding value of k for which fg(x)=k has equal roots?

I've been going through this community and I Find this really helpful. About me(I know I should be precise but ya), I'm just a highschool studen...

Published: Sep 06, 2026

updates

How do I graph (-2,30) on a polar grid? [closed]

I tried to graph the point $(-2,30)$ on a polar graph and I think I got it wrong, how should it be graphed?

Published: Sep 06, 2026

general

Number of lines to connect $n \times n$ dots

The following is a popular riddle: Draw a $3 \times 3$ grid, and connect all the dots using only $4$ straight consecutive lines. The solution is to think ...

Published: Sep 06, 2026

general

Uniqueness of hamiltonian cycle

Let G be a graph on $n$ vertices, where $n \geq 8$ and with minimum degree at least $n/2$. Does $G$ have at least 2 distinct Hamilton cycles? (Two Hamilto...

Published: Sep 06, 2026

news

Solution of tanx = x?

How do I find the solutions of tanx = x upto any number of decimals? (Of course, there is the graphical method but it just helps in finding the approximat...

Published: Sep 06, 2026

news

derivative of cost function for Logistic Regression

I am going over the lectures on Machine Learning at Coursera. I am struggling with the following. How can the partial derivative of $$J(\theta)=-\frac{1}{...

Published: Sep 06, 2026

general

Rotate triangle ABC around the origin

How do you get from triangle ABC (blue) to triangle ABC (red) The instructions are to rotate it $270$ degrees I am trying to help a friend but forgot how ...

Published: Sep 06, 2026

general

What is the opposite of a cross term?

When we multiply out $(x + y)(x + y)$, we refer to the two $xy$ terms as "cross terms". Is there a corresponding term for the $x^2$ and $y^2$ terms?

Published: Sep 06, 2026

general

What is the difference between a sound argument and a valid argument?

In my notes, these are the definitions of a valid argument An argument form is valid if and only if whenever the premises are all true, then conclusion is...

Published: Sep 06, 2026

news

How do I write $e^{(-x/2)}$ as a summation?

I am new to power series. I know how to write $e^x$ as a summation, but i do not know how that helps me.

Published: Sep 06, 2026