In first-order ODEs, we say that a differential equation in the form $$\frac{\mathrm d y}{\mathrm d x}=f(x,y)$$ is said to be homogeneous if the function ...

Suppose there are 15 rooms among which a person in present in one room. If i pick 5 rooms out of them, what is the probability that the person is present ...

How many numbers from $1$ to $99999$ have a digit-sum of $8$? Why is the answer ${8+4\choose 4}$? Does the following method work? Answer is the number of ...

This theorem is obviously correct. Now I try to prove it by well-ordering principle. But I don't know where to start the proving....

I would like to find an equation that I can put into excel to calculate the coordinates for the center of the circle. Given $P_1\equiv (a=33855.05, b=2112...

How many 8-permutation are there of the letters of the word 'ADDRESSES'? My textbook suggests that we should divide the situation into cases whe...

Recently, I stumbled over a few things in very basic Lie group / Lie algebra theory concerning matrix groups. Basically, my question is: Is there a way to...

With the following information, I am to write the equation of the polynomial: Degree 3, zeros at $x=-2$, $x=1$, $x=3$, y intercept: $0,-4$ I know that the...

I'm having trouble with differentials. I've been trying to learn about them online using great resources like PatrickJMT but I'm having tro...

I am just starting dynamical systems and came across the following problem in my textbook. Considering the discrete time logistic growth model, $$N_{t+1} ...