If we have a Graph with Euler Circuit can we the consider it as a special Euler Path that start and end in the same Node? I am asking because the Conditio...

Questions: (a) What's $a_5$? (b) Find a formula for $a_n$ in terms of $a_{n - 1}$ (c) Find a formula for $a_n$ in terms of $n$ and use (b) to prove y...

I needed to evaluate the surjectivity of cuberoot(x) and used Wolfram-Alpha for that. To my surprise, cuberoot(x) is different than x^1/3, as can be seen ...

Particle, initially at rest travels in a straight line and its acceleration satisfies $$a=0.1(t-5)^2 $$for $0\leq t\leq5$ Find its average speed. during t...

I've recently read about the Fundamental Theorem of Arithmetic and I think that I have just about understood the proof. What I found quite interestin...

Suppose $X$ has $N$ elements and $Y$ has $M$ elements. How many one to one function are there from $X$ to $Y$? How many onto function are there from $X$ t...

Given a geometric sequence where the $5$th term $= 162$ and the $8$th term $= -4374$, determine the first three terms of the sequence. I am unclear how to...

$X$ is a continuous random variable with probability density function $f(x)= \dfrac{2x}{15}$ where $1≤x≤4$. What is the median of X?

$$W = \int_{x_i}^{x_f} F_x dx + \int_{y_i}^{y_f} F_y dy \int_{z_i}^{z_f} F_z dz$$ same as saying $$E = m\int_{0}^{x_f} a_x dx + m\int_{0}^{y_f} a_y dy + m...

In the book by Serge Lang, titled 'Introduction to Linear Algebra', there is given on pg. #88, as below: Let $A = (a_{ij}), B = (b_{jk})$ & ...