Velvet Star Monitor

updates

"Simplest" symbolic equation with "most complex" symbolic answer

The below was inspired by this question, in which the OP was surprised that the "simple" equation $x^3 + x = 1$ could have such a "complex&...

Read Journal

updates

range of signed binary number system

I am a bit confused about the range of values for signed binary system. If I have $3$ bit to represent a number system, then number range will be given by...

Read Journal

updates

Use moment generating functions to find the distribution of $Y$?

Suppose that $X_1,X_2,\dotsc,X_n$ is a random sample of size $n = 5$ of independent random variables from an exponential distribution with parameter $\bet...

Read Journal

updates

Number patterns - finding the pattern

The number pattern is $$1,3,6,10,15,\dots$$ Find formula for this pattern. And thus find the 50th pattern. I have problems in trying to come out with thes...

Read Journal

updates

Exact meaning of "consists of"

What does consists of mean exactly, say in an arithmetic progression of length $n$ consists of prime numbers? Are there only prime numbers or must there b...

Read Journal

updates

How to find $\lim_{x \to 0^+} x^{\sqrt{x}}$ using L'Hospital's Rule.

I am trying to find $\lim_{x \to 0^+} x^{\sqrt{x}}$ using L'Hospital's Rule. I've differentiate the function, but it doesn't seem like...

Read Journal

updates

Computing a combined average (mean) of values

My textbook on descriptive statistics says that when we have a data set of m members, the mean is calculated like this: x-bar = 1/m (Σfixi) where sigma su...

Read Journal

updates

Is there/need there be a mathematical definition of a "direction"?

I recall learning the phrase "a vector is something with magnitude and direction" many years ago. It dawned on me that "magnitudes" are well defined as nu...

Read Journal

updates

(f o g) o f composition function

If $f$ represents the function $f(x)$ and $g$ represents the functions $g(x)$, is $(f \circ g)\circ f$ essentially $f(g(f(x)))$? I know that: $(f \circ g)...

Read Journal

updates

Sigma notation calculus, how to answer without calculator [closed]

How do I answer this without using a calculator? $$\sum_{x=1}^{20}8x^{3}$$

Read Journal