updates
Finding rate of change of angle of elevation
Question- From a building of height $48$ m, a man is walking away at a speed of $2$ m/s. Find the rate of change of angle of elevation, when he is at a di...
Read Journal Category
Updates
updates
Infinitely many primes of the form $4n+3$
I've found at least 3 other posts$^*$ regarding this theorem, but the posts don't address the issues that I have. Below is a proof that for infi...
Read Journal
updates
Logical disjunction truth table
The truth table for a logical disjunction shows that there is only one situation where the result can be false, being when both statements are false. As l...
Read Journal
updates
L'Hospital's Rule application with raised exponents.
I am having a little trouble going about: $$\lim_{x\to \infty} \left(\frac{14x}{14x+10}\right)^{10x}$$ Using $\ln$ properties we can bring down the $10x$ ...
Read Journal
updates
Joint density problem. Two uniform distributions
This is the problem: An insurer estimates that Smith's time until death is uniformly distributed on the interval [0,5], and Jone's time until de...
Read Journal
updates
Integrate $\left(x^2e^{x^2}\right)$
$\int\left(x^2e^{x^2}\right)$ First I integrated $$x^2e^{x^2}$$ to get $$F(x)=\frac{x^3}{3}\cdot\frac{1}{2x}\cdot e^{x^2}=\frac{x^3}{3}\cdot\frac{e^{x^2}}...
Read Journal
updates
Calculate angle between two lines
We have four points: a, b, c and d. We only know length of line cd and line ab. We also know that points c and d have same x coordinate, also points a and...
Read Journal
updates
Converting from base $10$ to base $2$
I am attempting to solve the following two questions. The first question I believe I have done correctly and I am looking to confirm this answer. The seco...
Read Journal
updates
Is there such thing as a "3-dimensional surface"?
The reason I'm asking this question: I work at the National Museum of Mathematics and, amidst my sundry duties (which generally have nothing to do wi...
Read Journal
updates
Does the 0th percentile exist?
For me it seems that it does. Here is my reasoning, please correct me if I'm wrong: We have 3 definitions of a percentile, let's check if the 0t...
Read Journal