Recent content by docnet

If each person gets a dedicated bidet cloth to dry off after using the bidet, it makes TP unnecessary. Many modern bidets have a variety of ways to control water pressure, spread, nozzle angle, movement, and etc. I find they are more hygienic and less irritating than TP as well.

+1 for bidet attachments

For nonzero ##a##, ##a^0=1##, because $$\frac{a^n}{a^n}=a^{n-n}=a^0.$$ For any ##a##, ##a^1=a##, because $$a^1\cdot a^1=a^{1+1}=a^2.$$

does it come with the grilled fish? not a fan of crustaceans, but looks scrumptious

hint: you can get an expression for ##R-h## in terms of ##R## and ##\theta## using basic trigonometry.

Maybe not obvious, but definitely derivable. Start with the double angle identity: $$\tan(2\theta) = \frac{2\tan(\theta)}{1 - \tan^2(\theta)}.$$ Let ##\theta = \arctan\left(\frac{1}{2}\right)##. Then, ##\tan(\theta) = \frac{1}{2}##. Substituting into the double-angle identity...

how do you read the signs (thai?) if you moved from the U.S.? It doesn't seem an easy language to learn

Simply, the answer to the "why" is that the sine function is defined that way. If you calculate it based on the y-axis, it would be a different function. Here is ##\sin(x)## graphed together with ##\cos(x)##. ##\sin(x)##, with the current definition, has very useful applications in physics and...

I'm getting $$\text{area}=200 \arcsin\left(\frac{4}{5}\right) + 50 \arcsin\left(\frac{3}{5}\right) - 125\pi + 200$$ as the exact solution using integration. I don't know if there is any simple trick.

What's better, cardio or weight training, if you could only choose one?

Hi there. I'm a frequent enjoyer of spicy foods. Buffalo wings, tabasco, Thai food, chips, you name it. I find that my sleep and mood improve after I ingest spicy foods. I've been experimenting with different sources as well, from jalapeno peppers to pure capsaicin extract, at 16 million...

You're probably technically correct, but people more often seem to use plural when referring to ABBA. For example: https://abbasite.com uses "their" when referring to ABBA. :oldbiggrin:

I wasn't implying anything about your physique at all. I just wanted to post something drastically out of the norm for entertainment. For clarity, you seem to be in an exceptionally fit shape, kudos for that. My dad is around the same age, he works out every day, and he's not as strong or flexible.

😓

It must be as ##x=\frac{r}{n}## and ##\Delta x = \frac{1}{n}##. The boundaries are ##0## and ##1## because $$0< r \leq n\Leftrightarrow 0<\frac{r}{n}\leq 1\Leftrightarrow 0<x\leq 1,$$ which goes along with $$\sum_{r=1}^n\frac{1}{n}=1$$ for the traditional right Riemann sum $$\sum_{r=1}^n...